Finite Group Databasebeta

← #28292997

Subgroups — #28292997

Order 13568.

7900 conjugacy classes of subgroups.

The subgroup lattice has 2008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289232C214yesmaximal, complemented
2#20289230C214yesmaximal, complemented
3#20289116C212yesmaximal, complemented
4#20289114C212yesmaximal, complemented
5#20289090C212yesmaximal, complemented
6#20289088C212yesmaximal, complemented
7#20289084C214yesmaximal, complemented
8#20288951C214yesmaximal, complemented
9#20288750C212yesmaximal, complemented
10#20288748C212yesmaximal, complemented
11#20288743C214yesmaximal, complemented
12#20288628C211yesmaximal, characteristic, complemented
13#20288627C212yesmaximal, complemented
14#20288592C212yesmaximal, complemented
15#20288584C212yesmaximal, complemented
16#20288568C212yesmaximal, complemented
17#20288560C212yesmaximal, complemented
18#20288493C211yesmaximal, characteristic, complemented
19#20288488C212yesmaximal, complemented
20#20288488C211yesmaximal, characteristic, complemented
21#20288478C212yesmaximal, complemented
22#20288473C212yesmaximal, complemented
23#20288385C212yesmaximal, complemented
24#20288381C214yesmaximal, complemented
25#20288379C212yesmaximal, complemented
26#20288008C211yesmaximal, characteristic, complemented
27C2×#16811174C211yesmaximal, characteristic, complemented
28#532×D53C211yesmaximal, characteristic, complemented
29C53×#3511C211yesmaximal, characteristic, complemented
30C2×#13133263C2212yescomplemented
31C2×#13133263C2214yescomplemented
32C2×#13133263C2212yescomplemented
33C22×#11719949C2212yescomplemented
34C2×#41×D53C2212yescomplemented
35#16811369C2218yescomplemented
36#16811365C2218yescomplemented
37#16811364C2218yescomplemented
38#16811363C2218yescomplemented
39#16811358C2214yescomplemented
40#16811358C2214yescomplemented
41#16811356C2214yescomplemented
42#16811355C2214yescomplemented
43#16811347C2212yescomplemented
44#16811345C2214yescomplemented
45#16811339C2212yescomplemented
46#16811336C2214yescomplemented
47#16811336C2214yescomplemented
48#16811334C2212yescomplemented
49#16811329C2214yescomplemented
50#16811326C2214yescomplemented
51#16811324C2218yescomplemented
52#16811321C2214yescomplemented
53#16811321C2214yescomplemented
54#16811317C2214yescomplemented
55#16811317C2214yescomplemented
56#16811295C2212yescomplemented
57#16811295C2214yescomplemented
58#16811295C2214yescomplemented
59#16811295C2212yescomplemented
60#16811294C2214yescomplemented
61#16811294C2212yescomplemented
62#16811294C2214yescomplemented
63#16811294C2212yescomplemented
64#16811292C2214yescomplemented
65#16811291C2214yescomplemented
66#16811285C2214yescomplemented
67#16811284C2214yescomplemented
68#16811283C2214yescomplemented
69#16811276C2212yescomplemented
70#16811275C2214yescomplemented
71#16811275C2214yescomplemented
72#16811274C2214yescomplemented
73#16811270C2214yescomplemented
74#16811270C2214yescomplemented
75#16811268C2214yescomplemented
76#16811268C2218yescomplemented
77#16811266C2214yescomplemented
78#16811266C2218yescomplemented
79#16811265C2218yescomplemented
80#16811264C2214yescomplemented
81#16811264C2214yescomplemented
82#16811264C2214yescomplemented
83#16811264C2214yescomplemented
84#16811264C2214yescomplemented
85#16811264C2218yescomplemented
86#16811262C2218yescomplemented
87#16811261C2214yescomplemented
88D4×D212C2212yescomplemented
89D4×D212C2212yescomplemented
90D4×D212C2212yescomplemented
91D4×D212C2212yescomplemented
92D4×D212C2218yescomplemented
93D4×D212C2214yescomplemented
94D4×D212C2214yescomplemented
95D4×D212C2214yescomplemented
96D4×D212C2214yescomplemented
97#16811257C2214yescomplemented
98#16811257C2214yescomplemented
99#16811257C2214yescomplemented
100#16811257C2218yescomplemented
101#16811257C2214yescomplemented
102#16811257C2214yescomplemented
103#16811257C2214yescomplemented
104#16811257C2214yescomplemented
105#16811247C2214yescomplemented
106#16811246C2214yescomplemented
107#16811245C2214yescomplemented
108#16811229C2214yescomplemented
109#16811229C2214yescomplemented
110#16811226C2214yescomplemented
111#16811224C2214yescomplemented
112#16811213C2218yescomplemented
113#16811212C2218yescomplemented
114#16811212C2218yescomplemented
115#16811209C2218yescomplemented
116#16811207C2218yescomplemented
117#16811206C2218yescomplemented
118#16811204C2214yescomplemented
119#16811204C2212yescomplemented
120#16811203C2218yescomplemented
121#16811203C2214yescomplemented
122#16811203C2214yescomplemented
123#16811192C2212yescomplemented
124#16811192C2214yescomplemented
125#16811192C2214yescomplemented
126#16811192C2214yescomplemented
127#16811191C2214yescomplemented
128#16811191C2218yescomplemented
129#16811191C2214yescomplemented
130#16811191C2214yescomplemented
131#16811189C2214yescomplemented
132#16811189C2214yescomplemented
133#16811187C2212yescomplemented
134#16811187C2214yescomplemented
135#16811184C2218yescomplemented
136#16811181C2218yescomplemented
137#16811178C2212yescomplemented
138#16811177C2211yescharacteristic, complemented
139#16811177C2211yescharacteristic, complemented
140#16811176C2211yescharacteristic, complemented
141#16811174C2212yescomplemented
142#16811174C2212yescomplemented
143#16811174C2212yescomplemented
144#16811174C2212yescomplemented
145#16811174C2211yescharacteristic, complemented
146#16811174C2212yescomplemented
147#16811174C2212yescomplemented
148#16811174C2212yescomplemented
149#16811174C2212yescomplemented
150#16811174C2212yescomplemented
151#16811174C2212yescomplemented
152#16811173C2212yescomplemented
153#16811173C2211yescharacteristic, complemented
154#16811172C2212yescomplemented
155#16811171C2211yescharacteristic, complemented
156#16811170C2211yescharacteristic, complemented
157#16811170C2211yescharacteristic, complemented
158#16811170C2212yescomplemented
159#16811170C2212yescomplemented
160#16811169C2211yescharacteristic, complemented
161#16811169C2212yescomplemented
162#16811168C2212yescomplemented
163#16811168C2212yescomplemented
164C4⋊Q8×D53C2211yescharacteristic, complemented
165C2×#13133214C2212yescomplemented
166C2×#13133214C2211yescharacteristic, complemented
167#127×D53C2212yescomplemented
168#127×D53C2211yescharacteristic, complemented
169#16811160C2211yescharacteristic, complemented
170#16811160C2211yescharacteristic, complemented
171#16811155C2211yescharacteristic, complemented
172#16811155C2211yescharacteristic, complemented
173#16811153C2212yescomplemented
174#16811153C2212yescomplemented
175#16811151C2212yescomplemented
176#16811151C2212yescomplemented
177C2×#13133206C2212yescomplemented
178#124×D53C2212yescomplemented
179#16811136C2214yescomplemented
180#16811135C2211yescharacteristic, complemented
181#16811135C2214yescomplemented
182#16811132C2212yescomplemented
183#16811132C2212yescomplemented
184#16811132C2218yescomplemented
185#16811130C2211yescharacteristic, complemented
186C2×#13133192C2212yescomplemented
187C2×#13133192C2214yescomplemented
188C2×#13133192C2212yescomplemented
189#121×D53C2214yescomplemented
190#121×D53C2212yescomplemented
191#121×D53C2218yescomplemented
192#121×D53C2212yescomplemented
193#16811105C2214yescomplemented
194#16811104C2212yescomplemented
195#16811097C2214yescomplemented
196#16811095C2214yescomplemented
197C4×#11719945C2212yescomplemented
198C4×#11719945C2212yescomplemented
199C4×#11719945C2211yescharacteristic, complemented
200C2×#13133179C2212yescomplemented
201C2×#13133179C2212yescomplemented
202C4×D4×D53C2212yescomplemented
203C4×D4×D53C2212yescomplemented
204C2×C42×D53C2211yescharacteristic, complemented
205C53×#556C2212yescomplemented
206C53×#555C2212yescomplemented
207C53×#554C2212yescomplemented
208C53×#553C2214yescomplemented
209C53×#548C2214yescomplemented
210C53×#547C2212yescomplemented
211C53×#542C2214yescomplemented
212C53×#537C2212yescomplemented
213C53×#533C2212yescomplemented
214C53×#532C2212yescomplemented
215C53×#532C2211yescharacteristic, complemented
216C2×C4⋊Q8×C53C2211yescharacteristic, complemented
217C53×#520C2212yescomplemented
218C4×#41×C53C2211yescharacteristic, complemented
219#13133263—48no—
220#13133263—48no—
221#13133263—416no—
222C2×#11719949—48no—
223C2×#11719949C2314yes—
224C2×#11719949C2314yes—
225C2×#11719949C2312yes—
226C2×#11719949C2314yes—
227C2×#11719949C2314yes—
228C2×#11719949C2314yes—
229C2×#11719949C2314yes—
230C2×#11719949C2314yes—
231C2×#11719945C2312yes—
232C2×#11719945C2311yescharacteristic
233C2×#11719945C2312yes—
234C2×#11719945C2318yes—
235C2×#11719945C2314yes—
236C2×#11719945C2314yes—
237C2×#11719945C2312yes—
238C2×#11719945C2314yes—
239C2×#11719947C2312yes—
240C2×#11719947C2314yes—
241#41×D53—48no—
242C2×Q8×D53C2312yes—
243C22×D212C2312yes—
244C22×D212C2314yes—
245C22×D212C2314yes—
246C22×D212C2318yes—
247C22×D212C2314yes—
248C22×D212C2312yes—
249C22×D212C2314yes—
250C22×D212C2314yes—
251C22×D212C2312yes—
252C2×D4×D53C2312yes—
253C2×D4×D53C2318yes—
254C2×D4×D53C2318yes—
255C2×D4×D53C2314yes—
256C2×D4×D53C2314yes—
257C2×D4×D53C2318yes—
258C2×D4×D53C2314yes—
259C2×D4×D53C2312yes—
260C2×D4×D53C2314yes—
261C2×D4×D53C2314yes—
262C2×D4×D53C2318yes—
263C2×D4×D53C2312yes—
264C22×C4×D53C2311yescharacteristic
265C22×C4×D53C2311yescharacteristic
266C22×C4×D53C2311yescharacteristic
267C22×C4×D53C2314yes—
268C22×C4×D53C2314yes—
269#13133217C2311yescharacteristic
270#13133216C2311yescharacteristic
271#13133216C2312yes—
272#13133216C2311yescharacteristic
273#13133216C2312yes—
274#13133215C2311yescharacteristic
275#13133215C2312yes—
276#13133214C2314yes—
277#13133214C2312yes—
278#13133214C2312yes—
279#13133214C2314yes—
280#13133214C2314yes—
281#13133214C2318yes—
282#13133214C2312yes—
283#13133214C2311yescharacteristic
284#13133214C2312yes—
285#13133213C2318yes—
286#13133213C2314yes—
287#13133213C2314yes—
288#13133213C2312yes—
289#13133213C2312yes—
290#13133213C2314yes—
291#13133213C2312yes—
292#13133213C2311yescharacteristic
293#13133212C2318yes—
294#13133212C2318yes—
295#13133212C2312yes—
296#13133212C2312yes—
297#13133211C2318yes—
298#13133210C2312yes—
299#13133210C2312yes—
300#13133208C2311yescharacteristic
301#13133208C2314yes—
302#13133208C2311yescharacteristic
303#13133207C2312yes—
304#13133207C2312yes—
305#13133206C2311yescharacteristic
306#13133206C2312yes—
307#13133206C2314yes—
308#13133206C2318yes—
309#13133206C2314yes—
310#13133206C2314yes—
311#13133206C2314yes—
312#13133206C2314yes—
313#13133206C2314yes—
314#13133205C2318yes—
315#13133205C2314yes—
316#13133205C2318yes—
317#13133205C2312yes—
318#13133204C2311yescharacteristic
319#13133204C2312yes—
320#13133203C2312yes—
321#13133203C2318yes—
322#13133203C2318yes—
323#13133203C2312yes—
324#13133203C2314yes—
325#13133203C2314yes—
326#13133202C2312yes—
327#13133202C2318yes—
328#13133202C2318yes—
329#13133202C2318yes—
330#13133202C2318yes—
331#13133202C2318yes—
332#13133202C2318yes—
333#13133202C2312yes—
334#13133201C2312yes—
335#13133201C2318yes—
336#13133200C2318yes—
337#13133199C2312yes—
338#13133199C2318yes—
339#13133199C2318yes—
340#13133199C2318yes—
341#13133199C2312yes—
342#13133198C2312yes—
343#13133197C2314yes—
344#13133197C2318yes—
345#13133197C2314yes—
346#13133197C2311yescharacteristic
347#13133197C2311yescharacteristic
348#13133195C2318yes—
349#13133195C2318yes—
350#13133195C2312yes—
351#13133195C2312yes—
352#13133194C2312yes—
353#13133194C2312yes—
354#13133193C2314yes—
355#13133193C2318yes—
356#13133193C2311yescharacteristic
357#13133193C2311yescharacteristic
358#13133192C2318yes—
359#13133192C2312yes—
360#13133192C2318yes—
361#13133192C2314yes—
362#13133192C2314yes—
363#13133192C2318yes—
364#13133192C2318yes—
365#13133192C2318yes—
366#13133192C2318yes—
367#13133192C2314yes—
368#13133192C2314yes—
369#13133192C2314yes—
370#13133192C2314yes—
371#13133192C2314yes—
372#13133192C2318yes—
373#13133192C2314yes—
374#13133192C2314yes—
375#13133192C2314yes—
376#13133192C2314yes—
377#13133192C2314yes—
378#13133192C2312yes—
379#13133192C2311yescharacteristic
380#13133192C2314yes—
381#13133192C2314yes—
382#13133192C2314yes—
383#13133192C2311yescharacteristic
384#13133191C2318yes—
385#13133191C2318yes—
386#13133191C2318yes—
387#13133191C2314yes—
388#13133191C2312yes—
389#13133191C2314yes—
390#13133191C2314yes—
391#13133191C2318yes—
392#13133191C2314yes—
393#13133191C2312yes—
394#13133190C2318yes—
395#13133190C2318yes—
396#13133190C2318yes—
397#13133190C2318yes—
398#13133190C2318yes—
399#13133190C2318yes—
400#13133190C2318yes—
401#13133190C2318yes—
402#13133190C2318yes—
403#13133190C2314yes—
404#13133190C2314yes—
405#13133190C2312yes—
406#13133190C2312yes—
407#13133189C2318yes—
408#13133189C2312yes—
409#13133189C2314yes—
410#13133189C2314yes—
411#13133189C2312yes—
412#13133188C2312yes—
413#13133188C2318yes—
414#13133188C2311yescharacteristic
415#13133188C2312yes—
416#13133188C2311yescharacteristic
417#13133187C2318yes—
418#13133187C2318yes—
419#13133187C2318yes—
420#13133187C2318yes—
421#13133187C2318yes—
422#13133187C2318yes—
423#13133187C2318yes—
424#13133187C2318yes—
425#13133187C2318yes—
426#13133187C2318yes—
427#13133187C2318yes—
428#13133187C2318yes—
429#13133187C2312yes—
430#13133185C2318yes—
431#13133185C2318yes—
432#13133185C2318yes—
433#13133185C2312yes—
434#13133185C2318yes—
435Q8×Dic53C2314yes—
436C4×Dic106C2312yes—
437C4×Dic106C2311yescharacteristic
438C4×Dic106C2312yes—
439C4×Dic106C2311yescharacteristic
440C4×Dic106C2312yes—
441C4×Dic106C2312yes—
442#13133182C2314yes—
443C4×D212C2312yes—
444C4×D212C2318yes—
445C4×D212C2318yes—
446C4×D212C2314yes—
447C4×D212C2312yes—
448C4×D212C2318yes—
449C4×D212C2311yescharacteristic
450C4×D212C2312yes—
451C4×D212C2312yes—
452C4×D212C2314yes—
453C4×D212C2312yes—
454C4×D212C2312yes—
455C4×D212C2311yescharacteristic
456D4×Dic53C2312yes—
457D4×Dic53C2312yes—
458#13133179C2312yes—
459#13133179C2314yes—
460#13133179C2314yes—
461#13133179C2318yes—
462#13133179C2314yes—
463#13133179C2314yes—
464#13133179C2314yes—
465#13133179C2314yes—
466#13133179C2314yes—
467#13133179C2314yes—
468#13133179C2314yes—
469#13133179C2314yes—
470#13133179C2312yes—
471#13133179C2314yes—
472#13133179C2314yes—
473C4×C22⋊D53C2312yes—
474C4×C22⋊D53C2312yes—
475C4×C22⋊D53C2312yes—
476C4×C22⋊D53C2312yes—
477C4×C22⋊D53C2314yes—
478C4×C22⋊D53C2318yes—
479C4×C22⋊D53C2314yes—
480C4×C22⋊D53C2312yes—
481C4×C22⋊D53C2312yes—
482C4×C22⋊D53C2312yes—
483C4×C22⋊D53C2318yes—
484C4×C22⋊D53C2312yes—
485C4×C22⋊D53C2312yes—
486C4×C22⋊D53C2312yes—
487#13133177C2314yes—
488#13133177C2318yes—
489#13133177C2314yes—
490#13133176C2312yes—
491#13133176C2311yescharacteristic
492#13133176C2312yes—
493#13133175C2314yes—
494#13133175C2314yes—
495#13133174C2318yes—
496#13133174C2312yes—
497#13133174C2312yes—
498#13133174C2312yes—
499#13133174C2312yes—
500#13133174C2312yes—
501C4⋊C4×D53C2314yes—
502C4⋊C4×D53C2318yes—
503C4⋊C4×D53C2312yes—
504C4⋊C4×D53C2312yes—
505C2×#11719921C2318yes—
506C2×#11719921C2314yes—
507C2×#11719921C2314yes—
508C22⋊C4×D53C2318yes—
509C22⋊C4×D53C2314yes—
510C22⋊C4×D53C2318yes—
511C22⋊C4×D53C2318yes—
512C22⋊C4×D53C2314yes—
513C2×C4×Dic53C2311yescharacteristic
514C2×C4×Dic53C2311yescharacteristic
515C2×C4×Dic53C2311yescharacteristic
516C42×D53C2311yescharacteristic
517C42×D53C2311yescharacteristic
518C42×D53C2311yescharacteristic
519C42×D53C2311yescharacteristic
520C42×D53C2311yescharacteristic
521C42×D53C2311yescharacteristic
522C42×D53C2311yescharacteristic
523C42×D53C2311yescharacteristic
524C42×D53C2312yes—
525C2×#41×C53C2311yescharacteristic
526C2×#41×C53C2312yes—
527C2×#41×C53C2314yes—
528C22×Q8×C53C2312yes—
529C4⋊Q8×C53C2312yes—
530C4⋊Q8×C53C2312yes—
531C4⋊Q8×C53C2312yes—
532C4⋊Q8×C53C2312yes—
533C4⋊Q8×C53C2311yescharacteristic
534#127×C53C2311yescharacteristic
535#126×C53C2318yes—
536#125×C53C2314yes—
537#124×C53C2314yes—
538#124×C53C2318yes—
539#124×C53C2312yes—
540#123×C53C2318yes—
541C22⋊Q8×C53C2314yes—
542C22⋊Q8×C53C2314yes—
543C22⋊Q8×C53C2314yes—
544C22⋊Q8×C53C2318yes—
545#121×C53C2314yes—
546#121×C53C2314yes—
547#121×C53C2312yes—
548#121×C53C2312yes—
549#121×C53C2314yes—
550#121×C53C2318yes—
551C4×Q8×C53C2314yes—
552C4×Q8×C53C2311yescharacteristic
553C4×Q8×C53C2311yescharacteristic
554C4×Q8×C53C2314yes—
555C4×D4×C53C2314yes—
556C4×D4×C53C2318yes—
557C4×D4×C53C2312yes—
558C4×D4×C53C2314yes—
559C4×D4×C53C2312yes—
560C4×D4×C53C2311yescharacteristic
561C4×D4×C53C2312yes—
562C4×D4×C53C2312yes—
563C4×D4×C53C2311yescharacteristic
564#117×C53C2311yescharacteristic
565#117×C53C2312yes—
566#117×C53C2314yes—
567#117×C53C2314yes—
568C2×C4⋊C4×C53C2314yes—
569C2×C4⋊C4×C53C2312yes—
570C2×C4⋊C4×C53C2312yes—
571C2×C42×C53C2311yescharacteristic
572C2×C42×C53C2312yes—
573C23×D53C2411yescharacteristic
574C23×D53C2414yes—
575C23×D53C2414yes—
576C23×D53C2418yes—
577C23×D53C2418yes—
578#41×C53—28no—
579#41×C53—24no—
580#41×C53—48no—
581C2×Q8×C53—44no—
582C2×Q8×C53C2411yescharacteristic
583C2×Q8×C53C2412yes—
584C2×Q8×C53C2414yes—
585C2×Q8×C53C2414yes—
586C2×D4×C53C2412yes—
587C2×D4×C53C2414yes—
588C2×D4×C53C2412yes—
589C2×D4×C53C2411yescharacteristic
590C2×D4×C53C2412yes—
591C2×D4×C53C2412yes—
592C2×D4×C53C2418yes—
593C22×C4×C53C2411yescharacteristic
594C22×C4×C53C2412yes—
595C22×C4×C53C2412yes—
596C22×C4×C53C2411yescharacteristic
597C22×C4×C53C2412yes—
598C22×C4×C53C2414yes—
599C22×C4×C53C2414yes—
600C22×C4×C53C2418yes—
601C22×C4×C53C2411yescharacteristic
602C2×C22⋊D53C2414yes—
603C2×C22⋊D53C2412yes—
604C2×C22⋊D53C2414yes—
605C2×C22⋊D53C2412yes—
606C2×C22⋊D53C2412yes—
607C2×C22⋊D53C2414yes—
608C2×C22⋊D53C2418yes—
609C2×C22⋊D53C2412yes—
610C2×C22⋊D53C2412yes—
611C2×C22⋊D53C2414yes—
612C2×C22⋊D53C2418yes—
613C2×C22⋊D53C2418yes—
614C2×C22⋊D53C2418yes—
615C2×C22⋊D53C2414yes—
616C22×Dic53C2411yescharacteristic
617C22×Dic53C2411yescharacteristic
618C22×Dic53C2411yescharacteristic
619C22×Dic53C2414yes—
620#11719949—216no—
621#11719949—48no—
622#11719949—48no—
623#11719949—44no—
624#11719949—48no—
625#11719949—48no—
626#11719949—48no—
627#11719949—48no—
628Q8×D53—44no—
629#11719947—44no—
630#11719947—48no—
631D4×D53—28no—
632D4×D53—44no—
633D4×D53—48no—
634D4×D53—44no—
635D4×D53—48no—
636D4×D53—48no—
637D4×D53—48no—
638D4×D53—416no—
639D4×D53—416no—
640D4×D53—48no—
641D4×D53—416no—
642D4×D53—416no—
643#11719945—28no—
644#11719945—24no—
645#11719945—28no—
646#11719945—416no—
647#11719945—48no—
648#11719945—48no—
649#11719945—48no—
650#11719945—44no—
651C2×D212—28no—
652C2×D212—44no—
653C2×D212—48no—
654C2×D212—44no—
655C2×D212—48no—
656C2×D212—48no—
657C2×D212—48no—
658C2×D212—48no—
659C2×D212—416no—
660C2×D212C2414yes—
661C2×D212C2412yes—
662C2×D212C2414yes—
663C2×D212C2414yes—
664C2×D212C2412yes—
665C2×D212C2418yes—
666C2×D212C2412yes—
667C2×D212C2414yes—
668C2×D212C2412yes—
669C2×D212C2411yescharacteristic
670C2×D212C2414yes—
671C2×D212C2412yes—
672C2×D212C2418yes—
673C2×D212C2414yes—
674C2×D212C2418yes—
675C2×D212C2418yes—
676C2×D212C2414yes—
677C2×D212C2418yes—
678C2×D212C2418yes—
679C2×D212C2418yes—
680C2×C4×D53—24no—
681C2×C4×D53—24no—
682C2×C4×D53—48no—
683C2×C4×D53—42no—
684C2×C4×D53—48no—
685C2×C4×D53C2411yescharacteristic
686C2×C4×D53C2411yescharacteristic
687C2×C4×D53C2411yescharacteristic
688C2×C4×D53C2411yescharacteristic
689C2×C4×D53C2411yescharacteristic
690C2×C4×D53C2411yescharacteristic
691C2×C4×D53C2411yescharacteristic
692C2×C4×D53C2411yescharacteristic
693C2×C4×D53C2411yescharacteristic
694C2×C4×D53C2412yes—
695C2×C4×D53C2412yes—
696C2×C4×D53C2412yes—
697C2×C4×D53C2418yes—
698C2×C4×D53C2414yes—
699C2×C4×D53C2411yescharacteristic
700C2×C4×D53C2411yescharacteristic
701C2×C4×D53C2414yes—
702C2×C4×D53C2414yes—
703C2×C4×D53C2418yes—
704C2×C4×D53C2418yes—
705C2×C4×D53C2418yes—
706C2×C4×D53C2418yes—
707C2×C4×D53C2411yescharacteristic
708C2×Dic106C2412yes—
709C2×Dic106C2412yes—
710C2×Dic106C2411yescharacteristic
711C2×Dic106C2412yes—
712C2×Dic106C2414yes—
713C4⋊C4×C53C2411yescharacteristic
714C4⋊C4×C53C2414yes—
715C4⋊C4×C53C2414yes—
716C4⋊C4×C53C2414yes—
717C4⋊C4×C53C2418yes—
718C4⋊C4×C53C2414yes—
719C4⋊C4×C53C2411yescharacteristic
720C4⋊C4×C53C2412yes—
721C4⋊C4×C53C2412yes—
722C4⋊C4×C53C2412yes—
723C4⋊C4×C53C2412yes—
724C4⋊C4×C53C2418yes—
725C22⋊C4×C53C2412yes—
726C22⋊C4×C53C2418yes—
727C22⋊C4×C53C2412yes—
728C22⋊C4×C53C2412yes—
729C22⋊C4×C53C2418yes—
730C22⋊C4×C53C2418yes—
731C22⋊C4×C53C2414yes—
732C22⋊C4×C53C2414yes—
733C42×C53C2411yescharacteristic
734C42×C53C2412yes—
735C42×C53C2411yescharacteristic
736C42×C53C2412yes—
737C42×C53C2411yescharacteristic
738C42×C53C2411yescharacteristic
739C42×C53C2412yes—
740C42×C53C2418yes—
741C22⋊Dic53C2412yes—
742C22⋊Dic53C2412yes—
743C22⋊Dic53C2414yes—
744C22⋊Dic53C2414yes—
745C22⋊Dic53C2412yes—
746C22⋊Dic53C2412yes—
747C22⋊Dic53C2412yes—
748#11719921C2412yes—
749#11719921C2414yes—
750#11719921C2418yes—
751#11719921C2418yes—
752#11719921C2414yes—
753#11719921C2414yes—
754#11719921C2414yes—
755#11719921C2418yes—
756#11719921C2418yes—
757#11719921C2412yes—
758#11719921C2418yes—
759#11719921C2418yes—
760#11719921C2418yes—
761#11719921C2418yes—
762#11719921C2412yes—
763#11719921C2412yes—
764#11719921C2412yes—
765#11719921C2412yes—
766#11719921C2412yes—
767#11719921C2412yes—
768#11719921C2412yes—
769#11719921C2412yes—
770#11719921C2418yes—
771#11719921C2418yes—
772#11719921C2418yes—
773C4⋊Dic53C2411yescharacteristic
774C4⋊Dic53C2412yes—
775C4⋊Dic53C2412yes—
776C4⋊Dic53C2418yes—
777C4⋊Dic53C2411yescharacteristic
778C4⋊Dic53C2412yes—
779C4⋊Dic53C2412yes—
780C4⋊Dic53C2412yes—
781C4⋊Dic53C2412yes—
782#11719919C2412yes—
783#11719919C2414yes—
784#11719919C2414yes—
785#11719919C2418yes—
786#11719919C2412yes—
787#11719919C2412yes—
788#11719919C2412yes—
789#11719919C2412yes—
790#11719919C2412yes—
791#11719919C2412yes—
792#11719919C2412yes—
793#11719919C2412yes—
794#11719919C2412yes—
795C4×Dic53C2411yescharacteristic
796C4×Dic53C2411yescharacteristic
797C4×Dic53C2411yescharacteristic
798C4×Dic53C2411yescharacteristic
799C4×Dic53C2411yescharacteristic
800C4×Dic53C2411yescharacteristic
801C4×Dic53C2411yescharacteristic
802C4×Dic53C2411yescharacteristic
803C4×Dic53C2411yescharacteristic
804C4×Dic53C2411yescharacteristic
805C4×Dic53C2411yescharacteristic
806C4×Dic53C2411yescharacteristic
807C4×Dic53C2412yes—
808C4×Dic53C2412yes—
809C4×Dic53C2412yes—
810C4×Dic53C2418yes—
811C23×C53C2514yes—
812C23×C53C2512yes—
813C23×C53C2511yescharacteristic
814C22×D53—22no—
815C22×D53—28no—
816C22×D53—22no—
817C22×D53—28no—
818C22×D53—41no—
819C22×D53—44no—
820C22×D53—44no—
821C22×D53—44no—
822C22×D53—44no—
823C22×D53—48no—
824C22×D53—48no—
825C22×D53—48no—
826C22×D53—48no—
827C22×D53—48no—
828C22×D53—48no—
829C22×D53C2511yescharacteristic
830C22×D53C2518yes—
831C22×D53C2514yes—
832C22×D53C2512yes—
833C22×D53C2511yescharacteristic
834Q8×C53—24no—
835Q8×C53—28no—
836Q8×C53—22no—
837Q8×C53—44no—
838D4×C53—24no—
839D4×C53—28no—
840D4×C53—24no—
841D4×C53—22no—
842D4×C53—24no—
843D4×C53—24no—
844D4×C53—48no—
845C2×C4×C53—22no—
846C2×C4×C53—28no—
847C2×C4×C53—24no—
848C2×C4×C53—24no—
849C2×C4×C53—22no—
850C2×C4×C53—24no—
851C2×C4×C53—44no—
852C2×C4×C53—48no—
853C2×C4×C53H(5,𝔽2)14yescomplemented
854C2×C4×C53C2514yes—
855C2×C4×C53C2512yes—
856C2×C4×C53C2512yes—
857C2×C4×C53C2512yes—
858C2×C4×C53C2518yes—
859C2×C4×C53C2511yescharacteristic
860C2×C4×C53C2511yescharacteristic
861C2×C4×C53C2511yescharacteristic
862C2×C4×C53C2511yescharacteristic
863C2×C4×C53C2511yescharacteristic
864C2×C4×C53C2511yescharacteristic
865C22⋊D53—24no—
866C22⋊D53—28no—
867C22⋊D53—24no—
868C22⋊D53—24no—
869C22⋊D53—28no—
870C22⋊D53—48no—
871C22⋊D53—48no—
872C22⋊D53—48no—
873C22⋊D53—44no—
874C22⋊D53—44no—
875C22⋊D53—42no—
876C22⋊D53—42no—
877C22⋊D53—48no—
878C22⋊D53—44no—
879C2×Dic53—22no—
880C2×Dic53—22no—
881C2×Dic53—44no—
882C2×Dic53—41no—
883C2×Dic53C2511yescharacteristic
884C2×Dic53C2514yes—
885C2×Dic53C2511yescharacteristic
886C2×Dic53C2512yes—
887C2×Dic53C2512yes—
888C2×Dic53C2512yes—
889C2×Dic53C2511yescharacteristic
890C2×Dic53C2511yescharacteristic
891C2×Dic53C2511yescharacteristic
892C2×Dic53C2511yescharacteristic
893D212—24no—
894D212—216no—
895D212—28no—
896D212—28no—
897D212—22no—
898D212—24no—
899D212—24no—
900D212—28no—
901D212—28no—
902D212—24no—
903D212—48no—
904D212—48no—
905D212—44no—
906D212—48no—
907D212—48no—
908D212—48no—
909D212—44no—
910D212—48no—
911D212—42no—
912D212—44no—
913C4×D53—22no—
914C4×D53—22no—
915C4×D53—22no—
916C4×D53—22no—
917C4×D53—22no—
918C4×D53—22no—
919C4×D53—28no—
920C4×D53—24no—
921C4×D53—24no—
922C4×D53—22no—
923C4×D53—22no—
924C4×D53—24no—
925C4×D53—22no—
926C4×D53—216no—
927C4×D53—41no—
928C4×D53—41no—
929C4×D53—44no—
930C4×D53—44no—
931C4×D53—48no—
932C4×D53—48no—
933C4×D53—48no—
934C4×D53—48no—
935C4×D53H(5,𝔽2)14yescomplemented
936Dic106—22no—
937Dic106—24no—
938Dic106—24no—
939Dic106—42no—
940Dic106—44no—
941#62834—531nomaximal, Sylow
942C22×C53—21no—
943C22×C53—21no—
944C22×C53—24no—
945C22×C53—22no—
946C22×C53—24no—
947C22×C53—22no—
948C22×C53—24no—
949C22×C53—22no—
950C22×C53C2×H(5,𝔽2)12yes—
951C22×C53C2611yescharacteristic
952C2×D53—21no—
953C2×D53—21no—
954C2×D53—21no—
955C2×D53—21no—
956C2×D53—28no—
957C2×D53—24no—
958C2×D53—22no—
959C2×D53—22no—
960C2×D53—28no—
961C2×D53—24no—
962C2×D53—21no—
963C2×D53—22no—
964C2×D53—28no—
965C2×D53—24no—
966C2×D53—44no—
967C2×D53—88no—
968C2×D53—88no—
969C2×D53—168no—
970C2×D53—168no—
971C2×D53C2×H(5,𝔽2)12yes—
972C4×C53—22no—
973C4×C53—24no—
974C4×C53—21no—
975C4×C53—28no—
976C4×C53—22no—
977C4×C53—22no—
978C4×C53—21no—
979C4×C53C2×H(5,𝔽2)12yes—
980C4×C53C2×H(5,𝔽2)12yes—
981C4×C53C2×H(5,𝔽2)12yes—
982C4×C53#58512yes—
983Dic53—24no—
984Dic53—22no—
985Dic53—22no—
986Dic53—21no—
987Dic53—21no—
988Dic53—21no—
989Dic53—21no—
990Dic53—22no—
991Dic53—21no—
992Dic53C2×H(5,𝔽2)12yes—
993#3558—534no—
994#3558—534no—
995#3549—532no—
996#3548—532no—
997#3546—532no—
998#3546—532no—
999#3546—534no—
1000#3537—534no—
1001#3519—532no—
1002#3519—532no—
1003#3519—534no—
1004#3511—532no—
1005#3511—531no—
1006#3511D5311yescharacteristic, complemented
1007#3508—532no—
1008#3508—532no—
1009#3506—532no—
1010#3506—532no—
1011#3498—532no—
1012#3498—531no—
1013#3498—531no—
1014#3496—532no—
1015#3496—532no—
1016#3488—534no—
1017#3488—532no—
1018#3488—532no—
1019#3444—531no—
1020C2×#532—531no—
1021C2×#532—531no—
1022C2×C53—22no—
1023C2×C53—44no—
1024C2×C53—42no—
1025C2×C53C22×H(5,𝔽2)11yescharacteristic
1026C2×C53C22×H(5,𝔽2)11yescharacteristic
1027C2×C53C2×#58511yescharacteristic
1028D53—22no—
1029D53—41no—
1030D53—48no—
1031D53—44no—
1032D53—42no—
1033C2×H(5,𝔽2)—534no—
1034C2×H(5,𝔽2)—532no—
1035C2×H(5,𝔽2)—532no—
1036C22×#41—532no—
1037C22×#41—532no—
1038#562—538no—
1039H(3,𝔽4)—538no—
1040#560—538no—
1041#560—538no—
1042#559—534no—
1043#559—534no—
1044#559—534no—
1045#559—534no—
1046#556—532no—
1047#556—534no—
1048#556C2×D5312yescomplemented
1049#555—532no—
1050#555—534no—
1051#555—534no—
1052#555C2×D5312yescomplemented
1053#554—532no—
1054#554—534no—
1055#554C2×D5312yescomplemented
1056#553—538no—
1057#553—534no—
1058#553—534no—
1059#553—534no—
1060#553—534no—
1061#553—534no—
1062#553C2×D5314yescomplemented
1063#550—534no—
1064#550—534no—
1065#550—534no—
1066#550—534no—
1067#550—532no—
1068#550—532no—
1069#550—534no—
1070#550—532no—
1071#550—534no—
1072#550—532no—
1073#548—534no—
1074#548—534no—
1075#548—534no—
1076#548C2×D5314yescomplemented
1077#547—532no—
1078#547—534no—
1079#547—534no—
1080#547—534no—
1081#547C2×D5312yescomplemented
1082#546—534no—
1083#546—534no—
1084#546—538no—
1085#546—538no—
1086#546—534no—
1087#546—534no—
1088#546—538no—
1089#546—534no—
1090#546—534no—
1091#546—534no—
1092#546—534no—
1093#546—534no—
1094#546—538no—
1095#546—534no—
1096#546—538no—
1097D42—538no—
1098D42—534no—
1099D42—534no—
1100D42—534no—
1101D42—534no—
1102D42—534no—
1103D42—534no—
1104D42—534no—
1105D42—538no—
1106D42—534no—
1107D42—534no—
1108D42—532no—
1109D42—532no—
1110D42—534no—
1111D42—534no—
1112D42—532no—
1113D42—532no—
1114#542—534no—
1115#542—534no—
1116#542—534no—
1117#542C2×D5314yescomplemented
1118#540—534no—
1119#540—534no—
1120#540—534no—
1121#540—534no—
1122#538—538no—
1123#538—538no—
1124#538—538no—
1125#538—538no—
1126#538—538no—
1127#538—538no—
1128#537—534no—
1129#537—534no—
1130#537—538no—
1131#537—532no—
1132#537—534no—
1133#537C2×D5312yescomplemented
1134#535—532no—
1135#535—534no—
1136#535—534no—
1137#535—538no—
1138#535—534no—
1139#535—534no—
1140#535—534no—
1141#535—534no—
1142#535—532no—
1143#535—534no—
1144#535—534no—
1145#535—534no—
1146#534—538no—
1147#534—538no—
1148#533—532no—
1149#533—531no—
1150#533—531no—
1151#533—531no—
1152#533C2×D5312yescomplemented
1153#532—532no—
1154#532—531no—
1155#532—532no—
1156#532—532no—
1157#532—531no—
1158#532—532no—
1159#532—532no—
1160#532—532no—
1161#532—532no—
1162#532—532no—
1163#532—532no—
1164#532—532no—
1165#532—532no—
1166#532—531no—
1167#532—532no—
1168#532—532no—
1169#532—532no—
1170#532—532no—
1171#532—532no—
1172#532—531no—
1173#532—531no—
1174#532—531no—
1175#532—532no—
1176#532C2×D5311yescharacteristic, complemented
1177#532C2×D5312yescomplemented
1178C2×C4⋊Q8—531no—
1179C2×C4⋊Q8C2×D5311yescharacteristic, complemented
1180C2×#127—531no—
1181C2×#127—532no—
1182C2×#127—531no—
1183C2×#127—532no—
1184#529—531no—
1185#529—531no—
1186#529—532no—
1187#529—532no—
1188#529—531no—
1189#529—531no—
1190#529—532no—
1191#529—532no—
1192C2×#124—532no—
1193C2×#124—532no—
1194#525—531no—
1195#525—534no—
1196#525—532no—
1197#525—532no—
1198#525—538no—
1199#525—531no—
1200#525—534no—
1201C2×#121—532no—
1202C2×#121—532no—
1203C2×#121—534no—
1204C2×#121—538no—
1205C2×#121—532no—
1206C2×#121—532no—
1207C2×#121—534no—
1208#520—534no—
1209#520—532no—
1210#520C2×D5312yescomplemented
1211#518—534no—
1212#518—534no—
1213C4×#41—531no—
1214C4×#41—532no—
1215C4×#41—532no—
1216C4×#41C2×D5311yescharacteristic, complemented
1217C2×C4×D4—532no—
1218C2×C4×D4—532no—
1219C2×C4×D4—532no—
1220C2×C4×D4—532no—
1221C22×C42—531no—
1222C53#6283411yescharacteristic, complemented, Sylow
1223H(5,𝔽2)—2128no—
1224H(5,𝔽2)—2128no—
1225H(5,𝔽2)—21216no—
1226C2×#41—534no—
1227C2×#41—534no—
1228C2×#41—534no—
1229C2×#41—534no—
1230C2×#41—534no—
1231C2×#41—532no—
1232C2×#41—534no—
1233C2×#41—534no—
1234C2×#41—534no—
1235C2×#41—532no—
1236C2×#41—532no—
1237C2×#41—531no—
1238C2×#41—532no—
1239C2×#41—532no—
1240C2×#41—538no—
1241C2×#41—534no—
1242C2×#41—534no—
1243C2×#41—534no—
1244C2×#41—2128no—
1245C2×#41—2128no—
1246C2×#41C22×D5311yescharacteristic
1247C2×#41C22×D5312yes—
1248C2×#41C22×D5314yes—
1249C22×Q8—532no—
1250C22×Q8C22×D5312yes—
1251C22×D4—532no—
1252C22×D4—532no—
1253C22×D4—534no—
1254C22×D4—534no—
1255C22×D4—538no—
1256C22×D4—538no—
1257C22×D4—538no—
1258C22×D4—538no—
1259C22×D4—534no—
1260C22×D4—532no—
1261C22×D4—534no—
1262C22×D4—534no—
1263C22×D4—532no—
1264C22×D4—532no—
1265C22×D4—534no—
1266C22×D4—534no—
1267C22×D4—538no—
1268C22×D4—534no—
1269C22×D4—532no—
1270C22×D4—534no—
1271C22×D4—534no—
1272C23×C4—531no—
1273C23×C4—531no—
1274C23×C4—534no—
1275C23×C4—534no—
1276C23×C4—531no—
1277C4⋊Q8—532no—
1278C4⋊Q8—531no—
1279C4⋊Q8—532no—
1280C4⋊Q8—532no—
1281C4⋊Q8—531no—
1282C4⋊Q8—531no—
1283C4⋊Q8—531no—
1284C4⋊Q8C22×D5311yescharacteristic
1285C4⋊Q8C22×D5312yes—
1286C4⋊Q8C22×D5312yes—
1287C4⋊Q8C22×D5312yes—
1288C4⋊Q8C22×D5312yes—
1289#127—532no—
1290#127—532no—
1291#127—532no—
1292#127—534no—
1293#127—534no—
1294#127—534no—
1295#127—531no—
1296#127—538no—
1297#127—531no—
1298#127—532no—
1299#127—532no—
1300#127—532no—
1301#127—532no—
1302#127—534no—
1303#127—534no—
1304#127—534no—
1305#127—538no—
1306#127C22×D5311yescharacteristic
1307#126—532no—
1308#126—532no—
1309#126—538no—
1310#126—538no—
1311#126—532no—
1312#126—532no—
1313#126—538no—
1314#126C22×D5318yes—
1315#125—532no—
1316#125—531no—
1317#125—531no—
1318#125—532no—
1319#125—534no—
1320#125C22×D5314yes—
1321#124—534no—
1322#124—534no—
1323#124—534no—
1324#124—532no—
1325#124—534no—
1326#124—531no—
1327#124—534no—
1328#124—534no—
1329#124—538no—
1330#124—532no—
1331#124—531no—
1332#124—534no—
1333#124—534no—
1334#124—532no—
1335#124—532no—
1336#124—538no—
1337#124—538no—
1338#124—532no—
1339#124—534no—
1340#124—538no—
1341#124—538no—
1342#124C22×D5312yes—
1343#124C22×D5314yes—
1344#124C22×D5318yes—
1345#123—532no—
1346#123—538no—
1347#123—532no—
1348#123—532no—
1349#123—538no—
1350#123—538no—
1351#123—538no—
1352#123—538no—
1353#123—538no—
1354#123—538no—
1355#123—532no—
1356#123—532no—
1357#123—532no—
1358#123—538no—
1359#123—538no—
1360#123—538no—
1361#123—538no—
1362#123C22×D5318yes—
1363C22⋊Q8—531no—
1364C22⋊Q8—531no—
1365C22⋊Q8—534no—
1366C22⋊Q8—538no—
1367C22⋊Q8—531no—
1368C22⋊Q8—532no—
1369C22⋊Q8—531no—
1370C22⋊Q8—532no—
1371C22⋊Q8—538no—
1372C22⋊Q8—534no—
1373C22⋊Q8—534no—
1374C22⋊Q8—538no—
1375C22⋊Q8—538no—
1376C22⋊Q8—532no—
1377C22⋊Q8—532no—
1378C22⋊Q8C22×D5314yes—
1379C22⋊Q8C22×D5314yes—
1380C22⋊Q8C22×D5314yes—
1381C22⋊Q8C22×D5318yes—
1382#121—531no—
1383#121—532no—
1384#121—534no—
1385#121—534no—
1386#121—532no—
1387#121—532no—
1388#121—538no—
1389#121—538no—
1390#121—532no—
1391#121—531no—
1392#121—532no—
1393#121—532no—
1394#121—538no—
1395#121—534no—
1396#121—534no—
1397#121—534no—
1398#121—534no—
1399#121—538no—
1400#121—538no—
1401#121—538no—
1402#121—531no—
1403#121—534no—
1404#121—534no—
1405#121—534no—
1406#121—532no—
1407#121—534no—
1408#121—534no—
1409#121—534no—
1410#121—532no—
1411#121—534no—
1412#121—534no—
1413#121—538no—
1414#121—534no—
1415#121—534no—
1416#121—538no—
1417#121—538no—
1418#121—531no—
1419#121—534no—
1420#121—534no—
1421#121—534no—
1422#121—534no—
1423#121—534no—
1424#121—538no—
1425#121—538no—
1426#121—538no—
1427#121—538no—
1428#121—534no—
1429#121—534no—
1430#121—538no—
1431#121—538no—
1432#121—538no—
1433#121—532no—
1434#121—532no—
1435#121—538no—
1436#121—538no—
1437#121—538no—
1438#121—538no—
1439#121—538no—
1440#121—538no—
1441#121C22×D5312yes—
1442#121C22×D5312yes—
1443#121C22×D5318yes—
1444#121C22×D5314yes—
1445#121C22×D5314yes—
1446#121C22×D5314yes—
1447#120—532no—
1448#120—538no—
1449#120—538no—
1450#120—538no—
1451#120—538no—
1452#120—532no—
1453#120—538no—
1454#120—538no—
1455#120—538no—
1456#120—538no—
1457#120—538no—
1458#120—538no—
1459#120—538no—
1460#120—538no—
1461#120—538no—
1462#120—538no—
1463#120—538no—
1464#120—538no—
1465C4×Q8—534no—
1466C4×Q8—534no—
1467C4×Q8—532no—
1468C4×Q8—531no—
1469C4×Q8—532no—
1470C4×Q8—531no—
1471C4×Q8—532no—
1472C4×Q8—532no—
1473C4×Q8C22×D5311yescharacteristic
1474C4×Q8C22×D5311yescharacteristic
1475C4×Q8C22×D5314yes—
1476C4×Q8C22×D5314yes—
1477C4×D4—532no—
1478C4×D4—532no—
1479C4×D4—534no—
1480C4×D4—534no—
1481C4×D4—532no—
1482C4×D4—532no—
1483C4×D4—532no—
1484C4×D4—532no—
1485C4×D4—532no—
1486C4×D4—532no—
1487C4×D4—532no—
1488C4×D4—532no—
1489C4×D4—532no—
1490C4×D4—532no—
1491C4×D4—538no—
1492C4×D4—538no—
1493C4×D4—532no—
1494C4×D4—534no—
1495C4×D4—534no—
1496C4×D4—534no—
1497C4×D4—534no—
1498C4×D4—534no—
1499C4×D4—534no—
1500C4×D4—534no—
1501C4×D4—532no—
1502C4×D4—534no—
1503C4×D4—534no—
1504C4×D4—534no—
1505C4×D4—538no—
1506C4×D4—534no—
1507C4×D4—534no—
1508C4×D4—534no—
1509C4×D4—534no—
1510C4×D4—538no—
1511C4×D4—532no—
1512C4×D4—532no—
1513C4×D4—532no—
1514C4×D4—532no—
1515C4×D4—532no—
1516C4×D4—532no—
1517C4×D4—531no—
1518C4×D4—531no—
1519C4×D4—538no—
1520C4×D4—538no—
1521C4×D4—534no—
1522C4×D4—538no—
1523C4×D4—534no—
1524C4×D4C22×D5312yes—
1525C4×D4C22×D5312yes—
1526C4×D4C22×D5312yes—
1527C4×D4C22×D5312yes—
1528C4×D4C22×D5311yescharacteristic
1529C4×D4C22×D5311yescharacteristic
1530C4×D4C22×D5314yes—
1531C4×D4C22×D5318yes—
1532C4×D4C22×D5314yes—
1533#117—532no—
1534#117—531no—
1535#117—532no—
1536#117—534no—
1537#117—534no—
1538#117—532no—
1539#117—532no—
1540#117—532no—
1541#117—532no—
1542#117—532no—
1543#117—538no—
1544#117C22×D5311yescharacteristic
1545#117C22×D5312yes—
1546#117C22×D5314yes—
1547#117C22×D5314yes—
1548C2×C4⋊C4—532no—
1549C2×C4⋊C4—532no—
1550C2×C4⋊C4—538no—
1551C2×C4⋊C4—534no—
1552C2×C4⋊C4C22×D5312yes—
1553C2×C4⋊C4C22×D5312yes—
1554C2×C4⋊C4C22×D5314yes—
1555C2×C22⋊C4—534no—
1556C2×C22⋊C4—534no—
1557C2×C22⋊C4—538no—
1558C2×C22⋊C4—534no—
1559C2×C22⋊C4—534no—
1560C2×C22⋊C4—538no—
1561C2×C22⋊C4—538no—
1562C2×C22⋊C4—538no—
1563C2×C42—531no—
1564C2×C42—531no—
1565C2×C42—531no—
1566C2×C42—531no—
1567C2×C42—531no—
1568C2×C42—532no—
1569C2×C42—531no—
1570C2×C42—531no—
1571C2×C42—531no—
1572C2×C42—531no—
1573C2×C42—531no—
1574C2×C42—531no—
1575C2×C42C22×D5312yes—
1576C2×C42C22×D5311yescharacteristic
1577C24—531no—
1578C24—534no—
1579C24—534no—
1580C24—538no—
1581C24—538no—
1582#41—28no—
1583#41—24no—
1584#41—48no—
1585#41—1068no—
1586#41—10616no—
1587#41—1068no—
1588#41—1064no—
1589#41—2124no—
1590#41—2128no—
1591#41—2128no—
1592#41—2128no—
1593#41—21216no—
1594#41—2128no—
1595#41—2128no—
1596#41—2124no—
1597#41—2128no—
1598#41—2128no—
1599#41—2124no—
1600#41—2128no—
1601#41—2128no—
1602#41—2128no—
1603C2×Q8—44no—
1604C2×Q8—532no—
1605C2×Q8—531no—
1606C2×Q8—532no—
1607C2×Q8—532no—
1608C2×Q8—534no—
1609C2×Q8—2124no—
1610C2×Q8C23×D5314yes—
1611C2×Q8C23×D5311yescharacteristic
1612C2×Q8C23×D5312yes—
1613C2×Q8C23×D5314yes—
1614C2×D4—534no—
1615C2×D4—532no—
1616C2×D4—532no—
1617C2×D4—532no—
1618C2×D4—534no—
1619C2×D4—532no—
1620C2×D4—532no—
1621C2×D4—534no—
1622C2×D4—538no—
1623C2×D4—534no—
1624C2×D4—538no—
1625C2×D4—534no—
1626C2×D4—538no—
1627C2×D4—538no—
1628C2×D4—534no—
1629C2×D4—532no—
1630C2×D4—538no—
1631C2×D4—532no—
1632C2×D4—531no—
1633C2×D4—534no—
1634C2×D4—532no—
1635C2×D4—534no—
1636C2×D4—534no—
1637C2×D4—532no—
1638C2×D4—532no—
1639C2×D4—534no—
1640C2×D4—538no—
1641C2×D4—534no—
1642C2×D4—538no—
1643C2×D4—538no—
1644C2×D4—538no—
1645C2×D4—534no—
1646C2×D4—538no—
1647C2×D4—538no—
1648C2×D4—1068no—
1649C2×D4—1068no—
1650C2×D4—2124no—
1651C2×D4—2128no—
1652C2×D4—2124no—
1653C2×D4—2128no—
1654C2×D4—2128no—
1655C2×D4—2128no—
1656C2×D4—2128no—
1657C2×D4—21216no—
1658C2×D4—2124no—
1659C2×D4—2128no—
1660C2×D4—2124no—
1661C2×D4—2128no—
1662C2×D4—2128no—
1663C2×D4—2128no—
1664C2×D4—21216no—
1665C2×D4—2128no—
1666C2×D4—21216no—
1667C2×D4—21216no—
1668C2×D4—21216no—
1669C2×D4C23×D5312yes—
1670C2×D4C23×D5312yes—
1671C2×D4C23×D5314yes—
1672C2×D4C23×D5312yes—
1673C2×D4C23×D5311yescharacteristic
1674C2×D4C23×D5312yes—
1675C2×D4C23×D5318yes—
1676C22×C4—531no—
1677C22×C4—531no—
1678C22×C4—531no—
1679C22×C4—531no—
1680C22×C4—534no—
1681C22×C4—531no—
1682C22×C4—531no—
1683C22×C4—531no—
1684C22×C4—531no—
1685C22×C4—531no—
1686C22×C4—531no—
1687C22×C4—531no—
1688C22×C4—531no—
1689C22×C4—531no—
1690C22×C4—532no—
1691C22×C4—532no—
1692C22×C4—532no—
1693C22×C4—538no—
1694C22×C4—534no—
1695C22×C4—531no—
1696C22×C4—531no—
1697C22×C4—534no—
1698C22×C4—538no—
1699C22×C4—534no—
1700C22×C4—538no—
1701C22×C4—538no—
1702C22×C4—538no—
1703C22×C4—1064no—
1704C22×C4—1064no—
1705C22×C4—2122no—
1706C22×C4—2128no—
1707C22×C4—2128no—
1708C22×C4C23×D5311yescharacteristic
1709C22×C4C23×D5311yescharacteristic
1710C22×C4C23×D5312yes—
1711C22×C4C23×D5312yes—
1712C22×C4C23×D5312yes—
1713C22×C4C23×D5314yes—
1714C22×C4C23×D5314yes—
1715C22×C4C23×D5318yes—
1716C22×C4C23×D5311yescharacteristic
1717C4⋊C4—532no—
1718C4⋊C4—531no—
1719C4⋊C4—534no—
1720C4⋊C4—532no—
1721C4⋊C4—532no—
1722C4⋊C4—534no—
1723C4⋊C4—538no—
1724C4⋊C4—538no—
1725C4⋊C4—532no—
1726C4⋊C4—531no—
1727C4⋊C4—532no—
1728C4⋊C4—532no—
1729C4⋊C4—532no—
1730C4⋊C4—532no—
1731C4⋊C4—532no—
1732C4⋊C4—532no—
1733C4⋊C4—532no—
1734C4⋊C4—532no—
1735C4⋊C4—532no—
1736C4⋊C4—532no—
1737C4⋊C4—532no—
1738C4⋊C4—532no—
1739C4⋊C4C23×D5314yes—
1740C4⋊C4C23×D5312yes—
1741C4⋊C4C23×D5312yes—
1742C4⋊C4C23×D5318yes—
1743C4⋊C4C23×D5311yescharacteristic
1744C4⋊C4C23×D5314yes—
1745C4⋊C4C23×D5314yes—
1746C4⋊C4C23×D5314yes—
1747C4⋊C4C23×D5318yes—
1748C4⋊C4C23×D5311yescharacteristic
1749C4⋊C4C23×D5312yes—
1750C4⋊C4C23×D5312yes—
1751C22⋊C4—532no—
1752C22⋊C4—532no—
1753C22⋊C4—534no—
1754C22⋊C4—534no—
1755C22⋊C4—532no—
1756C22⋊C4—532no—
1757C22⋊C4—532no—
1758C22⋊C4—532no—
1759C22⋊C4—532no—
1760C22⋊C4—538no—
1761C22⋊C4—534no—
1762C22⋊C4—538no—
1763C22⋊C4—538no—
1764C22⋊C4—538no—
1765C22⋊C4—538no—
1766C22⋊C4—538no—
1767C22⋊C4—534no—
1768C22⋊C4—538no—
1769C22⋊C4—534no—
1770C22⋊C4—538no—
1771C22⋊C4—534no—
1772C22⋊C4—532no—
1773C22⋊C4—532no—
1774C22⋊C4—532no—
1775C22⋊C4—532no—
1776C22⋊C4—532no—
1777C22⋊C4—532no—
1778C22⋊C4—538no—
1779C22⋊C4—538no—
1780C22⋊C4—538no—
1781C22⋊C4—532no—
1782C22⋊C4—532no—
1783C22⋊C4C23×D5318yes—
1784C22⋊C4C23×D5318yes—
1785C22⋊C4C23×D5314yes—
1786C22⋊C4C23×D5314yes—
1787C22⋊C4C23×D5312yes—
1788C22⋊C4C23×D5312yes—
1789C22⋊C4C23×D5312yes—
1790C22⋊C4C23×D5318yes—
1791C42—531no—
1792C42—531no—
1793C42—531no—
1794C42—531no—
1795C42—531no—
1796C42—531no—
1797C42—531no—
1798C42—531no—
1799C42—531no—
1800C42—531no—
1801C42—531no—
1802C42—531no—
1803C42—532no—
1804C42—532no—
1805C42—532no—
1806C42—538no—
1807C42C23×D5311yescharacteristic
1808C42C23×D5311yescharacteristic
1809C42C23×D5311yescharacteristic
1810C42C23×D5311yescharacteristic
1811C42C23×D5312yes—
1812C42C23×D5312yes—
1813C42C23×D5312yes—
1814C42C23×D5318yes—
1815C23—531no—
1816C23—532no—
1817C23—538no—
1818C23—534no—
1819C23—531no—
1820C23—1068no—
1821C23—1062no—
1822C23—1068no—
1823C23—1062no—
1824C23—2128no—
1825C23—2128no—
1826C23—2128no—
1827C23—2128no—
1828C23—2128no—
1829C23—2128no—
1830C23—2124no—
1831C23—2124no—
1832C23—2124no—
1833C23—2124no—
1834C23—2121no—
1835C23C24×D5312yes—
1836C23C24×D5314yes—
1837C23C24×D5311yescharacteristic
1838Q8—28no—
1839Q8—24no—
1840Q8—22no—
1841Q8—44no—
1842Q8—1064no—
1843Q8—1064no—
1844Q8—1062no—
1845Q8—2124no—
1846Q8—2122no—
1847D4—24no—
1848D4—28no—
1849D4—24no—
1850D4—22no—
1851D4—24no—
1852D4—24no—
1853D4—48no—
1854D4—1064no—
1855D4—10616no—
1856D4—1068no—
1857D4—1064no—
1858D4—1064no—
1859D4—1064no—
1860D4—1068no—
1861D4—1064no—
1862D4—1068no—
1863D4—1068no—
1864D4—1068no—
1865D4—1062no—
1866D4—1064no—
1867D4—1068no—
1868D4—1064no—
1869D4—2124no—
1870D4—2128no—
1871D4—2128no—
1872D4—2128no—
1873D4—2128no—
1874D4—2128no—
1875D4—2124no—
1876D4—2128no—
1877D4—2124no—
1878D4—2122no—
1879D4—2124no—
1880D4—2128no—
1881D4—2128no—
1882D4—2128no—
1883D4—2128no—
1884D4—2124no—
1885D4—2124no—
1886D4—2122no—
1887D4—2122no—
1888C2×C4—22no—
1889C2×C4—24no—
1890C2×C4—28no—
1891C2×C4—24no—
1892C2×C4—22no—
1893C2×C4—24no—
1894C2×C4—44no—
1895C2×C4—48no—
1896C2×C4—531no—
1897C2×C4—534no—
1898C2×C4—532no—
1899C2×C4—531no—
1900C2×C4—531no—
1901C2×C4—531no—
1902C2×C4—531no—
1903C2×C4—531no—
1904C2×C4—534no—
1905C2×C4—532no—
1906C2×C4—532no—
1907C2×C4—1062no—
1908C2×C4—10616no—
1909C2×C4—1062no—
1910C2×C4—1062no—
1911C2×C4—1062no—
1912C2×C4—1062no—
1913C2×C4—1064no—
1914C2×C4—1062no—
1915C2×C4—1062no—
1916C2×C4—1062no—
1917C2×C4—1062no—
1918C2×C4—1068no—
1919C2×C4—1064no—
1920C2×C4—1062no—
1921C2×C4—1062no—
1922C2×C4—1064no—
1923C2×C4—2121no—
1924C2×C4—2121no—
1925C2×C4—2124no—
1926C2×C4—2128no—
1927C2×C4—2124no—
1928C2×C4—2128no—
1929C2×C4—2128no—
1930C2×C4—2128no—
1931C2×C4—2121no—
1932C2×C4—2124no—
1933C2×C4#1313326314yescomplemented
1934C2×C4C24×D5311yescharacteristic
1935C2×C4C24×D5311yescharacteristic
1936C2×C4C24×D5318yes—
1937C2×C4C24×D5312yes—
1938C2×C4C24×D5314yes—
1939C2×C4C24×D5312yes—
1940C2×C4C24×D5312yes—
1941C2×C4C24×D5311yescharacteristic
1942C2×C4C24×D5311yescharacteristic
1943C2×C4C24×D5311yescharacteristic
1944C2×C4C24×D5311yescharacteristic
1945C22—21no—
1946C22—21no—
1947C22—22no—
1948C22—24no—
1949C22—24no—
1950C22—22no—
1951C22—22no—
1952C22—24no—
1953C22—532no—
1954C22—8488no—
1955C22—8488no—
1956C22—1061no—
1957C22—1061no—
1958C22—1061no—
1959C22—1068no—
1960C22—1062no—
1961C22—1064no—
1962C22—1061no—
1963C22—1064no—
1964C22—1062no—
1965C22—1068no—
1966C22—1061no—
1967C22—1062no—
1968C22—1068no—
1969C22—1064no—
1970C22—4248no—
1971C22—4248no—
1972C22—2124no—
1973C22C2×#1313326312yes—
1974C22C25×D5311yescharacteristic
1975C4—22no—
1976C4—21no—
1977C4—28no—
1978C4—22no—
1979C4—24no—
1980C4—21no—
1981C4—22no—
1982C4—532no—
1983C4—1061no—
1984C4—1062no—
1985C4—1061no—
1986C4—1061no—
1987C4—1062no—
1988C4—1064no—
1989C4—1061no—
1990C4—1061no—
1991C4—1062no—
1992C4H(5,𝔽2)×D5312yes—
1993C4C2×#1313326312yes—
1994C4C2×#1313326312yes—
1995C4#1681146012yes—
1996C2—22no—
1997C2—42no—
1998C2—44no—
1999C2—1062no—
2000C2—2122no—
2001C2—2128no—
2002C2—2124no—
2003C2—2121no—
2004C2C2×H(5,𝔽2)×D5311yescharacteristic
2005C2C22×#1313326311yescharacteristic
2006C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3511C2
hypercenter#3511D53
hypocenterC53#62834
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3511

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20289232C2semidirect
2. #20289230C2semidirect
3. #20289116C2semidirect
4. #20289114C2semidirect
5. #20289090C2semidirect
6. #20289088C2semidirect
7. #20289084C2semidirect
8. #20288951C2semidirect
9. #20288750C2semidirect
10. #20288748C2semidirect
11. #20288743C2semidirect
12. #20288628C2semidirect
13. #20288627C2semidirect
14. #20288592C2semidirect
15. #20288584C2semidirect
16. #20288568C2semidirect
17. #20288560C2semidirect
18. #20288493C2semidirect
19. #20288488C2semidirect
20. #20288488C2semidirect
21. #20288478C2semidirect
22. #20288473C2semidirect
23. #20288385C2semidirect
24. #20288381C2semidirect
25. #20288379C2semidirect
26. #20288008C2semidirect
27. C2×#16811174C2semidirect
28. #532×D53C2semidirect
29. C53×#3511C2semidirect
30. C2×#13133263C22semidirect
31. C2×#13133263C22semidirect
32. C2×#13133263C22semidirect
33. C22×#11719949C22semidirect
34. C2×#41×D53C22semidirect
35. #16811369C22semidirect
36. #16811365C22semidirect
37. #16811364C22semidirect
38. #16811363C22semidirect
39. #16811358C22semidirect
40. #16811358C22semidirect
41. #16811356C22semidirect
42. #16811355C22semidirect
43. #16811347C22semidirect
44. #16811345C22semidirect
45. #16811339C22semidirect
46. #16811336C22semidirect
47. #16811336C22semidirect
48. #16811334C22semidirect
49. #16811329C22semidirect
50. #16811326C22semidirect
51. #16811324C22semidirect
52. #16811321C22semidirect
53. #16811321C22semidirect
54. #16811317C22semidirect
55. #16811317C22semidirect
56. #16811295C22semidirect
57. #16811295C22semidirect
58. #16811295C22semidirect
59. #16811295C22semidirect
60. #16811294C22semidirect
61. #16811294C22semidirect
62. #16811294C22semidirect
63. #16811294C22semidirect
64. #16811292C22semidirect
65. #16811291C22semidirect
66. #16811285C22semidirect
67. #16811284C22semidirect
68. #16811283C22semidirect
69. #16811276C22semidirect
70. #16811275C22semidirect
71. #16811275C22semidirect
72. #16811274C22semidirect
73. #16811270C22semidirect
74. #16811270C22semidirect
75. #16811268C22semidirect
76. #16811268C22semidirect
77. #16811266C22semidirect
78. #16811266C22semidirect
79. #16811265C22semidirect
80. #16811264C22semidirect
81. #16811264C22semidirect
82. #16811264C22semidirect
83. #16811264C22semidirect
84. #16811264C22semidirect
85. #16811264C22semidirect
86. #16811262C22semidirect
87. #16811261C22semidirect
88. D4×D212C22semidirect
89. D4×D212C22semidirect
90. D4×D212C22semidirect
91. D4×D212C22semidirect
92. D4×D212C22semidirect
93. D4×D212C22semidirect
94. D4×D212C22semidirect
95. D4×D212C22semidirect
96. D4×D212C22semidirect
97. #16811257C22semidirect
98. #16811257C22semidirect
99. #16811257C22semidirect
100. #16811257C22semidirect
101. #16811257C22semidirect
102. #16811257C22semidirect
103. #16811257C22semidirect
104. #16811257C22semidirect
105. #16811247C22semidirect
106. #16811246C22semidirect
107. #16811245C22semidirect
108. #16811229C22semidirect
109. #16811229C22semidirect
110. #16811226C22semidirect
111. #16811224C22semidirect
112. #16811213C22semidirect
113. #16811212C22semidirect
114. #16811212C22semidirect
115. #16811209C22semidirect
116. #16811207C22semidirect
117. #16811206C22semidirect
118. #16811204C22semidirect
119. #16811204C22semidirect
120. #16811203C22semidirect
121. #16811203C22semidirect
122. #16811203C22semidirect
123. #16811192C22semidirect
124. #16811192C22semidirect
125. #16811192C22semidirect
126. #16811192C22semidirect
127. #16811191C22semidirect
128. #16811191C22semidirect
129. #16811191C22semidirect
130. #16811191C22semidirect
131. #16811189C22semidirect
132. #16811189C22semidirect
133. #16811187C22semidirect
134. #16811187C22semidirect
135. #16811184C22semidirect
136. #16811181C22semidirect
137. #16811178C22semidirect
138. #16811177C22semidirect
139. #16811177C22semidirect
140. #16811176C22semidirect
141. #16811174C22semidirect
142. #16811174C22semidirect
143. #16811174C22semidirect
144. #16811174C22semidirect
145. #16811174C22semidirect
146. #16811174C22semidirect
147. #16811174C22semidirect
148. #16811174C22semidirect
149. #16811174C22semidirect
150. #16811174C22semidirect
151. #16811174C22semidirect
152. #16811173C22semidirect
153. #16811173C22semidirect
154. #16811172C22semidirect
155. #16811171C22semidirect
156. #16811170C22semidirect
157. #16811170C22semidirect
158. #16811170C22semidirect
159. #16811170C22semidirect
160. #16811169C22semidirect
161. #16811169C22semidirect
162. #16811168C22semidirect
163. #16811168C22semidirect
164. C4⋊Q8×D53C22semidirect
165. C2×#13133214C22semidirect
166. C2×#13133214C22semidirect
167. #127×D53C22semidirect
168. #127×D53C22semidirect
169. #16811160C22semidirect
170. #16811160C22semidirect
171. #16811155C22semidirect
172. #16811155C22semidirect
173. #16811153C22semidirect
174. #16811153C22semidirect
175. #16811151C22semidirect
176. #16811151C22semidirect
177. C2×#13133206C22semidirect
178. #124×D53C22semidirect
179. #16811136C22semidirect
180. #16811135C22semidirect
181. #16811135C22semidirect
182. #16811132C22semidirect
183. #16811132C22semidirect
184. #16811132C22semidirect
185. #16811130C22semidirect
186. C2×#13133192C22semidirect
187. C2×#13133192C22semidirect
188. C2×#13133192C22semidirect
189. #121×D53C22semidirect
190. #121×D53C22semidirect
191. #121×D53C22semidirect
192. #121×D53C22semidirect
193. #16811105C22semidirect
194. #16811104C22semidirect
195. #16811097C22semidirect
196. #16811095C22semidirect
197. C4×#11719945C22semidirect
198. C4×#11719945C22semidirect
199. C4×#11719945C22semidirect
200. C2×#13133179C22semidirect
201. C2×#13133179C22semidirect
202. C4×D4×D53C22semidirect
203. C4×D4×D53C22semidirect
204. C2×C42×D53C22semidirect
205. C53×#556C22semidirect
206. C53×#555C22semidirect
207. C53×#554C22semidirect
208. C53×#553C22semidirect
209. C53×#548C22semidirect
210. C53×#547C22semidirect
211. C53×#542C22semidirect
212. C53×#537C22semidirect
213. C53×#533C22semidirect
214. C53×#532C22semidirect
215. C53×#532C22semidirect
216. C2×C4⋊Q8×C53C22semidirect
217. C53×#520C22semidirect
218. C4×#41×C53C22semidirect
853. C2×C4×C53H(5,𝔽2)semidirect
935. C4×D53H(5,𝔽2)semidirect
1006. #3511D53semidirect
1048. #556C2×D53semidirect
1052. #555C2×D53semidirect
1055. #554C2×D53semidirect
1062. #553C2×D53semidirect
1076. #548C2×D53semidirect
1081. #547C2×D53semidirect
1117. #542C2×D53semidirect
1133. #537C2×D53semidirect
1152. #533C2×D53semidirect
1176. #532C2×D53semidirect
1177. #532C2×D53semidirect
1179. C2×C4⋊Q8C2×D53semidirect
1210. #520C2×D53semidirect
1216. C4×#41C2×D53semidirect
1222. C53#62834semidirect
1933. C2×C4#13133263semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202892322
#202892302
#202891162
#202891142
#202890902
#202890882
#202890842
#202889512
#202887502
#202887482
#202887432
#202886282
#202886272
#202885922
#202885842
#202885682
#202885602
#202884932
#202884882
#202884782
#202884732
#202883852
#202883812
#202883792
#202880082
C2×#168111742
#532×D532
C53×#35112
#6283453