Finite Group Databasebeta

← #28293278

Subgroups — #28293278

Order 13568.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288826C214yesmaximal, complemented
2#20288737C2112yesmaximal, complemented
3#20288715C214yesmaximal, complemented
4#20288657C2112yesmaximal, complemented
5#20288637C213yesmaximal, complemented
6#20288591C213yesmaximal, complemented
7#20288541C211yesmaximal, characteristic, complemented
8#20288493C211yesmaximal, characteristic, complemented
9#20288450C216yesmaximal, complemented
10#20288384C212yesmaximal, complemented
11#20288131C216yesmaximal, complemented
12#20288105C213yesmaximal, complemented
13C2×#16811228C213yesmaximal, complemented
14C4×#13133263C212yesmaximal, complemented
15C53×#3428C211yesmaximal, characteristic, complemented
16C2×#13133263C2212yes—
17#16811358C22112yescomplemented
18#16811349C2214yescomplemented
19#16811336C22112yescomplemented
20#16811332C22112yescomplemented
21#16811323C22112yescomplemented
22#16811322C22124yescomplemented
23#16811321C22112yescomplemented
24#16811317C22112yescomplemented
25#16811314C22112yescomplemented
26#16811297C22124yescomplemented
27#16811295C2214yescomplemented
28#16811294C22112yescomplemented
29#16811292C2214yescomplemented
30#16811284C2214yescomplemented
31#16811274C22112yescomplemented
32#16811269C22124yescomplemented
33#16811263C22124yescomplemented
34#16811261C22112yescomplemented
35D4×D212C22112yescomplemented
36D4×C22⋊D53C22112yescomplemented
37#16811251C2216yescomplemented
38#16811245C22112yescomplemented
39#16811244C2216yescomplemented
40#16811244C2216yescomplemented
41#16811235C2211yescharacteristic, complemented
42#16811235C2213yescomplemented
43#16811228C22112yescomplemented
44#16811228C2213yescomplemented
45#16811228C2216yescomplemented
46#16811228C2216yescomplemented
47#16811228C22112yescomplemented
48#16811228C2216yescomplemented
49#16811228C2213yescomplemented
50#16811224C22112yescomplemented
51#16811220C22112yescomplemented
52#16811211C22112yescomplemented
53#16811206C22124yescomplemented
54#16811201C2216yescomplemented
55#16811192C2216yescomplemented
56#16811187C2216yescomplemented
57#16811180C2213yescomplemented
58#16811173C22112yescomplemented
59#16811173C2213yescomplemented
60#16811170C22112yescomplemented
61C2×#13133214C2213yescomplemented
62#16811160C22112yescomplemented
63#16811157C22112yescomplemented
64#16811151C22112yescomplemented
65#16811151C22112yescomplemented
66C2×#13133209C2213yescomplemented
67#16811134C2216yescomplemented
68#16811132C22124yescomplemented
69C2×#13133202C22112yescomplemented
70C2×#13133191C2216yescomplemented
71C2×#13133190C22112yescomplemented
72#16811106C2212yes—
73#16811105C2214yescomplemented
74#16811103C2216yescomplemented
75#16811097C2216yescomplemented
76#16811095C22112yescomplemented
77C4×#11719949C2214yescomplemented
78C4×#11719945C2216yescomplemented
79C2×C4×D212C2216yescomplemented
80C4×D4×D53C22112yescomplemented
81C22×#41×C53C2211yescharacteristic
82C53×#520C2216yescomplemented
83C53×#520C2212yescomplemented
84C53×#519C2212yescomplemented
85C53×#518C2216yescomplemented
86C4×#41×C53C2211yescharacteristic
87C4×#41×C53C2211yescharacteristic
88C4×#41×C53C2213yescomplemented
89C4×#41×C53C2213yescomplemented
90C2×#117×C53C2213yescomplemented
91C2×#117×C53C2213yescomplemented
92#13133263—216no—
93C2×#11719949C2314yes—
94C2×#11719945C2316yes—
95C2×#11719945C23124yes—
96C22×D212C2316yes—
97C22×D212C23112yes—
98C22×C22⋊D53C23112yes—
99C2×D4×D53C23112yes—
100C22×C4×D53C23112yes—
101#13133217C2311yescharacteristic
102#13133217C2316yes—
103#13133216C23112yes—
104#13133214C23112yes—
105#13133214C2313yes—
106#13133214C2316yes—
107#13133213C23112yes—
108#13133212C23112yes—
109#13133212C23112yes—
110#13133211C23124yes—
111#13133210C23112yes—
112#13133210C2314yes—
113#13133209C23112yes—
114#13133209C2313yes—
115#13133209C2316yes—
116#13133209C2311yescharacteristic
117#13133208C23112yes—
118#13133207C23112yes—
119#13133207C2314yes—
120#13133206C23112yes—
121#13133205C23124yes—
122#13133205C2316yes—
123#13133203C23112yes—
124#13133203C23112yes—
125#13133202C23112yes—
126#13133202C23124yes—
127#13133202C23124yes—
128#13133202C23112yes—
129#13133202C23124yes—
130#13133200C23124yes—
131#13133200C23112yes—
132#13133199C23112yes—
133#13133199C23112yes—
134#13133196C23112yes—
135#13133196C2312yes—
136#13133196C2316yes—
137#13133195C23112yes—
138#13133195C23112yes—
139#13133194C23124yes—
140#13133193C23112yes—
141#13133192C23112yes—
142#13133192C23112yes—
143#13133191C23124yes—
144#13133191C23112yes—
145#13133191C23112yes—
146#13133191C23112yes—
147#13133191C2316yes—
148#13133191C23112yes—
149#13133191C2316yes—
150#13133190C23112yes—
151#13133190C23124yes—
152#13133190C23124yes—
153#13133190C23112yes—
154#13133190C23124yes—
155#13133189C23124yes—
156#13133188C23112yes—
157#13133187C23124yes—
158#13133186C23112yes—
159#13133185C23124yes—
160Q8×Dic53C2314yes—
161C4×Dic106C23112yes—
162C4×Dic106C2312yes—
163C4×Dic106C2316yes—
164C4×D212C23124yes—
165C4×D212C23112yes—
166C4×D212C23112yes—
167C4×D212C2316yes—
168C4×D212C23112yes—
169C4×D212C23112yes—
170C4×D212C2316yes—
171D4×Dic53C23112yes—
172#13133179C23112yes—
173#13133179C23112yes—
174C4×C22⋊D53C23112yes—
175C4×C22⋊D53C23112yes—
176C4×C22⋊D53C23124yes—
177C4×C22⋊D53C23112yes—
178C4×C22⋊D53C23112yes—
179#13133177C23124yes—
180#13133176C2316yes—
181#13133175C23112yes—
182#13133174C23124yes—
183#13133174C23112yes—
184C2×C4⋊Dic53C2316yes—
185C2×#11719919C23112yes—
186C4⋊C4×D53C23112yes—
187C2×#11719921C23112yes—
188C2×#11719921C23112yes—
189C22⋊C4×D53C23124yes—
190C42×D53C23112yes—
191C2×#41×C53—28no—
192C2×#41×C53C2311yescharacteristic
193C2×#41×C53C2313yes—
194C2×#41×C53C2313yes—
195C2×#41×C53C2311yescharacteristic
196C22×Q8×C53C2311yescharacteristic
197C22×D4×C53C2313yes—
198C23×C4×C53C2313yes—
199C4×Q8×C53C2312yes—
200C4×Q8×C53C2312yes—
201C4×Q8×C53C2316yes—
202C4×Q8×C53C2316yes—
203C4×D4×C53C23112yes—
204C4×D4×C53C2316yes—
205C4×D4×C53C2316yes—
206C4×D4×C53C2316yes—
207C4×D4×C53C23112yes—
208C4×D4×C53C2316yes—
209#117×C53C2311yescharacteristic
210#117×C53C2313yes—
211#117×C53C2313yes—
212#117×C53C2313yes—
213#117×C53C2313yes—
214#117×C53C2313yes—
215#117×C53C2316yes—
216#117×C53C2316yes—
217#117×C53C2316yes—
218#117×C53C2316yes—
219C2×C4⋊C4×C53C2316yes—
220C2×C4⋊C4×C53C2316yes—
221C2×C22⋊C4×C53C2316yes—
222C2×C22⋊C4×C53C2316yes—
223C2×C42×C53C2313yes—
224C2×C42×C53C2313yes—
225C2×C42×C53C2316yes—
226C24×C53C2413yes—
227C23×D53C24112yes—
228#41×C53—24no—
229#41×C53—212no—
230#41×C53—212no—
231#41×C53#4118yescomplemented
232C2×Q8×C53—24no—
233C2×Q8×C53C2413yes—
234C2×Q8×C53C2411yescharacteristic
235C2×D4×C53—212no—
236C2×D4×C53C2416yes—
237C2×D4×C53C2413yes—
238C2×D4×C53C2413yes—
239C22×C4×C53—212no—
240C22×C4×C53C2413yes—
241C22×C4×C53C2413yes—
242C22×C4×C53C2413yes—
243C22×C4×C53C2411yescharacteristic
244C22×C4×C53C2413yes—
245C22×C4×C53C2416yes—
246C22×C4×C53C2416yes—
247C22×C4×C53C24112yes—
248C22×C4×C53C2413yes—
249C2×C22⋊D53—812no—
250C2×C22⋊D53C24112yes—
251C2×C22⋊D53C24112yes—
252C2×C22⋊D53C24124yes—
253C2×C22⋊D53C24112yes—
254C22×Dic53C24112yes—
255#11719949—216no—
256D4×D53—248no—
257#11719945—224no—
258#11719945—824no—
259C2×D212—224no—
260C2×D212—812no—
261C2×D212C24112yes—
262C2×D212C2416yes—
263C2×D212C24124yes—
264C2×D212C24112yes—
265C2×C4×D53—812no—
266C2×C4×D53C24112yes—
267C2×C4×D53C24112yes—
268C2×C4×D53C24112yes—
269C2×C4×D53C24124yes—
270C2×Dic106C2412yes—
271C2×Dic106C24112yes—
272C4⋊C4×C53C2416yes—
273C4⋊C4×C53C2412yes—
274C4⋊C4×C53C2416yes—
275C4⋊C4×C53C2416yes—
276C4⋊C4×C53C2416yes—
277C4⋊C4×C53C2416yes—
278C22⋊C4×C53C2412yes—
279C22⋊C4×C53C2416yes—
280C22⋊C4×C53C2416yes—
281C22⋊C4×C53C2416yes—
282C22⋊C4×C53C2416yes—
283C22⋊C4×C53C2416yes—
284C42×C53C2411yescharacteristic
285C42×C53C2413yes—
286C42×C53C2413yes—
287C42×C53C2411yescharacteristic
288C42×C53C2416yes—
289C42×C53C24112yes—
290C42×C53C2416yes—
291C22⋊Dic53C24112yes—
292C22⋊Dic53C2414yes—
293C22⋊Dic53C24112yes—
294#11719921C24112yes—
295#11719921C24124yes—
296#11719921C24112yes—
297#11719921C24112yes—
298#11719921C24124yes—
299#11719921C24112yes—
300#11719921C24112yes—
301#11719921C24112yes—
302C4⋊Dic53C24112yes—
303C4⋊Dic53C2416yes—
304C4⋊Dic53C2412yes—
305C4⋊Dic53C2414yes—
306C4⋊Dic53C24112yes—
307#11719919C24112yes—
308#11719919C24112yes—
309#11719919C24124yes—
310#11719919C2414yes—
311#11719919C24112yes—
312#11719919C2414yes—
313#11719919C2414yes—
314C4×Dic53C2414yes—
315C4×Dic53C24112yes—
316C4×Dic53C24112yes—
317C23×C53—26no—
318C23×C53—46no—
319C23×C53C2513yes—
320C23×C53C2511yescharacteristic
321C23×C53C2513yes—
322C22×D53—224no—
323C22×D53—412no—
324C22×D53—412no—
325C22×D53C25112yes—
326Q8×C53—26no—
327Q8×C53C2×#4114yes—
328D4×C53—212no—
329D4×C53—26no—
330D4×C53C2×#41112yes—
331C2×C4×C53—26no—
332C2×C4×C53—22no—
333C2×C4×C53—26no—
334C2×C4×C53—26no—
335C2×C4×C53—26no—
336C2×C4×C53—46no—
337C2×C4×C53—46no—
338C2×C4×C53—412no—
339C2×C4×C53C2×#41112yes—
340C2×C4×C53C2516yes—
341C2×C4×C53C2516yes—
342C2×C4×C53C2512yes—
343C2×C4×C53C2512yes—
344C2×C4×C53C2511yescharacteristic
345C2×C4×C53C2513yes—
346C2×C4×C53C2511yescharacteristic
347C2×C4×C53C2513yes—
348C22⋊D53—224no—
349C22⋊D53—412no—
350C22⋊D53—424no—
351C22⋊D53—412no—
352C2×Dic53—412no—
353C2×Dic53C2514yes—
354C2×Dic53C25112yes—
355C2×Dic53C2514yes—
356D212—212no—
357D212—224no—
358D212—412no—
359D212—424no—
360C4×D53—224no—
361C4×D53—412no—
362C4×D53—424no—
363C4×D53—412no—
364Dic106—24no—
365Dic106—412no—
366#62858—531nomaximal, Sylow
367C22×C53—26no—
368C22×C53—21no—
369C22×C53—23no—
370C22×C53—26no—
371C22×C53—22no—
372C22×C53—86no—
373C22×C53C22×#4116yes—
374C22×C53C2611yescharacteristic
375C2×D53—212no—
376C2×D53—212no—
377C2×D53—212no—
378C2×D53—824no—
379C4×C53—21no—
380C4×C53—23no—
381C4×C53—26no—
382C4×C53—22no—
383C4×C53—26no—
384C4×C53—22no—
385C4×C53C22×#4112yes—
386C4×C53C22×#4116yes—
387Dic53—24no—
388Dic53—24no—
389Dic53—212no—
390#3524—534no—
391#3519—5312no—
392#3517—534no—
393#3513—5312no—
394#3512—533no—
395#3508—533no—
396#3504—531no—
397#3498—531no—
398#3494—536no—
399#3488—532no—
400#3460—536no—
401#3455—533no—
402C2×#540—533no—
403C4×H(5,𝔽2)—532no—
404#3428D5311yescharacteristic, complemented
405C2×C53—26no—
406C2×C53—43no—
407C2×C53—41no—
408C2×C53C23×#4111yescharacteristic
409C2×C53H(7,𝔽2)12yes—
410D53—412no—
411C2×H(5,𝔽2)—532no—
412C22×#41C2×D5311yescharacteristic
413#559—5312no—
414#557—534no—
415#555—5312no—
416#554—5312no—
417#553—5324no—
418#553—5312no—
419#553—5312no—
420#553—5312no—
421#552—5312no—
422#551—5324no—
423#550—534no—
424#550—534no—
425#550—5312no—
426#548—534no—
427#547—5312no—
428#546—5312no—
429#546—5324no—
430#546—5324no—
431D42—5312no—
432D42—5312no—
433#544—536no—
434#542—5312no—
435#542—536no—
436#542—536no—
437#541—531no—
438#541—533no—
439#540—5312no—
440#540—533no—
441#540—536no—
442#540—536no—
443#540—536no—
444#540—5312no—
445#540—5312no—
446#540—533no—
447#539—5312no—
448#538—5324no—
449#538—5312no—
450#537—536no—
451#535—536no—
452#535—536no—
453#533—533no—
454#532—5312no—
455#532—533no—
456#532—5312no—
457C2×#127—533no—
458#529—5312no—
459#529—5312no—
460#529—5312no—
461#529—5312no—
462C2×#125—533no—
463#525—536no—
464#525—5324no—
465C2×#123—5312no—
466C2×#121—536no—
467C2×#121—5312no—
468#520—532no—
469#520—534no—
470#520—536no—
471#520C2×D5316yescomplemented
472#520C2×D5312yescomplemented
473#519C2×D5312yescomplemented
474#518—5312no—
475#518—536no—
476#518C2×D5316yescomplemented
477C4×#41—534no—
478C4×#41—536no—
479C4×#41C2×D5311yescharacteristic
480C4×#41C2×D5311yescharacteristic
481C4×#41C2×D5313yescomplemented
482C4×#41C2×D5313yescomplemented
483C2×C4×D4—5312no—
484C2×C4×D4—536no—
485C2×#117C2×D5313yescomplemented
486C2×#117C2×D5313yescomplemented
487C53#6285811yescharacteristic, complemented, Sylow
488H(5,𝔽2)—10616no—
489C2×#41—28no—
490C2×#41—534no—
491C2×#41—536no—
492C2×#41—5324no—
493C2×#41C22×D5313yes—
494C2×#41C22×D5313yes—
495C2×#41C22×D5311yescharacteristic
496C2×#41C22×D5311yescharacteristic
497C22×Q8C22×D5311yescharacteristic
498C22×D4—5312no—
499C22×D4—5312no—
500C22×D4—536no—
501C22×D4—5312no—
502C22×D4C22×D5313yes—
503C23×C4—5312no—
504C23×C4C22×D5313yes—
505C4⋊Q8—5312no—
506C4⋊Q8—531no—
507C4⋊Q8—536no—
508#127—5312no—
509#127—533no—
510#127—536no—
511#127—5312no—
512#126—5312no—
513#126—5312no—
514#126—534no—
515#126—5312no—
516#126—5324no—
517#125—534no—
518#125—5312no—
519#125—5312no—
520#125—533no—
521#125—536no—
522#125—5312no—
523#125—531no—
524#124—5312no—
525#124—5312no—
526#124—5312no—
527#124—536no—
528#124—5324no—
529#123—5312no—
530#123—5324no—
531#123—5312no—
532#123—5324no—
533#123—5324no—
534#123—5324no—
535#123—5312no—
536#123—5312no—
537#123—5312no—
538C22⋊Q8—5312no—
539C22⋊Q8—532no—
540C22⋊Q8—536no—
541C22⋊Q8—5312no—
542C22⋊Q8—5312no—
543C22⋊Q8—5312no—
544C22⋊Q8—5324no—
545#121—5324no—
546#121—5312no—
547#121—536no—
548#121—5312no—
549#121—5312no—
550#121—5312no—
551#121—536no—
552#121—5312no—
553#121—5324no—
554#121—5312no—
555#121—5312no—
556#121—5312no—
557#121—5324no—
558#121—5324no—
559#121—5324no—
560#121—5312no—
561#120—5312no—
562#120—5324no—
563#120—5324no—
564C4×Q8—534no—
565C4×Q8—532no—
566C4×Q8—536no—
567C4×Q8—5312no—
568C4×Q8C22×D5312yes—
569C4×Q8C22×D5312yes—
570C4×Q8C22×D5316yes—
571C4×Q8C22×D5316yes—
572C4×D4—5312no—
573C4×D4—5312no—
574C4×D4—5312no—
575C4×D4—5312no—
576C4×D4—5312no—
577C4×D4—5324no—
578C4×D4—5312no—
579C4×D4—5312no—
580C4×D4—5324no—
581C4×D4—5312no—
582C4×D4—536no—
583C4×D4—5312no—
584C4×D4—5312no—
585C4×D4—536no—
586C4×D4—5324no—
587C4×D4—5312no—
588C4×D4C22×D5316yes—
589C4×D4C22×D5316yes—
590C4×D4C22×D53112yes—
591C4×D4C22×D5316yes—
592C4×D4C22×D53112yes—
593C4×D4C22×D5316yes—
594#117—536no—
595#117—5312no—
596#117—5312no—
597#117—5324no—
598#117C22×D5311yescharacteristic
599#117C22×D5313yes—
600#117C22×D5313yes—
601#117C22×D5313yes—
602#117C22×D5313yes—
603#117C22×D5313yes—
604#117C22×D5316yes—
605#117C22×D5316yes—
606#117C22×D5316yes—
607#117C22×D5316yes—
608C2×C4⋊C4—536no—
609C2×C4⋊C4—5312no—
610C2×C4⋊C4—5312no—
611C2×C4⋊C4C22×D5316yes—
612C2×C4⋊C4C22×D5316yes—
613C2×C22⋊C4—5312no—
614C2×C22⋊C4—5312no—
615C2×C22⋊C4—5324no—
616C2×C22⋊C4C22×D5316yes—
617C2×C22⋊C4C22×D5316yes—
618C2×C42—5312no—
619C2×C42C22×D5313yes—
620C2×C42C22×D5313yes—
621C2×C42C22×D5316yes—
622C24—5312no—
623C24C23×D5313yes—
624#41—24no—
625#41—212no—
626#41—212no—
627#41—10616no—
628#41—10624no—
629#41—42424no—
630#41#1171994518yescomplemented
631C2×Q8—24no—
632C2×Q8—532no—
633C2×Q8—5312no—
634C2×Q8C23×D5313yes—
635C2×Q8C23×D5311yescharacteristic
636C2×D4—212no—
637C2×D4—5312no—
638C2×D4—5312no—
639C2×D4—5312no—
640C2×D4—5324no—
641C2×D4—5312no—
642C2×D4—536no—
643C2×D4—5324no—
644C2×D4—5312no—
645C2×D4—10648no—
646C2×D4—10624no—
647C2×D4—42412no—
648C2×D4—42412no—
649C2×D4C23×D5316yes—
650C2×D4C23×D5313yes—
651C2×D4C23×D5313yes—
652C22×C4—212no—
653C22×C4—5312no—
654C22×C4—5312no—
655C22×C4—5312no—
656C22×C4—5312no—
657C22×C4—5324no—
658C22×C4—42412no—
659C22×C4C23×D5313yes—
660C22×C4C23×D5313yes—
661C22×C4C23×D5313yes—
662C22×C4C23×D5313yes—
663C22×C4C23×D5311yescharacteristic
664C22×C4C23×D5316yes—
665C22×C4C23×D5316yes—
666C22×C4C23×D53112yes—
667C22×C4C23×D5313yes—
668C4⋊C4—5312no—
669C4⋊C4—536no—
670C4⋊C4—5312no—
671C4⋊C4—5312no—
672C4⋊C4—5324no—
673C4⋊C4—532no—
674C4⋊C4—534no—
675C4⋊C4—5312no—
676C4⋊C4—534no—
677C4⋊C4—534no—
678C4⋊C4—5312no—
679C4⋊C4—534no—
680C4⋊C4C23×D5316yes—
681C4⋊C4C23×D5316yes—
682C4⋊C4C23×D5312yes—
683C4⋊C4C23×D5316yes—
684C4⋊C4C23×D5316yes—
685C4⋊C4C23×D5316yes—
686C22⋊C4—5312no—
687C22⋊C4—534no—
688C22⋊C4—5312no—
689C22⋊C4—5312no—
690C22⋊C4—5324no—
691C22⋊C4—5312no—
692C22⋊C4—5312no—
693C22⋊C4—5324no—
694C22⋊C4—5312no—
695C22⋊C4—5312no—
696C22⋊C4—5312no—
697C22⋊C4C23×D5316yes—
698C22⋊C4C23×D5312yes—
699C22⋊C4C23×D5316yes—
700C22⋊C4C23×D5316yes—
701C22⋊C4C23×D5316yes—
702C22⋊C4C23×D5316yes—
703C42—534no—
704C42—5312no—
705C42—5312no—
706C42C23×D5316yes—
707C42C23×D5311yescharacteristic
708C42C23×D5313yes—
709C42C23×D5313yes—
710C42C23×D5311yescharacteristic
711C42C23×D53112yes—
712C42C23×D5316yes—
713C23—26no—
714C23—46no—
715C23—5312no—
716C23—10624no—
717C23—21212no—
718C23—21212no—
719C23C24×D5311yescharacteristic
720C23C24×D5313yes—
721C23C24×D5313yes—
722Q8—26no—
723Q8—1064no—
724Q8—21212no—
725Q8C2×#1171994514yes—
726D4—212no—
727D4—26no—
728D4—10624no—
729D4—10612no—
730D4—10624no—
731D4—21212no—
732D4—21224no—
733D4—21212no—
734D4—21224no—
735D4—21212no—
736D4C2×#11719945112yes—
737C2×C4—26no—
738C2×C4—22no—
739C2×C4—26no—
740C2×C4—26no—
741C2×C4—26no—
742C2×C4—46no—
743C2×C4—46no—
744C2×C4—412no—
745C2×C4—534no—
746C2×C4—534no—
747C2×C4—5312no—
748C2×C4—10624no—
749C2×C4—21212no—
750C2×C4—21224no—
751C2×C4—21212no—
752C2×C4—21212no—
753C2×C4C2×#11719945112yes—
754C2×C4C24×D5312yes—
755C2×C4C24×D5316yes—
756C2×C4C24×D5313yes—
757C2×C4C24×D5316yes—
758C2×C4C24×D5312yes—
759C2×C4C24×D5311yescharacteristic
760C2×C4C24×D5313yes—
761C2×C4C24×D5311yescharacteristic
762C22—26no—
763C22—21no—
764C22—23no—
765C22—26no—
766C22—22no—
767C22—86no—
768C22—10612no—
769C22—10612no—
770C22—10612no—
771C22—42424no—
772C22C22×#1171994516yes—
773C22C25×D5311yescharacteristic
774C4—21no—
775C4—23no—
776C4—22no—
777C4—26no—
778C4—22no—
779C4—26no—
780C4—1064no—
781C4—10612no—
782C4—1064no—
783C4C22×#1171994512yes—
784C4C22×#1171994516yes—
785C2—26no—
786C2—41no—
787C2—43no—
788C2—21212no—
789C2C23×#1171994511yescharacteristic
790C2#2028952612yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3428C2
hypercenter#3428D53
hypocenterC53#62858
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #20288826C2semidirect
2. #20288737C2semidirect
3. #20288715C2semidirect
4. #20288657C2semidirect
5. #20288637C2semidirect
6. #20288591C2semidirect
7. #20288541C2semidirect
8. #20288493C2semidirect
9. #20288450C2semidirect
10. #20288384C2semidirect
11. #20288131C2semidirect
12. #20288105C2semidirect
13. C2×#16811228C2semidirect
14. C4×#13133263C2semidirect
15. C53×#3428C2semidirect
17. #16811358C22semidirect
18. #16811349C22semidirect
19. #16811336C22semidirect
20. #16811332C22semidirect
21. #16811323C22semidirect
22. #16811322C22semidirect
23. #16811321C22semidirect
24. #16811317C22semidirect
25. #16811314C22semidirect
26. #16811297C22semidirect
27. #16811295C22semidirect
28. #16811294C22semidirect
29. #16811292C22semidirect
30. #16811284C22semidirect
31. #16811274C22semidirect
32. #16811269C22semidirect
33. #16811263C22semidirect
34. #16811261C22semidirect
35. D4×D212C22semidirect
36. D4×C22⋊D53C22semidirect
37. #16811251C22semidirect
38. #16811245C22semidirect
39. #16811244C22semidirect
40. #16811244C22semidirect
41. #16811235C22semidirect
42. #16811235C22semidirect
43. #16811228C22semidirect
44. #16811228C22semidirect
45. #16811228C22semidirect
46. #16811228C22semidirect
47. #16811228C22semidirect
48. #16811228C22semidirect
49. #16811228C22semidirect
50. #16811224C22semidirect
51. #16811220C22semidirect
52. #16811211C22semidirect
53. #16811206C22semidirect
54. #16811201C22semidirect
55. #16811192C22semidirect
56. #16811187C22semidirect
57. #16811180C22semidirect
58. #16811173C22semidirect
59. #16811173C22semidirect
60. #16811170C22semidirect
61. C2×#13133214C22semidirect
62. #16811160C22semidirect
63. #16811157C22semidirect
64. #16811151C22semidirect
65. #16811151C22semidirect
66. C2×#13133209C22semidirect
67. #16811134C22semidirect
68. #16811132C22semidirect
69. C2×#13133202C22semidirect
70. C2×#13133191C22semidirect
71. C2×#13133190C22semidirect
73. #16811105C22semidirect
74. #16811103C22semidirect
75. #16811097C22semidirect
76. #16811095C22semidirect
77. C4×#11719949C22semidirect
78. C4×#11719945C22semidirect
79. C2×C4×D212C22semidirect
80. C4×D4×D53C22semidirect
82. C53×#520C22semidirect
83. C53×#520C22semidirect
84. C53×#519C22semidirect
85. C53×#518C22semidirect
88. C4×#41×C53C22semidirect
89. C4×#41×C53C22semidirect
90. C2×#117×C53C22semidirect
91. C2×#117×C53C22semidirect
231. #41×C53#41semidirect
404. #3428D53semidirect
471. #520C2×D53semidirect
472. #520C2×D53semidirect
473. #519C2×D53semidirect
476. #518C2×D53semidirect
481. C4×#41C2×D53semidirect
482. C4×#41C2×D53semidirect
485. C2×#117C2×D53semidirect
486. C2×#117C2×D53semidirect
487. C53#62858semidirect
630. #41#11719945semidirect

Maximal subgroups

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

subgroupindex
#202888262
#202887372
#202887152
#202886572
#202886372
#202885912
#202885412
#202884932
#202884502
#202883842
#202881312
#202881052
C2×#168112282
C4×#131332632
C53×#34282
#6285853