Finite Group Databasebeta

← #28293039

Subgroups — #28293039

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289310C214yesmaximal, complemented
2#20289301C214yesmaximal, complemented
3#20289183C214yesmaximal, complemented
4#20289084C214yesmaximal, complemented
5#20289024C218yesmaximal, complemented
6#20288719C214yesmaximal, complemented
7#20288664C214yesmaximal, complemented
8#20288642C218yesmaximal, complemented
9#20288619C214yesmaximal, complemented
10#20288613C211yesmaximal, characteristic, complemented
11#20288596C211yesmaximal, characteristic, complemented
12#20288588C214yesmaximal, complemented
13#20288586C211yesmaximal, characteristic, complemented
14#20288508C211yesmaximal, characteristic, complemented
15#20288505C211yesmaximal, characteristic, complemented
16#20288497C211yesmaximal, characteristic, complemented
17#20288490C211yesmaximal, characteristic, complemented
18#20288374C211yesmaximal, characteristic, complemented
19#20288371C211yesmaximal, characteristic, complemented
20#20288360C211yesmaximal, characteristic, complemented
21#20288358C211yesmaximal, characteristic, complemented
22#20288012C211yesmaximal, characteristic, complemented
23#20288008C211yesmaximal, characteristic, complemented
24C2×#16811172C211yesmaximal, characteristic, complemented
25C53×#3510C211yesmaximal, characteristic, complemented
26C2×#13133265C2211yescharacteristic, complemented
27C2×#13133264C2211yescharacteristic, complemented
28C2×#13133263C2211yescharacteristic
29C2×#13133262C2211yescharacteristic
30C22×#11719949C2211yescharacteristic, complemented
31C22×#11719947C2211yescharacteristic, complemented
32#16811369C2218yescomplemented
33#16811367C2218yescomplemented
34#16811364C2218yescomplemented
35#16811363C2218yescomplemented
36#16811358C2214yescomplemented
37#16811356C2214yescomplemented
38#16811355C2218yescomplemented
39#16811351C2214yescomplemented
40#16811346C2214yescomplemented
41#16811345C2214yescomplemented
42#16811336C2218yescomplemented
43#16811331C2218yescomplemented
44#16811324C2218yescomplemented
45#16811324C2218yescomplemented
46#16811324C2218yescomplemented
47#16811319C2218yescomplemented
48#16811306C2218yescomplemented
49#16811300C2218yescomplemented
50#16811297C2218yescomplemented
51#16811296C2218yescomplemented
52#16811295C2214yescomplemented
53#16811295C2214yescomplemented
54#16811294C2218yescomplemented
55#16811294C2214yescomplemented
56#16811293C2214yescomplemented
57#16811291C2214yescomplemented
58#16811291C2214yescomplemented
59#16811286C2214yescomplemented
60#16811285C2214yescomplemented
61#16811285C2214yescomplemented
62#16811285C2214yescomplemented
63#16811281C2214yescomplemented
64#16811281C2214yescomplemented
65#16811279C2214yescomplemented
66#16811277C2214yescomplemented
67#16811277C2214yescomplemented
68#16811276C2214yescomplemented
69#16811275C2214yescomplemented
70#16811275C2214yescomplemented
71#16811271C2218yescomplemented
72#16811268C2218yescomplemented
73#16811268C2214yescomplemented
74#16811268C2214yescomplemented
75#16811268C2214yescomplemented
76#16811266C2214yescomplemented
77#16811266C2214yescomplemented
78#16811265C2218yescomplemented
79#16811265C2218yescomplemented
80#16811264C2214yescomplemented
81#16811263C2218yescomplemented
82#16811263C2218yescomplemented
83#16811257C2214yescomplemented
84#16811255C2218yes—
85#16811247C2214yescomplemented
86#16811239C2218yescomplemented
87#16811239C2218yescomplemented
88#16811231C2214yescomplemented
89#16811228C2218yescomplemented
90#16811225C2218yescomplemented
91#16811225C2218yescomplemented
92#16811225C2218yescomplemented
93#16811224C2214yescomplemented
94#16811217C2218yescomplemented
95#16811214C2218yescomplemented
96#16811213C2218yescomplemented
97#16811212C2218yescomplemented
98#16811207C2218yescomplemented
99#16811206C2218yescomplemented
100#16811203C2218yescomplemented
101#16811199C2211yescharacteristic
102#16811199C2211yescharacteristic, complemented
103#16811199C2212yescomplemented
104#16811198C2212yescomplemented
105#16811197C2211yescharacteristic
106#16811193C2212yescomplemented
107#16811193C2212yescomplemented
108#16811192C2211yescharacteristic
109#16811192C2214yescomplemented
110#16811192C2212yescomplemented
111#16811192C2211yescharacteristic, complemented
112#16811191C2218yescomplemented
113#16811191C2212yescomplemented
114#16811191C2212yescomplemented
115#16811190C2211yescharacteristic, complemented
116#16811188C2214yescomplemented
117#16811186C2212yescomplemented
118#16811185C2214yescomplemented
119#16811184C2214yescomplemented
120#16811178C2212yescomplemented
121#16811177C2212yescomplemented
122#16811177C2214yescomplemented
123#16811176C2211yescharacteristic, complemented
124#16811174C2212yescomplemented
125#16811173C2211yescharacteristic
126#16811173C2212yescomplemented
127#16811172C2214yescomplemented
128#16811172C2214yescomplemented
129#16811172C2212yescomplemented
130#16811172C2214yescomplemented
131#16811172C2212yescomplemented
132#16811172C2214yescomplemented
133#16811172C2212yescomplemented
134#16811170C2212yescomplemented
135#16811170C2214yescomplemented
136#16811169C2211yescharacteristic
137C2×#13133215C2211yescharacteristic, complemented
138C4⋊Q8×D53C2212yescomplemented
139C2×#13133213C2211yescharacteristic
140#127×D53C2212yescomplemented
141#16811160C2212yescomplemented
142#16811160C2214yescomplemented
143#16811159C2214yescomplemented
144#16811158C2212yescomplemented
145#16811158C2212yescomplemented
146#16811158C2214yescomplemented
147#16811155C2212yescomplemented
148#16811153C2214yescomplemented
149#16811151C2214yescomplemented
150C2×#13133205C2211yescharacteristic, complemented
151C2×#13133205C2212yescomplemented
152#124×D53C2212yescomplemented
153#16811136C2214yescomplemented
154#16811135C2211yescharacteristic
155#16811135C2211yescharacteristic, complemented
156#16811135C2211yescharacteristic, complemented
157#16811135C2214yescomplemented
158#16811132C2214yescomplemented
159#16811130C2211yescharacteristic, complemented
160#16811129C2214yescomplemented
161C2×#13133201C2214yescomplemented
162#123×D53C2214yescomplemented
163C2×#13133190C2214yescomplemented
164#16811103C2218yescomplemented
165#16811100C2211yescharacteristic, complemented
166#16811097C2211yescharacteristic, complemented
167#16811095C2218yescomplemented
168C4×#11719949C2214yescomplemented
169C4×#11719945C2211yescharacteristic, complemented
170C4×#11719945C2214yescomplemented
171#16811091C2211yescharacteristic
172#16811091C2211yescharacteristic, complemented
173C2×#13133177C2214yescomplemented
174C2×C42×D53C2211yescharacteristic, complemented
175C53×#559C2214yescomplemented
176C53×#556C2214yescomplemented
177C53×#551C2218yescomplemented
178C53×#542C2214yescomplemented
179C53×#536C2211yescharacteristic, complemented
180C53×#535C2211yescharacteristic
181C53×#533C2211yescharacteristic, complemented
182C53×#529C2214yescomplemented
183C2×#124×C53C2211yescharacteristic, complemented
184C53×#519C2211yescharacteristic, complemented
185C53×#518C2211yescharacteristic, complemented
186C4×#41×C53C2211yescharacteristic, complemented
187#13133265—44no—
188#13133264—44no—
189#13133263—44no—
190#13133262—44no—
191C2×#11719949—44no—
192C2×#11719949C2314yes—
193C2×#11719949C2312yes—
194C2×#11719949C2314yes—
195C2×#11719949C2312yes—
196C2×#11719949C2312yes—
197C2×#11719949C2314yes—
198C2×#11719945C2311yescharacteristic
199C2×#11719945C2311yescharacteristic
200C2×#11719945C2311yescharacteristic
201C2×#11719945C2314yes—
202C2×#11719945C2318yes—
203C2×#11719945C2314yes—
204C2×#11719945C2312yes—
205C2×#11719945C2312yes—
206C2×#11719947—44no—
207C2×#11719947C2314yes—
208C2×#11719947C2312yes—
209C2×#11719947C2314yes—
210C2×#11719947C2314yes—
211C2×#11719947C2312yes—
212C2×#11719947C2312yes—
213C22×Dic106C2311yescharacteristic
214C22×Dic106C2312yes—
215C2×Q8×D53C2312yes—
216C2×Q8×D53C2312yes—
217C2×Q8×D53C2312yes—
218C22×D212C2311yescharacteristic
219C22×D212C2312yes—
220C22×D212C2312yes—
221C22×C22⋊D53C2314yes—
222C22×C22⋊D53C2312yes—
223C22×C22⋊D53C2314yes—
224C2×D4×D53C2318yes—
225C2×D4×D53C2312yes—
226C2×D4×D53C2312yes—
227C2×D4×D53C2314yes—
228C2×D4×D53C2312yes—
229C23×Dic53C2312yes—
230C22×C4×D53C2311yescharacteristic
231C22×C4×D53C2312yes—
232C22×C4×D53C2312yes—
233#13133217C2312yes—
234#13133217C2312yes—
235#13133217C2311yescharacteristic
236#13133216C2318yes—
237#13133216C2312yes—
238#13133215C2312yes—
239#13133215C2314yes—
240#13133215C2311yescharacteristic
241#13133215C2312yes—
242#13133215C2312yes—
243#13133214C2312yes—
244#13133214C2318yes—
245#13133214C2312yes—
246#13133214C2311yescharacteristic
247#13133213C2312yes—
248#13133213C2318yes—
249#13133213C2318yes—
250#13133213C2314yes—
251#13133213C2311yescharacteristic
252#13133213C2312yes—
253#13133213C2312yes—
254#13133212C2314yes—
255#13133212C2318yes—
256#13133212C2318yes—
257#13133212C2318yes—
258#13133212C2314yes—
259#13133212C2314yes—
260#13133211C2318yes—
261#13133210C2314yes—
262#13133209C2318yes—
263#13133208C2312yes—
264#13133208C2314yes—
265#13133207C2318yes—
266#13133207C2318yes—
267#13133207C2314yes—
268#13133206C2312yes—
269#13133206C2318yes—
270#13133206C2314yes—
271#13133206C2311yescharacteristic
272#13133205C2312yes—
273#13133205C2312yes—
274#13133205C2318yes—
275#13133205C2314yes—
276#13133205C2318yes—
277#13133205C2312yes—
278#13133205C2312yes—
279#13133205C2311yescharacteristic
280#13133205C2312yes—
281#13133205C2312yes—
282#13133205C2311yescharacteristic
283#13133204C2312yes—
284#13133204C2311yescharacteristic
285#13133203C2314yes—
286#13133203C2318yes—
287#13133203C2318yes—
288#13133203C2318yes—
289#13133202C2318yes—
290#13133202C2318yes—
291#13133202C2318yes—
292#13133202C2318yes—
293#13133202C2318yes—
294#13133202C2314yes—
295#13133202C2314yes—
296#13133202C2314yes—
297#13133201C2314yes—
298#13133201C2318yes—
299#13133201C2318yes—
300#13133201C2318yes—
301#13133201C2314yes—
302#13133201C2318yes—
303#13133201C2312yes—
304#13133201C2312yes—
305#13133201C2312yes—
306#13133200C2318yes—
307#13133200C2314yes—
308#13133199C2318yes—
309#13133199C2318yes—
310#13133199C2318yes—
311#13133199C2318yes—
312#13133199C2314yes—
313#13133198C2312yes—
314#13133197C2314yes—
315#13133197C2314yes—
316#13133197C2318yes—
317#13133197C2312yes—
318#13133197C2312yes—
319#13133197C2312yes—
320#13133197C2318yes—
321#13133195C2318yes—
322#13133195C2318yes—
323#13133195C2314yes—
324#13133194C2318yes—
325#13133194C2318yes—
326#13133194C2318yes—
327#13133194C2314yes—
328#13133193C2314yes—
329#13133193C2312yes—
330#13133193C2318yes—
331#13133193C2314yes—
332#13133192C2312yes—
333#13133192C2318yes—
334#13133192C2318yes—
335#13133192C2318yes—
336#13133192C2312yes—
337#13133192C2314yes—
338#13133192C2318yes—
339#13133192C2314yes—
340#13133192C2318yes—
341#13133192C2312yes—
342#13133192C2314yes—
343#13133191C2318yes—
344#13133191C2314yes—
345#13133191C2318yes—
346#13133191C2318yes—
347#13133191C2318yes—
348#13133190C2318yes—
349#13133190C2318yes—
350#13133190C2318yes—
351#13133190C2318yes—
352#13133190C2318yes—
353#13133190C2318yes—
354#13133190C2318yes—
355#13133190C2318yes—
356#13133190C2318yes—
357#13133190C2318yes—
358#13133190C2318yes—
359#13133190C2318yes—
360#13133190C2318yes—
361#13133190C2314yes—
362#13133189C2318yes—
363#13133189C2318yes—
364#13133189C2314yes—
365#13133189C2318yes—
366#13133188C2312yes—
367#13133188C2314yes—
368#13133187C2318yes—
369#13133187C2318yes—
370#13133187C2318yes—
371#13133187C2318yes—
372#13133187C2314yes—
373#13133187C2318yes—
374#13133187C2314yes—
375#13133187C2312yes—
376#13133187C2312yes—
377#13133187C2312yes—
378#13133186C2314yes—
379#13133185C2318yes—
380#13133185C2312yes—
381Q8×Dic53C2314yes—
382C4×Dic106C2312yes—
383C4×Dic106C2314yes—
384C4×Dic106C2318yes—
385C4×Dic106C2314yes—
386C4×Dic106C2314yes—
387#13133182C2314yes—
388#13133182C2312yes—
389#13133182C2312yes—
390C4×D212C2312yes—
391C4×D212C2314yes—
392C4×D212C2314yes—
393C4×D212C2314yes—
394C4×D212C2314yes—
395C4×D212C2318yes—
396C4×D212C2314yes—
397C4×D212C2318yes—
398C4×D212C2318yes—
399C4×D212C2314yes—
400D4×Dic53C2318yes—
401#13133179C2314yes—
402#13133179C2314yes—
403#13133179C2314yes—
404#13133179C2312yes—
405#13133179C2314yes—
406#13133179C2318yes—
407#13133179C2312yes—
408C4×C22⋊D53C2314yes—
409C4×C22⋊D53C2314yes—
410C4×C22⋊D53C2314yes—
411C4×C22⋊D53C2318yes—
412C4×C22⋊D53C2314yes—
413C4×C22⋊D53C2314yes—
414#13133177C2318yes—
415#13133177C2318yes—
416#13133177C2314yes—
417#13133177C2318yes—
418#13133177C2318yes—
419#13133177C2318yes—
420#13133177C2318yes—
421#13133177C2314yes—
422#13133177C2318yes—
423#13133177C2318yes—
424#13133176C2314yes—
425#13133176C2311yescharacteristic
426#13133175C2318yes—
427#13133175C2314yes—
428#13133175C2314yes—
429#13133175C2314yes—
430#13133174C2314yes—
431#13133174C2318yes—
432#13133174C2314yes—
433#13133174C2312yes—
434#13133174C2312yes—
435#13133174C2312yes—
436#13133173C2314yes—
437C2×C4⋊Dic53C2318yes—
438C2×#11719919C2314yes—
439C4⋊C4×D53C2318yes—
440C4⋊C4×D53C2318yes—
441C2×#11719921C2318yes—
442C2×#11719921C2318yes—
443C2×#11719921C2314yes—
444C22⋊C4×D53C2318yes—
445C22⋊C4×D53C2318yes—
446C22⋊C4×D53C2314yes—
447C2×C4×Dic53C2312yes—
448C2×C4×Dic53C2311yescharacteristic
449C42×D53C2312yes—
450C42×D53C2312yes—
451C42×D53C2312yes—
452C42×D53C2312yes—
453C42×D53C2312yes—
454C42×D53C2312yes—
455C42×D53C2312yes—
456C2×#41×C53C2311yescharacteristic
457C22×Q8×C53C2311yescharacteristic
458C22×D4×C53C2311yescharacteristic
459C4⋊Q8×C53C2312yes—
460C4⋊Q8×C53C2312yes—
461#127×C53C2312yes—
462#126×C53C2318yes—
463#126×C53C2318yes—
464#125×C53C2312yes—
465#124×C53C2312yes—
466#124×C53C2314yes—
467#124×C53C2312yes—
468#124×C53C2312yes—
469#124×C53C2312yes—
470#124×C53C2318yes—
471#123×C53C2318yes—
472#123×C53C2318yes—
473#123×C53C2314yes—
474C22⋊Q8×C53C2314yes—
475C22⋊Q8×C53C2314yes—
476C22⋊Q8×C53C2318yes—
477#121×C53C2314yes—
478#120×C53C2314yes—
479C4×Q8×C53C2312yes—
480C4×Q8×C53C2314yes—
481C4×Q8×C53C2314yes—
482C4×Q8×C53C2314yes—
483C4×D4×C53C2314yes—
484C4×D4×C53C2312yes—
485C4×D4×C53C2314yes—
486C4×D4×C53C2314yes—
487C4×D4×C53C2318yes—
488#117×C53C2311yescharacteristic
489#117×C53C2312yes—
490#117×C53C2311yescharacteristic
491#117×C53C2318yes—
492#117×C53C2314yes—
493#117×C53C2311yescharacteristic
494C2×C22⋊C4×C53C2314yes—
495C2×C22⋊C4×C53C2314yes—
496C2×C42×C53C2311yescharacteristic
497C2×C42×C53C2312yes—
498C24×C53C2412yes—
499C23×D53C2412yes—
500C23×D53C2411yescharacteristic
501C23×D53C2414yes—
502C23×D53C2414yes—
503#41×C53—24no—
504C2×Q8×C53—24no—
505C2×Q8×C53C2412yes—
506C2×Q8×C53C2412yes—
507C2×Q8×C53C2411yescharacteristic
508C2×Q8×C53C2414yes—
509C2×D4×C53—24no—
510C2×D4×C53C2412yes—
511C2×D4×C53C2412yes—
512C2×D4×C53C2412yes—
513C2×D4×C53C2411yescharacteristic
514C2×D4×C53C2418yes—
515C22×C4×C53C2412yes—
516C22×C4×C53C2412yes—
517C22×C4×C53C2412yes—
518C22×C4×C53C2414yes—
519C22×C4×C53C2418yes—
520C22×C4×C53C2411yescharacteristic
521C2×C22⋊D53—48no—
522C2×C22⋊D53—44no—
523C2×C22⋊D53—48no—
524C2×C22⋊D53C2418yes—
525C2×C22⋊D53C2414yes—
526C2×C22⋊D53C2412yes—
527C2×C22⋊D53C2412yes—
528C2×C22⋊D53C2412yes—
529C2×C22⋊D53C2418yes—
530C2×C22⋊D53C2418yes—
531C2×C22⋊D53C2414yes—
532C2×C22⋊D53C2414yes—
533C2×C22⋊D53C2414yes—
534C2×C22⋊D53C2418yes—
535C2×C22⋊D53C2414yes—
536C2×C22⋊D53C2414yes—
537C22×Dic53—44no—
538C22×Dic53C2412yes—
539C22×Dic53C2411yescharacteristic
540C22×Dic53C2412yes—
541C22×Dic53C2414yes—
542C22×Dic53C2418yes—
543C22×Dic53C2414yes—
544#11719949—48no—
545#11719949—48no—
546#11719949—48no—
547#11719949—44no—
548#11719949—44no—
549#11719949—44no—
550Q8×D53—44no—
551Q8×D53—44no—
552Q8×D53—44no—
553#11719947—48no—
554#11719947—48no—
555#11719947—44no—
556#11719947—44no—
557#11719947—44no—
558#11719947—48no—
559D4×D53—44no—
560D4×D53—44no—
561D4×D53—44no—
562D4×D53—416no—
563D4×D53—48no—
564#11719945—24no—
565#11719945—24no—
566#11719945—24no—
567#11719945—48no—
568#11719945—416no—
569#11719945—44no—
570#11719945—44no—
571#11719945—48no—
572C2×D212—24no—
573C2×D212—44no—
574C2×D212—44no—
575C2×D212C2411yescharacteristic
576C2×D212C2412yes—
577C2×D212C2411yescharacteristic
578C2×D212C2412yes—
579C2×D212C2411yescharacteristic
580C2×D212C2414yes—
581C2×D212C2414yes—
582C2×D212C2418yes—
583C2×D212C2414yes—
584C2×D212C2414yes—
585C2×D212C2418yes—
586C2×D212C2414yes—
587C2×D212C2414yes—
588C2×D212C2418yes—
589C2×C4×D53—24no—
590C2×C4×D53—44no—
591C2×C4×D53—44no—
592C2×C4×D53C2412yes—
593C2×C4×D53C2412yes—
594C2×C4×D53C2412yes—
595C2×C4×D53C2412yes—
596C2×C4×D53C2414yes—
597C2×C4×D53C2414yes—
598C2×C4×D53C2412yes—
599C2×C4×D53C2412yes—
600C2×C4×D53C2412yes—
601C2×C4×D53C2412yes—
602C2×C4×D53C2412yes—
603C2×C4×D53C2414yes—
604C2×C4×D53C2418yes—
605C2×C4×D53C2414yes—
606C2×C4×D53C2418yes—
607C2×C4×D53C2414yes—
608C2×C4×D53C2414yes—
609C2×C4×D53C2414yes—
610C2×Dic106—24no—
611C2×Dic106—44no—
612C2×Dic106C2411yescharacteristic
613C2×Dic106C2412yes—
614C2×Dic106C2411yescharacteristic
615C2×Dic106C2414yes—
616C2×Dic106C2411yescharacteristic
617C2×Dic106C2412yes—
618C2×Dic106C2414yes—
619C2×Dic106C2414yes—
620C4⋊C4×C53C2414yes—
621C4⋊C4×C53C2412yes—
622C4⋊C4×C53C2412yes—
623C4⋊C4×C53C2414yes—
624C4⋊C4×C53C2412yes—
625C4⋊C4×C53C2418yes—
626C4⋊C4×C53C2418yes—
627C4⋊C4×C53C2414yes—
628C4⋊C4×C53C2414yes—
629C22⋊C4×C53C2412yes—
630C22⋊C4×C53C2412yes—
631C22⋊C4×C53C2418yes—
632C22⋊C4×C53C2418yes—
633C22⋊C4×C53C2418yes—
634C22⋊C4×C53C2412yes—
635C22⋊C4×C53C2414yes—
636C22⋊C4×C53C2418yes—
637C22⋊C4×C53C2418yes—
638C42×C53C2411yescharacteristic
639C42×C53C2412yes—
640C42×C53C2414yes—
641C42×C53C2411yescharacteristic
642C42×C53C2412yes—
643C42×C53C2418yes—
644C42×C53C2412yes—
645C42×C53C2412yes—
646C22⋊Dic53C2412yes—
647C22⋊Dic53C2414yes—
648C22⋊Dic53C2418yes—
649C22⋊Dic53C2414yes—
650#11719921C2414yes—
651#11719921C2414yes—
652#11719921C2418yes—
653#11719921C2418yes—
654#11719921C2414yes—
655#11719921C2418yes—
656#11719921C2418yes—
657#11719921C2418yes—
658#11719921C2418yes—
659#11719921C2418yes—
660#11719921C2414yes—
661#11719921C2414yes—
662#11719921C2414yes—
663#11719921C2414yes—
664#11719921C2414yes—
665#11719921C2414yes—
666#11719921C2414yes—
667#11719921C2414yes—
668#11719921C2418yes—
669#11719921C2414yes—
670#11719921C2414yes—
671C4⋊Dic53C2414yes—
672C4⋊Dic53C2418yes—
673C4⋊Dic53C2414yes—
674C4⋊Dic53C2418yes—
675C4⋊Dic53C2414yes—
676C4⋊Dic53C2414yes—
677C4⋊Dic53C2412yes—
678C4⋊Dic53C2414yes—
679#11719919C2414yes—
680#11719919C2414yes—
681#11719919C2418yes—
682#11719919C2418yes—
683#11719919C2418yes—
684#11719919C2418yes—
685#11719919C2414yes—
686#11719919C2414yes—
687#11719919C2414yes—
688#11719919C2414yes—
689#11719919C2414yes—
690C4×Dic53C2411yescharacteristic
691C4×Dic53C2411yescharacteristic
692C4×Dic53C2412yes—
693C4×Dic53C2412yes—
694C4×Dic53C2412yes—
695C4×Dic53C2412yes—
696C4×Dic53C2412yes—
697C4×Dic53C2414yes—
698C4×Dic53C2412yes—
699C4×Dic53C2414yes—
700C4×Dic53C2414yes—
701C4×Dic53C2418yes—
702C23×C53—24no—
703C23×C53—44no—
704C23×C53C2514yes—
705C23×C53C2512yes—
706C23×C53C2511yescharacteristic
707C22×D53—22no—
708C22×D53—24no—
709C22×D53—42no—
710C22×D53—44no—
711C22×D53—44no—
712C22×D53—44no—
713C22×D53—48no—
714C22×D53—48no—
715C22×D53C2512yes—
716C22×D53C2512yes—
717C22×D53C2512yes—
718C22×D53C2514yes—
719C22×D53C2512yes—
720Q8×C53—22no—
721Q8×C53—24no—
722Q8×C53—24no—
723Q8×C53—44no—
724D4×C53—24no—
725D4×C53—22no—
726D4×C53—24no—
727D4×C53—24no—
728D4×C53—48no—
729C2×C4×C53—24no—
730C2×C4×C53—24no—
731C2×C4×C53—42no—
732C2×C4×C53—44no—
733C2×C4×C53—48no—
734C2×C4×C53H(5,𝔽2)14yes—
735C2×C4×C53C2512yes—
736C2×C4×C53C2514yes—
737C2×C4×C53C2514yes—
738C2×C4×C53C2512yes—
739C2×C4×C53C2514yes—
740C2×C4×C53C2512yes—
741C2×C4×C53C2514yes—
742C2×C4×C53C2511yescharacteristic
743C2×C4×C53C2511yescharacteristic
744C22⋊D53—24no—
745C22⋊D53—24no—
746C22⋊D53—24no—
747C22⋊D53—28no—
748C22⋊D53—216no—
749C22⋊D53—44no—
750C22⋊D53—44no—
751C22⋊D53—44no—
752C22⋊D53—48no—
753C22⋊D53—44no—
754C22⋊D53—44no—
755C22⋊D53—48no—
756C22⋊D53—48no—
757C2×Dic53—24no—
758C2×Dic53—22no—
759C2×Dic53—24no—
760C2×Dic53—44no—
761C2×Dic53—48no—
762C2×Dic53—44no—
763C2×Dic53C2512yes—
764C2×Dic53C2512yes—
765C2×Dic53C2514yes—
766C2×Dic53C2512yes—
767C2×Dic53C2514yes—
768C2×Dic53C2512yes—
769C2×Dic53C2512yes—
770C2×Dic53C2512yes—
771D212—24no—
772D212—24no—
773D212—22no—
774D212—22no—
775D212—22no—
776D212—44no—
777D212—48no—
778D212—44no—
779D212—48no—
780D212—44no—
781D212—48no—
782D212—44no—
783D212—44no—
784D212—44no—
785C4×D53—24no—
786C4×D53—24no—
787C4×D53—24no—
788C4×D53—24no—
789C4×D53—24no—
790C4×D53—24no—
791C4×D53—24no—
792C4×D53—28no—
793C4×D53—28no—
794C4×D53—42no—
795C4×D53—42no—
796C4×D53—48no—
797C4×D53—44no—
798C4×D53—48no—
799C4×D53—44no—
800C4×D53—44no—
801C4×D53—44no—
802C4×D53—44no—
803Dic106—24no—
804Dic106—24no—
805Dic106—22no—
806Dic106—22no—
807Dic106—22no—
808Dic106—28no—
809Dic106—44no—
810Dic106—44no—
811#62836—531nomaximal, Sylow
812C22×C53—22no—
813C22×C53—24no—
814C22×C53—22no—
815C22×C53—28no—
816C22×C53—24no—
817C22×C53—84no—
818C22×C53C2×H(5,𝔽2)12yes—
819C22×C53C2611yescharacteristic
820C2×D53—22no—
821C2×D53—22no—
822C2×D53—22no—
823C2×D53—22no—
824C2×D53—24no—
825C2×D53—22no—
826C2×D53—22no—
827C2×D53—24no—
828C2×D53—24no—
829C2×D53—24no—
830C2×D53—28no—
831C2×D53—44no—
832C2×D53—84no—
833C2×D53—164no—
834C2×D53—164no—
835C4×C53—22no—
836C4×C53—24no—
837C4×C53—24no—
838C4×C53—22no—
839C4×C53—24no—
840C4×C53—22no—
841C4×C53—24no—
842C4×C53C2×H(5,𝔽2)12yes—
843C4×C53C2×H(5,𝔽2)12yes—
844Dic53—24no—
845Dic53—22no—
846Dic53—22no—
847Dic53—22no—
848Dic53—22no—
849Dic53—24no—
850Dic53—22no—
851Dic53#58514yes—
852#3562—534no—
853#3562—534no—
854#3554—534no—
855#3546—534no—
856#3542—538no—
857#3517—534no—
858#3514—534no—
859#3513—538no—
860#3511—534no—
861#3510—531no—
862#3510D5311yescharacteristic, complemented
863#3509—531no—
864#3508—534no—
865#3508—531no—
866#3500—531no—
867#3500—531no—
868#3499—531no—
869#3498—531no—
870#3487—531no—
871#3487—531no—
872#3485—531no—
873#3485—531no—
874#3444—531no—
875#3444—531no—
876C2×#532—531no—
877C2×C53—22no—
878C2×C53—42no—
879C2×C53—44no—
880C2×C53C22×H(5,𝔽2)11yescharacteristic
881C2×C53C2×#58512yes—
882D53—42no—
883D53—42no—
884D53—44no—
885D53—42no—
886D53—42no—
887C2×2−1+4—531no—
888C2×2−1+4—531no—
889C2×H(5,𝔽2)—531no—
890C2×H(5,𝔽2)—531no—
891C22×#41—531no—
892C22×#41—531no—
893#562—538no—
894#562—538no—
895#560—538no—
896#560—538no—
897#559—538no—
898#559—534no—
899#559—534no—
900#559C2×D5314yescomplemented
901#557—534no—
902#556—534no—
903#556—534no—
904#556C2×D5314yescomplemented
905#555—538no—
906#554—538no—
907#553—538no—
908#553—538no—
909#553—538no—
910#553—538no—
911#552—538no—
912#551—538no—
913#551—538no—
914#551—538no—
915#551C2×D5318yescomplemented
916#550—534no—
917#550—534no—
918#550—534no—
919#550—534no—
920#550—534no—
921#550—538no—
922#550—534no—
923D4×Q8—534no—
924#548—534no—
925#548—534no—
926#548—534no—
927#548—534no—
928#548—534no—
929#548—534no—
930#547—534no—
931#547—538no—
932#547—534no—
933#547—534no—
934#547—534no—
935#547—534no—
936#546—534no—
937#546—534no—
938#546—538no—
939#546—538no—
940#546—534no—
941#546—534no—
942#546—534no—
943#546—534no—
944#546—538no—
945#546—538no—
946#546—538no—
947D42—534no—
948D42—538no—
949#542—534no—
950#542—538no—
951#542—538no—
952#542C2×D5314yescomplemented
953#541—534no—
954#540—538no—
955#540—538no—
956#540—538no—
957#540—534no—
958#540—538no—
959#539—538no—
960#539—538no—
961#538—538no—
962#538—538no—
963#538—538no—
964#538—538no—
965#537—538no—
966#536—531no—
967#536—532no—
968#536—532no—
969#536—532no—
970#536—531no—
971#536—531no—
972#536—532no—
973#536C2×D5311yescharacteristic, complemented
974#535—531no—
975#535—532no—
976#535—532no—
977#535—532no—
978#535—538no—
979#535—534no—
980#535—531no—
981#535—531no—
982#535—534no—
983#535—532no—
984#535C2×D5311yescharacteristic
985#534—534no—
986#534—534no—
987#533—532no—
988#533—532no—
989#533—534no—
990#533—531no—
991#533C2×D5311yescharacteristic, complemented
992#532—531no—
993#532—532no—
994#532—534no—
995#532—534no—
996#532—534no—
997#532—534no—
998#532—532no—
999#532—532no—
1000#532—532no—
1001#532—532no—
1002#532—534no—
1003#532—531no—
1004#532—532no—
1005C2×C4⋊Q8—531no—
1006C2×C4⋊Q8—532no—
1007C2×#127—531no—
1008C2×#127—532no—
1009#529—532no—
1010#529—532no—
1011#529—534no—
1012#529—534no—
1013#529—534no—
1014#529—532no—
1015#529—534no—
1016#529—532no—
1017#529—534no—
1018#529C2×D5314yescomplemented
1019C2×#124—532no—
1020C2×#124—531no—
1021C2×#124—532no—
1022C2×#124C2×D5311yescharacteristic, complemented
1023#525—531no—
1024#525—534no—
1025#525—534no—
1026#525—534no—
1027#525—531no—
1028#525—531no—
1029#525—531no—
1030#525—534no—
1031C2×#123—534no—
1032C2×#123—534no—
1033C2×#121—534no—
1034#520—538no—
1035#519—531no—
1036#519C2×D5311yescharacteristic, complemented
1037#518—538no—
1038#518—531no—
1039#518C2×D5311yescharacteristic, complemented
1040C4×#41—534no—
1041C4×#41—531no—
1042C4×#41—531no—
1043C4×#41—531no—
1044C4×#41—534no—
1045C4×#41C2×D5311yescharacteristic, complemented
1046C2×C4×D4—534no—
1047C22×C42—531no—
1048C53#6283611yescharacteristic, complemented, Sylow
10492−1+4—2124no—
10502−1+4—2124no—
1051H(5,𝔽2)—2124no—
1052H(5,𝔽2)—2124no—
1053C2×#41—534no—
1054C2×#41—534no—
1055C2×#41—534no—
1056C2×#41—532no—
1057C2×#41—532no—
1058C2×#41—532no—
1059C2×#41—534no—
1060C2×#41—534no—
1061C2×#41—534no—
1062C2×#41—532no—
1063C2×#41—532no—
1064C2×#41—532no—
1065C2×#41—531no—
1066C2×#41—531no—
1067C2×#41—531no—
1068C2×#41—534no—
1069C2×#41—538no—
1070C2×#41—534no—
1071C2×#41—532no—
1072C2×#41—532no—
1073C2×#41—2124no—
1074C2×#41—2124no—
1075C2×#41C22×D5311yescharacteristic
1076C22×Q8—532no—
1077C22×Q8—532no—
1078C22×Q8—532no—
1079C22×Q8—531no—
1080C22×Q8—532no—
1081C22×Q8C22×D5311yescharacteristic
1082C22×D4—534no—
1083C22×D4—532no—
1084C22×D4—534no—
1085C22×D4—538no—
1086C22×D4—534no—
1087C22×D4—532no—
1088C22×D4—532no—
1089C22×D4—532no—
1090C22×D4—531no—
1091C22×D4—532no—
1092C22×D4—532no—
1093C22×D4C22×D5311yescharacteristic
1094C23×C4—532no—
1095C23×C4—531no—
1096C23×C4—532no—
1097C23×C4—532no—
1098C4⋊Q8—531no—
1099C4⋊Q8—532no—
1100C4⋊Q8—532no—
1101C4⋊Q8—534no—
1102C4⋊Q8—532no—
1103C4⋊Q8—538no—
1104C4⋊Q8—532no—
1105C4⋊Q8—532no—
1106C4⋊Q8—531no—
1107C4⋊Q8—532no—
1108C4⋊Q8C22×D5312yes—
1109C4⋊Q8C22×D5312yes—
1110#127—531no—
1111#127—532no—
1112#127—532no—
1113#127—534no—
1114#127—538no—
1115#127—532no—
1116#127—538no—
1117#127—532no—
1118#127—531no—
1119#127—532no—
1120#127—538no—
1121#127C22×D5312yes—
1122#126—534no—
1123#126—534no—
1124#126—534no—
1125#126—538no—
1126#126—538no—
1127#126—538no—
1128#126—534no—
1129#126—538no—
1130#126C22×D5318yes—
1131#126C22×D5318yes—
1132#125—534no—
1133#125—532no—
1134#125—534no—
1135#125—538no—
1136#125—538no—
1137#125—538no—
1138#125C22×D5312yes—
1139#124—532no—
1140#124—531no—
1141#124—534no—
1142#124—538no—
1143#124—532no—
1144#124—531no—
1145#124—538no—
1146#124—534no—
1147#124—538no—
1148#124—538no—
1149#124—531no—
1150#124—532no—
1151#124—532no—
1152#124—534no—
1153#124—532no—
1154#124—532no—
1155#124—538no—
1156#124—531no—
1157#124—532no—
1158#124—532no—
1159#124—538no—
1160#124C22×D5312yes—
1161#124C22×D5312yes—
1162#124C22×D5314yes—
1163#124C22×D5312yes—
1164#124C22×D5312yes—
1165#124C22×D5318yes—
1166#123—532no—
1167#123—534no—
1168#123—538no—
1169#123—538no—
1170#123—534no—
1171#123—534no—
1172#123—534no—
1173#123—538no—
1174#123—538no—
1175#123—538no—
1176#123—538no—
1177#123—532no—
1178#123—532no—
1179#123—534no—
1180#123—534no—
1181#123—538no—
1182#123—538no—
1183#123—538no—
1184#123—532no—
1185#123—534no—
1186#123—538no—
1187#123—538no—
1188#123—538no—
1189#123—538no—
1190#123—538no—
1191#123C22×D5314yes—
1192#123C22×D5318yes—
1193#123C22×D5318yes—
1194C22⋊Q8—532no—
1195C22⋊Q8—534no—
1196C22⋊Q8—534no—
1197C22⋊Q8—538no—
1198C22⋊Q8—534no—
1199C22⋊Q8—532no—
1200C22⋊Q8—532no—
1201C22⋊Q8—532no—
1202C22⋊Q8—538no—
1203C22⋊Q8—534no—
1204C22⋊Q8—534no—
1205C22⋊Q8—538no—
1206C22⋊Q8—538no—
1207C22⋊Q8—538no—
1208C22⋊Q8—534no—
1209C22⋊Q8—538no—
1210C22⋊Q8—538no—
1211C22⋊Q8—538no—
1212C22⋊Q8C22×D5314yes—
1213C22⋊Q8C22×D5314yes—
1214C22⋊Q8C22×D5318yes—
1215#121—534no—
1216#121—532no—
1217#121—538no—
1218#121—534no—
1219#121—538no—
1220#121—538no—
1221#121—534no—
1222#121—538no—
1223#121—538no—
1224#121—538no—
1225#121—538no—
1226#121—532no—
1227#121—532no—
1228#121—532no—
1229#121—534no—
1230#121—538no—
1231#121—534no—
1232#121—534no—
1233#121—538no—
1234#121—538no—
1235#121—538no—
1236#121—538no—
1237#121—538no—
1238#121—538no—
1239#121—538no—
1240#121—538no—
1241#121—534no—
1242#121—538no—
1243#121—538no—
1244#121—538no—
1245#121—538no—
1246#121—538no—
1247#121—538no—
1248#121—538no—
1249#121—538no—
1250#121—538no—
1251#121C22×D5314yes—
1252#120—534no—
1253#120—532no—
1254#120—538no—
1255#120—532no—
1256#120—532no—
1257#120—532no—
1258#120—534no—
1259#120—534no—
1260#120—538no—
1261#120—538no—
1262#120—538no—
1263#120—538no—
1264#120—538no—
1265#120C22×D5314yes—
1266C4×Q8—534no—
1267C4×Q8—532no—
1268C4×Q8—532no—
1269C4×Q8—534no—
1270C4×Q8—534no—
1271C4×Q8—532no—
1272C4×Q8—534no—
1273C4×Q8—534no—
1274C4×Q8—538no—
1275C4×Q8C22×D5314yes—
1276C4×Q8C22×D5312yes—
1277C4×Q8C22×D5314yes—
1278C4×Q8C22×D5314yes—
1279C4×D4—538no—
1280C4×D4—534no—
1281C4×D4—534no—
1282C4×D4—534no—
1283C4×D4—534no—
1284C4×D4—534no—
1285C4×D4—538no—
1286C4×D4—534no—
1287C4×D4—534no—
1288C4×D4—532no—
1289C4×D4—534no—
1290C4×D4—532no—
1291C4×D4—538no—
1292C4×D4—534no—
1293C4×D4—538no—
1294C4×D4—538no—
1295C4×D4—538no—
1296C4×D4—538no—
1297C4×D4—534no—
1298C4×D4—534no—
1299C4×D4—538no—
1300C4×D4—538no—
1301C4×D4—538no—
1302C4×D4—538no—
1303C4×D4—534no—
1304C4×D4—534no—
1305C4×D4—534no—
1306C4×D4—534no—
1307C4×D4—534no—
1308C4×D4—532no—
1309C4×D4—538no—
1310C4×D4—534no—
1311C4×D4—538no—
1312C4×D4—538no—
1313C4×D4C22×D5314yes—
1314C4×D4C22×D5312yes—
1315C4×D4C22×D5318yes—
1316C4×D4C22×D5314yes—
1317C4×D4C22×D5314yes—
1318#117—531no—
1319#117—534no—
1320#117—534no—
1321#117—534no—
1322#117—534no—
1323#117—538no—
1324#117—534no—
1325#117—534no—
1326#117—532no—
1327#117—532no—
1328#117—532no—
1329#117—534no—
1330#117—538no—
1331#117C22×D5311yescharacteristic
1332#117C22×D5311yescharacteristic
1333#117C22×D5311yescharacteristic
1334#117C22×D5312yes—
1335#117C22×D5314yes—
1336#117C22×D5318yes—
1337C2×C4⋊C4—534no—
1338C2×C4⋊C4—538no—
1339C2×C4⋊C4—538no—
1340C2×C4⋊C4—538no—
1341C2×C22⋊C4—534no—
1342C2×C22⋊C4—538no—
1343C2×C22⋊C4—538no—
1344C2×C22⋊C4—534no—
1345C2×C22⋊C4—538no—
1346C2×C22⋊C4—538no—
1347C2×C22⋊C4C22×D5314yes—
1348C2×C22⋊C4C22×D5314yes—
1349C2×C42—532no—
1350C2×C42—531no—
1351C2×C42—532no—
1352C2×C42—532no—
1353C2×C42—532no—
1354C2×C42—532no—
1355C2×C42—532no—
1356C2×C42—532no—
1357C2×C42—532no—
1358C2×C42C22×D5312yes—
1359C2×C42C22×D5311yescharacteristic
1360C24—532no—
1361C24—531no—
1362C24—534no—
1363C24—534no—
1364C24C23×D5312yes—
1365#41—24no—
1366#41—1064no—
1367#41—1064no—
1368#41—1064no—
1369#41—2128no—
1370#41—2124no—
1371#41—2124no—
1372#41—2128no—
1373#41—21216no—
1374#41—2128no—
1375#41—2128no—
1376#41—2128no—
1377#41—2128no—
1378#41—2124no—
1379#41—2124no—
1380#41—2124no—
1381#41—2128no—
1382#41—2128no—
1383#41—2124no—
1384#41—2124no—
1385#41—2124no—
1386C2×Q8—24no—
1387C2×Q8—534no—
1388C2×Q8—531no—
1389C2×Q8—532no—
1390C2×Q8—532no—
1391C2×Q8—531no—
1392C2×Q8—531no—
1393C2×Q8—534no—
1394C2×Q8—534no—
1395C2×Q8—1064no—
1396C2×Q8—2124no—
1397C2×Q8—2124no—
1398C2×Q8—2124no—
1399C2×Q8—2124no—
1400C2×Q8C23×D5311yescharacteristic
1401C2×Q8C23×D5312yes—
1402C2×Q8C23×D5312yes—
1403C2×Q8C23×D5314yes—
1404C2×D4—24no—
1405C2×D4—534no—
1406C2×D4—538no—
1407C2×D4—532no—
1408C2×D4—532no—
1409C2×D4—532no—
1410C2×D4—534no—
1411C2×D4—538no—
1412C2×D4—538no—
1413C2×D4—534no—
1414C2×D4—534no—
1415C2×D4—538no—
1416C2×D4—534no—
1417C2×D4—534no—
1418C2×D4—531no—
1419C2×D4—532no—
1420C2×D4—532no—
1421C2×D4—531no—
1422C2×D4—531no—
1423C2×D4—534no—
1424C2×D4—534no—
1425C2×D4—534no—
1426C2×D4—538no—
1427C2×D4—538no—
1428C2×D4—534no—
1429C2×D4—534no—
1430C2×D4—534no—
1431C2×D4—538no—
1432C2×D4—1064no—
1433C2×D4—2124no—
1434C2×D4—2124no—
1435C2×D4—2124no—
1436C2×D4—2124no—
1437C2×D4—2124no—
1438C2×D4—21216no—
1439C2×D4—2128no—
1440C2×D4—2124no—
1441C2×D4—2128no—
1442C2×D4—2128no—
1443C2×D4C23×D5312yes—
1444C2×D4C23×D5311yescharacteristic
1445C2×D4C23×D5312yes—
1446C2×D4C23×D5312yes—
1447C2×D4C23×D5318yes—
1448C22×C4—532no—
1449C22×C4—531no—
1450C22×C4—532no—
1451C22×C4—534no—
1452C22×C4—538no—
1453C22×C4—534no—
1454C22×C4—532no—
1455C22×C4—532no—
1456C22×C4—532no—
1457C22×C4—532no—
1458C22×C4—534no—
1459C22×C4—534no—
1460C22×C4—532no—
1461C22×C4—532no—
1462C22×C4—532no—
1463C22×C4—532no—
1464C22×C4—532no—
1465C22×C4—534no—
1466C22×C4—538no—
1467C22×C4—534no—
1468C22×C4—538no—
1469C22×C4—534no—
1470C22×C4—534no—
1471C22×C4—534no—
1472C22×C4—1064no—
1473C22×C4—2124no—
1474C22×C4—2124no—
1475C22×C4—2124no—
1476C22×C4C23×D5312yes—
1477C22×C4C23×D5312yes—
1478C22×C4C23×D5312yes—
1479C22×C4C23×D5314yes—
1480C22×C4C23×D5318yes—
1481C22×C4C23×D5311yescharacteristic
1482C4⋊C4—534no—
1483C4⋊C4—534no—
1484C4⋊C4—538no—
1485C4⋊C4—534no—
1486C4⋊C4—534no—
1487C4⋊C4—538no—
1488C4⋊C4—538no—
1489C4⋊C4—538no—
1490C4⋊C4—538no—
1491C4⋊C4—534no—
1492C4⋊C4—534no—
1493C4⋊C4—532no—
1494C4⋊C4—534no—
1495C4⋊C4—534no—
1496C4⋊C4—534no—
1497C4⋊C4—534no—
1498C4⋊C4—534no—
1499C4⋊C4—534no—
1500C4⋊C4—538no—
1501C4⋊C4C23×D5318yes—
1502C4⋊C4C23×D5314yes—
1503C4⋊C4C23×D5314yes—
1504C4⋊C4C23×D5314yes—
1505C4⋊C4C23×D5312yes—
1506C4⋊C4C23×D5312yes—
1507C4⋊C4C23×D5312yes—
1508C4⋊C4C23×D5314yes—
1509C4⋊C4C23×D5318yes—
1510C22⋊C4—532no—
1511C22⋊C4—534no—
1512C22⋊C4—538no—
1513C22⋊C4—534no—
1514C22⋊C4—534no—
1515C22⋊C4—534no—
1516C22⋊C4—534no—
1517C22⋊C4—538no—
1518C22⋊C4—538no—
1519C22⋊C4—538no—
1520C22⋊C4—538no—
1521C22⋊C4—538no—
1522C22⋊C4—538no—
1523C22⋊C4—538no—
1524C22⋊C4—534no—
1525C22⋊C4—534no—
1526C22⋊C4—534no—
1527C22⋊C4—538no—
1528C22⋊C4—534no—
1529C22⋊C4—534no—
1530C22⋊C4—534no—
1531C22⋊C4—534no—
1532C22⋊C4—534no—
1533C22⋊C4—534no—
1534C22⋊C4—534no—
1535C22⋊C4C23×D5312yes—
1536C22⋊C4C23×D5318yes—
1537C22⋊C4C23×D5318yes—
1538C22⋊C4C23×D5312yes—
1539C22⋊C4C23×D5318yes—
1540C22⋊C4C23×D5318yes—
1541C22⋊C4C23×D5312yes—
1542C22⋊C4C23×D5318yes—
1543C22⋊C4C23×D5314yes—
1544C42—531no—
1545C42—532no—
1546C42—532no—
1547C42—531no—
1548C42—532no—
1549C42—532no—
1550C42—532no—
1551C42—534no—
1552C42—534no—
1553C42—532no—
1554C42—534no—
1555C42—538no—
1556C42C23×D5311yescharacteristic
1557C42C23×D5311yescharacteristic
1558C42C23×D5312yes—
1559C42C23×D5312yes—
1560C42C23×D5312yes—
1561C42C23×D5314yes—
1562C42C23×D5312yes—
1563C42C23×D5318yes—
1564C23—24no—
1565C23—44no—
1566C23—532no—
1567C23—532no—
1568C23—534no—
1569C23—532no—
1570C23—532no—
1571C23—1064no—
1572C23—1062no—
1573C23—2124no—
1574C23—2124no—
1575C23—2128no—
1576C23—2128no—
1577C23—2124no—
1578C23—2122no—
1579C23C24×D5312yes—
1580C23C24×D5314yes—
1581C23C24×D5311yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—44no—
1586Q8—1068no—
1587Q8—1064no—
1588Q8—1064no—
1589Q8—1062no—
1590Q8—1062no—
1591Q8—1062no—
1592Q8—2124no—
1593Q8—2124no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—22no—
1598D4—48no—
1599D4—1068no—
1600D4—10616no—
1601D4—1064no—
1602D4—1064no—
1603D4—1064no—
1604D4—1064no—
1605D4—1064no—
1606D4—1062no—
1607D4—1062no—
1608D4—1062no—
1609D4—2128no—
1610D4—2124no—
1611D4—2128no—
1612D4—2124no—
1613D4—2128no—
1614D4—2124no—
1615D4—2124no—
1616D4—2124no—
1617D4—2124no—
1618D4—2128no—
1619D4—2124no—
1620D4—2124no—
1621D4—2124no—
1622D4—2128no—
1623D4—2124no—
1624D4—2128no—
1625D4—2124no—
1626C2×C4—24no—
1627C2×C4—24no—
1628C2×C4—42no—
1629C2×C4—44no—
1630C2×C4—48no—
1631C2×C4—532no—
1632C2×C4—534no—
1633C2×C4—532no—
1634C2×C4—532no—
1635C2×C4—532no—
1636C2×C4—532no—
1637C2×C4—534no—
1638C2×C4—532no—
1639C2×C4—1064no—
1640C2×C4—1064no—
1641C2×C4—1068no—
1642C2×C4—1068no—
1643C2×C4—1064no—
1644C2×C4—1062no—
1645C2×C4—1064no—
1646C2×C4—1064no—
1647C2×C4—1064no—
1648C2×C4—1064no—
1649C2×C4—1064no—
1650C2×C4—1064no—
1651C2×C4—2122no—
1652C2×C4—2122no—
1653C2×C4—2128no—
1654C2×C4—2124no—
1655C2×C4—2124no—
1656C2×C4—2124no—
1657C2×C4—2124no—
1658C2×C4—2124no—
1659C2×C4—2128no—
1660C2×C4—2128no—
1661C2×C4—2124no—
1662C2×C4—2124no—
1663C2×C4#1313326314yes—
1664C2×C4C24×D5312yes—
1665C2×C4C24×D5314yes—
1666C2×C4C24×D5312yes—
1667C2×C4C24×D5314yes—
1668C2×C4C24×D5314yes—
1669C2×C4C24×D5312yes—
1670C2×C4C24×D5314yes—
1671C2×C4C24×D5311yescharacteristic
1672C2×C4C24×D5311yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—24no—
1676C22—24no—
1677C22—28no—
1678C22—84no—
1679C22—8484no—
1680C22—8484no—
1681C22—1062no—
1682C22—1062no—
1683C22—1062no—
1684C22—1062no—
1685C22—1064no—
1686C22—1062no—
1687C22—1062no—
1688C22—1064no—
1689C22—1064no—
1690C22—1064no—
1691C22—1068no—
1692C22—4244no—
1693C22—2124no—
1694C22C2×#1313326312yes—
1695C22C25×D5311yescharacteristic
1696C4—22no—
1697C4—24no—
1698C4—22no—
1699C4—24no—
1700C4—24no—
1701C4—22no—
1702C4—24no—
1703C4—534no—
1704C4—1062no—
1705C4—1062no—
1706C4—1062no—
1707C4—1062no—
1708C4—1064no—
1709C4—1062no—
1710C4—1064no—
1711C4C2×#1313326312yes—
1712C4C2×#1313326312yes—
1713C2—22no—
1714C2—44no—
1715C2—42no—
1716C2—2122no—
1717C2—2122no—
1718C2—2124no—
1719C2—2122no—
1720C2—2122no—
1721C2C22×#1313326311yescharacteristic
1722C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3510C2
hypercenter#3510D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3510

Complements

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

NH ≅ G/Ntype
1. #20289310C2semidirect
2. #20289301C2semidirect
3. #20289183C2semidirect
4. #20289084C2semidirect
5. #20289024C2semidirect
6. #20288719C2semidirect
7. #20288664C2semidirect
8. #20288642C2semidirect
9. #20288619C2semidirect
10. #20288613C2semidirect
11. #20288596C2semidirect
12. #20288588C2semidirect
13. #20288586C2semidirect
14. #20288508C2semidirect
15. #20288505C2semidirect
16. #20288497C2semidirect
17. #20288490C2semidirect
18. #20288374C2semidirect
19. #20288371C2semidirect
20. #20288360C2semidirect
21. #20288358C2semidirect
22. #20288012C2semidirect
23. #20288008C2semidirect
24. C2×#16811172C2semidirect
25. C53×#3510C2semidirect
26. C2×#13133265C22semidirect
27. C2×#13133264C22semidirect
30. C22×#11719949C22semidirect
31. C22×#11719947C22semidirect
32. #16811369C22semidirect
33. #16811367C22semidirect
34. #16811364C22semidirect
35. #16811363C22semidirect
36. #16811358C22semidirect
37. #16811356C22semidirect
38. #16811355C22semidirect
39. #16811351C22semidirect
40. #16811346C22semidirect
41. #16811345C22semidirect
42. #16811336C22semidirect
43. #16811331C22semidirect
44. #16811324C22semidirect
45. #16811324C22semidirect
46. #16811324C22semidirect
47. #16811319C22semidirect
48. #16811306C22semidirect
49. #16811300C22semidirect
50. #16811297C22semidirect
51. #16811296C22semidirect
52. #16811295C22semidirect
53. #16811295C22semidirect
54. #16811294C22semidirect
55. #16811294C22semidirect
56. #16811293C22semidirect
57. #16811291C22semidirect
58. #16811291C22semidirect
59. #16811286C22semidirect
60. #16811285C22semidirect
61. #16811285C22semidirect
62. #16811285C22semidirect
63. #16811281C22semidirect
64. #16811281C22semidirect
65. #16811279C22semidirect
66. #16811277C22semidirect
67. #16811277C22semidirect
68. #16811276C22semidirect
69. #16811275C22semidirect
70. #16811275C22semidirect
71. #16811271C22semidirect
72. #16811268C22semidirect
73. #16811268C22semidirect
74. #16811268C22semidirect
75. #16811268C22semidirect
76. #16811266C22semidirect
77. #16811266C22semidirect
78. #16811265C22semidirect
79. #16811265C22semidirect
80. #16811264C22semidirect
81. #16811263C22semidirect
82. #16811263C22semidirect
83. #16811257C22semidirect
85. #16811247C22semidirect
86. #16811239C22semidirect
87. #16811239C22semidirect
88. #16811231C22semidirect
89. #16811228C22semidirect
90. #16811225C22semidirect
91. #16811225C22semidirect
92. #16811225C22semidirect
93. #16811224C22semidirect
94. #16811217C22semidirect
95. #16811214C22semidirect
96. #16811213C22semidirect
97. #16811212C22semidirect
98. #16811207C22semidirect
99. #16811206C22semidirect
100. #16811203C22semidirect
102. #16811199C22semidirect
103. #16811199C22semidirect
104. #16811198C22semidirect
106. #16811193C22semidirect
107. #16811193C22semidirect
109. #16811192C22semidirect
110. #16811192C22semidirect
111. #16811192C22semidirect
112. #16811191C22semidirect
113. #16811191C22semidirect
114. #16811191C22semidirect
115. #16811190C22semidirect
116. #16811188C22semidirect
117. #16811186C22semidirect
118. #16811185C22semidirect
119. #16811184C22semidirect
120. #16811178C22semidirect
121. #16811177C22semidirect
122. #16811177C22semidirect
123. #16811176C22semidirect
124. #16811174C22semidirect
126. #16811173C22semidirect
127. #16811172C22semidirect
128. #16811172C22semidirect
129. #16811172C22semidirect
130. #16811172C22semidirect
131. #16811172C22semidirect
132. #16811172C22semidirect
133. #16811172C22semidirect
134. #16811170C22semidirect
135. #16811170C22semidirect
137. C2×#13133215C22semidirect
138. C4⋊Q8×D53C22semidirect
140. #127×D53C22semidirect
141. #16811160C22semidirect
142. #16811160C22semidirect
143. #16811159C22semidirect
144. #16811158C22semidirect
145. #16811158C22semidirect
146. #16811158C22semidirect
147. #16811155C22semidirect
148. #16811153C22semidirect
149. #16811151C22semidirect
150. C2×#13133205C22semidirect
151. C2×#13133205C22semidirect
152. #124×D53C22semidirect
153. #16811136C22semidirect
155. #16811135C22semidirect
156. #16811135C22semidirect
157. #16811135C22semidirect
158. #16811132C22semidirect
159. #16811130C22semidirect
160. #16811129C22semidirect
161. C2×#13133201C22semidirect
162. #123×D53C22semidirect
163. C2×#13133190C22semidirect
164. #16811103C22semidirect
165. #16811100C22semidirect
166. #16811097C22semidirect
167. #16811095C22semidirect
168. C4×#11719949C22semidirect
169. C4×#11719945C22semidirect
170. C4×#11719945C22semidirect
172. #16811091C22semidirect
173. C2×#13133177C22semidirect
174. C2×C42×D53C22semidirect
175. C53×#559C22semidirect
176. C53×#556C22semidirect
177. C53×#551C22semidirect
178. C53×#542C22semidirect
179. C53×#536C22semidirect
181. C53×#533C22semidirect
182. C53×#529C22semidirect
183. C2×#124×C53C22semidirect
184. C53×#519C22semidirect
185. C53×#518C22semidirect
186. C4×#41×C53C22semidirect
862. #3510D53semidirect
900. #559C2×D53semidirect
904. #556C2×D53semidirect
915. #551C2×D53semidirect
952. #542C2×D53semidirect
973. #536C2×D53semidirect
991. #533C2×D53semidirect
1018. #529C2×D53semidirect
1022. C2×#124C2×D53semidirect
1036. #519C2×D53semidirect
1039. #518C2×D53semidirect
1045. C4×#41C2×D53semidirect
1048. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893102
#202893012
#202891832
#202890842
#202890242
#202887192
#202886642
#202886422
#202886192
#202886132
#202885962
#202885882
#202885862
#202885082
#202885052
#202884972
#202884902
#202883742
#202883712
#202883602
#202883582
#202880122
#202880082
C2×#168111722
C53×#35102
#6283653