Finite Group Databasebeta

← #8094497

Subgroups — #8094497

Order 512.

4669 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53133C214yesmaximal, complemented
2#53031C212yesmaximal, complemented
3#53023C214yesmaximal, complemented
4#53017C212yesmaximal, complemented
5#52991C212yesmaximal, complemented
6#52968C212yesmaximal, complemented
7#52603C214yesmaximal, complemented
8#52568C214yesmaximal, complemented
9#46190C212yesmaximal, complemented
10#46180C214yesmaximal, complemented
11#46147C212yesmaximal, complemented
12#45696C212yesmaximal, complemented
13#45648C214yesmaximal, complemented
14#45488C212yesmaximal, complemented
15#45474C214yesmaximal, complemented
16#45456C214yesmaximal
17#35566C212yesmaximal, complemented
18#35544C212yesmaximal, complemented
19#35544C212yesmaximal, complemented
20#35265C212yesmaximal, complemented
21#35253C212yesmaximal, complemented
22#35224C212yesmaximal, complemented
23#34946C211yesmaximal, characteristic
24#34809C211yesmaximal, characteristic
25C2×#2486C211yesmaximal, characteristic
26C2×#563C2214yes—
27C2×#544C2212yes—
28C2×#533C2211yescharacteristic
29C22×#123C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2864C2214yescomplemented
34#2859C2214yescomplemented
35#2857C2214yescomplemented
36#2851C2214yescomplemented
37#2848C2218yes—
38#2843C2218yescomplemented
39#2841C2214yescomplemented
40#2839C2218yescomplemented
41#2838C2218yescomplemented
42#2836C2218yescomplemented
43#2835C2214yescomplemented
44#2833C2218yescomplemented
45#2833C2214yescomplemented
46#2831C2218yescomplemented
47#2822C2214yescomplemented
48#2817C2214yescomplemented
49#2817C2214yescomplemented
50#2814C2218yes—
51#2791C2218yescomplemented
52#2787C2218yescomplemented
53#2775C2218yescomplemented
54#2771C2214yescomplemented
55#2769C2214yescomplemented
56#2766C2218yescomplemented
57#2765C2218yescomplemented
58#2764C2214yescomplemented
59#2764C2214yescomplemented
60#2745C2218yescomplemented
61#2738C2218yescomplemented
62#2734C2214yescomplemented
63#2724C2214yes—
64#2722C2214yescomplemented
65#2718C2218yes—
66#2717C2214yes—
67#2713C2218yescomplemented
68#2707C2218yes—
69#2698C2218yescomplemented
70#2698C2218yescomplemented
71#2695C2218yes—
72#2689C2218yescomplemented
73#2680C2218yes—
74#2674C2218yes—
75#2647C2214yescomplemented
76#2647C2214yescomplemented
77#2629C2214yescomplemented
78#2628C2214yescomplemented
79#2627C2218yes—
80#2584C2214yescomplemented
81#2584C2214yescomplemented
82#2567C2214yescomplemented
83#2563C2211yescharacteristic
84#2563C2211yescharacteristic
85#2562C2212yes—
86#2562C2212yes—
87#2561C2212yes—
88#2561C2212yes—
89#2552C2214yescomplemented
90#2551C2214yescomplemented
91#2550C2214yescomplemented
92#2550C2214yescomplemented
93#2549C2218yes—
94#2547C2211yescharacteristic
95#2547C2211yescharacteristic
96#2546C2214yescomplemented
97#2509C2214yescomplemented
98#2508C2214yescomplemented
99#2507C2214yescomplemented
100#2506C2214yescomplemented
101#2505C2218yes—
102#2503C2212yes—
103#2497C2214yescomplemented
104#2497C2214yescomplemented
105#2497C2214yescomplemented
106#2497C2214yescomplemented
107#2496C2214yescomplemented
108#2496C2214yescomplemented
109#2496C2214yescomplemented
110#2496C2214yescomplemented
111#2495C2214yescomplemented
112#2495C2214yescomplemented
113#2495C2214yescomplemented
114#2495C2214yescomplemented
115#2494C2214yescomplemented
116#2494C2214yescomplemented
117#2494C2214yescomplemented
118#2494C2214yescomplemented
119#2493C2218yes—
120#2493C2218yes—
121#2487C2211yescharacteristic
122#2487C2211yescharacteristic
123#2486C2212yes—
124#2486C2212yes—
125#2486C2211yescharacteristic
126#2486C2212yes—
127#2486C2211yescharacteristic
128#2486C2212yes—
129#2486C2212yes—
130#2486C2212yes—
131#2486C2212yes—
132#2486C2212yes—
133#2485C2212yes—
134#2485C2212yes—
135#2484C2212yes—
136#2483C2212yes—
137#2482C2212yes—
138#2480C2218yes—
139#2480C2218yes—
140#2473C2218yes—
141#2442C2214yescomplemented
142#2442C2214yescomplemented
143#2442C2214yescomplemented
144#2442C2214yescomplemented
145#2442C2214yescomplemented
146#2441C2214yescomplemented
147#2440C2218yes—
148#2440C2214yescomplemented
149#2440C2214yescomplemented
150#2440C2214yescomplemented
151#2440C2214yescomplemented
152#2440C2214yescomplemented
153#2439C2214yescomplemented
154#2438C2218yes—
155#2437C2218yes—
156#2435C2212yes—
157#2405C2212yes—
158#2398C2212yes—
159#2398C2212yes—
160#2395C2212yes—
161#2395C2212yes—
162C2×#398C2212yes—
163C2×#397C2212yes—
164#2378C2218yescomplemented
165#2376C2214yes—
166#2317C2212yes—
167#2317C2212yes—
168#2317C2212yes—
169#2317C2212yes—
170#2316C2212yes—
171#2316C2212yes—
172C4×#124C2212yes—
173C4×#124C2212yes—
174C4×#123C2212yes—
175C4×#123C2212yes—
176#2296C2212yes—
177C2×#389C2212yes—
178#2280C2212yes—
179#2280C2212yes—
180#2280C2212yes—
181#2280C2211yescharacteristic
182C2×#381C2212yes—
183C2×#380C2212yes—
184C2×#380C2211yescharacteristic
185#2274C2212yes—
186C4×#117C2211yescharacteristic
187C23×D4C2311yescharacteristic
188C24×C4C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2312yes—
191#563—416no—
192#544—48no—
193#533—44no—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2318yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×#126C2318yes—
200C2×#126C2318yes—
201C2×#125C2312yes—
202C2×#125C2318yes—
203C2×#125C2314yes—
204C2×#125C2314yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#123—48no—
208C2×#123C2314yes—
209C2×#123C2312yes—
210C2×#123C2312yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×D4—44no—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—44no—
232C2×#117C2312yes—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2312yes—
239C22×C4⋊C4—44no—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2311yescharacteristic
253C22×C22⋊C4C2314yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#401C2318yes—
259#401C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2314yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2312yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2312yes—
277#399C2318yes—
278#399C2312yes—
279#399C2312yes—
280#398C2312yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2312yes—
298#398C2318yes—
299#398C2314yes—
300#397C2312yes—
301#397C2312yes—
302#397C2312yes—
303#397C2312yes—
304#397C2312yes—
305#397C2314yes—
306#397C2318yes—
307#397C2318yes—
308#397C2314yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2312yes—
316#397C2318yes—
317#397C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#395C2318yes—
323#395C2318yes—
324#395C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#394C2314yes—
330#394C2314yes—
331#394C2314yes—
332#394C2314yes—
333#393C2312yes—
334#393C2312yes—
335#393C2312yes—
336#393C2312yes—
337#393C2318yes—
338#391C2318yes—
339#391C2312yes—
340#391C2318yes—
341#391C2318yes—
342#391C2312yes—
343#390C2312yes—
344#390C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2312yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#386C2312yes—
403#386C2312yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2312yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2312yes—
418#384C2318yes—
419#384C2314yes—
420#384C2314yes—
421#384C2314yes—
422#384C2314yes—
423#383C2318yes—
424#383C2318yes—
425#382C2312yes—
426#382C2312yes—
427#382C2314yes—
428#382C2314yes—
429#382C2314yes—
430#382C2314yes—
431#382C2318yes—
432#381C2314yes—
433#381C2314yes—
434#381C2312yes—
435#381C2314yes—
436#381C2314yes—
437#381C2314yes—
438#381C2314yes—
439#381C2312yes—
440#381C2314yes—
441#381C2312yes—
442#380C2312yes—
443#380C2312yes—
444#380C2312yes—
445#380C2312yes—
446#380C2312yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2314yes—
455#380C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2312yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#379C2314yes—
471#379C2314yes—
472#379C2314yes—
473#379C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2312yes—
494#376C2312yes—
495C2×#95C2312yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C43C2312yes—
499C25C2411yescharacteristic
500C25C2411yescharacteristic
501C22×Q8C2412yes—
502C22×Q8C2412yes—
503C22×Q8C2418yes—
504C22×D4—24no—
505C22×D4—42no—
506C22×D4—42no—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—28no—
514C23×C4—28no—
515C23×C4—44no—
516C23×C4—44no—
517C23×C4—44no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2414yes—
530C23×C4C2411yescharacteristic
531C23×C4C2414yes—
532C23×C4C2412yes—
533C23×C4C2414yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2411yescharacteristic
537C4⋊Q8—42no—
538C4⋊Q8—42no—
539C4⋊Q8—48no—
540C4⋊Q8—48no—
541C4⋊Q8—416no—
542#126—416no—
543#126—416no—
544#125—44no—
545#125—48no—
546#125—48no—
547#125—416no—
548#124—28no—
549#124—44no—
550#123—216no—
551#123—28no—
552#123—48no—
553#123—44no—
554#123—48no—
555#123—48no—
556C22⋊Q8—416no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559C22⋊Q8—416no—
560C22⋊Q8—416no—
561C22⋊Q8—416no—
562C4×Q8—44no—
563C4×Q8—44no—
564C4×D4—42no—
565C4×D4—42no—
566C4×D4—42no—
567C4×D4—42no—
568C4×D4—42no—
569C4×D4—42no—
570C4×D4—42no—
571C4×D4—42no—
572#117—28no—
573#117—28no—
574#117—28no—
575#117—28no—
576#117—44no—
577#117—44no—
578#117—44no—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—44no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—42no—
586C2×C4⋊C4—42no—
587C2×C4⋊C4—48no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4—42no—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C22⋊C4—44no—
636C2×C22⋊C4—48no—
637C2×C22⋊C4—44no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2411yescharacteristic
654C2×C22⋊C4C2411yescharacteristic
655C2×C22⋊C4C2411yescharacteristic
656C2×C22⋊C4C2411yescharacteristic
657C2×C22⋊C4C2411yescharacteristic
658C2×C22⋊C4C2411yescharacteristic
659C2×C22⋊C4C2411yescharacteristic
660C2×C22⋊C4C2411yescharacteristic
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C42—24no—
673C2×C42—44no—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2414yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2418yes—
686C2×C42C2414yes—
687C2×C42C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2418yes—
694#95C2412yes—
695#95C2412yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2412yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730C24—22no—
731C24—22no—
732C24—22no—
733C24—22no—
734C24—24no—
735C24—22no—
736C24—24no—
737C24—42no—
738C24—41no—
739C24—42no—
740C24C2511yescharacteristic
741C24C2511yescharacteristic
742C24C2511yescharacteristic
743C24C2511yescharacteristic
744C24C2511yescharacteristic
745C2×Q8—24no—
746C2×Q8—42no—
747C2×Q8—42no—
748C2×Q8—42no—
749C2×Q8—44no—
750C2×Q8—48no—
751C2×Q8—48no—
752C2×Q8—48no—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—416no—
765C2×D4H(5,𝔽2)14yes—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—22no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—41no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—42no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—42no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—416no—
809C22×C4—416no—
810C22×C4—816no—
811C22×C4H(5,𝔽2)14yes—
812C22×C42−1+418yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2511yescharacteristic
820C22×C4C2518yes—
821C22×C4C2511yescharacteristic
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—216no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—41no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—24no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—41no—
892C22⋊C4—41no—
893C22⋊C4—41no—
894C22⋊C4—41no—
895C22⋊C4—41no—
896C22⋊C4—41no—
897C22⋊C4—41no—
898C22⋊C4—41no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—42no—
909C22⋊C4—44no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—22no—
914C42—28no—
915C42—28no—
916C42—24no—
917C42—28no—
918C42—28no—
919C42—44no—
920C42—48no—
921C42—44no—
922C42—42no—
923C42—48no—
924C23—21no—
925C23—21no—
926C23—22no—
927C23—28no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—21no—
936C23—21no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—21no—
941C23—21no—
942C23—22no—
943C23—21no—
944C23—22no—
945C23—48no—
946C23—48no—
947C23—44no—
948C23—48no—
949C23—44no—
950C23—44no—
951C23—44no—
952C23—82no—
953C23—84no—
954C23C2×H(5,𝔽2)12yes—
955C23C2×H(5,𝔽2)12yes—
956C23C2×H(5,𝔽2)12yes—
957C23C2×2−1+414yes—
958C23#58512yes—
959C23C2611yescharacteristic
960Q8—84no—
961Q8—84no—
962Q8—168no—
963D4—44no—
964D4—44no—
965D4—44no—
966D4—44no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—28no—
987C2×C4—21no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—21no—
1002C2×C4—28no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—44no—
1020C2×C4—44no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—84no—
1026C2×C4—82no—
1027C2×C4—88no—
1028C2×C4—88no—
1029C2×C4—88no—
1030C2×C4—88no—
1031C2×C4—84no—
1032C2×C4#563116yescomplemented
1033C2×C4C2×H(5,𝔽2)12yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C2×C4C2×H(5,𝔽2)12yes—
1036C2×C4C2×2−1+414yes—
1037C2×C4C2×2−1+414yes—
1038C22—22no—
1039C22—22no—
1040C22—24no—
1041C22—24no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—416no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—41no—
1060C22—42no—
1061C22—42no—
1062C22—41no—
1063C22—88no—
1064C22C2×#56314yes—
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C22×H(5,𝔽2)11yescharacteristic
1067C22C22×2−1+412yes—
1068C22C2×#58511yescharacteristic
1069C222−1+612yes—
1070C4—22no—
1071C4—41no—
1072C4—48no—
1073C4—44no—
1074C4—44no—
1075C4—41no—
1076C4—44no—
1077C4—41no—
1078C4—44no—
1079C4—44no—
1080C4—44no—
1081C4—48no—
1082C4—44no—
1083C4—44no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4C2×#56314yes—
1089C4C2×#56314yes—
1090C2—24no—
1091C2—42no—
1092C2—42no—
1093C2—42no—
1094C2—81no—
1095C2C22×#56311yescharacteristic
1096C2#6281811yescharacteristic
1097C2#6288611yescharacteristic
1098C2#6291512yes—
1099C2#6292812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53133C2semidirect
2. #53031C2semidirect
3. #53023C2semidirect
4. #53017C2semidirect
5. #52991C2semidirect
6. #52968C2semidirect
7. #52603C2semidirect
8. #52568C2semidirect
9. #46190C2semidirect
10. #46180C2semidirect
11. #46147C2semidirect
12. #45696C2semidirect
13. #45648C2semidirect
14. #45488C2semidirect
15. #45474C2semidirect
17. #35566C2semidirect
18. #35544C2semidirect
19. #35544C2semidirect
20. #35265C2semidirect
21. #35253C2semidirect
22. #35224C2semidirect
33. #2864C22semidirect
34. #2859C22semidirect
35. #2857C22semidirect
36. #2851C22semidirect
38. #2843C22semidirect
39. #2841C22semidirect
40. #2839C22semidirect
41. #2838C22semidirect
42. #2836C22semidirect
43. #2835C22semidirect
44. #2833C22semidirect
45. #2833C22semidirect
46. #2831C22semidirect
47. #2822C22semidirect
48. #2817C22semidirect
49. #2817C22semidirect
51. #2791C22semidirect
52. #2787C22semidirect
53. #2775C22semidirect
54. #2771C22semidirect
55. #2769C22semidirect
56. #2766C22semidirect
57. #2765C22semidirect
58. #2764C22semidirect
59. #2764C22semidirect
60. #2745C22semidirect
61. #2738C22semidirect
62. #2734C22semidirect
64. #2722C22semidirect
67. #2713C22semidirect
69. #2698C22semidirect
70. #2698C22semidirect
72. #2689C22semidirect
75. #2647C22semidirect
76. #2647C22semidirect
77. #2629C22semidirect
78. #2628C22semidirect
80. #2584C22semidirect
81. #2584C22semidirect
82. #2567C22semidirect
89. #2552C22semidirect
90. #2551C22semidirect
91. #2550C22semidirect
92. #2550C22semidirect
96. #2546C22semidirect
97. #2509C22semidirect
98. #2508C22semidirect
99. #2507C22semidirect
100. #2506C22semidirect
103. #2497C22semidirect
104. #2497C22semidirect
105. #2497C22semidirect
106. #2497C22semidirect
107. #2496C22semidirect
108. #2496C22semidirect
109. #2496C22semidirect
110. #2496C22semidirect
111. #2495C22semidirect
112. #2495C22semidirect
113. #2495C22semidirect
114. #2495C22semidirect
115. #2494C22semidirect
116. #2494C22semidirect
117. #2494C22semidirect
118. #2494C22semidirect
141. #2442C22semidirect
142. #2442C22semidirect
143. #2442C22semidirect
144. #2442C22semidirect
145. #2442C22semidirect
146. #2441C22semidirect
148. #2440C22semidirect
149. #2440C22semidirect
150. #2440C22semidirect
151. #2440C22semidirect
152. #2440C22semidirect
153. #2439C22semidirect
164. #2378C22semidirect
1032. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#531332
#530312
#530232
#530172
#529912
#529682
#526032
#525682
#461902
#461802
#461472
#456962
#456482
#454882
#454742
#454562
#355662
#355442
#352652
#352532
#352242
#349462
#348092
C2×#24862