Finite Group Databasebeta

← #7678797

Subgroups — #7678797

Order 512.

4550 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59876C214yesmaximal, complemented
2#59443C214yesmaximal, complemented
3#59251C214yesmaximal, complemented
4#59246C214yesmaximal, complemented
5#45431C212yesmaximal, complemented
6#45431C212yesmaximal, complemented
7#45218C214yesmaximal, complemented
8#45163C212yesmaximal, complemented
9#45065C214yesmaximal, complemented
10#44979C212yesmaximal, complemented
11#39288C218yesmaximal, complemented
12#39151C214yesmaximal, complemented
13#36523C214yesmaximal, complemented
14#35630C212yesmaximal, complemented
15#35628C212yesmaximal
16#35179C211yesmaximal, characteristic, complemented
17#35160C212yesmaximal
18#34947C211yesmaximal, characteristic
19#34938C211yesmaximal, characteristic, complemented
20#34215C211yesmaximal, characteristic, complemented
21#34213C212yesmaximal, complemented
22#34189C211yesmaximal, characteristic
23C2×#2356C211yesmaximal, characteristic, complemented
24C4×#536C211yesmaximal, characteristic
25C2×#536C2211yescharacteristic
26C2×#533C2212yes—
27C2×#533C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30#2855C2214yes—
31#2852C2218yes—
32#2793C2218yes—
33#2777C2218yes—
34#2776C2218yes—
35#2776C2218yes—
36#2762C2218yes—
37#2762C2218yes—
38#2759C2218yes—
39#2758C2218yes—
40#2758C2218yes—
41#2745C2218yes—
42#2716C2218yes—
43#2689C2218yes—
44#2643C2218yes—
45#2627C2214yes—
46#2605C2218yes—
47#2605C2218yes—
48#2604C2218yes—
49#2594C2218yes—
50#2592C2214yes—
51#2592C2214yes—
52#2582C2214yes—
53#2581C2212yes—
54#2581C2212yes—
55#2577C2218yes—
56#2573C2218yes—
57#2570C2218yes—
58#2568C2214yes—
59#2568C2214yes—
60#2568C2212yes—
61#2568C2211yescharacteristic
62#2567C2212yes—
63#2567C2211yescharacteristic
64#2566C2212yes—
65#2565C2212yes—
66#2565C2214yes—
67#2564C2212yes—
68#2564C2212yes—
69#2563C2211yescharacteristic
70#2552C2212yes—
71#2551C2212yes—
72#2550C2212yes—
73#2550C2212yes—
74#2549C2212yes—
75#2549C2212yes—
76#2542C2211yescharacteristic
77#2533C2218yes—
78#2533C2218yes—
79#2532C2218yes—
80#2528C2218yes—
81#2528C2218yes—
82#2527C2218yes—
83#2525C2218yes—
84#2523C2218yes—
85#2514C2214yes—
86#2514C2214yes—
87#2514C2214yes—
88#2514C2214yes—
89#2514C2214yes—
90#2514C2218yes—
91#2513C2214yes—
92#2512C2214yes—
93#2511C2214yes—
94#2511C2214yes—
95#2511C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2497C2214yes—
99#2496C2214yes—
100#2495C2214yes—
101#2494C2214yes—
102#2493C2218yes—
103#2493C2218yes—
104#2492C2214yes—
105#2492C2214yes—
106#2489C2214yes—
107#2489C2214yes—
108#2488C2218yes—
109#2488C2218yes—
110#2465C2218yes—
111#2446C2218yes—
112#2440C2214yes—
113#2417C2214yes—
114#2399C2212yes—
115#2399C2212yes—
116#2396C2212yes—
117#2396C2212yes—
118#2373C2218yes—
119#2370C2214yes—
120#2370C2214yes—
121#2369C2214yes—
122#2368C2214yes—
123#2368C2214yes—
124#2365C2214yes—
125#2357C2212yes—
126#2357C2212yes—
127#2356C2212yes—
128#2356C2212yes—
129#2356C2214yes—
130#2356C2218yes—
131#2356C2212yes—
132#2356C2214yes—
133#2356C2212yes—
134#2356C2212yes—
135#2356C2212yes—
136#2355C2214yes—
137#2355C2214yes—
138#2355C2214yes—
139#2355C2214yes—
140#2355C2214yes—
141#2353C2214yes—
142#2353C2214yes—
143Q8×C4⋊C4C2214yes—
144#2331C2212yes—
145#2331C2212yes—
146#2329C2218yes—
147#2327C2212yes—
148#2326C2212yes—
149#2323C2214yes—
150#2322C2214yes—
151#2317C2211yescharacteristic
152#2317C2212yes—
153#2317C2212yes—
154#2314C2214yes—
155#2311C2211yescharacteristic
156#2311C2212yes—
157#2310C2211yescharacteristic
158#2310C2212yes—
159C4×C4⋊Q8C2212yes—
160C4×C4⋊Q8C2214yes—
161C4×#125C2214yes—
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2214yes—
165C4×C22⋊Q8C2218yes—
166C4×#123C2214yes—
167#2297C2212yes—
168#2296C2212yes—
169C2×#391C2212yes—
170C2×#387C2214yes—
171#2285C2212yes—
172#2285C2211yescharacteristic
173#2283C2212yes—
174#2283C2212yes—
175C2×#383C2212yes—
176C2×#382C2211yescharacteristic
177#2274C2212yes—
178#2274C2212yes—
179C4×#117C2211yescharacteristic
180C2×C4×C4⋊C4C2212yes—
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×#376C2212yes—
183C22×#41C2311yescharacteristic
184C23×Q8C2311yescharacteristic
185#536—28no—
186#533—216no—
187#533—28no—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2314yes—
194C2×#126C2318yes—
195C2×#125C2312yes—
196C2×#125C2312yes—
197C2×#125C2312yes—
198C2×#124C2312yes—
199C2×#123C2314yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C4×#41—28no—
207C2×C4×Q8—28no—
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2312yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2318yes—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2312yes—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2312yes—
223C2×#117C2311yescharacteristic
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2311yescharacteristic
227C2×#117C2312yes—
228C2×#117C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2312yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2314yes—
237C22×C42C2311yescharacteristic
238#401C2318yes—
239#401C2318yes—
240#401C2318yes—
241#400C2312yes—
242#400C2312yes—
243#400C2314yes—
244#400C2314yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#399C2312yes—
259#399C2312yes—
260#398C2314yes—
261#398C2318yes—
262#398C2318yes—
263#398C2314yes—
264#398C2314yes—
265#398C2314yes—
266#398C2314yes—
267#398C2314yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#396C2314yes—
274#396C2314yes—
275#396C2318yes—
276#395C2312yes—
277#395C2312yes—
278#395C2314yes—
279#395C2314yes—
280#395C2314yes—
281#395C2314yes—
282#395C2314yes—
283#395C2314yes—
284#393C2312yes—
285#393C2312yes—
286#393C2318yes—
287#393C2318yes—
288#391C2312yes—
289#391C2312yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2312yes—
300#391C2314yes—
301#391C2318yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2318yes—
306#391C2318yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#391C2318yes—
311#391C2318yes—
312#391C2314yes—
313#391C2314yes—
314#390C2312yes—
315#390C2312yes—
316#390C2312yes—
317#390C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2318yes—
332#389C2318yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#387C2314yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#386C2314yes—
380#386C2314yes—
381#386C2314yes—
382#386C2318yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2314yes—
390#385C2314yes—
391#384C2314yes—
392#384C2312yes—
393#384C2314yes—
394#384C2312yes—
395#384C2312yes—
396#384C2312yes—
397#384C2314yes—
398#383C2318yes—
399#383C2318yes—
400#383C2318yes—
401#383C2318yes—
402#383C2314yes—
403#383C2314yes—
404#383C2314yes—
405#383C2314yes—
406#382C2312yes—
407#382C2312yes—
408#382C2314yes—
409#382C2312yes—
410#382C2318yes—
411#382C2318yes—
412#382C2312yes—
413#382C2312yes—
414#382C2314yes—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2312yes—
418#382C2312yes—
419#381C2314yes—
420#381C2318yes—
421#381C2314yes—
422#381C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2312yes—
430#380C2312yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2318yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472#376C2312yes—
473#376C2314yes—
474#376C2314yes—
475#376C2314yes—
476#376C2318yes—
477#376C2314yes—
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2314yes—
481C2×#95C2312yes—
482C2×#95C2312yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C43C2312yes—
486C2×#41—24no—
487C2×#41—24no—
488C2×#41—24no—
489C22×Q8—24no—
490C22×Q8—24no—
491C22×Q8—24no—
492C22×Q8C2412yes—
493C22×Q8C2412yes—
494C22×Q8C2411yescharacteristic
495C22×Q8C2414yes—
496C22×Q8C2412yes—
497C22×Q8C2414yes—
498C22×Q8C2412yes—
499C22×D4C2412yes—
500C22×D4C2411yescharacteristic
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2412yes—
506C23×C4C2414yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C4⋊Q8—28no—
513C4⋊Q8—28no—
514C4⋊Q8—24no—
515C4⋊Q8—24no—
516C4⋊Q8—28no—
517C4⋊Q8—48no—
518#126—416no—
519#125—28no—
520#125—28no—
521#125—28no—
522#124—28no—
523#123—216no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—48no—
530C4×Q8—28no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—28no—
534C4×Q8—24no—
535C4×Q8—24no—
536C4×Q8—216no—
537C4×Q8—216no—
538C4×Q8—28no—
539C4×Q8—28no—
540C4×Q8—416no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—24no—
544C4×D4—24no—
545#117—24no—
546#117—28no—
547#117—28no—
548#117—24no—
549#117—28no—
550#117#4118yes—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—28no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—44no—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2412yes—
616C2×C42—28no—
617C2×C42—28no—
618C2×C42—28no—
619C2×C42—48no—
620C2×C42#4118yes—
621C2×C42C2412yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2418yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2418yes—
635C2×C42C2418yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2418yes—
640C2×C42C2418yes—
641C2×C42C2411yescharacteristic
642C2×C42C2412yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646#95C2412yes—
647#95C2411yescharacteristic
648#95C2411yescharacteristic
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2412yes—
656#95C2411yescharacteristic
657#95C2411yescharacteristic
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2412yes—
663#95C2412yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2412yes—
669#95C2412yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698C24C2512yes—
699C24C2511yescharacteristic
700#41—416no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—22no—
704C2×Q8—28no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—22no—
708C2×Q8—28no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—24no—
712C2×Q8—24no—
713C2×Q8—22no—
714C2×Q8—28no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8—44no—
720C2×Q8—416no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—44no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—42no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—42no—
750C22×C4C2×#4114yes—
751C22×C4C2×#4114yes—
752C22×C4C2×#4114yes—
753C22×C4C2×#4114yes—
754C22×C42−1+414yes—
755C22×C4C2514yes—
756C22×C4C2512yes—
757C22×C4C2518yes—
758C22×C4C2512yes—
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2512yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2511yescharacteristic
771C22×C4C2511yescharacteristic
772C22×C4C2514yes—
773C22×C4C2511yescharacteristic
774C22×C4C2512yes—
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—216no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—42no—
808C4⋊C4—42no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C4⋊C4—48no—
817C4⋊C4—44no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4C2×#4118yes—
823C22⋊C4—24no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—24no—
829C22⋊C4—216no—
830C22⋊C4—28no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4C2×#4118yes—
838C42—24no—
839C42—24no—
840C42—24no—
841C42—24no—
842C42—28no—
843C42—28no—
844C42—24no—
845C42—24no—
846C42—24no—
847C42—28no—
848C42—28no—
849C42—24no—
850C42—216no—
851C42—48no—
852C42—44no—
853C42—48no—
854C42—48no—
855C42—48no—
856C42—48no—
857C42—44no—
858C42C2×#4114yes—
859C42C2×#4114yes—
860C42C2×#4114yes—
861C42C2×#4114yes—
862C42C2×#4118yes—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—24no—
869C23—24no—
870C23C22×#4112yes—
871C23C22×#4112yes—
872C23C2×2−1+412yes—
873C23C2611yescharacteristic
874Q8—416no—
875Q8—48no—
876Q8—48no—
877Q8—44no—
878Q8—88no—
879Q8—84no—
880Q8—84no—
881D4—48no—
882D4—44no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—84no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4—88no—
940C2×C4#556116yes—
941C2×C4C22×#4112yes—
942C2×C4C22×#4112yes—
943C2×C4C22×#4112yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4118yes—
946C2×C4C22×#4112yes—
947C2×C4C22×#4112yes—
948C2×C4C22×#4112yes—
949C2×C4C22×#4112yes—
950C2×C4C2×2−1+412yes—
951C2×C4C2×2−1+412yes—
952C2×C4#58514yes—
953C22—24no—
954C22—22no—
955C22—22no—
956C22—24no—
957C22—44no—
958C22—42no—
959C22—42no—
960C22—44no—
961C22—42no—
962C22C2×#55614yes—
963C22C23×#4111yescharacteristic
964C22C23×#4111yescharacteristic
965C22C22×2−1+411yescharacteristic
966C22C2×#58512yes—
967C222−1+612yes—
968C4—24no—
969C4—28no—
970C4—22no—
971C4—22no—
972C4—22no—
973C4—22no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4—42no—
981C4—44no—
982C4—42no—
983C4—44no—
984C4—44no—
985C4—48no—
986C4—42no—
987C4—44no—
988C4C2×#55614yes—
989C4C2×#55614yes—
990C2—24no—
991C2—82no—
992C2C22×#55611yescharacteristic
993C2#6281511yescharacteristic
994C2#6286011yescharacteristic
995C2#6293212yes—
996C2#6299312yes—
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. #59876C2semidirect
2. #59443C2semidirect
3. #59251C2semidirect
4. #59246C2semidirect
5. #45431C2semidirect
6. #45431C2semidirect
7. #45218C2semidirect
8. #45163C2semidirect
9. #45065C2semidirect
10. #44979C2semidirect
11. #39288C2semidirect
12. #39151C2semidirect
13. #36523C2semidirect
14. #35630C2semidirect
16. #35179C2semidirect
19. #34938C2semidirect
20. #34215C2semidirect
21. #34213C2semidirect
23. C2×#2356C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#594432
#592512
#592462
#454312
#452182
#451632
#450652
#449792
#392882
#391512
#365232
#356302
#356282
#351792
#351602
#349472
#349382
#342152
#342132
#341892
C2×#23562
C4×#5362