Finite Group Databasebeta

← #8094891

Subgroups — #8094891

Order 512.

4616 conjugacy classes of subgroups.

The subgroup lattice has 1065 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53119C214yesmaximal, complemented
2#53114C214yesmaximal, complemented
3#53100C212yesmaximal, complemented
4#53081C212yesmaximal, complemented
5#52989C212yesmaximal, complemented
6#52987C212yesmaximal, complemented
7#52453C214yesmaximal, complemented
8#52431C214yesmaximal, complemented
9#46349C214yesmaximal, complemented
10#46346C212yesmaximal, complemented
11#46341C214yesmaximal, complemented
12#46329C212yesmaximal, complemented
13#46325C214yesmaximal, complemented
14#46196C212yesmaximal, complemented
15#46180C214yesmaximal, complemented
16#46147C212yesmaximal, complemented
17#35574C212yesmaximal, complemented
18#35519C212yesmaximal, complemented
19#35517C212yesmaximal
20#35267C212yesmaximal, complemented
21#35265C212yesmaximal, complemented
22#35160C212yesmaximal, complemented
23#34955C211yesmaximal, characteristic
24#34953C211yesmaximal, characteristic, complemented
25C2×#2546C211yesmaximal, characteristic, complemented
26C2×#563C2214yes—
27C2×#533C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C22×C4⋊Q8C2212yes—
30C22×C4⋊Q8C2211yescharacteristic
31C2×#520C2212yes—
32C22×C4×Q8C2211yescharacteristic
33#2864C2214yes—
34#2863C2214yes—
35#2860C2214yes—
36#2859C2214yes—
37#2852C2218yes—
38#2839C2218yes—
39#2836C2218yes—
40#2836C2218yes—
41#2834C2218yes—
42#2833C2214yes—
43#2833C2214yes—
44#2832C2214yes—
45#2831C2218yes—
46#2830C2214yes—
47#2827C2218yes—
48#2823C2214yes—
49#2822C2214yes—
50#2821C2218yes—
51#2799C2214yes—
52#2794C2214yes—
53#2793C2218yes—
54#2789C2214yes—
55#2775C2218yes—
56#2770C2218yes—
57#2766C2218yes—
58#2765C2218yes—
59#2759C2218yes—
60#2758C2218yes—
61#2734C2214yes—
62#2731C2214yes—
63#2729C2218yes—
64#2728C2214yes—
65#2728C2214yes—
66#2724C2214yes—
67#2716C2218yes—
68#2713C2218yes—
69#2707C2218yes—
70#2702C2218yes—
71#2698C2218yes—
72#2698C2218yes—
73#2677C2218yes—
74#2674C2218yes—
75#2647C2214yes—
76#2647C2214yes—
77#2645C2214yes—
78#2644C2214yes—
79#2643C2218yes—
80#2592C2212yes—
81#2592C2212yes—
82#2591C2212yes—
83#2591C2212yes—
84#2584C2212yes—
85#2584C2212yes—
86#2583C2212yes—
87#2583C2212yes—
88#2582C2214yes—
89#2581C2214yes—
90#2580C2214yes—
91#2579C2218yes—
92#2568C2211yescharacteristic
93#2568C2211yescharacteristic
94#2567C2211yescharacteristic
95#2567C2211yescharacteristic
96#2548C2211yescharacteristic
97#2548C2211yescharacteristic
98#2546C2212yes—
99#2546C2212yes—
100#2546C2211yescharacteristic
101#2546C2212yes—
102#2546C2212yes—
103#2546C2212yes—
104#2546C2212yes—
105#2546C2212yes—
106#2546C2212yes—
107#2546C2211yescharacteristic
108#2538C2214yes—
109#2514C2214yes—
110#2513C2214yes—
111#2512C2214yes—
112#2511C2214yes—
113#2510C2218yes—
114#2509C2214yes—
115#2508C2214yes—
116#2507C2214yes—
117#2506C2214yes—
118#2505C2218yes—
119#2504C2212yes—
120#2502C2212yes—
121#2497C2214yes—
122#2497C2214yes—
123#2496C2214yes—
124#2496C2214yes—
125#2495C2214yes—
126#2495C2214yes—
127#2494C2214yes—
128#2494C2214yes—
129#2487C2214yes—
130#2486C2214yes—
131#2485C2214yes—
132#2485C2214yes—
133#2481C2218yes—
134#2473C2218yes—
135#2452C2214yes—
136#2452C2214yes—
137#2451C2214yes—
138#2451C2214yes—
139#2450C2218yes—
140#2449C2218yes—
141#2448C2214yes—
142#2447C2214yes—
143#2446C2214yes—
144#2445C2214yes—
145#2444C2218yes—
146#2443C2218yes—
147#2442C2214yes—
148#2441C2214yes—
149#2440C2214yes—
150#2440C2214yes—
151#2440C2214yes—
152#2439C2214yes—
153#2439C2214yes—
154#2439C2214yes—
155#2436C2212yes—
156#2434C2212yes—
157#2409C2218yes—
158#2399C2212yes—
159#2399C2212yes—
160#2398C2212yes—
161#2398C2212yes—
162C2×#398C2212yes—
163C2×#398C2212yes—
164#2381C2214yes—
165#2378C2218yes—
166#2317C2212yes—
167#2317C2212yes—
168#2317C2212yes—
169#2316C2212yes—
170#2311C2212yes—
171#2311C2212yes—
172#2311C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×#124C2212yes—
176C4×#124C2212yes—
177#2297C2212yes—
178#2297C2212yes—
179#2296C2212yes—
180#2296C2212yes—
181C2×#391C2212yes—
182C2×#389C2212yes—
183C2×#389C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2312yes—
188C23×Q8C2311yescharacteristic
189C23×Q8C2312yes—
190#563—416no—
191#533—44no—
192#532—44no—
193C2×C4⋊Q8—44no—
194C2×C4⋊Q8—48no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#126C2318yes—
210C2×#126C2318yes—
211C2×#125C2318yes—
212C2×#125C2312yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#123C2318yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2318yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224#520—48no—
225C2×C4×Q8—44no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#401C2318yes—
259#401C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2312yes—
265#400C2312yes—
266#400C2312yes—
267#400C2312yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#399C2318yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2312yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#398C2312yes—
292#398C2318yes—
293#398C2312yes—
294#398C2318yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2312yes—
299#398C2314yes—
300#398C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#395C2314yes—
319#395C2318yes—
320#395C2312yes—
321#395C2312yes—
322#395C2312yes—
323#395C2312yes—
324#395C2318yes—
325#395C2318yes—
326#395C2314yes—
327#394C2312yes—
328#394C2318yes—
329#394C2312yes—
330#394C2318yes—
331#394C2312yes—
332#394C2312yes—
333#393C2314yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2318yes—
352#391C2314yes—
353#391C2314yes—
354#391C2318yes—
355#391C2318yes—
356#391C2314yes—
357#391C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2318yes—
387#389C2314yes—
388#389C2318yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2314yes—
394#389C2318yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2314yes—
446#385C2314yes—
447#385C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2314yes—
451#384C2314yes—
452#384C2314yes—
453#383C2318yes—
454#383C2318yes—
455#382C2312yes—
456#382C2312yes—
457#382C2314yes—
458#382C2314yes—
459#382C2314yes—
460#382C2318yes—
461#381C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#380C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492#376C2312yes—
493#376C2312yes—
494C2×#95C2312yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C43C2312yes—
498C43C2312yes—
499C2×#41—28no—
500C2×#41—28no—
501C2×#41—28no—
502C22×Q8—24no—
503C22×Q8—42no—
504C22×Q8—44no—
505C22×Q8—42no—
506C22×Q8—44no—
507C22×Q8—44no—
508C22×Q8C2412yes—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2412yes—
513C22×Q8C2414yes—
514C22×Q8C2414yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×D4C2414yes—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C23×C4C2414yes—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2414yes—
526C23×C4C2411yescharacteristic
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2418yes—
531C23×C4C2411yescharacteristic
532C4⋊Q8—216no—
533C4⋊Q8—28no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—42no—
539C4⋊Q8—42no—
540C4⋊Q8—48no—
541C4⋊Q8—42no—
542C4⋊Q8—48no—
543C4⋊Q8—48no—
544C4⋊Q8—44no—
545#127—42no—
546#126—416no—
547#126—416no—
548#125—44no—
549#125—416no—
550#124—28no—
551#124—44no—
552#124—44no—
553#123—416no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—416no—
557C22⋊Q8—416no—
558C22⋊Q8—416no—
559#121—44no—
560#121—44no—
561C4×Q8—42no—
562C4×Q8—42no—
563C4×Q8—42no—
564C4×Q8—42no—
565C4×Q8—42no—
566C4×Q8—42no—
567C4×Q8—42no—
568C4×Q8—42no—
569C4×Q8—44no—
570C4×Q8—44no—
571C4×Q8—48no—
572C4×D4—48no—
573C4×D4—44no—
574C4×D4—44no—
575C4×D4—416no—
576#117—28no—
577#117—28no—
578#117—28no—
579#117—48no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—48no—
583C2×C4⋊C4—48no—
584C2×C4⋊C4—48no—
585C2×C4⋊C4—42no—
586C2×C4⋊C4—42no—
587C2×C4⋊C4—42no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C42—24no—
661C2×C42—24no—
662C2×C42—24no—
663C2×C42—44no—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2414yes—
695#95C2412yes—
696#95C2412yes—
697#95C2414yes—
698#95C2412yes—
699#95C2412yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730C24C2514yes—
731C24C2511yescharacteristic
732#41—432no—
733C2×Q8—24no—
734C2×Q8—22no—
735C2×Q8—22no—
736C2×Q8—22no—
737C2×Q8—24no—
738C2×Q8—28no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—22no—
742C2×Q8—22no—
743C2×Q8—28no—
744C2×Q8—41no—
745C2×Q8—41no—
746C2×Q8—41no—
747C2×Q8—41no—
748C2×Q8—41no—
749C2×Q8—41no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—42no—
756C2×Q8—44no—
757C2×Q8—44no—
758C2×Q8—416no—
759C2×Q8—816no—
760C2×Q8H(5,𝔽2)14yes—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—44no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—28no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—44no—
788C22×C4—42no—
789C22×C4—44no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—44no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—44no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4H(5,𝔽2)14yes—
800C22×C42−1+418yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2518yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2518yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—28no—
839C4⋊C4—48no—
840C4⋊C4—41no—
841C4⋊C4—41no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—41no—
846C4⋊C4—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—22no—
905C42—22no—
906C42—22no—
907C42—28no—
908C42—28no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—28no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—48no—
917C42—42no—
918C42—42no—
919C23—21no—
920C23—21no—
921C23—22no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23C2×H(5,𝔽2)12yes—
930C23C2×2−1+414yes—
931C23C2611yescharacteristic
932Q8—44no—
933Q8—44no—
934Q8—44no—
935Q8—44no—
936Q8—48no—
937Q8—84no—
938Q8—88no—
939Q8—88no—
940Q8—84no—
941D4—416no—
942D4—48no—
943D4—84no—
944D4—84no—
945C2×C4—28no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—21no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—416no—
1003C2×C4—416no—
1004C2×C4—82no—
1005C2×C4—82no—
1006C2×C4—88no—
1007C2×C4—168no—
1008C2×C4#563116yescomplemented
1009C2×C4C2×H(5,𝔽2)12yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4C2×H(5,𝔽2)12yes—
1012C2×C4C2×H(5,𝔽2)12yes—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×2−1+414yes—
1015C2×C4C2×2−1+414yes—
1016C2×C4#58512yes—
1017C22—22no—
1018C22—22no—
1019C22—24no—
1020C22—24no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22C2×#56314yes—
1029C22C22×H(5,𝔽2)11yescharacteristic
1030C22C22×H(5,𝔽2)11yescharacteristic
1031C22C22×2−1+412yes—
1032C22C2×#58511yescharacteristic
1033C222−1+612yes—
1034C4—22no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—41no—
1039C4—41no—
1040C4—48no—
1041C4—44no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—41no—
1048C4—44no—
1049C4—44no—
1050C4—44no—
1051C4—48no—
1052C4—44no—
1053C4—44no—
1054C4—44no—
1055C4C2×#56314yes—
1056C4C2×#56314yes—
1057C2—24no—
1058C2—84no—
1059C2C22×#56311yescharacteristic
1060C2#6281811yescharacteristic
1061C2#6288611yescharacteristic
1062C2#6291312yes—
1063C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53119C2semidirect
2. #53114C2semidirect
3. #53100C2semidirect
4. #53081C2semidirect
5. #52989C2semidirect
6. #52987C2semidirect
7. #52453C2semidirect
8. #52431C2semidirect
9. #46349C2semidirect
10. #46346C2semidirect
11. #46341C2semidirect
12. #46329C2semidirect
13. #46325C2semidirect
14. #46196C2semidirect
15. #46180C2semidirect
16. #46147C2semidirect
17. #35574C2semidirect
18. #35519C2semidirect
20. #35267C2semidirect
21. #35265C2semidirect
22. #35160C2semidirect
24. #34953C2semidirect
25. C2×#2546C2semidirect
1008. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#531192
#531142
#531002
#530812
#529892
#529872
#524532
#524312
#463492
#463462
#463412
#463292
#463252
#461962
#461802
#461472
#355742
#355192
#355172
#352672
#352652
#351602
#349552
#349532
C2×#25462