Finite Group Databasebeta

← #28292677

Subgroups — #28292677

Order 13568.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288630C214yesmaximal, complemented
2#20288620C214yesmaximal, complemented
3#20288613C211yesmaximal, characteristic, complemented
4#20288611C211yesmaximal, characteristic, complemented
5#20288609C211yesmaximal, characteristic, complemented
6#20288600C211yesmaximal, characteristic, complemented
7#20288596C211yesmaximal, characteristic, complemented
8#20288590C211yesmaximal, characteristic, complemented
9#20288586C211yesmaximal, characteristic, complemented
10#20288576C214yesmaximal, complemented
11#20288563C214yesmaximal, complemented
12#20288546C218yesmaximal, complemented
13#20288311C214yesmaximal, complemented
14#20288307C214yesmaximal, complemented
15#20288270C218yesmaximal, complemented
16#20288102C214yesmaximal, complemented
17#20288047C211yesmaximal, characteristic, complemented
18#20288046C211yesmaximal, characteristic, complemented
19#20288009C214yesmaximal, complemented
20#533×D53C211yesmaximal, characteristic, complemented
21C2×#16811172C211yesmaximal, characteristic, complemented
22#20287917C211yesmaximal, characteristic, complemented
23#20287913C211yesmaximal, characteristic, complemented
24C4×#41×D53C211yesmaximal, characteristic, complemented
25C53×#3510C211yesmaximal, characteristic, complemented
26C22×#11719949C2211yescharacteristic
27C22×#11719947C2211yescharacteristic
28C2×#41×D53C2211yescharacteristic
29#16811358C2214yescomplemented
30#16811356C2214yescomplemented
31#16811356C2214yescomplemented
32#16811355C2214yescomplemented
33#16811355C2214yescomplemented
34#16811351C2214yescomplemented
35#16811348C2214yescomplemented
36#16811346C2214yescomplemented
37#16811345C2214yescomplemented
38#16811345C2214yescomplemented
39#16811342C2214yescomplemented
40#16811342C2214yescomplemented
41#16811340C2218yescomplemented
42#16811335C2218yescomplemented
43#16811327C2218yescomplemented
44#16811324C2218yescomplemented
45#16811324C2218yescomplemented
46#16811323C2218yescomplemented
47#16811322C2218yescomplemented
48#16811318C2218yescomplemented
49#16811318C2218yescomplemented
50#16811318C2218yescomplemented
51#16811317C2218yescomplemented
52#16811310C2218yescomplemented
53#16811309C2218yescomplemented
54#16811306C2218yescomplemented
55#16811306C2218yescomplemented
56#16811302C2218yescomplemented
57#16811300C2218yescomplemented
58#16811299C2218yescomplemented
59#16811294C2214yescomplemented
60#16811293C2214yescomplemented
61#16811283C2218yescomplemented
62#16811281C2218yescomplemented
63#16811271C2218yescomplemented
64#16811263C2218yescomplemented
65#16811260C2218yescomplemented
66#16811247C2214yescomplemented
67#16811244C2214yescomplemented
68#16811242C2214yescomplemented
69#16811233C2214yescomplemented
70#16811231C2214yescomplemented
71#16811226C2214yescomplemented
72#16811224C2214yescomplemented
73#16811219C2218yescomplemented
74#16811214C2218yescomplemented
75#16811209C2218yescomplemented
76#16811207C2218yescomplemented
77#16811203C2214yescomplemented
78#16811202C2214yescomplemented
79#16811199C2211yescharacteristic
80#16811198C2212yescomplemented
81#16811197C2211yescharacteristic
82#16811194C2211yescharacteristic
83#16811193C2212yescomplemented
84#16811192C2211yescharacteristic
85#16811191C2212yescomplemented
86#16811190C2211yescharacteristic
87#16811187C2211yescharacteristic
88#16811186C2212yescomplemented
89#16811184C2214yes—
90#16811183C2214yes—
91#16811180C2211yescharacteristic, complemented
92#16811179C2212yescomplemented
93#16811178C2212yescomplemented
94#16811177C2214yescomplemented
95#16811177C2214yescomplemented
96#16811176C2211yescharacteristic, complemented
97#16811176C2211yescharacteristic, complemented
98#16811175C2214yescomplemented
99#16811175C2214yescomplemented
100#16811174C2212yescomplemented
101#16811172C2212yes—
102#16811172C2214yes—
103#16811172C2212yes—
104#16811172C2212yescomplemented
105#16811172C2212yescomplemented
106#16811172C2214yescomplemented
107#16811172C2212yescomplemented
108#16811172C2212yescomplemented
109#16811171C2212yescomplemented
110#16811170C2214yescomplemented
111#16811168C2214yescomplemented
112C2×#13133215C2211yescharacteristic, complemented
113C4⋊Q8×D53C2212yescomplemented
114C2×#13133213C2211yescharacteristic, complemented
115#16811159C2218yescomplemented
116#16811158C2214yescomplemented
117#16811157C2214yescomplemented
118#16811156C2218yescomplemented
119#16811156C2218yescomplemented
120#16811156C2218yescomplemented
121#16811152C2214yescomplemented
122#16811152C2218yescomplemented
123#16811151C2218yescomplemented
124#16811150C2218yescomplemented
125#16811150C2218yescomplemented
126#125×D53C2212yescomplemented
127C2×#13133205C2211yescharacteristic, complemented
128#16811136C2214yescomplemented
129#16811133C2214yescomplemented
130#16811132C2218yescomplemented
131#16811131C2214yes—
132#16811131C2218yescomplemented
133#16811129C2214yes—
134C22⋊Q8×D53C2214yes—
135C2×#13133190C2214yes—
136#16811105C2214yescomplemented
137#16811105C2214yescomplemented
138#16811102C2214yescomplemented
139#16811102C2214yescomplemented
140#16811101C2211yescharacteristic, complemented
141#16811100C2211yescharacteristic, complemented
142#16811100C2211yescharacteristic, complemented
143#16811098C2211yescharacteristic, complemented
144#16811097C2214yes—
145#16811097C2211yescharacteristic, complemented
146#16811097C2211yescharacteristic, complemented
147#16811096C2214yes—
148#41×Dic53C2211yescharacteristic
149C4×#11719949C2214yescomplemented
150C4×#11719949C2212yescomplemented
151C4×#11719949C2214yescomplemented
152C4×#11719945C2211yescharacteristic
153C4×#11719945C2212yescomplemented
154#16811091C2211yescharacteristic
155#16811091C2218yescomplemented
156#16811091C2212yescomplemented
157C4×#11719947C2214yes—
158C4×#11719947C2218yescomplemented
159C4×#11719947C2214yescomplemented
160C4×#11719947C2214yescomplemented
161C4×#11719947C2212yescomplemented
162C4×Q8×D53C2214yescomplemented
163C4×Q8×D53C2212yescomplemented
164C2×#13133177C2214yescomplemented
165C4×D4×D53C2214yes—
166C4×D4×D53C2212yescomplemented
167C2×#13133173C2214yescomplemented
168#117×D53C2211yescharacteristic
169#117×D53C2211yescharacteristic
170#117×D53C2211yescharacteristic
171#117×D53C2214yescomplemented
172#117×D53C2212yescomplemented
173C2×C42×D53C2211yescharacteristic
174C2×C42×D53C2212yescomplemented
175C53×#559C2214yescomplemented
176C53×#556C2214yescomplemented
177C53×#551C2218yescomplemented
178C53×#542C2214yescomplemented
179C53×#536C2211yescharacteristic
180C53×#535C2211yescharacteristic
181C53×#533C2211yescharacteristic, complemented
182C53×#529C2214yescomplemented
183C2×#124×C53C2211yescharacteristic, complemented
184C53×#519C2211yescharacteristic, complemented
185C53×#518C2211yescharacteristic, complemented
186C4×#41×C53C2211yescharacteristic
187C2×#11719949—28no—
188C2×#11719949C2312yes—
189C2×#11719949C2312yes—
190C2×#11719949C2311yescharacteristic
191C2×#11719949C2312yes—
192C2×#11719949C2312yes—
193C2×#11719945C2311yescharacteristic
194C2×#11719945C2312yes—
195C2×#11719945C2318yes—
196C2×#11719947—28no—
197C2×#11719947C2312yes—
198C2×#11719947C2312yes—
199C2×#11719947C2311yescharacteristic
200C2×#11719947C2312yes—
201C2×#11719947C2312yes—
202C2×#11719947C2312yes—
203C2×#11719947C2318yes—
204#41×D53—28no—
205C22×Dic106C2311yescharacteristic
206C2×Q8×D53C2311yescharacteristic
207C2×Q8×D53C2314yes—
208C22×D212C2312yes—
209C22×D212C2311yescharacteristic
210C22×C22⋊D53C2312yes—
211C22×C22⋊D53C2314yes—
212C2×D4×D53C2312yes—
213C2×D4×D53C2311yescharacteristic
214C23×Dic53C2312yes—
215C22×C4×D53C2312yes—
216C22×C4×D53C2312yes—
217C22×C4×D53C2312yes—
218C22×C4×D53C2314yes—
219C22×C4×D53C2311yescharacteristic
220#13133217C2312yes—
221#13133217C2312yes—
222#13133216C2314yes—
223#13133216C2312yes—
224#13133216C2312yes—
225#13133215C2314yes—
226#13133215C2312yes—
227#13133215C2314yes—
228#13133215C2312yes—
229#13133215C2312yes—
230#13133215C2312yes—
231#13133214C2312yes—
232#13133213C2312yes—
233#13133213C2314yes—
234#13133213C2312yes—
235#13133213C2312yes—
236#13133213C2312yes—
237#13133212C2318yes—
238#13133212C2318yes—
239#13133212C2318yes—
240#13133212C2318yes—
241#13133211C2318yes—
242#13133211C2318yes—
243#13133210C2318yes—
244#13133210C2318yes—
245#13133210C2318yes—
246#13133210C2318yes—
247#13133209C2318yes—
248#13133209C2312yes—
249#13133208C2318yes—
250#13133208C2312yes—
251#13133208C2312yes—
252#13133207C2314yes—
253#13133207C2318yes—
254#13133207C2318yes—
255#13133207C2318yes—
256#13133207C2314yes—
257#13133207C2318yes—
258#13133206C2318yes—
259#13133206C2312yes—
260#13133206C2312yes—
261#13133205C2312yes—
262#13133205C2314yes—
263#13133205C2312yes—
264#13133205C2312yes—
265#13133205C2312yes—
266#13133204C2312yes—
267#13133204C2312yes—
268#13133203C2318yes—
269#13133203C2318yes—
270#13133203C2318yes—
271#13133203C2318yes—
272#13133202C2318yes—
273#13133202C2318yes—
274#13133202C2318yes—
275#13133201C2318yes—
276#13133201C2314yes—
277#13133201C2318yes—
278#13133200C2314yes—
279#13133200C2318yes—
280#13133200C2318yes—
281#13133199C2318yes—
282#13133199C2318yes—
283#13133199C2318yes—
284#13133199C2318yes—
285#13133199C2318yes—
286#13133198C2314yes—
287#13133197C2314yes—
288#13133197C2314yes—
289#13133196C2314yes—
290#13133196C2314yes—
291#13133195C2318yes—
292#13133195C2318yes—
293#13133195C2318yes—
294#13133195C2314yes—
295#13133195C2314yes—
296#13133194C2318yes—
297#13133194C2318yes—
298#13133194C2314yes—
299#13133194C2318yes—
300#13133194C2314yes—
301#13133193C2318yes—
302#13133193C2314yes—
303#13133193C2314yes—
304#13133192C2318yes—
305#13133192C2314yes—
306#13133191C2318yes—
307#13133191C2314yes—
308#13133190C2318yes—
309#13133190C2318yes—
310#13133190C2318yes—
311#13133190C2318yes—
312#13133190C2318yes—
313#13133190C2318yes—
314#13133190C2318yes—
315#13133190C2318yes—
316#13133190C2318yes—
317#13133189C2318yes—
318#13133189C2318yes—
319#13133189C2318yes—
320#13133188C2318yes—
321#13133188C2318yes—
322#13133188C2314yes—
323#13133187C2314yes—
324#13133187C2318yes—
325#13133186C2314yes—
326#13133185C2314yes—
327#13133185C2318yes—
328Q8×Dic53C2312yes—
329Q8×Dic53C2314yes—
330Q8×Dic53C2314yes—
331Q8×Dic53C2314yes—
332C4×Dic106C2318yes—
333C4×Dic106C2314yes—
334C4×Dic106C2314yes—
335C4×Dic106C2314yes—
336C4×Dic106C2312yes—
337C4×Dic106C2314yes—
338C4×Dic106C2314yes—
339C4×Dic106C2314yes—
340#13133182C2318yes—
341#13133182C2314yes—
342#13133182C2314yes—
343#13133182C2312yes—
344#13133182C2314yes—
345#13133182C2314yes—
346#13133182C2314yes—
347#13133182C2314yes—
348C4×D212C2318yes—
349C4×D212C2314yes—
350C4×D212C2314yes—
351C4×D212C2312yes—
352C4×D212C2318yes—
353C4×D212C2314yes—
354D4×Dic53C2312yes—
355D4×Dic53C2314yes—
356D4×Dic53C2314yes—
357D4×Dic53C2314yes—
358D4×Dic53C2318yes—
359#13133179C2314yes—
360#13133179C2318yes—
361#13133179C2312yes—
362#13133179C2314yes—
363#13133179C2318yes—
364#13133179C2318yes—
365#13133179C2318yes—
366#13133179C2314yes—
367C4×C22⋊D53C2318yes—
368C4×C22⋊D53C2314yes—
369C4×C22⋊D53C2318yes—
370C4×C22⋊D53C2314yes—
371C4×C22⋊D53C2314yes—
372C4×C22⋊D53C2318yes—
373C4×C22⋊D53C2318yes—
374#13133177C2314yes—
375#13133177C2318yes—
376#13133177C2314yes—
377#13133177C2318yes—
378#13133177C2318yes—
379#13133177C2314yes—
380#13133177C2318yes—
381#13133177C2318yes—
382#13133177C2318yes—
383#13133177C2318yes—
384#13133177C2318yes—
385#13133177C2318yes—
386#13133177C2318yes—
387#13133176C2314yes—
388#13133176C2311yescharacteristic
389#13133176C2311yescharacteristic
390#13133176C2311yescharacteristic
391#13133176C2312yes—
392#13133175C2318yes—
393#13133175C2312yes—
394#13133175C2312yes—
395#13133175C2312yes—
396#13133175C2314yes—
397#13133175C2318yes—
398#13133174C2318yes—
399#13133174C2318yes—
400#13133174C2318yes—
401#13133174C2312yes—
402#13133174C2312yes—
403#13133174C2312yes—
404#13133174C2312yes—
405#13133174C2312yes—
406#13133173C2318yes—
407#13133173C2314yes—
408#13133173C2314yes—
409#13133173C2318yes—
410#13133173C2318yes—
411#13133173C2312yes—
412#13133173C2312yes—
413#13133173C2312yes—
414#13133173C2314yes—
415#13133173C2318yes—
416C2×#11719919C2318yes—
417C2×#11719919C2314yes—
418C4⋊C4×D53C2318yes—
419C4⋊C4×D53C2314yes—
420C4⋊C4×D53C2314yes—
421C4⋊C4×D53C2314yes—
422C4⋊C4×D53C2312yes—
423C4⋊C4×D53C2312yes—
424C4⋊C4×D53C2312yes—
425C4⋊C4×D53C2314yes—
426C2×C22⋊Dic53C2314yes—
427C2×#11719921C2314yes—
428C22⋊C4×D53C2314yes—
429C22⋊C4×D53C2314yes—
430C22⋊C4×D53C2312yes—
431C22⋊C4×D53C2312yes—
432C22⋊C4×D53C2312yes—
433C22⋊C4×D53C2314yes—
434C2×C4×Dic53C2312yes—
435C2×C4×Dic53C2311yescharacteristic
436C2×C4×Dic53C2314yes—
437C2×C4×Dic53C2312yes—
438C2×C4×Dic53C2318yes—
439C42×D53C2311yescharacteristic
440C42×D53C2311yescharacteristic
441C42×D53C2312yes—
442C42×D53C2312yes—
443C42×D53C2311yescharacteristic
444C42×D53C2311yescharacteristic
445C42×D53C2312yes—
446C42×D53C2314yes—
447C42×D53C2314yes—
448C42×D53C2312yes—
449C42×D53C2312yes—
450C42×D53C2312yes—
451C42×D53C2312yes—
452C42×D53C2318yes—
453C2×#41×C53C2311yescharacteristic
454C22×Q8×C53C2311yescharacteristic
455C22×D4×C53C2311yescharacteristic
456C4⋊Q8×C53C2312yes—
457C4⋊Q8×C53C2312yes—
458#127×C53C2312yes—
459#126×C53C2318yes—
460#126×C53C2318yes—
461#125×C53C2312yes—
462#124×C53C2318yes—
463#124×C53C2312yes—
464#124×C53C2312yes—
465#124×C53C2314yes—
466#124×C53C2312yes—
467#124×C53C2312yes—
468#123×C53C2318yes—
469#123×C53C2318yes—
470#123×C53C2314yes—
471C22⋊Q8×C53C2318yes—
472C22⋊Q8×C53C2314yes—
473C22⋊Q8×C53C2314yes—
474#121×C53C2314yes—
475#120×C53C2314yes—
476C4×Q8×C53C2312yes—
477C4×Q8×C53C2314yes—
478C4×Q8×C53C2314yes—
479C4×Q8×C53C2314yes—
480C4×D4×C53C2314yes—
481C4×D4×C53C2314yes—
482C4×D4×C53C2312yes—
483C4×D4×C53C2314yes—
484C4×D4×C53C2318yes—
485#117×C53C2311yescharacteristic
486#117×C53C2312yes—
487#117×C53C2311yescharacteristic
488#117×C53C2314yes—
489#117×C53C2311yescharacteristic
490#117×C53C2318yes—
491C2×C22⋊C4×C53C2314yes—
492C2×C22⋊C4×C53C2314yes—
493C2×C42×C53C2311yescharacteristic
494C2×C42×C53C2312yes—
495C24×C53C2412yes—
496C23×D53C2412yes—
497C23×D53C2412yes—
498C23×D53C2411yescharacteristic
499#41×C53—24no—
500C2×Q8×C53—24no—
501C2×Q8×C53C2412yes—
502C2×Q8×C53C2412yes—
503C2×Q8×C53C2411yescharacteristic
504C2×Q8×C53C2414yes—
505C2×D4×C53—24no—
506C2×D4×C53C2412yes—
507C2×D4×C53C2412yes—
508C2×D4×C53C2412yes—
509C2×D4×C53C2411yescharacteristic
510C2×D4×C53C2418yes—
511C22×C4×C53C2412yes—
512C22×C4×C53C2412yes—
513C22×C4×C53C2412yes—
514C22×C4×C53C2414yes—
515C22×C4×C53C2418yes—
516C22×C4×C53C2411yescharacteristic
517C2×C22⋊D53—28no—
518C2×C22⋊D53—48no—
519C2×C22⋊D53C2418yes—
520C2×C22⋊D53C2414yes—
521C2×C22⋊D53C2412yes—
522C2×C22⋊D53C2412yes—
523C2×C22⋊D53C2414yes—
524C2×C22⋊D53C2412yes—
525C2×C22⋊D53C2418yes—
526C2×C22⋊D53C2418yes—
527C2×C22⋊D53C2418yes—
528C22×Dic53—28no—
529C22×Dic53C2412yes—
530C22×Dic53C2414yes—
531C22×Dic53C2412yes—
532C22×Dic53C2414yes—
533C22×Dic53C2412yes—
534C22×Dic53C2414yes—
535C22×Dic53C2418yes—
536C22×Dic53C2411yescharacteristic
537#11719949—24no—
538#11719949—28no—
539#11719949—28no—
540#11719949—28no—
541#11719949—28no—
542Q8×D53—24no—
543Q8×D53—48no—
544#11719947—28no—
545#11719947—24no—
546#11719947—28no—
547#11719947—28no—
548#11719947—28no—
549#11719947—28no—
550#11719947—416no—
551D4×D53—28no—
552D4×D53—24no—
553#11719945—24no—
554#11719945—28no—
555#11719945—416no—
556C2×D212—28no—
557C2×D212—24no—
558C2×D212C2414yes—
559C2×D212C2414yes—
560C2×D212C2412yes—
561C2×D212C2412yes—
562C2×D212C2412yes—
563C2×D212C2411yescharacteristic
564C2×D212C2418yes—
565C2×C4×D53—28no—
566C2×C4×D53—28no—
567C2×C4×D53—48no—
568C2×C4×D53—44no—
569C2×C4×D53#4118yescomplemented
570C2×C4×D53C2412yes—
571C2×C4×D53C2412yes—
572C2×C4×D53C2412yes—
573C2×C4×D53C2414yes—
574C2×C4×D53C2412yes—
575C2×C4×D53C2414yes—
576C2×C4×D53C2412yes—
577C2×C4×D53C2414yes—
578C2×C4×D53C2414yes—
579C2×C4×D53C2412yes—
580C2×C4×D53C2412yes—
581C2×C4×D53C2414yes—
582C2×C4×D53C2414yes—
583C2×C4×D53C2414yes—
584C2×C4×D53C2418yes—
585C2×C4×D53C2418yes—
586C2×C4×D53C2411yescharacteristic
587C2×C4×D53C2411yescharacteristic
588C2×C4×D53C2411yescharacteristic
589C2×C4×D53C2411yescharacteristic
590C2×Dic106—24no—
591C2×Dic106C2414yes—
592C2×Dic106C2412yes—
593C2×Dic106C2412yes—
594C2×Dic106C2411yescharacteristic
595C2×Dic106C2412yes—
596C2×Dic106C2414yes—
597C2×Dic106C2414yes—
598C4⋊C4×C53C2414yes—
599C4⋊C4×C53C2412yes—
600C4⋊C4×C53C2412yes—
601C4⋊C4×C53C2414yes—
602C4⋊C4×C53C2412yes—
603C4⋊C4×C53C2418yes—
604C4⋊C4×C53C2418yes—
605C4⋊C4×C53C2414yes—
606C4⋊C4×C53C2414yes—
607C22⋊C4×C53C2412yes—
608C22⋊C4×C53C2412yes—
609C22⋊C4×C53C2418yes—
610C22⋊C4×C53C2418yes—
611C22⋊C4×C53C2418yes—
612C22⋊C4×C53C2412yes—
613C22⋊C4×C53C2414yes—
614C22⋊C4×C53C2418yes—
615C22⋊C4×C53C2418yes—
616C42×C53C2411yescharacteristic
617C42×C53C2412yes—
618C42×C53C2414yes—
619C42×C53C2411yescharacteristic
620C42×C53C2412yes—
621C42×C53C2418yes—
622C42×C53C2412yes—
623C42×C53C2412yes—
624C22⋊Dic53C2412yes—
625C22⋊Dic53C2412yes—
626C22⋊Dic53C2412yes—
627C22⋊Dic53C2414yes—
628C22⋊Dic53C2418yes—
629C22⋊Dic53C2418yes—
630C22⋊Dic53C2418yes—
631#11719921C2414yes—
632#11719921C2414yes—
633#11719921C2414yes—
634#11719921C2414yes—
635#11719921C2414yes—
636#11719921C2418yes—
637#11719921C2418yes—
638#11719921C2418yes—
639#11719921C2418yes—
640#11719921C2418yes—
641#11719921C2418yes—
642#11719921C2418yes—
643#11719921C2418yes—
644C4⋊Dic53C2412yes—
645C4⋊Dic53C2412yes—
646C4⋊Dic53C2414yes—
647C4⋊Dic53C2412yes—
648C4⋊Dic53C2418yes—
649C4⋊Dic53C2414yes—
650C4⋊Dic53C2414yes—
651C4⋊Dic53C2414yes—
652C4⋊Dic53C2418yes—
653#11719919C2414yes—
654#11719919C2414yes—
655#11719919C2414yes—
656#11719919C2414yes—
657#11719919C2414yes—
658#11719919C2414yes—
659#11719919C2414yes—
660#11719919C2414yes—
661#11719919C2414yes—
662#11719919C2414yes—
663#11719919C2414yes—
664#11719919C2418yes—
665#11719919C2418yes—
666#11719919C2418yes—
667#11719919C2418yes—
668#11719919C2418yes—
669#11719919C2418yes—
670C4×Dic53C2414yes—
671C4×Dic53C2412yes—
672C4×Dic53C2411yescharacteristic
673C4×Dic53C2414yes—
674C4×Dic53C2412yes—
675C4×Dic53C2414yes—
676C4×Dic53C2412yes—
677C4×Dic53C2411yescharacteristic
678C4×Dic53C2412yes—
679C4×Dic53C2412yes—
680C4×Dic53C2414yes—
681C4×Dic53C2414yes—
682C4×Dic53C2412yes—
683C4×Dic53C2414yes—
684C4×Dic53C2418yes—
685C4×Dic53C2412yes—
686C4×Dic53C2412yes—
687C4×Dic53C2418yes—
688C4×Dic53C2418yes—
689C23×C53—24no—
690C23×C53—44no—
691C23×C53C2514yes—
692C23×C53C2512yes—
693C23×C53C2511yescharacteristic
694C22×D53—24no—
695C22×D53—24no—
696C22×D53—42no—
697C22×D53—44no—
698C22×D53—44no—
699C22×D53C2×#4114yes—
700C22×D53C2514yes—
701C22×D53C2512yes—
702C22×D53C2511yescharacteristic
703C22×D53C2511yescharacteristic
704Q8×C53—22no—
705Q8×C53—24no—
706Q8×C53—24no—
707Q8×C53—44no—
708D4×C53—24no—
709D4×C53—22no—
710D4×C53—24no—
711D4×C53—24no—
712D4×C53—48no—
713C2×C4×C53—24no—
714C2×C4×C53—24no—
715C2×C4×C53—42no—
716C2×C4×C53—44no—
717C2×C4×C53—48no—
718C2×C4×C53C2×#4114yes—
719C2×C4×C53C2512yes—
720C2×C4×C53C2514yes—
721C2×C4×C53C2512yes—
722C2×C4×C53C2514yes—
723C2×C4×C53C2512yes—
724C2×C4×C53C2514yes—
725C2×C4×C53C2514yes—
726C2×C4×C53C2511yescharacteristic
727C2×C4×C53C2511yescharacteristic
728C22⋊D53—24no—
729C22⋊D53—24no—
730C22⋊D53—28no—
731C22⋊D53—28no—
732C22⋊D53—24no—
733C22⋊D53—216no—
734C22⋊D53—48no—
735C22⋊D53—48no—
736C22⋊D53—48no—
737C2×Dic53—24no—
738C2×Dic53—24no—
739C2×Dic53—28no—
740C2×Dic53—28no—
741C2×Dic53—28no—
742C2×Dic53—24no—
743C2×Dic53—48no—
744C2×Dic53C2×#4114yes—
745C2×Dic53C2514yes—
746C2×Dic53C2512yes—
747C2×Dic53C2514yes—
748C2×Dic53C2514yes—
749C2×Dic53C2514yes—
750C2×Dic53C2512yes—
751C2×Dic53C2511yescharacteristic
752C2×Dic53C2511yescharacteristic
753C2×Dic53C2512yes—
754D212—28no—
755D212—28no—
756D212—24no—
757D212—24no—
758D212—24no—
759D212—22no—
760D212—48no—
761C4×D53—24no—
762C4×D53—24no—
763C4×D53—24no—
764C4×D53—28no—
765C4×D53—28no—
766C4×D53—24no—
767C4×D53—28no—
768C4×D53—24no—
769C4×D53—44no—
770C4×D53—44no—
771C4×D53—42no—
772C4×D53—42no—
773C4×D53—48no—
774C4×D53—48no—
775C4×D53—44no—
776C4×D53—44no—
777C4×D53C2×#4114yes—
778C4×D53C2×#4114yes—
779C4×D53C2×#4114yes—
780C4×D53C2×#4114yes—
781Dic106—24no—
782Dic106—24no—
783Dic106—22no—
784Dic106—24no—
785Dic106—28no—
786Dic106—28no—
787Dic106—44no—
788#62815—531nomaximal, Sylow
789C22×C53—22no—
790C22×C53—24no—
791C22×C53—22no—
792C22×C53—24no—
793C22×C53—28no—
794C22×C53—84no—
795C22×C53C22×#4112yes—
796C22×C53C2611yescharacteristic
797C2×D53—22no—
798C2×D53—22no—
799C2×D53—24no—
800C2×D53—22no—
801C2×D53—24no—
802C2×D53—28no—
803C2×D53—44no—
804C2×D53—48no—
805C2×D53—84no—
806C2×D53C22×#4112yes—
807C2×D53C22×#4112yes—
808C4×C53—22no—
809C4×C53—24no—
810C4×C53—24no—
811C4×C53—24no—
812C4×C53—22no—
813C4×C53—22no—
814C4×C53—24no—
815C4×C53C22×#4112yes—
816C4×C53C22×#4112yes—
817Dic53—22no—
818Dic53—24no—
819Dic53—24no—
820Dic53—24no—
821Dic53—24no—
822Dic53—22no—
823Dic53C22×#4112yes—
824Dic53C22×#4112yes—
825Dic53#58514yes—
826#3512—534no—
827#3511—534no—
828#3510—531no—
829#3510—531no—
830#3510—531no—
831#3510D5311yescharacteristic, complemented
832#3509—531no—
833#3509—531no—
834#3508—531no—
835#3508—531no—
836#3507—534no—
837#3506—534no—
838#3505—538no—
839#3480—534no—
840#3480—534no—
841#3475—538no—
842#3455—534no—
843#3449—531no—
844#3449—531no—
845#3444—534no—
846C2×#533—531no—
847C2×#532—531no—
848#3428—531no—
849#3428—531no—
850C2×C4×#41—531no—
851C2×C53—22no—
852C2×C53—42no—
853C2×C53—44no—
854C2×C53C23×#4111yescharacteristic
855C2×C53C2×#58512yes—
856D53—22no—
857D53—22no—
858D53—42no—
859D53—44no—
860C22×#41—531no—
861C22×#41—531no—
862C22×#41—531no—
863#559—534no—
864#559—534no—
865#559—534no—
866#559—534no—
867#559—534no—
868#559C2×D5314yescomplemented
869#557—534no—
870#557—534no—
871#556—538no—
872#556—534no—
873#556—534no—
874#556—534no—
875#556—534no—
876#556—534no—
877#556C2×D5314yescomplemented
878#555—538no—
879#554—538no—
880#553—538no—
881#553—538no—
882#553—538no—
883#553—538no—
884#553—538no—
885#553—538no—
886#553—538no—
887#553—538no—
888#552—538no—
889#552—538no—
890#552—538no—
891#552—538no—
892#551—538no—
893#551—538no—
894#551—538no—
895#551C2×D5318yescomplemented
896#550—534no—
897#550—534no—
898#548—538no—
899#548—538no—
900#547—538no—
901#546—538no—
902#546—538no—
903#542—534no—
904#542—534no—
905#542—534no—
906#542C2×D5314yescomplemented
907#541—534no—
908#541—534no—
909#540—534no—
910#540—534no—
911#539—538no—
912#539—538no—
913#538—538no—
914#538—538no—
915#537—534no—
916#537—534no—
917#536—531no—
918#536—531no—
919#536—532no—
920#536—532no—
921#536—531no—
922#536C2×D5311yescharacteristic
923#535—531no—
924#535—531no—
925#535—532no—
926#535—532no—
927#535—531no—
928#535C2×D5311yescharacteristic
929#534—534no—
930#534—534no—
931#533—532no—
932#533—532no—
933#533—534no—
934#533—534no—
935#533—534no—
936#533—534no—
937#533—531no—
938#533—531no—
939#533—531no—
940#533C2×D5311yescharacteristic, complemented
941#532—532no—
942#532—532no—
943#532—532no—
944#532—532no—
945#532—534no—
946#532—534no—
947#532—532no—
948#532—532no—
949#532—532no—
950#532—532no—
951#532—534no—
952#532—534no—
953C2×C4⋊Q8—531no—
954C2×C4⋊Q8—532no—
955C2×#127—531no—
956#529—538no—
957#529—538no—
958#529—538no—
959#529—534no—
960#529—534no—
961#529—538no—
962#529—538no—
963#529—538no—
964#529—538no—
965#529—538no—
966#529—534no—
967#529C2×D5314yescomplemented
968C2×#125—532no—
969C2×#124—531no—
970C2×#124C2×D5311yescharacteristic, complemented
971#525—538no—
972#525—534no—
973#525—534no—
974#525—534no—
975#525—534no—
976#525—538no—
977C2×C22⋊Q8—534no—
978C2×#121—534no—
979#520—534no—
980#520—534no—
981#520—534no—
982#520—534no—
983#519—531no—
984#519—531no—
985#519—531no—
986#519C2×D5311yescharacteristic, complemented
987#518—531no—
988#518—534no—
989#518—531no—
990#518—531no—
991#518—534no—
992#518C2×D5311yescharacteristic, complemented
993C4×#41—531no—
994C4×#41—532no—
995C4×#41—534no—
996C4×#41—534no—
997C4×#41—534no—
998C4×#41—532no—
999C4×#41—534no—
1000C4×#41—534no—
1001C4×#41—538no—
1002C4×#41—531no—
1003C4×#41—532no—
1004C4×#41—538no—
1005C4×#41—531no—
1006C4×#41—532no—
1007C4×#41C2×D5311yescharacteristic
1008C2×C4×Q8—532no—
1009C2×C4×Q8—534no—
1010C2×C4×D4—534no—
1011C2×C4×D4—532no—
1012C2×C4×D4—534no—
1013C2×#117—531no—
1014C2×#117—531no—
1015C2×#117—531no—
1016C2×#117—532no—
1017C2×#117—534no—
1018C2×#117—534no—
1019C22×C42—531no—
1020C22×C42—532no—
1021C53#6281511yescharacteristic, complemented, Sylow
1022C2×#41—532no—
1023C2×#41—531no—
1024C2×#41—532no—
1025C2×#41—532no—
1026C2×#41—532no—
1027C2×#41—532no—
1028C2×#41—532no—
1029C2×#41—531no—
1030C2×#41—532no—
1031C2×#41—532no—
1032C2×#41—532no—
1033C2×#41—538no—
1034C2×#41—531no—
1035C2×#41—532no—
1036C2×#41—538no—
1037C2×#41—1068no—
1038C2×#41—1068no—
1039C2×#41—1068no—
1040C2×#41C22×D5311yescharacteristic
1041C22×Q8—531no—
1042C22×Q8—534no—
1043C22×Q8—531no—
1044C22×Q8C22×D5311yescharacteristic
1045C22×D4—532no—
1046C22×D4—534no—
1047C22×D4—532no—
1048C22×D4—531no—
1049C22×D4—532no—
1050C22×D4—531no—
1051C22×D4C22×D5311yescharacteristic
1052C23×C4—531no—
1053C23×C4—532no—
1054C23×C4—532no—
1055C23×C4—532no—
1056C23×C4—532no—
1057C23×C4—534no—
1058C4⋊Q8—532no—
1059C4⋊Q8—532no—
1060C4⋊Q8—534no—
1061C4⋊Q8—534no—
1062C4⋊Q8—532no—
1063C4⋊Q8—532no—
1064C4⋊Q8—532no—
1065C4⋊Q8—532no—
1066C4⋊Q8—534no—
1067C4⋊Q8—532no—
1068C4⋊Q8—532no—
1069C4⋊Q8C22×D5312yes—
1070C4⋊Q8C22×D5312yes—
1071#127—532no—
1072#127—532no—
1073#127—534no—
1074#127—532no—
1075#127—532no—
1076#127—532no—
1077#127C22×D5312yes—
1078#126—538no—
1079#126—538no—
1080#126—538no—
1081#126—538no—
1082#126—538no—
1083#126—538no—
1084#126—538no—
1085#126—538no—
1086#126—538no—
1087#126—538no—
1088#126C22×D5318yes—
1089#126C22×D5318yes—
1090#125—532no—
1091#125—532no—
1092#125—534no—
1093#125—534no—
1094#125—538no—
1095#125—538no—
1096#125—538no—
1097#125—538no—
1098#125—538no—
1099#125—532no—
1100#125—538no—
1101#125C22×D5312yes—
1102#124—538no—
1103#124—532no—
1104#124—532no—
1105#124—532no—
1106#124—532no—
1107#124—538no—
1108#124—538no—
1109#124—538no—
1110#124—538no—
1111#124—532no—
1112#124—532no—
1113#124—534no—
1114#124—532no—
1115#124—532no—
1116#124C22×D5312yes—
1117#124C22×D5312yes—
1118#124C22×D5314yes—
1119#124C22×D5318yes—
1120#124C22×D5312yes—
1121#124C22×D5312yes—
1122#123—534no—
1123#123—538no—
1124#123—534no—
1125#123—538no—
1126#123—538no—
1127#123—538no—
1128#123—538no—
1129#123—538no—
1130#123—538no—
1131#123—534no—
1132#123—538no—
1133#123—538no—
1134#123—538no—
1135#123—538no—
1136#123—538no—
1137#123C22×D5318yes—
1138#123C22×D5314yes—
1139#123C22×D5318yes—
1140C22⋊Q8—534no—
1141C22⋊Q8—534no—
1142C22⋊Q8—538no—
1143C22⋊Q8—534no—
1144C22⋊Q8—534no—
1145C22⋊Q8—534no—
1146C22⋊Q8—534no—
1147C22⋊Q8—534no—
1148C22⋊Q8—534no—
1149C22⋊Q8—538no—
1150C22⋊Q8—538no—
1151C22⋊Q8—538no—
1152C22⋊Q8—534no—
1153C22⋊Q8—534no—
1154C22⋊Q8—538no—
1155C22⋊Q8—538no—
1156C22⋊Q8—538no—
1157C22⋊Q8C22×D5314yes—
1158C22⋊Q8C22×D5314yes—
1159C22⋊Q8C22×D5318yes—
1160#121—534no—
1161#121—538no—
1162#121—538no—
1163#121—538no—
1164#121—538no—
1165#121—538no—
1166#121—534no—
1167#121—538no—
1168#121—534no—
1169#121—538no—
1170#121—538no—
1171#121—538no—
1172#121—538no—
1173#121—538no—
1174#121—538no—
1175#121—538no—
1176#121—538no—
1177#121—538no—
1178#121—538no—
1179#121C22×D5314yes—
1180#120—534no—
1181#120—538no—
1182#120—534no—
1183#120—538no—
1184#120—534no—
1185#120C22×D5314yes—
1186C4×Q8—532no—
1187C4×Q8—534no—
1188C4×Q8—534no—
1189C4×Q8—534no—
1190C4×Q8—534no—
1191C4×Q8—534no—
1192C4×Q8—534no—
1193C4×Q8—532no—
1194C4×Q8—534no—
1195C4×Q8—534no—
1196C4×Q8—534no—
1197C4×Q8—538no—
1198C4×Q8—534no—
1199C4×Q8—532no—
1200C4×Q8—534no—
1201C4×Q8—534no—
1202C4×Q8—534no—
1203C4×Q8—534no—
1204C4×Q8—534no—
1205C4×Q8—538no—
1206C4×Q8C22×D5312yes—
1207C4×Q8C22×D5314yes—
1208C4×Q8C22×D5314yes—
1209C4×Q8C22×D5314yes—
1210C4×D4—534no—
1211C4×D4—532no—
1212C4×D4—534no—
1213C4×D4—534no—
1214C4×D4—538no—
1215C4×D4—534no—
1216C4×D4—534no—
1217C4×D4—534no—
1218C4×D4—538no—
1219C4×D4—538no—
1220C4×D4—538no—
1221C4×D4—538no—
1222C4×D4—534no—
1223C4×D4—532no—
1224C4×D4—538no—
1225C4×D4—534no—
1226C4×D4—538no—
1227C4×D4—534no—
1228C4×D4—538no—
1229C4×D4—538no—
1230C4×D4—538no—
1231C4×D4—534no—
1232C4×D4—534no—
1233C4×D4—534no—
1234C4×D4—538no—
1235C4×D4—538no—
1236C4×D4—538no—
1237C4×D4—538no—
1238C4×D4—538no—
1239C4×D4—538no—
1240C4×D4—538no—
1241C4×D4—538no—
1242C4×D4—538no—
1243C4×D4—534no—
1244C4×D4—532no—
1245C4×D4—538no—
1246C4×D4—534no—
1247C4×D4—538no—
1248C4×D4—534no—
1249C4×D4C22×D5314yes—
1250C4×D4C22×D5312yes—
1251C4×D4C22×D5314yes—
1252C4×D4C22×D5314yes—
1253C4×D4C22×D5318yes—
1254#117—531no—
1255#117—532no—
1256#117—531no—
1257#117—531no—
1258#117—534no—
1259#117—532no—
1260#117—532no—
1261#117—532no—
1262#117—534no—
1263#117—538no—
1264#117—538no—
1265#117—532no—
1266#117—532no—
1267#117—532no—
1268#117—534no—
1269#117—538no—
1270#117—534no—
1271#117—534no—
1272#117—538no—
1273#117—538no—
1274#117—538no—
1275#117—532no—
1276#117—532no—
1277#117—532no—
1278#117—532no—
1279#117—532no—
1280#117—538no—
1281#117—538no—
1282#117—538no—
1283#117C22×D5311yescharacteristic
1284#117C22×D5312yes—
1285#117C22×D5311yescharacteristic
1286#117C22×D5314yes—
1287#117C22×D5311yescharacteristic
1288#117C22×D5318yes—
1289C2×C4⋊C4—538no—
1290C2×C4⋊C4—534no—
1291C2×C4⋊C4—532no—
1292C2×C4⋊C4—534no—
1293C2×C4⋊C4—532no—
1294C2×C4⋊C4—532no—
1295C2×C4⋊C4—538no—
1296C2×C4⋊C4—534no—
1297C2×C4⋊C4—534no—
1298C2×C4⋊C4—534no—
1299C2×C22⋊C4—534no—
1300C2×C22⋊C4—534no—
1301C2×C22⋊C4—532no—
1302C2×C22⋊C4—534no—
1303C2×C22⋊C4—532no—
1304C2×C22⋊C4—532no—
1305C2×C22⋊C4—534no—
1306C2×C22⋊C4—534no—
1307C2×C22⋊C4C22×D5314yes—
1308C2×C22⋊C4C22×D5314yes—
1309C2×C42—538no—
1310C2×C42—532no—
1311C2×C42—534no—
1312C2×C42—531no—
1313C2×C42—532no—
1314C2×C42—532no—
1315C2×C42—531no—
1316C2×C42—532no—
1317C2×C42—532no—
1318C2×C42—538no—
1319C2×C42—534no—
1320C2×C42—532no—
1321C2×C42—532no—
1322C2×C42—534no—
1323C2×C42—531no—
1324C2×C42—532no—
1325C2×C42—531no—
1326C2×C42—532no—
1327C2×C42—531no—
1328C2×C42C22×D5311yescharacteristic
1329C2×C42C22×D5312yes—
1330C24—531no—
1331C24—532no—
1332C24—532no—
1333C24C23×D5312yes—
1334#41—24no—
1335#41—1068no—
1336#41—1068no—
1337#41—1068no—
1338#41—1068no—
1339#41—1068no—
1340#41—1068no—
1341#41—1064no—
1342#41—1068no—
1343#41—1068no—
1344#41—1068no—
1345#41—1068no—
1346#41—1064no—
1347#41—1064no—
1348#41—21216no—
1349#41—21216no—
1350C2×Q8—24no—
1351C2×Q8—532no—
1352C2×Q8—534no—
1353C2×Q8—534no—
1354C2×Q8—532no—
1355C2×Q8—531no—
1356C2×Q8—532no—
1357C2×Q8—534no—
1358C2×Q8—1064no—
1359C2×Q8—1064no—
1360C2×Q8—2128no—
1361C2×Q8C23×D5312yes—
1362C2×Q8C23×D5311yescharacteristic
1363C2×Q8C23×D5312yes—
1364C2×Q8C23×D5314yes—
1365C2×D4—24no—
1366C2×D4—532no—
1367C2×D4—534no—
1368C2×D4—532no—
1369C2×D4—532no—
1370C2×D4—534no—
1371C2×D4—538no—
1372C2×D4—538no—
1373C2×D4—538no—
1374C2×D4—538no—
1375C2×D4—534no—
1376C2×D4—532no—
1377C2×D4—534no—
1378C2×D4—532no—
1379C2×D4—532no—
1380C2×D4—531no—
1381C2×D4—538no—
1382C2×D4—1068no—
1383C2×D4—1064no—
1384C2×D4—1068no—
1385C2×D4—1068no—
1386C2×D4—1064no—
1387C2×D4—2128no—
1388C2×D4C23×D5312yes—
1389C2×D4C23×D5312yes—
1390C2×D4C23×D5311yescharacteristic
1391C2×D4C23×D5312yes—
1392C2×D4C23×D5318yes—
1393C22×C4—531no—
1394C22×C4—538no—
1395C22×C4—531no—
1396C22×C4—531no—
1397C22×C4—531no—
1398C22×C4—531no—
1399C22×C4—532no—
1400C22×C4—532no—
1401C22×C4—534no—
1402C22×C4—534no—
1403C22×C4—532no—
1404C22×C4—534no—
1405C22×C4—538no—
1406C22×C4—532no—
1407C22×C4—532no—
1408C22×C4—532no—
1409C22×C4—532no—
1410C22×C4—534no—
1411C22×C4—534no—
1412C22×C4—532no—
1413C22×C4—534no—
1414C22×C4—534no—
1415C22×C4—532no—
1416C22×C4—532no—
1417C22×C4—534no—
1418C22×C4—534no—
1419C22×C4—534no—
1420C22×C4—538no—
1421C22×C4—538no—
1422C22×C4—1068no—
1423C22×C4—1068no—
1424C22×C4—1068no—
1425C22×C4—2124no—
1426C22×C4—2128no—
1427C22×C4C23×D5312yes—
1428C22×C4C23×D5312yes—
1429C22×C4C23×D5312yes—
1430C22×C4C23×D5314yes—
1431C22×C4C23×D5318yes—
1432C22×C4C23×D5311yescharacteristic
1433C4⋊C4—534no—
1434C4⋊C4—534no—
1435C4⋊C4—534no—
1436C4⋊C4—532no—
1437C4⋊C4—534no—
1438C4⋊C4—538no—
1439C4⋊C4—534no—
1440C4⋊C4—532no—
1441C4⋊C4—532no—
1442C4⋊C4—534no—
1443C4⋊C4—538no—
1444C4⋊C4—538no—
1445C4⋊C4—534no—
1446C4⋊C4—534no—
1447C4⋊C4—538no—
1448C4⋊C4—534no—
1449C4⋊C4—534no—
1450C4⋊C4—538no—
1451C4⋊C4—534no—
1452C4⋊C4—534no—
1453C4⋊C4—534no—
1454C4⋊C4—534no—
1455C4⋊C4—534no—
1456C4⋊C4—538no—
1457C4⋊C4—538no—
1458C4⋊C4—538no—
1459C4⋊C4C23×D5314yes—
1460C4⋊C4C23×D5312yes—
1461C4⋊C4C23×D5312yes—
1462C4⋊C4C23×D5318yes—
1463C4⋊C4C23×D5314yes—
1464C4⋊C4C23×D5312yes—
1465C4⋊C4C23×D5314yes—
1466C4⋊C4C23×D5314yes—
1467C4⋊C4C23×D5318yes—
1468C22⋊C4—532no—
1469C22⋊C4—532no—
1470C22⋊C4—532no—
1471C22⋊C4—534no—
1472C22⋊C4—538no—
1473C22⋊C4—538no—
1474C22⋊C4—538no—
1475C22⋊C4—534no—
1476C22⋊C4—534no—
1477C22⋊C4—534no—
1478C22⋊C4—534no—
1479C22⋊C4—538no—
1480C22⋊C4—538no—
1481C22⋊C4—538no—
1482C22⋊C4—534no—
1483C22⋊C4—538no—
1484C22⋊C4—538no—
1485C22⋊C4—538no—
1486C22⋊C4—538no—
1487C22⋊C4—538no—
1488C22⋊C4C23×D5312yes—
1489C22⋊C4C23×D5312yes—
1490C22⋊C4C23×D5312yes—
1491C22⋊C4C23×D5314yes—
1492C22⋊C4C23×D5318yes—
1493C22⋊C4C23×D5318yes—
1494C22⋊C4C23×D5318yes—
1495C22⋊C4C23×D5318yes—
1496C22⋊C4C23×D5318yes—
1497C42—534no—
1498C42—532no—
1499C42—531no—
1500C42—534no—
1501C42—534no—
1502C42—532no—
1503C42—532no—
1504C42—534no—
1505C42—531no—
1506C42—532no—
1507C42—532no—
1508C42—534no—
1509C42—534no—
1510C42—532no—
1511C42—538no—
1512C42—538no—
1513C42—538no—
1514C42—532no—
1515C42—532no—
1516C42C23×D5311yescharacteristic
1517C42C23×D5312yes—
1518C42C23×D5314yes—
1519C42C23×D5311yescharacteristic
1520C42C23×D5312yes—
1521C42C23×D5318yes—
1522C42C23×D5312yes—
1523C42C23×D5312yes—
1524C23—24no—
1525C23—44no—
1526C23—531no—
1527C23—531no—
1528C23—534no—
1529C23—532no—
1530C23—534no—
1531C23—1064no—
1532C23—1064no—
1533C23—2124no—
1534C23—2122no—
1535C23—2124no—
1536C23C24×D5312yes—
1537C23C24×D5314yes—
1538C23C24×D5311yescharacteristic
1539Q8—24no—
1540Q8—24no—
1541Q8—22no—
1542Q8—44no—
1543Q8—1064no—
1544Q8—1068no—
1545Q8—1068no—
1546Q8—1064no—
1547Q8—1064no—
1548Q8—1062no—
1549Q8—2124no—
1550D4—24no—
1551D4—24no—
1552D4—24no—
1553D4—22no—
1554D4—48no—
1555D4—1064no—
1556D4—1068no—
1557D4—1068no—
1558D4—1064no—
1559D4—10616no—
1560D4—1064no—
1561D4—1068no—
1562D4—1068no—
1563D4—1064no—
1564D4—1064no—
1565D4—1064no—
1566D4—1062no—
1567D4—2128no—
1568D4—2128no—
1569D4—2128no—
1570D4—2128no—
1571C2×C4—24no—
1572C2×C4—24no—
1573C2×C4—44no—
1574C2×C4—42no—
1575C2×C4—48no—
1576C2×C4—534no—
1577C2×C4—531no—
1578C2×C4—532no—
1579C2×C4—531no—
1580C2×C4—534no—
1581C2×C4—534no—
1582C2×C4—534no—
1583C2×C4—534no—
1584C2×C4—534no—
1585C2×C4—532no—
1586C2×C4—534no—
1587C2×C4—534no—
1588C2×C4—534no—
1589C2×C4—532no—
1590C2×C4—1064no—
1591C2×C4—1068no—
1592C2×C4—1068no—
1593C2×C4—1064no—
1594C2×C4—1064no—
1595C2×C4—1068no—
1596C2×C4—1064no—
1597C2×C4—1064no—
1598C2×C4—1068no—
1599C2×C4—1068no—
1600C2×C4—1064no—
1601C2×C4—1068no—
1602C2×C4—1064no—
1603C2×C4—1064no—
1604C2×C4—2124no—
1605C2×C4—2124no—
1606C2×C4—2122no—
1607C2×C4—2122no—
1608C2×C4—2124no—
1609C2×C4—2124no—
1610C2×C4—2128no—
1611C2×C4—2128no—
1612C2×C4—2128no—
1613C2×C4#41×D5314yes—
1614C2×C4C24×D5314yes—
1615C2×C4C24×D5312yes—
1616C2×C4C24×D5314yes—
1617C2×C4C24×D5312yes—
1618C2×C4C24×D5312yes—
1619C2×C4C24×D5314yes—
1620C2×C4C24×D5314yes—
1621C2×C4C24×D5311yescharacteristic
1622C2×C4C24×D5311yescharacteristic
1623C22—22no—
1624C22—22no—
1625C22—24no—
1626C22—24no—
1627C22—28no—
1628C22—84no—
1629C22—532no—
1630C22—532no—
1631C22—1062no—
1632C22—1062no—
1633C22—1064no—
1634C22—1062no—
1635C22—1064no—
1636C22—1068no—
1637C22—4244no—
1638C22—2124no—
1639C22—2128no—
1640C22C2×#41×D5312yes—
1641C22C25×D5311yescharacteristic
1642C4—22no—
1643C4—24no—
1644C4—22no—
1645C4—24no—
1646C4—24no—
1647C4—22no—
1648C4—24no—
1649C4—532no—
1650C4—532no—
1651C4—534no—
1652C4—1062no—
1653C4—1064no—
1654C4—1064no—
1655C4—1062no—
1656C4—1064no—
1657C4—1064no—
1658C4C2×#41×D5312yes—
1659C4C2×#41×D5312yes—
1660C2—22no—
1661C2—44no—
1662C2—42no—
1663C2—1062no—
1664C2—1062no—
1665C2—2124no—
1666C2—2122no—
1667C2C22×#41×D5311yescharacteristic
1668C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3510C2
hypercenter#3510D53
hypocenterC53#62815
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3510

Complements

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

NH ≅ G/Ntype
1. #20288630C2semidirect
2. #20288620C2semidirect
3. #20288613C2semidirect
4. #20288611C2semidirect
5. #20288609C2semidirect
6. #20288600C2semidirect
7. #20288596C2semidirect
8. #20288590C2semidirect
9. #20288586C2semidirect
10. #20288576C2semidirect
11. #20288563C2semidirect
12. #20288546C2semidirect
13. #20288311C2semidirect
14. #20288307C2semidirect
15. #20288270C2semidirect
16. #20288102C2semidirect
17. #20288047C2semidirect
18. #20288046C2semidirect
19. #20288009C2semidirect
20. #533×D53C2semidirect
21. C2×#16811172C2semidirect
22. #20287917C2semidirect
23. #20287913C2semidirect
24. C4×#41×D53C2semidirect
25. C53×#3510C2semidirect
29. #16811358C22semidirect
30. #16811356C22semidirect
31. #16811356C22semidirect
32. #16811355C22semidirect
33. #16811355C22semidirect
34. #16811351C22semidirect
35. #16811348C22semidirect
36. #16811346C22semidirect
37. #16811345C22semidirect
38. #16811345C22semidirect
39. #16811342C22semidirect
40. #16811342C22semidirect
41. #16811340C22semidirect
42. #16811335C22semidirect
43. #16811327C22semidirect
44. #16811324C22semidirect
45. #16811324C22semidirect
46. #16811323C22semidirect
47. #16811322C22semidirect
48. #16811318C22semidirect
49. #16811318C22semidirect
50. #16811318C22semidirect
51. #16811317C22semidirect
52. #16811310C22semidirect
53. #16811309C22semidirect
54. #16811306C22semidirect
55. #16811306C22semidirect
56. #16811302C22semidirect
57. #16811300C22semidirect
58. #16811299C22semidirect
59. #16811294C22semidirect
60. #16811293C22semidirect
61. #16811283C22semidirect
62. #16811281C22semidirect
63. #16811271C22semidirect
64. #16811263C22semidirect
65. #16811260C22semidirect
66. #16811247C22semidirect
67. #16811244C22semidirect
68. #16811242C22semidirect
69. #16811233C22semidirect
70. #16811231C22semidirect
71. #16811226C22semidirect
72. #16811224C22semidirect
73. #16811219C22semidirect
74. #16811214C22semidirect
75. #16811209C22semidirect
76. #16811207C22semidirect
77. #16811203C22semidirect
78. #16811202C22semidirect
80. #16811198C22semidirect
83. #16811193C22semidirect
85. #16811191C22semidirect
88. #16811186C22semidirect
91. #16811180C22semidirect
92. #16811179C22semidirect
93. #16811178C22semidirect
94. #16811177C22semidirect
95. #16811177C22semidirect
96. #16811176C22semidirect
97. #16811176C22semidirect
98. #16811175C22semidirect
99. #16811175C22semidirect
100. #16811174C22semidirect
104. #16811172C22semidirect
105. #16811172C22semidirect
106. #16811172C22semidirect
107. #16811172C22semidirect
108. #16811172C22semidirect
109. #16811171C22semidirect
110. #16811170C22semidirect
111. #16811168C22semidirect
112. C2×#13133215C22semidirect
113. C4⋊Q8×D53C22semidirect
114. C2×#13133213C22semidirect
115. #16811159C22semidirect
116. #16811158C22semidirect
117. #16811157C22semidirect
118. #16811156C22semidirect
119. #16811156C22semidirect
120. #16811156C22semidirect
121. #16811152C22semidirect
122. #16811152C22semidirect
123. #16811151C22semidirect
124. #16811150C22semidirect
125. #16811150C22semidirect
126. #125×D53C22semidirect
127. C2×#13133205C22semidirect
128. #16811136C22semidirect
129. #16811133C22semidirect
130. #16811132C22semidirect
132. #16811131C22semidirect
136. #16811105C22semidirect
137. #16811105C22semidirect
138. #16811102C22semidirect
139. #16811102C22semidirect
140. #16811101C22semidirect
141. #16811100C22semidirect
142. #16811100C22semidirect
143. #16811098C22semidirect
145. #16811097C22semidirect
146. #16811097C22semidirect
149. C4×#11719949C22semidirect
150. C4×#11719949C22semidirect
151. C4×#11719949C22semidirect
153. C4×#11719945C22semidirect
155. #16811091C22semidirect
156. #16811091C22semidirect
158. C4×#11719947C22semidirect
159. C4×#11719947C22semidirect
160. C4×#11719947C22semidirect
161. C4×#11719947C22semidirect
162. C4×Q8×D53C22semidirect
163. C4×Q8×D53C22semidirect
164. C2×#13133177C22semidirect
166. C4×D4×D53C22semidirect
167. C2×#13133173C22semidirect
171. #117×D53C22semidirect
172. #117×D53C22semidirect
174. C2×C42×D53C22semidirect
175. C53×#559C22semidirect
176. C53×#556C22semidirect
177. C53×#551C22semidirect
178. C53×#542C22semidirect
181. C53×#533C22semidirect
182. C53×#529C22semidirect
183. C2×#124×C53C22semidirect
184. C53×#519C22semidirect
185. C53×#518C22semidirect
569. C2×C4×D53#41semidirect
831. #3510D53semidirect
868. #559C2×D53semidirect
877. #556C2×D53semidirect
895. #551C2×D53semidirect
906. #542C2×D53semidirect
940. #533C2×D53semidirect
967. #529C2×D53semidirect
970. C2×#124C2×D53semidirect
986. #519C2×D53semidirect
992. #518C2×D53semidirect
1021. C53#62815semidirect

Maximal subgroups

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

subgroupindex
#202886302
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#202880092
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C2×#168111722
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C4×#41×D532
C53×#35102
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