Finite Group Databasebeta

← #8108043

Subgroups — #8108043

Order 512.

5014 conjugacy classes of subgroups.

The subgroup lattice has 1049 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53154C212yesmaximal, complemented
2#53129C214yesmaximal, complemented
3#53074C212yesmaximal, complemented
4#52979C214yesmaximal, complemented
5#45285C214yesmaximal, complemented
6#45187C214yesmaximal, complemented
7#45171C214yesmaximal, complemented
8#42983C212yesmaximal, complemented
9#42903C214yesmaximal, complemented
10#42897C214yesmaximal, complemented
11#42759C214yesmaximal, complemented
12#42673C212yesmaximal, complemented
13#42627C214yesmaximal, complemented
14#42563C214yesmaximal, complemented
15#36609C212yesmaximal, complemented
16#36151C212yesmaximal, complemented
17#36150C212yesmaximal, complemented
18#36121C212yesmaximal, complemented
19#35319C211yesmaximal, characteristic, complemented
20#35298C212yesmaximal, complemented
21#35288C212yesmaximal, complemented
22#35285C211yesmaximal, characteristic, complemented
23#34551C211yesmaximal, characteristic, complemented
24C2×#546C2214yes—
25C2×#541C2212yes—
26C2×#533C2211yescharacteristic
27C2×#533C2212yescomplemented
28C2×#532C2212yes—
29C22×#127C2211yescharacteristic
30#2868C2211yescharacteristic, complemented
31#2862C2212yescomplemented
32#2859C2211yescharacteristic, complemented
33#2858C2212yes—
34#2858C2212yes—
35#2858C2212yes—
36#2857C2212yes—
37#2857C2212yescomplemented
38#2856C2212yes—
39#2837C2218yescomplemented
40#2830C2214yescomplemented
41#2829C2218yescomplemented
42#2828C2218yescomplemented
43#2827C2218yescomplemented
44#2824C2218yescomplemented
45#2812C2214yes—
46#2803C2218yescomplemented
47#2797C2218yescomplemented
48#2782C2218yescomplemented
49#2781C2218yescomplemented
50#2779C2218yescomplemented
51#2753C2218yescomplemented
52#2750C2218yescomplemented
53#2743C2218yescomplemented
54#2736C2214yes—
55#2735C2214yes—
56#2735C2218yes—
57#2724C2214yescomplemented
58#2711C2218yescomplemented
59#2701C2218yescomplemented
60#2699C2214yescomplemented
61#2694C2218yescomplemented
62#2685C2218yes—
63#2685C2218yes—
64#2651C2218yescomplemented
65#2649C2218yescomplemented
66#2648C2218yescomplemented
67#2644C2214yescomplemented
68#2642C2212yescomplemented
69#2641C2212yes—
70#2641C2212yes—
71#2624C2214yescomplemented
72#2622C2218yes—
73#2621C2212yes—
74#2620C2214yescomplemented
75#2620C2214yescomplemented
76#2593C2214yescomplemented
77#2592C2214yescomplemented
78#2592C2214yescomplemented
79#2580C2214yescomplemented
80#2576C2218yescomplemented
81#2566C2214yescomplemented
82#2566C2214yescomplemented
83#2558C2218yescomplemented
84#2548C2214yes—
85#2548C2214yes—
86#2545C2214yescomplemented
87#2545C2214yescomplemented
88#2544C2214yes—
89#2540C2214yescomplemented
90#2536C2214yes—
91#2513C2214yescomplemented
92#2513C2214yescomplemented
93#2513C2214yescomplemented
94#2506C2214yescomplemented
95#2506C2214yescomplemented
96#2500C2214yescomplemented
97#2500C2214yescomplemented
98#2496C2214yes—
99#2496C2214yes—
100#2490C2218yescomplemented
101#2490C2214yescomplemented
102#2490C2214yescomplemented
103#2489C2214yes—
104#2489C2214yescomplemented
105#2483C2214yes—
106#2480C2218yes—
107#2480C2218yes—
108#2454C2214yescomplemented
109#2454C2214yescomplemented
110#2453C2214yescomplemented
111#2453C2214yescomplemented
112#2448C2214yescomplemented
113#2448C2214yescomplemented
114#2448C2214yescomplemented
115#2448C2214yescomplemented
116#2447C2214yescomplemented
117#2447C2214yescomplemented
118#2447C2214yescomplemented
119#2445C2214yes—
120#2445C2214yes—
121#2435C2214yes—
122#2435C2214yes—
123#2435C2214yes—
124#2432C2214yescomplemented
125#2432C2214yescomplemented
126#2431C2214yes—
127#2428C2214yes—
128#2428C2214yes—
129#2427C2214yescomplemented
130#2427C2214yescomplemented
131#2426C2214yescomplemented
132#2426C2214yescomplemented
133#2426C2214yescomplemented
134#2421C2214yes—
135#2421C2214yescomplemented
136#2420C2214yescomplemented
137#2415C2214yes—
138#2415C2214yes—
139#2414C2214yescomplemented
140#2408C2214yes—
141#2408C2214yes—
142#2407C2214yescomplemented
143#2402C2212yescomplemented
144#2402C2211yescharacteristic, complemented
145#2401C2212yes—
146#2401C2212yescomplemented
147#2401C2212yescomplemented
148#2398C2212yes—
149#2398C2211yescharacteristic, complemented
150#2396C2211yescharacteristic
151#2396C2212yescomplemented
152#2395C2212yes—
153#2395C2212yes—
154#2395C2212yescomplemented
155#2392C2212yes—
156#2392C2211yescharacteristic
157#2367C2214yescomplemented
158#2367C2214yescomplemented
159#2367C2214yescomplemented
160#2363C2214yescomplemented
161#2362C2214yes—
162#2362C2214yescomplemented
163#2357C2214yescomplemented
164#2351C2214yescomplemented
165#2341C2214yescomplemented
166D4×C22⋊C4C2214yes—
167D4×C22⋊C4C2214yes—
168#2327C2212yescomplemented
169#2326C2214yescomplemented
170#2326C2214yescomplemented
171#2324C2214yescomplemented
172#2319C2214yescomplemented
173#2309C2212yes—
174#2309C2212yes—
175C4×C4⋊Q8C2212yescomplemented
176C4×C4⋊Q8C2212yescomplemented
177C4×#127C2212yes—
178C42×Q8C2211yescharacteristic, complemented
179C42×D4C2212yes—
180C42×D4C2211yescharacteristic, complemented
181C4×#117C2211yescharacteristic
182C4×#117C2212yescomplemented
183C22×#41C2314yes—
184C23×D4C2312yes—
185C23×D4C2314yes—
186#546—416no—
187#541—48no—
188#533—44no—
189#533—48no—
190#532—48no—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×#127—44no—
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#127C2314yes—
199C2×#126C2318yes—
200C2×#125C2314yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2318yes—
204C2×#124C2314yes—
205C2×#124C2314yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×#124C2314yes—
210C2×#124C2314yes—
211C2×#123C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#120C2318yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2314yes—
246C2×#117C2312yes—
247C22×C22⋊C4C2318yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250#401C2312yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2311yescharacteristic
256#400C2312yes—
257#400C2312yes—
258#400C2312yes—
259#400C2312yes—
260#400C2312yes—
261#400C2312yes—
262#400C2312yes—
263#399C2318yes—
264#399C2318yes—
265#399C2318yes—
266#399C2311yescharacteristic
267#399C2312yes—
268#398C2312yes—
269#398C2318yes—
270#398C2314yes—
271#398C2312yes—
272#398C2314yes—
273#398C2311yescharacteristic
274#398C2312yes—
275#398C2312yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2311yescharacteristic
290#397C2312yes—
291#397C2312yes—
292#397C2312yes—
293#397C2312yes—
294#397C2312yes—
295#397C2312yes—
296#397C2312yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2312yes—
302#396C2318yes—
303#396C2318yes—
304#396C2312yes—
305#396C2312yes—
306#395C2311yescharacteristic
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2312yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2312yes—
324#394C2318yes—
325#394C2318yes—
326#394C2312yes—
327#394C2312yes—
328#394C2311yescharacteristic
329#393C2312yes—
330#393C2318yes—
331#393C2311yescharacteristic
332#392C2318yes—
333#392C2318yes—
334#392C2318yes—
335#392C2311yescharacteristic
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2318yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2318yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2318yes—
367#390C2314yes—
368#390C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#384C2312yes—
420#384C2314yes—
421#384C2314yes—
422#382C2314yes—
423#382C2314yes—
424#382C2318yes—
425#382C2312yes—
426#381C2318yes—
427#381C2318yes—
428#380C2318yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2318yes—
434#379C2314yes—
435#379C2318yes—
436#379C2314yes—
437#379C2318yes—
438#379C2318yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2312yes—
477#376C2312yes—
478#376C2312yes—
479#376C2311yescharacteristic
480#376C2311yescharacteristic
481C43C2312yes—
482C43C2311yescharacteristic
483C43C2311yescharacteristic
484C25C2414yes—
485C2×#41—48no—
486C2×#41—48no—
487C2×#41—48no—
488C22×Q8C2414yes—
489C22×Q8C2414yes—
490C22×Q8C2411yescharacteristic
491C22×D4—28no—
492C22×D4—44no—
493C22×D4—48no—
494C22×D4—44no—
495C22×D4—48no—
496C22×D4—48no—
497C22×D4C2414yes—
498C22×D4C2414yes—
499C22×D4C2414yes—
500C22×D4C2412yes—
501C22×D4C2414yes—
502C22×D4C2411yescharacteristic
503C22×D4C2418yes—
504C22×D4C2418yes—
505C22×D4C2418yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C23×C4C2418yes—
512C23×C4C2418yes—
513C4⋊Q8—28no—
514C4⋊Q8—28no—
515C4⋊Q8—44no—
516C4⋊Q8—44no—
517#127—28no—
518#127—48no—
519#127—44no—
520#126—416no—
521#125—48no—
522#125—44no—
523#125—44no—
524#125—416no—
525#124—48no—
526#124—48no—
527#124—48no—
528#124—48no—
529#124—48no—
530#124—48no—
531#124—48no—
532#123—416no—
533C22⋊Q8—216no—
534C22⋊Q8—48no—
535C22⋊Q8—48no—
536C22⋊Q8—48no—
537C22⋊Q8—48no—
538#121—416no—
539#121—48no—
540#121—48no—
541#121—48no—
542#121—48no—
543#121—48no—
544#120—416no—
545C4×Q8—44no—
546C4×Q8—42no—
547C4×Q8—48no—
548C4×Q8—48no—
549C4×Q8—48no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×D4—28no—
553C4×D4—48no—
554C4×D4—48no—
555C4×D4—48no—
556C4×D4—48no—
557C4×D4—48no—
558C4×D4—44no—
559C4×D4—42no—
560C4×D4—44no—
561C4×D4—44no—
562#117—24no—
563#117—44no—
564#117—44no—
565#117—42no—
566#117—48no—
567#117—44no—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C22⋊C4—416no—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2411yescharacteristic
613C2×C22⋊C4C2411yescharacteristic
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C42—24no—
645C2×C42—28no—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2411yescharacteristic
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2411yescharacteristic
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2412yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2411yescharacteristic
692#95C2411yescharacteristic
693#95C2418yes—
694#95C2418yes—
695#95C2411yescharacteristic
696#95C2412yes—
697#95C2411yescharacteristic
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710C24—28no—
711C24—44no—
712C24—48no—
713C24—48no—
714C24—44no—
715C24C2518yes—
716C24C2512yes—
717C24C2511yescharacteristic
718#41—832no—
719C2×Q8—28no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—28no—
724C2×Q8—28no—
725C2×Q8—41no—
726C2×Q8—42no—
727C2×D4—24no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—41no—
741C2×D4—42no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—816no—
754C2×D4—832no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4H(5,𝔽2)14yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2518yes—
786C22×C4C2512yes—
787C22×C4C2518yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2518yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2512yes—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—216no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—41no—
807C4⋊C4—41no—
808C4⋊C4—42no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—41no—
815C4⋊C4—42no—
816C4⋊C4—41no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C22⋊C4—24no—
832C22⋊C4—216no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—42no—
838C22⋊C4—42no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—41no—
842C22⋊C4—41no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—42no—
852C22⋊C4—42no—
853C22⋊C4—42no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—24no—
875C42—22no—
876C42—22no—
877C42—22no—
878C42—24no—
879C42—24no—
880C42—22no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—22no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—44no—
891C42—48no—
892C42—48no—
893C42—48no—
894C42H(5,𝔽2)14yes—
895C23—21no—
896C23—21no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—28no—
906C23—28no—
907C23—28no—
908C23—28no—
909C23—22no—
910C23—28no—
911C23—22no—
912C23—22no—
913C23—88no—
914C23—816no—
915C23—816no—
916C23—164no—
917C23—164no—
918C23C2×H(5,𝔽2)12yes—
919C23C2611yescharacteristic
920Q8—44no—
921Q8—416no—
922Q8—416no—
923D4—48no—
924D4—44no—
925D4—416no—
926D4—416no—
927D4—416no—
928D4—88no—
929D4—816no—
930D4—816no—
931D4—168no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—22no—
975C2×C4—28no—
976C2×C4—22no—
977C2×C4—28no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—48no—
986C2×C4—816no—
987C2×C4—168no—
988C2×C4C2×H(5,𝔽2)12yes—
989C2×C4C2×H(5,𝔽2)12yes—
990C2×C4C2×H(5,𝔽2)12yes—
991C2×C4C2×H(5,𝔽2)14yes—
992C2×C4#58512yes—
993C2×C4#58514yes—
994C2×C4#58514yes—
995C22—22no—
996C22—24no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—42no—
1001C22—48no—
1002C22—42no—
1003C22—42no—
1004C22—48no—
1005C22—48no—
1006C22—48no—
1007C22—42no—
1008C22—42no—
1009C22—48no—
1010C22—42no—
1011C22—42no—
1012C22—48no—
1013C22—48no—
1014C22—1616no—
1015C22C22×H(5,𝔽2)11yescharacteristic
1016C22C22×H(5,𝔽2)11yescharacteristic
1017C22C2×#58511yescharacteristic
1018C22C2×#58512yes—
1019C22C2×#58512yes—
1020C4—22no—
1021C4—42no—
1022C4—48no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—48no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—48no—
1031C4—42no—
1032C4—42no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—42no—
1037C4—41no—
1038C4#355814yes—
1039C4#356218yes—
1040C2—42no—
1041C2—82no—
1042C2—88no—
1043C2C2×#355811yescharacteristic
1044C2C2×#356212yes—
1045C2#6283612yes—
1046C2#6283911yescharacteristic
1047C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53154C2semidirect
2. #53129C2semidirect
3. #53074C2semidirect
4. #52979C2semidirect
5. #45285C2semidirect
6. #45187C2semidirect
7. #45171C2semidirect
8. #42983C2semidirect
9. #42903C2semidirect
10. #42897C2semidirect
11. #42759C2semidirect
12. #42673C2semidirect
13. #42627C2semidirect
14. #42563C2semidirect
15. #36609C2semidirect
16. #36151C2semidirect
17. #36150C2semidirect
18. #36121C2semidirect
19. #35319C2semidirect
20. #35298C2semidirect
21. #35288C2semidirect
22. #35285C2semidirect
23. #34551C2semidirect
27. C2×#533C22semidirect
30. #2868C22semidirect
31. #2862C22semidirect
32. #2859C22semidirect
37. #2857C22semidirect
39. #2837C22semidirect
40. #2830C22semidirect
41. #2829C22semidirect
42. #2828C22semidirect
43. #2827C22semidirect
44. #2824C22semidirect
46. #2803C22semidirect
47. #2797C22semidirect
48. #2782C22semidirect
49. #2781C22semidirect
50. #2779C22semidirect
51. #2753C22semidirect
52. #2750C22semidirect
53. #2743C22semidirect
57. #2724C22semidirect
58. #2711C22semidirect
59. #2701C22semidirect
60. #2699C22semidirect
61. #2694C22semidirect
64. #2651C22semidirect
65. #2649C22semidirect
66. #2648C22semidirect
67. #2644C22semidirect
68. #2642C22semidirect
71. #2624C22semidirect
74. #2620C22semidirect
75. #2620C22semidirect
76. #2593C22semidirect
77. #2592C22semidirect
78. #2592C22semidirect
79. #2580C22semidirect
80. #2576C22semidirect
81. #2566C22semidirect
82. #2566C22semidirect
83. #2558C22semidirect
86. #2545C22semidirect
87. #2545C22semidirect
89. #2540C22semidirect
91. #2513C22semidirect
92. #2513C22semidirect
93. #2513C22semidirect
94. #2506C22semidirect
95. #2506C22semidirect
96. #2500C22semidirect
97. #2500C22semidirect
100. #2490C22semidirect
101. #2490C22semidirect
102. #2490C22semidirect
104. #2489C22semidirect
108. #2454C22semidirect
109. #2454C22semidirect
110. #2453C22semidirect
111. #2453C22semidirect
112. #2448C22semidirect
113. #2448C22semidirect
114. #2448C22semidirect
115. #2448C22semidirect
116. #2447C22semidirect
117. #2447C22semidirect
118. #2447C22semidirect
124. #2432C22semidirect
125. #2432C22semidirect
129. #2427C22semidirect
130. #2427C22semidirect
131. #2426C22semidirect
132. #2426C22semidirect
133. #2426C22semidirect
135. #2421C22semidirect
136. #2420C22semidirect
139. #2414C22semidirect
142. #2407C22semidirect
143. #2402C22semidirect
144. #2402C22semidirect
146. #2401C22semidirect
147. #2401C22semidirect
149. #2398C22semidirect
151. #2396C22semidirect
154. #2395C22semidirect
157. #2367C22semidirect
158. #2367C22semidirect
159. #2367C22semidirect
160. #2363C22semidirect
162. #2362C22semidirect
163. #2357C22semidirect
164. #2351C22semidirect
165. #2341C22semidirect
168. #2327C22semidirect
169. #2326C22semidirect
170. #2326C22semidirect
171. #2324C22semidirect
172. #2319C22semidirect
175. C4×C4⋊Q8C22semidirect
176. C4×C4⋊Q8C22semidirect
178. C42×Q8C22semidirect
180. C42×D4C22semidirect
182. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531542
#531292
#530742
#529792
#452852
#451872
#451712
#429832
#429032
#428972
#427592
#426732
#426272
#425632
#366092
#361512
#361502
#361212
#353192
#352982
#352882
#352852
#345512