Finite Group Databasebeta

← #8108045

Subgroups — #8108045

Order 512.

4288 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53147C212yesmaximal, complemented
2#53131C214yesmaximal, complemented
3#53030C212yesmaximal, complemented
4#52991C214yesmaximal, complemented
5#45253C214yesmaximal, complemented
6#45185C214yesmaximal, complemented
7#45118C214yesmaximal, complemented
8#42980C212yesmaximal
9#42956C214yesmaximal
10#42863C214yesmaximal, complemented
11#42728C214yesmaximal, complemented
12#42697C212yesmaximal, complemented
13#42636C214yesmaximal, complemented
14#42489C214yesmaximal, complemented
15#36574C212yesmaximal, complemented
16#36189C212yesmaximal, complemented
17#36189C212yesmaximal, complemented
18#36181C212yesmaximal, complemented
19#35319C211yesmaximal, characteristic, complemented
20#35286C212yesmaximal, complemented
21#35286C211yesmaximal, characteristic, complemented
22#35284C212yesmaximal, complemented
23#34551C211yesmaximal, characteristic
24C2×#552C2214yes—
25C2×#541C2212yes—
26#2868C2211yescharacteristic
27#2859C2212yes—
28#2859C2212yes—
29#2859C2212yes—
30#2859C2212yes—
31#2859C2211yescharacteristic
32#2857C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2841C2218yes—
36#2839C2218yes—
37#2839C2218yes—
38#2839C2218yes—
39#2839C2218yes—
40#2835C2214yes—
41#2822C2214yes—
42#2802C2218yes—
43#2794C2214yes—
44#2794C2218yes—
45#2792C2214yes—
46#2791C2218yes—
47#2771C2218yes—
48#2767C2218yes—
49#2767C2218yes—
50#2744C2218yes—
51#2743C2218yes—
52#2739C2218yes—
53#2726C2218yes—
54#2722C2218yes—
55#2722C2214yes—
56#2719C2218yes—
57#2695C2218yes—
58#2695C2218yes—
59#2693C2214yes—
60#2667C2218yes—
61#2655C2218yes—
62#2652C2218yes—
63#2647C2212yes—
64#2647C2212yes—
65#2647C2214yes—
66#2647C2214yes—
67#2647C2214yes—
68#2642C2212yes—
69#2629C2218yes—
70#2629C2214yes—
71#2621C2212yes—
72#2609C2214yes—
73#2584C2214yes—
74#2584C2214yes—
75#2581C2214yes—
76#2575C2218yes—
77#2571C2214yes—
78#2571C2214yes—
79#2571C2214yes—
80#2570C2214yes—
81#2570C2214yes—
82#2565C2214yes—
83#2553C2218yes—
84#2552C2214yes—
85#2552C2214yes—
86#2552C2214yes—
87#2517C2214yes—
88#2511C2214yes—
89#2511C2214yes—
90#2509C2214yes—
91#2509C2214yes—
92#2508C2214yes—
93#2508C2214yes—
94#2507C2214yes—
95#2507C2214yes—
96#2507C2214yes—
97#2507C2214yes—
98#2506C2214yes—
99#2506C2214yes—
100#2506C2214yes—
101#2506C2214yes—
102#2503C2214yes—
103#2499C2214yes—
104#2497C2214yes—
105#2497C2214yes—
106#2497C2214yes—
107#2497C2214yes—
108#2496C2214yes—
109#2496C2218yes—
110#2496C2214yes—
111#2496C2214yes—
112#2496C2214yes—
113#2487C2214yes—
114#2487C2214yes—
115#2486C2214yes—
116#2486C2214yes—
117#2475C2218yes—
118#2453C2214yes—
119#2453C2214yes—
120#2446C2214yes—
121#2446C2214yes—
122#2442C2214yes—
123#2442C2214yes—
124#2442C2214yes—
125#2442C2214yes—
126#2442C2214yes—
127#2442C2214yes—
128#2442C2214yes—
129#2442C2214yes—
130#2441C2214yes—
131#2441C2214yes—
132#2441C2218yes—
133#2429C2214yes—
134#2429C2214yes—
135#2423C2214yes—
136#2423C2214yes—
137#2417C2214yes—
138#2417C2214yes—
139#2402C2212yes—
140#2402C2211yescharacteristic
141#2401C2212yes—
142#2401C2212yes—
143#2401C2212yes—
144#2398C2211yescharacteristic
145#2398C2212yes—
146#2396C2211yescharacteristic
147#2396C2212yes—
148#2395C2212yes—
149#2395C2212yes—
150#2395C2212yes—
151#2392C2212yes—
152#2392C2211yescharacteristic
153#2370C2214yes—
154#2370C2214yes—
155#2360C2214yes—
156#2360C2214yes—
157#2352C2214yes—
158#2352C2214yes—
159#2351C2214yes—
160#2345C2214yes—
161#2345C2214yes—
162#2344C2214yes—
163#2344C2214yes—
164#2330C2214yes—
165#2327C2212yes—
166#2317C2214yes—
167#2317C2212yes—
168#2316C2212yes—
169#2316C2214yes—
170#2314C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174#2285C2211yescharacteristic
175#2285C2212yes—
176C2×#384C2212yes—
177C2×#384C2211yescharacteristic
178C42×Q8C2211yescharacteristic
179C42×D4C2212yes—
180C42×D4C2211yescharacteristic
181C4×#117C2212yes—
182C4×#117C2211yescharacteristic
183#552—416no—
184#541—48no—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×#126C2318yes—
189C2×#126C2318yes—
190C2×#125C2314yes—
191C2×#125C2318yes—
192C2×#125C2314yes—
193C2×#125C2314yes—
194C2×#125C2314yes—
195C2×#125C2312yes—
196C2×#125C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2312yes—
211C2×#117C2312yes—
212C2×#117C2311yescharacteristic
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2314yes—
216C2×#117C2311yescharacteristic
217C2×#117C2318yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2314yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225#401C2312yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2312yes—
240#400C2312yes—
241#400C2312yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2312yes—
249#400C2312yes—
250#400C2312yes—
251#400C2311yescharacteristic
252#400C2312yes—
253#399C2318yes—
254#399C2318yes—
255#399C2312yes—
256#399C2311yescharacteristic
257#398C2318yes—
258#398C2318yes—
259#398C2311yescharacteristic
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2314yes—
264#398C2312yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2312yes—
280#398C2312yes—
281#398C2312yes—
282#397C2312yes—
283#397C2314yes—
284#397C2318yes—
285#397C2314yes—
286#397C2311yescharacteristic
287#397C2312yes—
288#397C2312yes—
289#397C2312yes—
290#397C2312yes—
291#397C2312yes—
292#397C2312yes—
293#397C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2312yes—
298#396C2318yes—
299#396C2312yes—
300#396C2312yes—
301#395C2318yes—
302#395C2311yescharacteristic
303#394C2311yescharacteristic
304#394C2312yes—
305#394C2312yes—
306#394C2312yes—
307#394C2312yes—
308#393C2311yescharacteristic
309#393C2312yes—
310#392C2311yescharacteristic
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
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#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#386C2318yes—
385#386C2318yes—
386#385C2318yes—
387#385C2314yes—
388#385C2314yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#384C2312yes—
393#384C2312yes—
394#384C2312yes—
395#384C2314yes—
396#384C2314yes—
397#384C2314yes—
398#384C2314yes—
399#384C2314yes—
400#384C2318yes—
401#384C2314yes—
402#384C2312yes—
403#384C2314yes—
404#382C2312yes—
405#382C2314yes—
406#382C2314yes—
407#382C2314yes—
408#382C2314yes—
409#382C2314yes—
410#382C2318yes—
411#382C2312yes—
412#382C2314yes—
413#382C2318yes—
414#381C2318yes—
415#381C2318yes—
416#380C2314yes—
417#380C2314yes—
418#380C2318yes—
419#380C2318yes—
420#380C2318yes—
421#380C2318yes—
422#380C2314yes—
423#380C2314yes—
424#380C2318yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2312yes—
473#376C2311yescharacteristic
474#376C2312yes—
475#376C2311yescharacteristic
476#376C2312yes—
477C43C2312yes—
478C43C2311yescharacteristic
479C43C2311yescharacteristic
480C22×Q8C2414yes—
481C22×Q8C2411yescharacteristic
482C22×D4C2412yes—
483C22×D4C2411yescharacteristic
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2418yes—
490C23×C4C2414yes—
491C4⋊Q8—28no—
492C4⋊Q8—44no—
493C4⋊Q8—44no—
494#126—416no—
495#126—416no—
496#125—48no—
497#125—48no—
498#125—48no—
499#125—44no—
500#125—416no—
501#125—48no—
502#125—416no—
503#123—416no—
504C22⋊Q8—216no—
505C22⋊Q8—48no—
506C22⋊Q8—48no—
507C4×Q8—42no—
508C4×Q8—44no—
509C4×Q8—48no—
510C4×Q8—48no—
511C4×Q8—48no—
512C4×D4—28no—
513C4×D4—28no—
514C4×D4—28no—
515C4×D4—44no—
516C4×D4—42no—
517#117—24no—
518#117—28no—
519#117—28no—
520#117—44no—
521#117—42no—
522#117—416no—
523#117—48no—
524C2×C4⋊C4—216no—
525C2×C4⋊C4—48no—
526C2×C4⋊C4—48no—
527C2×C4⋊C4—44no—
528C2×C4⋊C4—48no—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2411yescharacteristic
595C2×C22⋊C4C2411yescharacteristic
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2418yes—
601C2×C42—28no—
602C2×C42—24no—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2412yes—
609C2×C42C2411yescharacteristic
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2412yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2418yes—
624C2×C42C2418yes—
625C2×C42C2418yes—
626C2×C42C2418yes—
627C2×C42C2411yescharacteristic
628#95C2412yes—
629#95C2412yes—
630#95C2412yes—
631#95C2412yes—
632#95C2412yes—
633#95C2412yes—
634#95C2412yes—
635#95C2412yes—
636#95C2412yes—
637#95C2412yes—
638#95C2412yes—
639#95C2412yes—
640#95C2411yescharacteristic
641#95C2412yes—
642#95C2412yes—
643#95C2412yes—
644#95C2412yes—
645#95C2412yes—
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2411yescharacteristic
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2412yes—
655#95C2412yes—
656#95C2411yescharacteristic
657#95C2411yescharacteristic
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2414yes—
677#95C2418yes—
678#95C2418yes—
679C24C2511yescharacteristic
680C24C2512yes—
681C2×Q8—28no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—41no—
685C2×Q8—42no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—41no—
690C2×D4—42no—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—24no—
695C22×C4—216no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—48no—
706C22×C4—48no—
707C22×C4—44no—
708C22×C4—48no—
709C22×C4H(5,𝔽2)14yes—
710C22×C42−1+418yes—
711C22×C4C2511yescharacteristic
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2511yescharacteristic
716C22×C4C2518yes—
717C22×C4C2512yes—
718C22×C4C2511yescharacteristic
719C22×C4C2512yes—
720C22×C4C2518yes—
721C22×C4C2518yes—
722C22×C4C2512yes—
723C22×C4C2518yes—
724C22×C4C2512yes—
725C22×C4C2512yes—
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C22×C4C2512yes—
730C22×C4C2511yescharacteristic
731C22×C4C2512yes—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—24no—
735C4⋊C4—216no—
736C4⋊C4—24no—
737C4⋊C4—216no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—41no—
758C4⋊C4—41no—
759C4⋊C4—48no—
760C4⋊C4—41no—
761C4⋊C4—42no—
762C4⋊C4—41no—
763C4⋊C4—42no—
764C4⋊C4—42no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C22⋊C4—28no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—216no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—42no—
795C22⋊C4—41no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—48no—
804C42—28no—
805C42—22no—
806C42—22no—
807C42—24no—
808C42—24no—
809C42—24no—
810C42—24no—
811C42—22no—
812C42—24no—
813C42—24no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—22no—
818C42—24no—
819C42—24no—
820C42—22no—
821C42—24no—
822C42—24no—
823C42—24no—
824C42—48no—
825C42—48no—
826C42—48no—
827C42—48no—
828C422−1+414yes—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—21no—
837C23—22no—
838C23—22no—
839C23C2×H(5,𝔽2)12yes—
840C23C2×2−1+414yes—
841C23C2611yescharacteristic
842Q8—44no—
843Q8—416no—
844D4—48no—
845D4—44no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—28no—
851C2×C4—216no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—28no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—28no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—28no—
898C2×C4—28no—
899C2×C4—48no—
900C2×C4—48no—
901C2×C4—48no—
902C2×C4—816no—
903C2×C4—164no—
904C2×C4C2×H(5,𝔽2)12yes—
905C2×C4C2×H(5,𝔽2)12yes—
906C2×C4C2×2−1+414yes—
907C2×C4C2×2−1+412yes—
908C2×C4C2×2−1+414yes—
909C2×C4C2×2−1+414yes—
910C2×C4#58512yes—
911C2×C4#58514yes—
912C22—22no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22C22×H(5,𝔽2)11yescharacteristic
925C22C22×2−1+411yescharacteristic
926C22C22×2−1+412yes—
927C22C2×#58511yescharacteristic
928C22C2×#58512yes—
929C4—22no—
930C4—24no—
931C4—42no—
932C4—48no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—48no—
939C4—48no—
940C4—42no—
941C4—42no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—48no—
946C4—41no—
947C4—42no—
948C4#355914yes—
949C4#356318yes—
950C2—42no—
951C2—44no—
952C2C2×#355911yescharacteristic
953C2C2×#356312yes—
954C2#6283512yes—
955C2#6283711yescharacteristic
956C2#6283911yescharacteristic
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. #53147C2semidirect
2. #53131C2semidirect
3. #53030C2semidirect
4. #52991C2semidirect
5. #45253C2semidirect
6. #45185C2semidirect
7. #45118C2semidirect
10. #42863C2semidirect
11. #42728C2semidirect
12. #42697C2semidirect
13. #42636C2semidirect
14. #42489C2semidirect
15. #36574C2semidirect
16. #36189C2semidirect
17. #36189C2semidirect
18. #36181C2semidirect
19. #35319C2semidirect
20. #35286C2semidirect
21. #35286C2semidirect
22. #35284C2semidirect

Maximal subgroups

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

subgroupindex
#531472
#531312
#530302
#529912
#452532
#451852
#451182
#429802
#429562
#428632
#427282
#426972
#426362
#424892
#365742
#361892
#361812
#353192
#352862
#352842
#345512