Finite Group Databasebeta

← #7746745

Subgroups — #7746745

Order 512.

4988 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45344C212yesmaximal, complemented
2#45336C212yesmaximal, complemented
3#45331C214yesmaximal, complemented
4#45322C214yesmaximal, complemented
5#45044C214yesmaximal, complemented
6#44984C214yesmaximal, complemented
7#44917C214yesmaximal, complemented
8#42853C214yesmaximal, complemented
9#42610C214yesmaximal, complemented
10#42587C214yesmaximal, complemented
11#36593C211yesmaximal, characteristic, complemented
12#36574C211yesmaximal, characteristic, complemented
13#36210C212yesmaximal, complemented
14#36209C211yesmaximal, characteristic, complemented
15D4×C4⋊Q8C211yesmaximal, characteristic, complemented
16D4×C4⋊Q8C212yesmaximal, complemented
17#35749C212yesmaximal, complemented
18#35747C214yesmaximal, complemented
19#35700C212yesmaximal
20#35699C214yesmaximal
21#35319C211yesmaximal, characteristic, complemented
22#35284C212yesmaximal, complemented
23#34551C211yesmaximal, characteristic
24#34216C212yesmaximal, complemented
25#34209C211yesmaximal, characteristic, complemented
26C2×#557C2212yes—
27C2×D4×Q8C2214yes—
28C2×D4×Q8C2212yes—
29C2×#541C2212yes—
30C22×C4⋊Q8C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C2×#519C2212yes—
33#2868C2212yes—
34#2868C2211yescharacteristic
35#2859C2211yescharacteristic
36#2859C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2833C2218yes—
41#2805C2218yes—
42#2787C2218yes—
43#2776C2218yes—
44#2774C2218yes—
45#2770C2218yes—
46#2766C2218yes—
47#2713C2218yes—
48#2713C2218yes—
49#2698C2218yes—
50#2690C2218yes—
51#2690C2218yes—
52#2689C2218yes—
53#2666C2218yes—
54#2652C2218yes—
55#2647C2214yes—
56#2642C2212yes—
57#2634C2214yes—
58#2629C2214yes—
59#2621C2214yes—
60#2621C2212yes—
61#2611C2214yes—
62#2606C2218yes—
63#2599C2214yes—
64#2587C2218yes—
65#2585C2218yes—
66#2584C2214yes—
67#2581C2212yes—
68#2562C2214yes—
69#2556C2218yes—
70#2552C2214yes—
71#2552C2214yes—
72#2552C2214yes—
73#2551C2214yes—
74#2551C2214yes—
75#2551C2214yes—
76#2550C2218yes—
77#2546C2214yes—
78#2546C2214yes—
79#2546C2212yes—
80#2546C2212yes—
81#2546C2214yes—
82#2536C2214yes—
83#2536C2212yes—
84#2514C2214yes—
85#2509C2214yes—
86#2509C2214yes—
87#2508C2214yes—
88#2508C2214yes—
89#2507C2214yes—
90#2507C2214yes—
91#2506C2214yes—
92#2506C2214yes—
93#2497C2214yes—
94#2497C2214yes—
95#2496C2214yes—
96#2496C2214yes—
97#2495C2214yes—
98#2495C2214yes—
99#2494C2214yes—
100#2494C2214yes—
101#2489C2214yes—
102#2485C2214yes—
103#2485C2214yes—
104#2475C2218yes—
105#2468C2218yes—
106#2466C2218yes—
107#2465C2218yes—
108#2462C2218yes—
109#2460C2218yes—
110#2453C2214yes—
111#2446C2214yes—
112#2446C2214yes—
113#2440C2214yes—
114#2440C2214yes—
115#2440C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2440C2214yes—
119#2434C2214yes—
120#2434C2214yes—
121#2434C2214yes—
122#2429C2214yes—
123#2429C2214yes—
124#2429C2218yes—
125#2421C2214yes—
126#2415C2214yes—
127#2415C2218yes—
128#2402C2211yescharacteristic
129#2402C2212yes—
130#2401C2212yes—
131#2401C2212yes—
132#2401C2212yes—
133#2399C2214yes—
134#2398C2211yescharacteristic
135#2398C2212yes—
136#2396C2212yes—
137#2396C2211yescharacteristic
138#2395C2212yes—
139#2395C2212yes—
140#2395C2212yes—
141#2392C2214yes—
142#2392C2212yes—
143#2392C2211yescharacteristic
144#2370C2214yes—
145#2370C2214yes—
146#2369C2214yes—
147#2369C2214yes—
148#2365C2214yes—
149#2365C2214yes—
150#2365C2214yes—
151#2365C2214yes—
152#2362C2214yes—
153#2356C2212yes—
154#2351C2212yes—
155Q8×C4⋊C4C2214yes—
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2214yes—
158D4×C4⋊C4C2214yes—
159#2347C2214yes—
160#2346C2214yes—
161#2345C2214yes—
162#2345C2214yes—
163#2344C2214yes—
164#2344C2214yes—
165Q8×C22⋊C4C2214yes—
166Q8×C22⋊C4C2214yes—
167#2331C2214yes—
168#2331C2214yes—
169#2330C2214yes—
170#2327C2212yes—
171#2327C2212yes—
172#2327C2212yes—
173#2316C2214yes—
174#2314C2214yes—
175#2310C2212yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183#2285C2212yes—
184#2285C2211yescharacteristic
185#2274C2214yes—
186C42×Q8C2211yescharacteristic
187C42×D4C2211yescharacteristic
188C42×D4C2212yes—
189C4×#117C2211yescharacteristic
190C4×#117C2212yes—
191C23×Q8C2312yes—
192C23×Q8C2314yes—
193#557—48no—
194D4×Q8—48no—
195D4×Q8—416no—
196#541—48no—
197C2×C4⋊Q8—28no—
198C2×C4⋊Q8—216no—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2318yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126C2318yes—
214C2×#125C2314yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×#125C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225#519—48no—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2318yes—
244C2×C4×D4C2314yes—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2314yes—
248C2×#117C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#401C2312yes—
259#401C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2311yescharacteristic
268#400C2318yes—
269#400C2318yes—
270#400C2312yes—
271#400C2312yes—
272#400C2312yes—
273#400C2312yes—
274#400C2312yes—
275#400C2312yes—
276#400C2312yes—
277#399C2311yescharacteristic
278#399C2312yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2312yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2312yes—
289#398C2314yes—
290#398C2318yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#398C2311yescharacteristic
297#398C2312yes—
298#398C2312yes—
299#398C2318yes—
300#397C2314yes—
301#397C2311yescharacteristic
302#397C2314yes—
303#397C2318yes—
304#397C2312yes—
305#397C2312yes—
306#397C2312yes—
307#397C2312yes—
308#397C2312yes—
309#397C2312yes—
310#397C2312yes—
311#397C2318yes—
312#397C2318yes—
313#396C2312yes—
314#396C2318yes—
315#396C2318yes—
316#396C2312yes—
317#396C2312yes—
318#395C2318yes—
319#395C2318yes—
320#395C2314yes—
321#395C2318yes—
322#395C2311yescharacteristic
323#395C2318yes—
324#395C2318yes—
325#395C2318yes—
326#394C2318yes—
327#394C2312yes—
328#394C2311yescharacteristic
329#394C2312yes—
330#394C2312yes—
331#394C2312yes—
332#394C2314yes—
333#393C2311yescharacteristic
334#393C2312yes—
335#392C2311yescharacteristic
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2318yes—
344#391C2318yes—
345#391C2314yes—
346#391C2318yes—
347#391C2318yes—
348#391C2318yes—
349#391C2314yes—
350#391C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2318yes—
385#389C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2312yes—
423#384C2314yes—
424#384C2314yes—
425#384C2314yes—
426#384C2314yes—
427#384C2314yes—
428#384C2314yes—
429#383C2314yes—
430#383C2318yes—
431#382C2314yes—
432#382C2312yes—
433#382C2312yes—
434#382C2314yes—
435#382C2318yes—
436#382C2314yes—
437#381C2318yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2318yes—
445#380C2318yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2318yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499#376C2311yescharacteristic
500#376C2311yescharacteristic
501#376C2312yes—
502#376C2312yes—
503#376C2314yes—
504C43C2311yescharacteristic
505C43C2311yescharacteristic
506C43C2312yes—
507C22×Q8—28no—
508C22×Q8—216no—
509C22×Q8—28no—
510C22×Q8—44no—
511C22×Q8—48no—
512C22×Q8—48no—
513C22×Q8C2411yescharacteristic
514C22×Q8C2412yes—
515C22×Q8C2414yes—
516C22×Q8C2414yes—
517C22×Q8C2412yes—
518C22×Q8C2418yes—
519C22×D4C2411yescharacteristic
520C22×D4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2414yes—
525C23×C4C2411yescharacteristic
526C23×C4C2412yes—
527C23×C4C2418yes—
528C4⋊Q8—28no—
529C4⋊Q8—216no—
530C4⋊Q8—216no—
531C4⋊Q8—216no—
532C4⋊Q8—216no—
533C4⋊Q8—24no—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—48no—
537C4⋊Q8—44no—
538C4⋊Q8—48no—
539C4⋊Q8—48no—
540C4⋊Q8—416no—
541C4⋊Q8#4118yes—
542#126—416no—
543#125—216no—
544#125—44no—
545#125—48no—
546#125—416no—
547#125—416no—
548C22⋊Q8—216no—
549C22⋊Q8—416no—
550C22⋊Q8—416no—
551C22⋊Q8—416no—
552C22⋊Q8—48no—
553C22⋊Q8—48no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—24no—
557C4×Q8—28no—
558C4×Q8—48no—
559C4×Q8—48no—
560C4×Q8—44no—
561C4×Q8—44no—
562C4×Q8—48no—
563C4×Q8—48no—
564C4×Q8—48no—
565C4×Q8—48no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—28no—
569C4×D4—24no—
570C4×D4—28no—
571C4×D4—48no—
572C4×D4—416no—
573#117—24no—
574#117—28no—
575#117—216no—
576#117—24no—
577#117—28no—
578#117—48no—
579#117—48no—
580#117—44no—
581C2×C4⋊C4—216no—
582C2×C4⋊C4—216no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C22⋊C4C2411yescharacteristic
636C2×C22⋊C4C2411yescharacteristic
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C42—28no—
657C2×C42—24no—
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2414yes—
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2418yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2418yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2412yes—
687#95C2411yescharacteristic
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2418yes—
701#95C2414yes—
702#95C2412yes—
703#95C2412yes—
704#95C2411yescharacteristic
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2411yescharacteristic
716#95C2411yescharacteristic
717#95C2412yes—
718#95C2412yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736C24C2511yescharacteristic
737C24C2512yes—
738C2×Q8—28no—
739C2×Q8—24no—
740C2×Q8—28no—
741C2×Q8—216no—
742C2×Q8—22no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—28no—
747C2×Q8—28no—
748C2×Q8—28no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—44no—
752C2×Q8—48no—
753C2×Q8—48no—
754C2×Q8—432no—
755C2×Q8—832no—
756C2×Q8C2×#4118yes—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—22no—
761C2×D4—24no—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—24no—
766C22×C4—28no—
767C22×C4—24no—
768C22×C4—24no—
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—216no—
778C22×C4—44no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4H(5,𝔽2)14yes—
782C22×C42−1+418yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2518yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2518yes—
797C22×C4C2514yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C4⋊C4—216no—
807C4⋊C4—216no—
808C4⋊C4—216no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—22no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—22no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—216no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—216no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4C2×#41116yes—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—216no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—216no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C42—24no—
879C42—24no—
880C42—24no—
881C42—22no—
882C42—24no—
883C42—22no—
884C42—22no—
885C42—22no—
886C42—28no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—216no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—44no—
899C42—44no—
900C42—44no—
901C42—48no—
902C42—48no—
903C42—48no—
904C42C2×#4114yes—
905C42H(5,𝔽2)14yes—
906C422−1+418yes—
907C23—21no—
908C23—22no—
909C23—21no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23C2×H(5,𝔽2)12yes—
918C23C2×2−1+414yes—
919C23C2611yescharacteristic
920Q8—28no—
921Q8—216no—
922Q8—416no—
923Q8—48no—
924Q8—416no—
925Q8—816no—
926D4—28no—
927D4—216no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—21no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—28no—
941C2×C4—216no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—28no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—28no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—416no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—816no—
985C2×C4C22×#4118yes—
986C2×C4C22×#4112yes—
987C2×C4C22×#4114yes—
988C2×C4C2×H(5,𝔽2)12yes—
989C2×C4C2×H(5,𝔽2)12yes—
990C2×C4C2×H(5,𝔽2)12yes—
991C2×C4C2×H(5,𝔽2)12yes—
992C2×C4C2×H(5,𝔽2)12yes—
993C2×C4C2×2−1+414yes—
994C2×C4C2×2−1+414yes—
995C2×C4C2×2−1+414yes—
996C2×C4C2×2−1+414yes—
997C2×C4C2×2−1+414yes—
998C22—22no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—41no—
1007C22—42no—
1008C22—41no—
1009C22—42no—
1010C22C23×#4111yescharacteristic
1011C22C22×H(5,𝔽2)11yescharacteristic
1012C22C22×H(5,𝔽2)11yescharacteristic
1013C22C22×2−1+412yes—
1014C22C22×2−1+412yes—
1015C4—22no—
1016C4—28no—
1017C4—24no—
1018C4—22no—
1019C4—22no—
1020C4—24no—
1021C4—24no—
1022C4—44no—
1023C4—42no—
1024C4—48no—
1025C4—42no—
1026C4—42no—
1027C4—41no—
1028C4—44no—
1029C4—41no—
1030C4—42no—
1031C4—44no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—48no—
1036C4#351914yes—
1037C4#352318yes—
1038C2—42no—
1039C2—44no—
1040C2C2×#351911yescharacteristic
1041C2C2×#352312yes—
1042C2#6283311yescharacteristic
1043C2#6283311yescharacteristic
1044C2#6283312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45344C2semidirect
2. #45336C2semidirect
3. #45331C2semidirect
4. #45322C2semidirect
5. #45044C2semidirect
6. #44984C2semidirect
7. #44917C2semidirect
8. #42853C2semidirect
9. #42610C2semidirect
10. #42587C2semidirect
11. #36593C2semidirect
12. #36574C2semidirect
13. #36210C2semidirect
14. #36209C2semidirect
15. D4×C4⋊Q8C2semidirect
16. D4×C4⋊Q8C2semidirect
17. #35749C2semidirect
18. #35747C2semidirect
21. #35319C2semidirect
22. #35284C2semidirect
24. #34216C2semidirect
25. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#453442
#453362
#453312
#453222
#450442
#449842
#449172
#428532
#426102
#425872
#365932
#365742
#362102
#362092
D4×C4⋊Q82
#357492
#357472
#357002
#356992
#353192
#352842
#345512
#342162
#342092