Finite Group Databasebeta

← #7646608

Subgroups — #7646608

Order 512.

4566 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42701C214yesmaximal, complemented
2#42698C214yesmaximal, complemented
3#42672C214yesmaximal, complemented
4#42665C214yesmaximal, complemented
5#39643C212yesmaximal, complemented
6#39609C212yesmaximal, complemented
7#39515C212yesmaximal, complemented
8#39478C212yesmaximal, complemented
9#39200C212yesmaximal, complemented
10#39159C212yesmaximal, complemented
11#38984C212yesmaximal, complemented
12#38933C212yesmaximal, complemented
13#37503C214yesmaximal, complemented
14#36999C218yesmaximal, complemented
15#35630C212yesmaximal, complemented
16#35628C212yesmaximal
17#35320C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic
19#35228C214yesmaximal, complemented
20#35182C212yesmaximal
21#35179C212yesmaximal, complemented
22#34947C211yesmaximal, characteristic
23#34938C211yesmaximal, characteristic, complemented
24#34213C211yesmaximal, characteristic, complemented
25C2×#2365C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic
27C2×#536C2212yes—
28C2×#533C2211yescharacteristic
29C2×#533C2212yes—
30C22×C4⋊Q8C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32C22×C4×Q8C2212yes—
33#2862C2212yes—
34#2862C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2855C2218yes—
38#2853C2218yes—
39#2839C2218yes—
40#2838C2218yes—
41#2799C2218yes—
42#2798C2218yes—
43#2774C2218yes—
44#2773C2218yes—
45#2767C2218yes—
46#2767C2218yes—
47#2766C2218yes—
48#2762C2218yes—
49#2759C2218yes—
50#2758C2218yes—
51#2755C2218yes—
52#2754C2218yes—
53#2747C2218yes—
54#2745C2218yes—
55#2742C2218yes—
56#2738C2218yes—
57#2666C2218yes—
58#2655C2218yes—
59#2654C2218yes—
60#2650C2218yes—
61#2647C2214yes—
62#2645C2214yes—
63#2642C2214yes—
64#2628C2214yes—
65#2627C2218yes—
66#2625C2214yes—
67#2623C2218yes—
68#2621C2214yes—
69#2592C2214yes—
70#2592C2214yes—
71#2582C2214yes—
72#2582C2214yes—
73#2581C2214yes—
74#2581C2214yes—
75#2568C2212yes—
76#2568C2214yes—
77#2568C2214yes—
78#2568C2212yes—
79#2568C2211yescharacteristic
80#2568C2214yes—
81#2568C2212yes—
82#2568C2212yes—
83#2567C2214yes—
84#2567C2211yescharacteristic
85#2566C2212yes—
86#2565C2214yes—
87#2565C2214yes—
88#2565C2212yes—
89#2564C2214yes—
90#2563C2211yescharacteristic
91#2552C2211yescharacteristic
92#2552C2211yescharacteristic
93#2551C2211yescharacteristic
94#2551C2211yescharacteristic
95#2550C2212yes—
96#2550C2212yes—
97#2549C2214yes—
98#2547C2212yes—
99#2547C2212yes—
100#2546C2212yes—
101#2546C2212yes—
102#2542C2211yescharacteristic
103#2525C2218yes—
104#2520C2218yes—
105#2514C2214yes—
106#2514C2214yes—
107#2514C2214yes—
108#2514C2214yes—
109#2511C2214yes—
110#2511C2214yes—
111#2511C2214yes—
112#2511C2214yes—
113#2511C2214yes—
114#2509C2214yes—
115#2508C2214yes—
116#2503C2214yes—
117#2503C2214yes—
118#2495C2214yes—
119#2494C2214yes—
120#2493C2218yes—
121#2493C2218yes—
122#2492C2214yes—
123#2492C2214yes—
124#2492C2214yes—
125#2489C2214yes—
126#2489C2214yes—
127#2488C2218yes—
128#2488C2218yes—
129#2486C2214yes—
130#2486C2214yes—
131#2451C2214yes—
132#2448C2214yes—
133#2448C2214yes—
134#2446C2214yes—
135#2446C2214yes—
136#2440C2212yes—
137#2440C2212yes—
138#2423C2214yes—
139#2423C2214yes—
140#2423C2214yes—
141#2421C2214yes—
142#2421C2214yes—
143#2417C2212yes—
144#2417C2212yes—
145#2399C2214yes—
146#2396C2214yes—
147#2370C2214yes—
148#2369C2212yes—
149#2365C2212yes—
150#2365C2212yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2214yes—
154#2365C2212yes—
155#2365C2214yes—
156#2355C2212yes—
157#2355C2214yes—
158Q8×C4⋊C4C2212yes—
159#2331C2214yes—
160#2329C2214yes—
161#2323C2214yes—
162#2320C2212yes—
163#2320C2214yes—
164#2319C2212yes—
165#2318C2214yes—
166#2317C2211yescharacteristic
167#2317C2211yescharacteristic
168#2317C2212yes—
169#2314C2212yes—
170#2314C2212yes—
171#2314C2214yes—
172#2311C2211yescharacteristic
173#2311C2211yescharacteristic
174#2310C2212yes—
175#2310C2212yes—
176#2310C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2212yes—
182#2297C2212yes—
183#2296C2212yes—
184#2295C2212yes—
185C2×#391C2212yes—
186#2293C2212yes—
187C2×#389C2212yes—
188#2290C2214yes—
189C2×#387C2214yes—
190#2285C2212yes—
191#2285C2212yes—
192#2285C2211yescharacteristic
193#2283C2212yes—
194#2274C2212yes—
195C4×#117C2211yescharacteristic
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C23×Q8C2312yes—
201#536—48no—
202#533—28no—
203#533—48no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#124C2314yes—
220C2×#123C2318yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C4×#41—28no—
230C2×C4×Q8—48no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2314yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C42C2312yes—
261C22×C42C2312yes—
262C22×C42C2314yes—
263C22×C42C2312yes—
264C22×C42C2311yescharacteristic
265#401C2318yes—
266#401C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2314yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2314yes—
310#396C2314yes—
311#395C2314yes—
312#395C2318yes—
313#395C2318yes—
314#395C2314yes—
315#395C2314yes—
316#395C2314yes—
317#395C2314yes—
318#393C2314yes—
319#393C2318yes—
320#393C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2314yes—
342#391C2318yes—
343#391C2318yes—
344#391C2318yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2312yes—
350#391C2318yes—
351#391C2318yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
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#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#383C2314yes—
448#383C2318yes—
449#383C2318yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2312yes—
454#382C2314yes—
455#382C2318yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#382C2318yes—
460#382C2312yes—
461#382C2314yes—
462#382C2312yes—
463#381C2318yes—
464#381C2318yes—
465#381C2318yes—
466#381C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2312yes—
519#376C2314yes—
520C2×#95C2312yes—
521C2×#95C2312yes—
522C2×#95C2314yes—
523C2×#95C2314yes—
524C43C2312yes—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C22×Q8—28no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×D4C2412yes—
539C22×D4C2411yescharacteristic
540C23×C4C2414yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2411yescharacteristic
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—48no—
562#125—28no—
563#125—44no—
564#125—44no—
565#124—48no—
566#123—416no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C4×Q8—24no—
576C4×Q8—24no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—24no—
589C4×D4—24no—
590#117—24no—
591#117—28no—
592#117—24no—
593#117—28no—
594#117—24no—
595#117—28no—
596#117—48no—
597C2×C4⋊C4—28no—
598C2×C4⋊C4—28no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—42no—
603C2×C4⋊C4—48no—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C42—28no—
680C2×C42—28no—
681C2×C42—44no—
682C2×C42—48no—
683C2×C42#4118yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2418yes—
699C2×C42C2418yes—
700C2×C42C2418yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2418yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#95C2414yes—
710#95C2418yes—
711#95C2412yes—
712#95C2412yes—
713#95C2414yes—
714#95C2418yes—
715#95C2412yes—
716#95C2412yes—
717#95C2418yes—
718#95C2418yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2512yes—
762C24C2511yescharacteristic
763#41—416no—
764C2×Q8—22no—
765C2×Q8—24no—
766C2×Q8—28no—
767C2×Q8—28no—
768C2×Q8—24no—
769C2×Q8—28no—
770C2×Q8—28no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—22no—
776C2×Q8—28no—
777C2×Q8—24no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—432no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—28no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—42no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4C2×#4114yes—
821C22×C4C2×#4114yes—
822C22×C4C2×#4114yes—
823C22×C4H(5,𝔽2)14yes—
824C22×C42−1+414yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2518yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—42no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C42−1+414yes—
907C22⋊C4—24no—
908C22⋊C4—28no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—28no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—28no—
937C42—24no—
938C42—44no—
939C42—48no—
940C42—48no—
941C42—42no—
942C42—42no—
943C42—48no—
944C42—48no—
945C42C2×#4114yes—
946C42C2×#4114yes—
947C42C2×#4114yes—
948C42C2×#4114yes—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23C22×#4112yes—
961C23C2×H(5,𝔽2)12yes—
962C23C2×2−1+412yes—
963C23C2611yescharacteristic
964Q8—416no—
965Q8—416no—
966Q8—44no—
967Q8—48no—
968Q8—84no—
969Q8—88no—
970Q8—88no—
971D4—48no—
972D4—44no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—44no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—416no—
1037C2×C4—48no—
1038C2×C4—48no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4#542116yes—
1043C2×C4C22×#4112yes—
1044C2×C4C22×#4112yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×2−1+414yes—
1052C2×C4C2×2−1+412yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4C2×2−1+412yes—
1055C2×C4#58512yes—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22C2×#54214yes—
1070C22C23×#4111yescharacteristic
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C22×2−1+411yescharacteristic
1073C22C22×2−1+411yescharacteristic
1074C22C2×#58511yescharacteristic
1075C222−1+611yescharacteristic
1076C222−1+611yescharacteristic
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—24no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—44no—
1085C4—44no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—42no—
1091C4—44no—
1092C4—42no—
1093C4—48no—
1094C4—42no—
1095C4—44no—
1096C4—42no—
1097C4—42no—
1098C4C2×#54214yes—
1099C4C2×#54214yes—
1100C4#350714yes—
1101C2—24no—
1102C2—82no—
1103C2C22×#54211yescharacteristic
1104C2C2×#350711yescharacteristic
1105C2#6286011yescharacteristic
1106C2#6292511yescharacteristic
1107C2#6293211yescharacteristic
1108C2#6294211yescharacteristic
1109C2#6294711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42701C2semidirect
2. #42698C2semidirect
3. #42672C2semidirect
4. #42665C2semidirect
5. #39643C2semidirect
6. #39609C2semidirect
7. #39515C2semidirect
8. #39478C2semidirect
9. #39200C2semidirect
10. #39159C2semidirect
11. #38984C2semidirect
12. #38933C2semidirect
13. #37503C2semidirect
14. #36999C2semidirect
15. #35630C2semidirect
17. #35320C2semidirect
19. #35228C2semidirect
21. #35179C2semidirect
23. #34938C2semidirect
24. #34213C2semidirect
25. C2×#2365C2semidirect

Maximal subgroups

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

subgroupindex
#427012
#426982
#426722
#426652
#396432
#396092
#395152
#394782
#392002
#391592
#389842
#389332
#375032
#369992
#356302
#356282
#353202
#353162
#352282
#351822
#351792
#349472
#349382
#342132
C2×#23652
#340602