Finite Group Databasebeta

← #7652625

Subgroups — #7652625

Order 512.

4628 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42899C214yesmaximal, complemented
2#42868C214yesmaximal, complemented
3#42863C214yesmaximal, complemented
4#42848C214yesmaximal, complemented
5#42022C218yesmaximal, complemented
6#40201C214yesmaximal, complemented
7#40099C214yesmaximal, complemented
8#39791C214yesmaximal, complemented
9#39226C214yesmaximal, complemented
10#38489C218yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35639C211yesmaximal, characteristic, complemented
14#35639C211yesmaximal, characteristic, complemented
15#35618C211yesmaximal, characteristic
16#35530C211yesmaximal, characteristic
17#35339C211yesmaximal, characteristic, complemented
18#35286C211yesmaximal, characteristic, complemented
19#35153C211yesmaximal, characteristic
20C2×#2565C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34816C211yesmaximal, characteristic, complemented
23#34276C211yesmaximal, characteristic, complemented
24#34276C211yesmaximal, characteristic, complemented
25#34249C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2864C2214yes—
36#2859C2214yes—
37#2854C2214yes—
38#2839C2218yes—
39#2837C2218yes—
40#2802C2218yes—
41#2796C2218yes—
42#2791C2218yes—
43#2790C2218yes—
44#2787C2218yes—
45#2783C2218yes—
46#2781C2218yes—
47#2777C2218yes—
48#2776C2218yes—
49#2773C2218yes—
50#2771C2218yes—
51#2767C2218yes—
52#2744C2218yes—
53#2721C2218yes—
54#2718C2218yes—
55#2694C2218yes—
56#2667C2218yes—
57#2664C2218yes—
58#2655C2218yes—
59#2654C2218yes—
60#2652C2218yes—
61#2651C2218yes—
62#2647C2214yes—
63#2647C2214yes—
64#2618C2214yes—
65#2596C2218yes—
66#2594C2218yes—
67#2585C2218yes—
68#2579C2214yes—
69#2579C2214yes—
70#2577C2218yes—
71#2575C2218yes—
72#2571C2214yes—
73#2570C2214yes—
74#2570C2214yes—
75#2569C2218yes—
76#2565C2214yes—
77#2565C2214yes—
78#2565C2214yes—
79#2565C2214yes—
80#2553C2218yes—
81#2552C2214yes—
82#2514C2212yes—
83#2514C2212yes—
84#2513C2212yes—
85#2513C2212yes—
86#2512C2212yes—
87#2512C2212yes—
88#2511C2212yes—
89#2511C2212yes—
90#2510C2214yes—
91#2510C2214yes—
92#2504C2212yes—
93#2503C2212yes—
94#2502C2212yes—
95#2501C2212yes—
96#2500C2212yes—
97#2500C2212yes—
98#2499C2212yes—
99#2499C2212yes—
100#2498C2218yes—
101#2498C2218yes—
102#2487C2214yes—
103#2487C2214yes—
104#2481C2214yes—
105#2481C2214yes—
106#2454C2214yes—
107#2454C2214yes—
108#2453C2214yes—
109#2453C2214yes—
110#2448C2214yes—
111#2448C2214yes—
112#2446C2214yes—
113#2446C2214yes—
114#2444C2218yes—
115#2443C2218yes—
116#2442C2218yes—
117#2442C2214yes—
118#2442C2214yes—
119#2441C2214yes—
120#2441C2214yes—
121#2429C2214yes—
122#2429C2214yes—
123#2426C2214yes—
124#2426C2214yes—
125#2423C2214yes—
126#2423C2214yes—
127#2423C2214yes—
128#2422C2214yes—
129#2421C2214yes—
130#2421C2214yes—
131#2421C2214yes—
132#2420C2214yes—
133#2401C2214yes—
134#2401C2214yes—
135C2×#398C2214yes—
136#2362C2214yes—
137#2362C2214yes—
138#2360C2214yes—
139#2360C2214yes—
140#2359C2218yes—
141#2359C2218yes—
142#2351C2214yes—
143#2351C2214yes—
144Q8×C4⋊C4C2214yes—
145Q8×C4⋊C4C2214yes—
146#2336C2218yes—
147#2335C2218yes—
148#2327C2212yes—
149#2327C2212yes—
150#2326C2212yes—
151#2326C2212yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2214yes—
156#2317C2211yescharacteristic
157#2316C2211yescharacteristic
158#2316C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162C4×C4⋊Q8C2212yes—
163C4×C4⋊Q8C2212yes—
164C4×#126C2214yes—
165C4×#126C2214yes—
166C4×#124C2212yes—
167C4×#124C2212yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2214yes—
177C2×#391C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#387C2214yes—
180#2285C2211yescharacteristic
181#2285C2211yescharacteristic
182C2×#384C2211yescharacteristic
183C2×#382C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190#537—44no—
191#536—28no—
192#536—28no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×#126C2314yes—
196C2×#126C2314yes—
197C2×#125—44no—
198C2×#125C2314yes—
199C2×#125C2314yes—
200C2×#125C2318yes—
201C2×#124C2312yes—
202C2×#124C2312yes—
203C2×#123C2314yes—
204C2×#123C2314yes—
205C2×#123C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2312yes—
213#520—44no—
214#520—44no—
215#519—28no—
216#519—44no—
217C2×C4×Q8—44no—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2314yes—
239C2×#117C2314yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2312yes—
256#401C2314yes—
257#401C2314yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2314yes—
293#397C2314yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2314yes—
300#397C2314yes—
301#397C2314yes—
302#397C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2318yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2318yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2318yes—
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#387C2318yes—
407#387C2318yes—
408#386C2314yes—
409#386C2314yes—
410#386C2312yes—
411#386C2312yes—
412#386C2318yes—
413#386C2312yes—
414#386C2314yes—
415#386C2314yes—
416#386C2312yes—
417#386C2314yes—
418#386C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2312yes—
422#385C2314yes—
423#385C2312yes—
424#385C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2312yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2318yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#383C2314yes—
443#383C2314yes—
444#382C2314yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2318yes—
452#382C2318yes—
453#382C2312yes—
454#382C2312yes—
455#381C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2318yes—
464#380C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493#376C2312yes—
494#376C2312yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2312yes—
499C43C2312yes—
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#4118yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2414yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C4⋊Q8—28no—
533C4⋊Q8—28no—
534#126—48no—
535#126—48no—
536#125—48no—
537#125—48no—
538#125—416no—
539#124—28no—
540#124—28no—
541#123—216no—
542#123—216no—
543#123—416no—
544C22⋊Q8—216no—
545C22⋊Q8—216no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548#121—44no—
549#121—44no—
550#121—48no—
551C4×Q8—216no—
552C4×Q8—216no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—44no—
559C4×Q8—44no—
560C4×Q8—44no—
561C4×D4—44no—
562C4×D4—44no—
563C4×D4—48no—
564C4×D4—48no—
565#117—216no—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—48no—
573#117—44no—
574#117—44no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—48no—
579C2×C4⋊C4—44no—
580C2×C4⋊C4—44no—
581C2×C4⋊C4—44no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C42—24no—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—44no—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2418yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2414yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685#95C2418yes—
686#95C2418yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728C24C2512yes—
729C24C2512yes—
730C24C2511yescharacteristic
731#41—416no—
732#41—416no—
733C2×Q8—232no—
734C2×Q8—22no—
735C2×Q8—22no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—22no—
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—22no—
744C2×Q8C2×#4118yes—
745C2×Q8C2×#4118yes—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—24no—
751C2×D4—24no—
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—44no—
759C2×D4—48no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—42no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4C2×#4118yes—
789C22×C4C2×#4114yes—
790C22×C4H(5,𝔽2)14yes—
791C22×C42−1+414yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C4⋊C4—216no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—216no—
820C4⋊C4—216no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—216no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—216no—
867C22⋊C4—216no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C42—216no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—22no—
896C42—24no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—24no—
901C42—28no—
902C42—48no—
903C42—44no—
904C42—44no—
905C42—44no—
906C42—44no—
907C42—44no—
908C42—44no—
909C42—44no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23C22×#4112yes—
923C23C2×H(5,𝔽2)12yes—
924C23C2×2−1+412yes—
925C23C2611yescharacteristic
926Q8—216no—
927Q8—216no—
928Q8—44no—
929Q8—44no—
930D4—48no—
931D4—48no—
932D4—44no—
933D4—44no—
934D4—164no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—216no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
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—22no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—28no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—22no—
987C2×C4—48no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—48no—
991C2×C4—48no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4—84no—
996C2×C4—164no—
997C2×C4—164no—
998C2×C4#539116yes—
999C2×C4C22×#4118yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C2×H(5,𝔽2)12yes—
1003C2×C4C2×H(5,𝔽2)12yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4#58514yes—
1007C22—24no—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—44no—
1012C22—44no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—44no—
1020C22—44no—
1021C22C2×#53914yes—
1022C22C23×#4111yescharacteristic
1023C22C22×H(5,𝔽2)11yescharacteristic
1024C22C22×2−1+411yescharacteristic
1025C22C2×#58512yes—
1026C222−1+612yes—
1027C4—28no—
1028C4—24no—
1029C4—44no—
1030C4—44no—
1031C4—44no—
1032C4—44no—
1033C4—42no—
1034C4—42no—
1035C4—44no—
1036C4—44no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4C2×#53914yes—
1048C4C2×#53914yes—
1049C2—24no—
1050C2—82no—
1051C2—82no—
1052C2C22×#53911yescharacteristic
1053C2#6283611yescharacteristic
1054C2#6288711yescharacteristic
1055C2#6292812yes—
1056C2#6300712yes—
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. #42899C2semidirect
2. #42868C2semidirect
3. #42863C2semidirect
4. #42848C2semidirect
5. #42022C2semidirect
6. #40201C2semidirect
7. #40099C2semidirect
8. #39791C2semidirect
9. #39226C2semidirect
10. #38489C2semidirect
11. #35673C2semidirect
12. #35673C2semidirect
13. #35639C2semidirect
14. #35639C2semidirect
17. #35339C2semidirect
18. #35286C2semidirect
20. C2×#2565C2semidirect
21. #34816C2semidirect
22. #34816C2semidirect
23. #34276C2semidirect
24. #34276C2semidirect
25. #34249C2semidirect

Maximal subgroups

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

subgroupindex
#428992
#428682
#428632
#428482
#420222
#402012
#400992
#397912
#392262
#384892
#356732
#356392
#356182
#355302
#353392
#352862
#351532
C2×#25652
#348162
#342762
#342492