Finite Group Databasebeta

← #7652627

Subgroups — #7652627

Order 512.

4666 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42924C214yesmaximal, complemented
2#42901C214yesmaximal, complemented
3#42727C214yesmaximal, complemented
4#42656C214yesmaximal, complemented
5#41444C218yesmaximal, complemented
6#40072C214yesmaximal, complemented
7#39913C214yesmaximal, complemented
8#39791C214yesmaximal, complemented
9#39155C214yesmaximal, complemented
10#38600C218yesmaximal, complemented
11#35672C211yesmaximal, characteristic, complemented
12#35668C211yesmaximal, characteristic, complemented
13#35633C211yesmaximal, characteristic
14#35630C211yesmaximal, characteristic, complemented
15#35627C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17#35307C211yesmaximal, characteristic, complemented
18#35286C211yesmaximal, characteristic, complemented
19#35151C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21C2×#2499C211yesmaximal, characteristic, complemented
22#34742C211yesmaximal, characteristic
23#34276C211yesmaximal, characteristic, complemented
24#34201C211yesmaximal, characteristic
25#34184C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2859C2214yescomplemented
36#2855C2214yes—
37#2855C2214yescomplemented
38#2838C2218yes—
39#2827C2218yes—
40#2810C2218yescomplemented
41#2802C2218yescomplemented
42#2789C2218yescomplemented
43#2787C2218yescomplemented
44#2783C2218yes—
45#2783C2218yes—
46#2775C2218yes—
47#2773C2218yes—
48#2767C2218yescomplemented
49#2757C2218yes—
50#2740C2218yes—
51#2739C2218yescomplemented
52#2738C2218yescomplemented
53#2723C2218yes—
54#2694C2218yes—
55#2690C2218yescomplemented
56#2666C2218yescomplemented
57#2664C2218yes—
58#2654C2218yes—
59#2652C2218yescomplemented
60#2649C2218yes—
61#2647C2214yescomplemented
62#2643C2218yes—
63#2626C2214yes—
64#2625C2214yescomplemented
65#2596C2218yes—
66#2590C2218yescomplemented
67#2585C2218yescomplemented
68#2571C2214yescomplemented
69#2571C2214yescomplemented
70#2570C2214yescomplemented
71#2568C2212yescomplemented
72#2567C2212yescomplemented
73#2567C2212yescomplemented
74#2566C2212yescomplemented
75#2565C2212yescomplemented
76#2565C2212yescomplemented
77#2565C2212yescomplemented
78#2552C2214yescomplemented
79#2542C2212yescomplemented
80#2534C2214yes—
81#2517C2218yescomplemented
82#2514C2214yescomplemented
83#2514C2214yescomplemented
84#2511C2214yescomplemented
85#2511C2214yescomplemented
86#2509C2214yescomplemented
87#2508C2214yescomplemented
88#2505C2218yes—
89#2499C2214yes—
90#2499C2214yes—
91#2499C2214yes—
92#2499C2214yes—
93#2497C2212yes—
94#2496C2212yes—
95#2495C2212yes—
96#2494C2212yes—
97#2493C2218yes—
98#2493C2214yes—
99#2493C2218yescomplemented
100#2488C2218yes—
101#2486C2214yes—
102#2484C2214yes—
103#2482C2214yes—
104#2480C2214yes—
105#2453C2214yescomplemented
106#2451C2214yescomplemented
107#2449C2218yes—
108#2447C2214yescomplemented
109#2446C2214yescomplemented
110#2442C2218yes—
111#2441C2214yes—
112#2441C2214yes—
113#2441C2214yescomplemented
114#2440C2214yescomplemented
115#2439C2214yes—
116#2439C2214yes—
117#2438C2218yes—
118#2429C2214yes—
119#2427C2214yes—
120#2423C2214yes—
121#2423C2214yes—
122#2423C2212yes—
123#2422C2212yes—
124#2421C2214yes—
125#2421C2214yes—
126#2421C2212yes—
127#2420C2212yes—
128#2419C2214yes—
129#2419C2218yes—
130#2418C2214yes—
131#2417C2214yes—
132#2415C2214yes—
133#2401C2214yes—
134#2395C2214yes—
135C2×#397C2214yes—
136#2363C2214yes—
137#2362C2214yes—
138#2362C2214yescomplemented
139#2360C2214yescomplemented
140#2359C2218yes—
141#2354C2214yes—
142#2352C2214yes—
143#2351C2214yescomplemented
144#2349C2218yes—
145#2349C2214yescomplemented
146#2336C2218yescomplemented
147#2329C2218yescomplemented
148#2327C2212yescomplemented
149#2326C2212yescomplemented
150#2321C2214yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2212yescomplemented
157#2317C2212yescomplemented
158#2316C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163C4×C4⋊Q8C2212yescomplemented
164C4×#126C2214yes—
165C4×#124C2212yescomplemented
166C4×#123C2214yes—
167C4×#123C2214yes—
168#2297C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172C2×#391C2211yescharacteristic
173C2×#391C2211yescharacteristic
174C2×#387C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177#2285C2212yescomplemented
178C2×#384C2211yescharacteristic
179C2×#382C2211yescharacteristic
180C2×#382C2212yescomplemented
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190#544—44no—
191#536—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×#126C2314yes—
196C2×#125C2312yes—
197C2×#125C2312yes—
198C2×#125C2318yes—
199C2×#124C2312yes—
200#525—28no—
201C2×#123C2314yes—
202C2×#123C2312yes—
203C2×#123C2314yes—
204C2×C22⋊Q8—44no—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2312yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×#121C2312yes—
212C2×#120C2312yes—
213#520—44no—
214#520—44no—
215#519—44no—
216C4×#41—28no—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×#117—44no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2314yes—
251C22×C4⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C42C2312yes—
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2312yes—
259#401C2318yes—
260#401C2314yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2318yes—
279#399C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2314yes—
295#397C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#396C2318yes—
305#396C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#395C2318yes—
311#394C2314yes—
312#394C2318yes—
313#394C2314yes—
314#393C2318yes—
315#391C2311yescharacteristic
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2311yescharacteristic
326#391C2318yes—
327#391C2312yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#390C2311yescharacteristic
332#390C2312yes—
333#390C2318yes—
334#390C2311yescharacteristic
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#386C2314yes—
400#386C2318yes—
401#386C2314yes—
402#386C2314yes—
403#386C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#385C2314yes—
409#385C2314yes—
410#385C2314yes—
411#385C2314yes—
412#385C2318yes—
413#385C2314yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#384C2312yes—
419#384C2311yescharacteristic
420#384C2312yes—
421#384C2312yes—
422#384C2312yes—
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2314yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#383C2314yes—
430#383C2318yes—
431#382C2311yescharacteristic
432#382C2312yes—
433#382C2312yes—
434#382C2311yescharacteristic
435#382C2314yes—
436#382C2312yes—
437#382C2312yes—
438#382C2318yes—
439#382C2318yes—
440#382C2312yes—
441#382C2312yes—
442#382C2318yes—
443#382C2312yes—
444#382C2312yes—
445#381C2314yes—
446#381C2314yes—
447#381C2312yes—
448#381C2312yes—
449#381C2318yes—
450#381C2314yes—
451#381C2312yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2318yes—
456#380C2314yes—
457#380C2318yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#379C2312yes—
466#379C2312yes—
467#379C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494#376C2312yes—
495C2×#95C2318yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
500C43C2312yes—
501C25C2411yescharacteristic
502C2×#41—24no—
503C2×#41—24no—
504C2×#41#4118yes—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2414yes—
512C22×D4C2412yes—
513C22×D4C2411yescharacteristic
514C22×D4C2414yes—
515C23×C4—24no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4C2412yes—
519C23×C4C2411yescharacteristic
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C4⋊Q8—28no—
533C4⋊Q8—44no—
534C4⋊Q8—44no—
535#126—48no—
536#125—416no—
537#125—44no—
538#125—44no—
539#124—28no—
540#123—28no—
541#123—216no—
542#123—48no—
543C22⋊Q8—28no—
544C22⋊Q8—216no—
545C22⋊Q8—48no—
546C22⋊Q8—416no—
547C22⋊Q8—48no—
548C22⋊Q8—48no—
549#121—28no—
550#120—28no—
551C4×Q8—28no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×D4—216no—
559C4×D4—28no—
560C4×D4—216no—
561C4×D4—44no—
562C4×D4—44no—
563C4×D4—48no—
564C4×D4—48no—
565#117—28no—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—24no—
573#117—48no—
574#117—48no—
575#117—48no—
576#117—44no—
577#117—44no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—48no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C22⋊C4—44no—
632C2×C22⋊C4—44no—
633C2×C22⋊C4—44no—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C42—28no—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—44no—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2418yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731C24—22no—
732C24—22no—
733C24—22no—
734C24—42no—
735C24—42no—
736C24C2512yes—
737C24C2512yes—
738C24C2511yescharacteristic
739#41—232no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—22no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—44no—
749C2×Q8—48no—
750C2×Q8—416no—
751C2×Q8C2×#4114yes—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—28no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4C2×#4118yes—
760C2×D4C2×#4114yes—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—22no—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—42no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—416no—
795C22×C4C2×#4118yes—
796C22×C4C2×#4114yes—
797C22×C4H(5,𝔽2)14yes—
798C22×C42−1+414yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—216no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C22⋊C4—28no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—28no—
872C22⋊C4—216no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—28no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—28no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C42—22no—
896C42—24no—
897C42—22no—
898C42—28no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—22no—
906C42—24no—
907C42—22no—
908C42—24no—
909C42—28no—
910C42—48no—
911C42—44no—
912C42—48no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—44no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—44no—
931C23—44no—
932C23—44no—
933C23—84no—
934C23—84no—
935C23C22×#4114yes—
936C23C22×#4112yes—
937C23C2×H(5,𝔽2)12yes—
938C23C2×2−1+412yes—
939C23C2611yescharacteristic
940Q8—28no—
941Q8—48no—
942Q8—48no—
943Q8—164no—
944D4—216no—
945D4—28no—
946D4—88no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—216no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—48no—
998C2×C4—44no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—84no—
1003C2×C4—88no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4—84no—
1007C2×C4—164no—
1008C2×C4—164no—
1009C2×C4#539116yes—
1010C2×C4C22×#4114yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×H(5,𝔽2)12yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4C2×2−1+412yes—
1017C2×C4#58514yes—
1018C22—24no—
1019C22—22no—
1020C22—22no—
1021C22—24no—
1022C22—28no—
1023C22—24no—
1024C22—42no—
1025C22—42no—
1026C22—44no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—88no—
1035C22C2×#53914yes—
1036C22C23×#4111yescharacteristic
1037C22C22×H(5,𝔽2)11yescharacteristic
1038C22C22×2−1+411yescharacteristic
1039C22C2×#58512yes—
1040C222−1+612yes—
1041C4—24no—
1042C4—24no—
1043C4—44no—
1044C4—42no—
1045C4—44no—
1046C4—42no—
1047C4—44no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—44no—
1056C4—42no—
1057C4—42no—
1058C4—44no—
1059C4—44no—
1060C4—42no—
1061C4C2×#53914yes—
1062C4C2×#53914yes—
1063C2—24no—
1064C2—44no—
1065C2—82no—
1066C2C22×#53911yescharacteristic
1067C2#6283611yescharacteristic
1068C2#6288711yescharacteristic
1069C2#6292812yes—
1070C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42924C2semidirect
2. #42901C2semidirect
3. #42727C2semidirect
4. #42656C2semidirect
5. #41444C2semidirect
6. #40072C2semidirect
7. #39913C2semidirect
8. #39791C2semidirect
9. #39155C2semidirect
10. #38600C2semidirect
11. #35672C2semidirect
12. #35668C2semidirect
14. #35630C2semidirect
15. #35627C2semidirect
16. #35532C2semidirect
17. #35307C2semidirect
18. #35286C2semidirect
19. #35151C2semidirect
20. #34814C2semidirect
21. C2×#2499C2semidirect
23. #34276C2semidirect
25. #34184C2semidirect
35. #2859C22semidirect
37. #2855C22semidirect
40. #2810C22semidirect
41. #2802C22semidirect
42. #2789C22semidirect
43. #2787C22semidirect
48. #2767C22semidirect
51. #2739C22semidirect
52. #2738C22semidirect
55. #2690C22semidirect
56. #2666C22semidirect
59. #2652C22semidirect
61. #2647C22semidirect
64. #2625C22semidirect
66. #2590C22semidirect
67. #2585C22semidirect
68. #2571C22semidirect
69. #2571C22semidirect
70. #2570C22semidirect
71. #2568C22semidirect
72. #2567C22semidirect
73. #2567C22semidirect
74. #2566C22semidirect
75. #2565C22semidirect
76. #2565C22semidirect
77. #2565C22semidirect
78. #2552C22semidirect
79. #2542C22semidirect
81. #2517C22semidirect
82. #2514C22semidirect
83. #2514C22semidirect
84. #2511C22semidirect
85. #2511C22semidirect
86. #2509C22semidirect
87. #2508C22semidirect
99. #2493C22semidirect
105. #2453C22semidirect
106. #2451C22semidirect
108. #2447C22semidirect
109. #2446C22semidirect
113. #2441C22semidirect
114. #2440C22semidirect
138. #2362C22semidirect
139. #2360C22semidirect
143. #2351C22semidirect
145. #2349C22semidirect
146. #2336C22semidirect
147. #2329C22semidirect
148. #2327C22semidirect
149. #2326C22semidirect
156. #2317C22semidirect
157. #2317C22semidirect
163. C4×C4⋊Q8C22semidirect
165. C4×#124C22semidirect
177. #2285C22semidirect
180. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#429242
#429012
#427272
#426562
#414442
#400722
#399132
#397912
#391552
#386002
#356722
#356682
#356332
#356302
#356272
#355322
#353072
#352862
#351512
#348142
C2×#24992
#347422
#342762
#342012
#341842