Finite Group Databasebeta

← #7644148

Subgroups — #7644148

Order 512.

4560 conjugacy classes of subgroups.

The subgroup lattice has 1027 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42701C214yesmaximal, complemented
2#42700C214yesmaximal, complemented
3#42692C214yesmaximal, complemented
4#42691C214yesmaximal, complemented
5#42526C214yesmaximal, complemented
6#42525C214yesmaximal, complemented
7#42513C214yesmaximal, complemented
8#42512C214yesmaximal, complemented
9#37464C214yesmaximal, complemented
10#37463C214yesmaximal, complemented
11#36980C214yesmaximal, complemented
12#36975C214yesmaximal, complemented
13#35628C212yesmaximal, complemented
14#35619C212yesmaximal, complemented
15#35545C212yesmaximal, complemented
16#35519C212yesmaximal, complemented
17#35179C211yesmaximal, characteristic, complemented
18#35178C211yesmaximal, characteristic
19#34642C211yesmaximal, characteristic, complemented
20#34637C211yesmaximal, characteristic
21#34213C211yesmaximal, characteristic, complemented
22#34206C211yesmaximal, characteristic
23C2×#2320C211yesmaximal, characteristic, complemented
24C2×#536C2212yes—
25C2×#533C2211yescharacteristic
26C2×#533C2212yes—
27C2×#532C2211yescharacteristic
28C2×#520C2212yes—
29C22×C4×Q8C2211yescharacteristic
30#2855C2214yes—
31#2854C2214yes—
32#2839C2218yes—
33#2838C2218yes—
34#2831C2218yes—
35#2830C2218yes—
36#2775C2218yes—
37#2774C2218yes—
38#2772C2218yes—
39#2770C2218yes—
40#2767C2218yes—
41#2766C2218yes—
42#2764C2218yes—
43#2763C2218yes—
44#2761C2218yes—
45#2759C2218yes—
46#2758C2218yes—
47#2757C2218yes—
48#2754C2218yes—
49#2737C2218yes—
50#2723C2218yes—
51#2698C2218yes—
52#2666C2218yes—
53#2665C2218yes—
54#2660C2212yes—
55#2660C2212yes—
56#2660C2212yes—
57#2660C2212yes—
58#2659C2212yes—
59#2659C2212yes—
60#2659C2212yes—
61#2659C2212yes—
62#2655C2218yes—
63#2652C2218yes—
64#2651C2218yes—
65#2650C2218yes—
66#2642C2212yes—
67#2641C2212yes—
68#2640C2212yes—
69#2640C2212yes—
70#2639C2212yes—
71#2639C2212yes—
72#2639C2212yes—
73#2639C2212yes—
74#2638C2218yes—
75#2637C2218yes—
76#2627C2214yes—
77#2618C2214yes—
78#2592C2214yes—
79#2592C2214yes—
80#2582C2212yes—
81#2582C2214yes—
82#2582C2212yes—
83#2581C2214yes—
84#2581C2214yes—
85#2580C2214yes—
86#2568C2214yes—
87#2568C2214yes—
88#2568C2212yes—
89#2567C2212yes—
90#2565C2214yes—
91#2548C2212yes—
92#2546C2212yes—
93#2545C2214yes—
94#2538C2212yes—
95#2538C2214yes—
96#2538C2212yes—
97#2536C2214yes—
98#2520C2218yes—
99#2515C2218yes—
100#2514C2214yes—
101#2513C2214yes—
102#2512C2214yes—
103#2511C2214yes—
104#2510C2218yes—
105#2503C2214yes—
106#2502C2214yes—
107#2499C2214yes—
108#2499C2214yes—
109#2497C2214yes—
110#2496C2214yes—
111#2495C2214yes—
112#2494C2214yes—
113#2492C2214yes—
114#2492C2214yes—
115#2489C2214yes—
116#2489C2214yes—
117#2488C2218yes—
118#2488C2218yes—
119#2481C2218yes—
120#2468C2218yes—
121#2465C2218yes—
122#2450C2218yes—
123#2449C2218yes—
124#2447C2214yes—
125#2447C2214yes—
126#2446C2214yes—
127#2446C2214yes—
128#2442C2214yes—
129#2441C2214yes—
130#2440C2214yes—
131#2439C2214yes—
132#2419C2218yes—
133#2419C2218yes—
134#2399C2214yes—
135#2399C2214yes—
136#2398C2214yes—
137#2398C2214yes—
138#2370C2214yes—
139#2369C2212yes—
140#2367C2214yes—
141#2366C2212yes—
142#2365C2212yes—
143#2365C2212yes—
144#2355C2214yes—
145#2355C2212yes—
146#2354C2212yes—
147#2352C2214yes—
148Q8×C4⋊C4C2212yes—
149D4×C4⋊C4C2212yes—
150#2329C2214yes—
151#2325C2214yes—
152#2320C2214yes—
153#2320C2214yes—
154#2320C2214yes—
155#2320C2214yes—
156#2317C2212yes—
157#2317C2212yes—
158#2311C2212yes—
159#2311C2212yes—
160#2310C2212yes—
161C4×C22⋊Q8C2214yes—
162C4×#121C2214yes—
163#2297C2212yes—
164#2297C2212yes—
165C2×#391C2211yescharacteristic
166C2×#391C2211yescharacteristic
167C2×#389C2211yescharacteristic
168C2×#389C2211yescharacteristic
169C2×#387C2212yes—
170C2×#387C2212yes—
171#2285C2212yes—
172#2285C2211yescharacteristic
173#2285C2211yescharacteristic
174C2×#383C2212yes—
175C2×#382C2212yes—
176#2274C2212yes—
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×#376C2211yescharacteristic
179C22×#41C2312yes—
180C23×Q8C2311yescharacteristic
181#536—48no—
182#533—28no—
183#533—48no—
184#532—28no—
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2312yes—
191C2×#127C2311yescharacteristic
192C2×#126C2318yes—
193C2×#125C2312yes—
194C2×#125C2312yes—
195C2×#125C2312yes—
196C2×#124C2312yes—
197C2×#124C2314yes—
198C2×#123C2318yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2318yes—
206C2×#121C2312yes—
207C2×#121C2312yes—
208#520—48no—
209C2×C4×Q8—28no—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2314yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241#401C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2314yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#399C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2314yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2318yes—
282#397C2318yes—
283#397C2314yes—
284#397C2314yes—
285#397C2314yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#395C2318yes—
292#395C2314yes—
293#395C2318yes—
294#395C2314yes—
295#395C2314yes—
296#395C2314yes—
297#395C2314yes—
298#395C2314yes—
299#395C2314yes—
300#395C2314yes—
301#394C2314yes—
302#394C2318yes—
303#394C2314yes—
304#394C2314yes—
305#394C2314yes—
306#393C2318yes—
307#393C2318yes—
308#393C2314yes—
309#393C2318yes—
310#393C2314yes—
311#393C2314yes—
312#393C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2318yes—
331#391C2318yes—
332#391C2312yes—
333#391C2312yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
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#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2314yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#384C2314yes—
404#384C2314yes—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2312yes—
410#384C2312yes—
411#383C2318yes—
412#383C2318yes—
413#383C2318yes—
414#382C2314yes—
415#382C2318yes—
416#382C2318yes—
417#382C2314yes—
418#382C2318yes—
419#382C2318yes—
420#382C2312yes—
421#382C2312yes—
422#382C2312yes—
423#382C2312yes—
424#381C2318yes—
425#381C2318yes—
426#381C2318yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#380C2312yes—
435#380C2314yes—
436#380C2314yes—
437#380C2318yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461#376C2312yes—
462#376C2312yes—
463#376C2312yes—
464#376C2312yes—
465C2×#95C2312yes—
466C2×#95C2311yescharacteristic
467C2×#95C2311yescharacteristic
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2312yes—
471C2×#95C2312yes—
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#95C2312yes—
476C2×#41—28no—
477C2×#41—28no—
478C2×#41—28no—
479C22×Q8—24no—
480C22×Q8—24no—
481C22×Q8—24no—
482C22×Q8C2412yes—
483C22×Q8C2412yes—
484C22×Q8C2412yes—
485C22×Q8C2412yes—
486C22×Q8C2412yes—
487C22×Q8C2414yes—
488C22×Q8C2414yes—
489C22×D4C2414yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C22×D4C2412yes—
493C23×C4C2414yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2411yescharacteristic
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2418yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C4⋊Q8—24no—
507C4⋊Q8—24no—
508C4⋊Q8—24no—
509C4⋊Q8—44no—
510C4⋊Q8—44no—
511C4⋊Q8—48no—
512#127—24no—
513#126—88no—
514#125—28no—
515#125—44no—
516#125—44no—
517#124—28no—
518#124—48no—
519#123—416no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—48no—
523C22⋊Q8—48no—
524C22⋊Q8—48no—
525C22⋊Q8—48no—
526C22⋊Q8—88no—
527#121—28no—
528#121—28no—
529C4×Q8—28no—
530C4×Q8—28no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—28no—
534C4×Q8—28no—
535C4×Q8—48no—
536C4×Q8—48no—
537C4×Q8—48no—
538C4×Q8—84no—
539C4×D4—28no—
540C4×D4—28no—
541C4×D4—48no—
542C4×D4—416no—
543C4×D4—84no—
544#117—28no—
545#117—28no—
546#117—28no—
547#117—48no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—28no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—48no—
553C2×C4⋊C4—82no—
554C2×C4⋊C4—82no—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C42—28no—
623C2×C42—24no—
624C2×C42—24no—
625C2×C42—82no—
626C2×C42#4118yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2418yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2414yes—
640C2×C42C2418yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#95C2412yes—
646#95C2412yes—
647#95C2412yes—
648#95C2412yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2414yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2418yes—
677#95C2414yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691C24C2514yes—
692C24C2511yescharacteristic
693#41—432no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—24no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—24no—
704C2×Q8—24no—
705C2×Q8—42no—
706C2×Q8—42no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—42no—
711C2×Q8—42no—
712C2×Q8—44no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—416no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—42no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4C2×#4114yes—
763C22×C4C2×#4114yes—
764C22×C4C2×#4114yes—
765C22×C4H(5,𝔽2)14yes—
766C22×C42−1+414yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2512yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—48no—
822C4⋊C4—42no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—42no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—48no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—44no—
853C22⋊C4—48no—
854C22⋊C4—44no—
855C42—28no—
856C42—28no—
857C42—28no—
858C42—24no—
859C42—24no—
860C42—28no—
861C42—28no—
862C42—24no—
863C42—24no—
864C42—44no—
865C42—44no—
866C42—48no—
867C42—48no—
868C42—48no—
869C42C2×#4114yes—
870C42C2×#4114yes—
871C42C2×#4114yes—
872C42C2×#4114yes—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23C22×#4112yes—
885C23C2×H(5,𝔽2)12yes—
886C23C2×2−1+412yes—
887C23C2611yescharacteristic
888Q8—48no—
889Q8—48no—
890Q8—48no—
891Q8—48no—
892Q8—84no—
893Q8—88no—
894Q8—88no—
895D4—48no—
896D4—416no—
897D4—48no—
898D4—84no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—44no—
953C2×C4—44no—
954C2×C4—48no—
955C2×C4—48no—
956C2×C4—416no—
957C2×C4—84no—
958C2×C4—82no—
959C2×C4—82no—
960C2×C4—84no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—168no—
964C2×C4#542116yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4C22×#4112yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C2×H(5,𝔽2)12yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C2×C4C2×2−1+412yes—
974C2×C4C2×2−1+412yes—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—44no—
988C22C2×#54214yes—
989C22C23×#4111yescharacteristic
990C22C22×H(5,𝔽2)11yescharacteristic
991C22C22×2−1+411yescharacteristic
992C22H(7,𝔽2)11yescharacteristic
993C222−1+611yescharacteristic
994C222−1+611yescharacteristic
995C222−1+611yescharacteristic
996C4—22no—
997C4—22no—
998C4—22no—
999C4—22no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4—44no—
1004C4—42no—
1005C4—44no—
1006C4—44no—
1007C4—42no—
1008C4—44no—
1009C4—42no—
1010C4—44no—
1011C4—44no—
1012C4—42no—
1013C4—44no—
1014C4—44no—
1015C4C2×#54214yes—
1016C4C2×#54214yes—
1017C2—24no—
1018C2—84no—
1019C2C22×#54211yescharacteristic
1020C2#6284511yescharacteristic
1021C2#6286011yescharacteristic
1022C2#6287811yescharacteristic
1023C2#6287911yescharacteristic
1024C2#6288811yescharacteristic
1025C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
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. #42700C2semidirect
3. #42692C2semidirect
4. #42691C2semidirect
5. #42526C2semidirect
6. #42525C2semidirect
7. #42513C2semidirect
8. #42512C2semidirect
9. #37464C2semidirect
10. #37463C2semidirect
11. #36980C2semidirect
12. #36975C2semidirect
13. #35628C2semidirect
14. #35619C2semidirect
15. #35545C2semidirect
16. #35519C2semidirect
17. #35179C2semidirect
19. #34642C2semidirect
21. #34213C2semidirect
23. C2×#2320C2semidirect

Maximal subgroups

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

subgroupindex
#427012
#427002
#426922
#426912
#425262
#425252
#425132
#425122
#374642
#374632
#369802
#369752
#356282
#356192
#355452
#355192
#351792
#351782
#346422
#346372
#342132
#342062
C2×#23202