Finite Group Databasebeta

← #7651259

Subgroups — #7651259

Order 512.

4612 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42772C214yesmaximal, complemented
2#42729C214yesmaximal, complemented
3#42665C214yesmaximal, complemented
4#42459C214yesmaximal, complemented
5#40811C218yesmaximal, complemented
6#40226C214yesmaximal, complemented
7#39905C214yesmaximal, complemented
8#39535C214yesmaximal, complemented
9#38933C214yesmaximal, complemented
10#38147C218yesmaximal, complemented
11#35649C211yesmaximal, characteristic
12#35640C211yesmaximal, characteristic, complemented
13#35630C211yesmaximal, characteristic, complemented
14#35628C211yesmaximal, characteristic, complemented
15#35620C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic
17#35312C211yesmaximal, characteristic, complemented
18#35308C211yesmaximal, characteristic
19#35182C211yesmaximal, characteristic, complemented
20C2×#2565C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34266C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34189C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2862C2212yes—
36#2861C2212yes—
37#2857C2212yes—
38#2853C2214yes—
39#2850C2212yes—
40#2839C2218yes—
41#2837C2218yes—
42#2800C2218yes—
43#2799C2218yes—
44#2798C2218yes—
45#2790C2218yes—
46#2772C2218yes—
47#2770C2218yes—
48#2767C2218yes—
49#2766C2218yes—
50#2766C2218yes—
51#2759C2218yes—
52#2754C2218yes—
53#2738C2218yes—
54#2738C2218yes—
55#2737C2218yes—
56#2718C2218yes—
57#2687C2218yes—
58#2654C2218yes—
59#2653C2218yes—
60#2652C2218yes—
61#2650C2218yes—
62#2647C2218yes—
63#2642C2212yes—
64#2640C2212yes—
65#2637C2218yes—
66#2623C2214yes—
67#2621C2212yes—
68#2620C2212yes—
69#2592C2214yes—
70#2591C2214yes—
71#2583C2214yes—
72#2568C2214yes—
73#2568C2212yes—
74#2566C2212yes—
75#2565C2214yes—
76#2565C2212yes—
77#2565C2214yes—
78#2565C2214yes—
79#2565C2214yes—
80#2563C2212yes—
81#2552C2214yes—
82#2552C2214yes—
83#2550C2214yes—
84#2550C2214yes—
85#2532C2218yes—
86#2530C2218yes—
87#2520C2218yes—
88#2514C2212yes—
89#2514C2214yes—
90#2514C2214yes—
91#2513C2212yes—
92#2512C2212yes—
93#2511C2212yes—
94#2511C2214yes—
95#2511C2214yes—
96#2510C2214yes—
97#2504C2214yes—
98#2502C2212yes—
99#2502C2214yes—
100#2501C2212yes—
101#2500C2212yes—
102#2499C2212yes—
103#2494C2218yes—
104#2493C2218yes—
105#2492C2214yes—
106#2492C2214yes—
107#2490C2214yes—
108#2490C2214yes—
109#2489C2214yes—
110#2489C2214yes—
111#2489C2214yes—
112#2489C2214yes—
113#2488C2218yes—
114#2488C2218yes—
115#2481C2214yes—
116#2458C2218yes—
117#2454C2212yes—
118#2453C2212yes—
119#2452C2212yes—
120#2451C2212yes—
121#2450C2214yes—
122#2450C2218yes—
123#2449C2214yes—
124#2448C2214yes—
125#2446C2214yes—
126#2443C2218yes—
127#2442C2214yes—
128#2439C2214yes—
129#2429C2214yes—
130#2427C2214yes—
131#2425C2218yes—
132#2423C2218yes—
133#2423C2214yes—
134#2423C2214yes—
135#2422C2214yes—
136#2421C2214yes—
137#2401C2214yes—
138#2396C2214yes—
139C2×#398C2214yes—
140#2367C2214yes—
141#2365C2214yes—
142#2362C2214yes—
143#2360C2218yes—
144#2360C2214yes—
145#2357C2214yes—
146#2356C2214yes—
147#2355C2214yes—
148#2353C2218yes—
149Q8×C4⋊C4C2214yes—
150#2335C2218yes—
151#2330C2214yes—
152#2322C2214yes—
153#2320C2218yes—
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2314C2214yes—
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163C4×C4⋊Q8C2214yes—
164C4×#126C2214yes—
165C4×C22⋊Q8C2214yes—
166C4×#123C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#387C2214yes—
178#2285C2211yescharacteristic
179C2×#384C2211yescharacteristic
180#2283C2214yes—
181C2×#382C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190#544—44no—
191#537—44no—
192#536—28no—
193#536—44no—
194#533—28no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#126C2314yes—
201C2×#125—44no—
202C2×#125C2312yes—
203C2×#125C2314yes—
204C2×#125C2314yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#123C2314yes—
210C2×#123C2318yes—
211C2×#123C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×#121C2314yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223#520—44no—
224C4×#41—28no—
225C2×C4×Q8—44no—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2318yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2314yes—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2314yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#401C2318yes—
259#401C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#399C2314yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2318yes—
298#397C2314yes—
299#397C2314yes—
300#396C2318yes—
301#396C2314yes—
302#396C2318yes—
303#396C2314yes—
304#396C2314yes—
305#395C2318yes—
306#395C2314yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2314yes—
314#391C2318yes—
315#391C2314yes—
316#391C2312yes—
317#391C2311yescharacteristic
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2311yescharacteristic
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2314yes—
335#391C2311yescharacteristic
336#391C2318yes—
337#391C2312yes—
338#391C2311yescharacteristic
339#391C2318yes—
340#391C2312yes—
341#390C2311yescharacteristic
342#390C2312yes—
343#390C2311yescharacteristic
344#390C2312yes—
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2311yescharacteristic
349#390C2312yes—
350#390C2311yescharacteristic
351#390C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
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#387C2314yes—
407#387C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2312yes—
412#386C2318yes—
413#386C2312yes—
414#386C2312yes—
415#386C2314yes—
416#386C2314yes—
417#386C2314yes—
418#386C2312yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2312yes—
424#385C2318yes—
425#385C2312yes—
426#385C2312yes—
427#385C2314yes—
428#385C2312yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2318yes—
440#383C2314yes—
441#383C2318yes—
442#383C2318yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2318yes—
451#382C2318yes—
452#382C2312yes—
453#381C2314yes—
454#381C2314yes—
455#381C2318yes—
456#380C2318yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2318yes—
461#380C2314yes—
462#380C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494#376C2318yes—
495#376C2312yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
500C43C2312yes—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2414yes—
515C22×Q8C2414yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2414yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2411yescharacteristic
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2414yes—
532C23×C4C2414yes—
533C23×C4C2411yescharacteristic
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539#126—48no—
540#125—28no—
541#125—48no—
542#125—48no—
543#125—44no—
544#125—44no—
545#124—28no—
546#124—44no—
547#123—216no—
548#123—416no—
549#123—48no—
550C22⋊Q8—216no—
551C22⋊Q8—216no—
552C22⋊Q8—48no—
553C22⋊Q8—48no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558#121—44no—
559#121—44no—
560#121—48no—
561C4×Q8—28no—
562C4×Q8—216no—
563C4×Q8—48no—
564C4×Q8—48no—
565C4×Q8—416no—
566C4×Q8—44no—
567C4×D4—28no—
568C4×D4—216no—
569C4×D4—44no—
570C4×D4—48no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—28no—
577#117—44no—
578#117#4118yes—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—48no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4—44no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
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⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2412yes—
660C2×C42—24no—
661C2×C42—24no—
662C2×C42—24no—
663C2×C42—28no—
664C2×C42—44no—
665C2×C42C2411yescharacteristic
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2418yes—
684C2×C42C2414yes—
685C2×C42C2418yes—
686C2×C42C2412yes—
687#95C2418yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2414yes—
707#95C2418yes—
708#95C2414yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730C24C2512yes—
731C24C2512yes—
732C24C2511yescharacteristic
733#41—416no—
734#41—416no—
735C2×Q8—22no—
736C2×Q8—28no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—22no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—28no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—48no—
752C2×Q8—416no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—44no—
766C2×D4—48no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—22no—
770C22×C4—22no—
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—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—42no—
795C22×C4—44no—
796C22×C4—48no—
797C22×C4C2×#4114yes—
798C22×C4H(5,𝔽2)14yes—
799C22×C42−1+414yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—216no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—48no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4C2×#4118yes—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—28no—
874C22⋊C4—216no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4C2×#4118yes—
894C42—22no—
895C42—22no—
896C42—24no—
897C42—28no—
898C42—24no—
899C42—22no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—28no—
909C42—48no—
910C42—48no—
911C42—44no—
912C42—44no—
913C42—48no—
914C42—48no—
915C42C2×#4118yes—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23C22×#4112yes—
929C23C2×H(5,𝔽2)12yes—
930C23C2×2−1+412yes—
931C23C2611yescharacteristic
932Q8—416no—
933Q8—48no—
934Q8—48no—
935Q8—44no—
936Q8—44no—
937Q8—164no—
938D4—48no—
939D4—48no—
940D4—44no—
941D4—44no—
942D4—164no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—28no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—48no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—88no—
1001C2×C4—84no—
1002C2×C4—84no—
1003C2×C4—84no—
1004C2×C4—84no—
1005C2×C4—164no—
1006C2×C4#542116yes—
1007C2×C4C22×#4118yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4C2×H(5,𝔽2)12yes—
1012C2×C4C2×2−1+412yes—
1013C2×C4C2×2−1+412yes—
1014C2×C4#58514yes—
1015C22—24no—
1016C22—22no—
1017C22—22no—
1018C22—24no—
1019C22—44no—
1020C22—44no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—44no—
1028C22—44no—
1029C22C2×#54214yes—
1030C22C23×#4111yescharacteristic
1031C22C22×H(5,𝔽2)11yescharacteristic
1032C22C22×2−1+411yescharacteristic
1033C22C2×#58512yes—
1034C222−1+612yes—
1035C4—24no—
1036C4—28no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4—44no—
1045C4—42no—
1046C4—42no—
1047C4—44no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—42no—
1052C4—44no—
1053C4—44no—
1054C4—44no—
1055C4C2×#54214yes—
1056C4C2×#54214yes—
1057C2—24no—
1058C2—82no—
1059C2—82no—
1060C2C22×#54211yescharacteristic
1061C2#6283611yescharacteristic
1062C2#6288711yescharacteristic
1063C2#6295612yes—
1064C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42772C2semidirect
2. #42729C2semidirect
3. #42665C2semidirect
4. #42459C2semidirect
5. #40811C2semidirect
6. #40226C2semidirect
7. #39905C2semidirect
8. #39535C2semidirect
9. #38933C2semidirect
10. #38147C2semidirect
12. #35640C2semidirect
13. #35630C2semidirect
14. #35628C2semidirect
15. #35620C2semidirect
17. #35312C2semidirect
19. #35182C2semidirect
20. C2×#2565C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34266C2semidirect
24. #34214C2semidirect
25. #34189C2semidirect

Maximal subgroups

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

subgroupindex
#427722
#427292
#426652
#424592
#408112
#402262
#399052
#395352
#389332
#381472
#356492
#356402
#356302
#356282
#356202
#355302
#353122
#353082
#351822
C2×#25652
#348162
#347452
#342662
#342142
#341892