Finite Group Databasebeta

← #7720086

Subgroups — #7720086

Order 512.

4982 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51057C218yesmaximal, complemented
2#51055C214yesmaximal, complemented
3#51054C214yesmaximal, complemented
4#45083C212yesmaximal, complemented
5#45056C212yesmaximal, complemented
6#44995C214yesmaximal, complemented
7#44979C212yesmaximal, complemented
8#44947C212yesmaximal, complemented
9#44905C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39769C212yesmaximal, complemented
12#37750C214yesmaximal, complemented
13#37749C214yesmaximal, complemented
14#37384C214yesmaximal, complemented
15#36134C212yesmaximal, complemented
16#36115C212yesmaximal, complemented
17#35326C214yesmaximal, complemented
18#35317C211yesmaximal, characteristic, complemented
19#35279C211yesmaximal, characteristic, complemented
20#35190C211yesmaximal, characteristic
21#34625C211yesmaximal, characteristic, complemented
22#34393C211yesmaximal, characteristic, complemented
23#34371C211yesmaximal, characteristic, complemented
24#34123C211yesmaximal, characteristic, complemented
25C2×#536C2214yes—
26C2×#533C2214yes—
27C2×#532C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C2×#529C2214yes—
30C2×C4×#41C2211yescharacteristic
31#2868C2212yes—
32#2858C2212yes—
33#2857C2214yes—
34#2857C2214yes—
35#2850C2214yes—
36#2850C2214yes—
37#2796C2218yes—
38#2794C2218yes—
39#2794C2218yes—
40#2777C2218yes—
41#2773C2218yes—
42#2768C2218yes—
43#2751C2218yes—
44#2748C2218yes—
45#2743C2218yes—
46#2741C2218yes—
47#2740C2218yes—
48#2738C2218yes—
49#2696C2218yes—
50#2695C2218yes—
51#2694C2218yes—
52#2693C2218yes—
53#2692C2218yes—
54#2690C2218yes—
55#2689C2218yes—
56#2687C2218yes—
57#2667C2212yes—
58#2666C2214yes—
59#2665C2212yes—
60#2660C2212yes—
61#2658C2212yes—
62#2658C2212yes—
63#2647C2212yes—
64#2642C2214yes—
65#2640C2214yes—
66#2635C2214yes—
67#2629C2212yes—
68#2628C2212yes—
69#2628C2214yes—
70#2611C2218yes—
71#2611C2218yes—
72#2604C2218yes—
73#2604C2218yes—
74#2598C2214yes—
75#2592C2214yes—
76#2580C2214yes—
77#2570C2214yes—
78#2570C2214yes—
79#2568C2211yescharacteristic
80#2568C2212yes—
81#2567C2212yes—
82#2564C2218yes—
83#2564C2218yes—
84#2563C2212yes—
85#2552C2214yes—
86#2548C2211yescharacteristic
87#2542C2212yes—
88#2542C2212yes—
89#2542C2211yescharacteristic
90#2542C2214yes—
91#2542C2212yes—
92#2541C2211yescharacteristic
93#2538C2214yes—
94#2513C2214yes—
95#2512C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2501C2214yes—
99#2501C2212yes—
100#2501C2212yes—
101#2500C2212yes—
102#2498C2218yes—
103#2498C2218yes—
104#2487C2214yes—
105#2477C2218yes—
106#2471C2218yes—
107#2471C2218yes—
108#2470C2218yes—
109#2467C2218yes—
110#2465C2218yes—
111#2458C2218yes—
112#2457C2218yes—
113#2450C2218yes—
114#2448C2214yes—
115#2447C2214yes—
116#2447C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2445C2214yes—
120#2441C2218yes—
121#2438C2218yes—
122#2431C2212yes—
123#2429C2214yes—
124#2429C2214yes—
125#2427C2214yes—
126#2426C2214yes—
127#2423C2218yes—
128#2409C2212yes—
129#2409C2212yes—
130#2407C2214yes—
131#2402C2212yes—
132#2399C2212yes—
133#2396C2214yes—
134#2381C2214yes—
135#2377C2214yes—
136#2366C2212yes—
137#2366C2214yes—
138#2365C2212yes—
139#2365C2212yes—
140#2365C2212yes—
141#2357C2212yes—
142#2356C2211yescharacteristic
143#2356C2211yescharacteristic
144#2354C2214yes—
145#2354C2214yes—
146#2353C2212yes—
147#2353C2212yes—
148Q8×C4⋊C4C2214yes—
149#2349C2211yescharacteristic
150#2349C2212yes—
151#2349C2211yescharacteristic
152#2346C2212yes—
153#2345C2214yes—
154#2343C2214yes—
155#2341C2212yes—
156Q8×C22⋊C4C2214yes—
157#2339C2212yes—
158#2339C2212yes—
159#2331C2212yes—
160#2331C2212yes—
161#2328C2212yes—
162#2327C2214yes—
163#2327C2214yes—
164#2326C2214yes—
165#2326C2212yes—
166#2326C2214yes—
167#2324C2214yes—
168#2318C2214yes—
169#2317C2212yes—
170#2313C2214yes—
171#2311C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×#125C2212yes—
174#2295C2212yes—
175#2290C2214yes—
176#2285C2211yescharacteristic
177#2283C2212yes—
178#2283C2211yescharacteristic
179#2283C2211yescharacteristic
180C42×D4C2212yes—
181C4×#117C2211yescharacteristic
182C2×#376C2212yes—
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×Q8C2312yes—
186#536—416no—
187#533—416no—
188#532—28no—
189C2×C4⋊Q8—28no—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×#127C2312yes—
199C2×#127C2311yescharacteristic
200#529—416no—
201C2×#126C2318yes—
202C2×#125C2312yes—
203C2×#125C2318yes—
204C2×#124C2312yes—
205C2×#124C2314yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#121C2314yes—
220C4×#41—28no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2318yes—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2318yes—
244C2×#117C2318yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C42C2312yes—
248C22×C42C2314yes—
249C22×C42C2311yescharacteristic
250#400C2318yes—
251#400C2318yes—
252#400C2314yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2318yes—
260#400C2318yes—
261#399C2314yes—
262#399C2318yes—
263#399C2318yes—
264#399C2314yes—
265#399C2314yes—
266#399C2314yes—
267#399C2318yes—
268#399C2314yes—
269#399C2318yes—
270#399C2314yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#396C2314yes—
288#396C2314yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#395C2314yes—
293#395C2314yes—
294#395C2314yes—
295#395C2314yes—
296#395C2314yes—
297#394C2314yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#393C2314yes—
302#393C2314yes—
303#393C2318yes—
304#393C2318yes—
305#393C2314yes—
306#392C2314yes—
307#392C2318yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2318yes—
318#391C2318yes—
319#391C2312yes—
320#391C2312yes—
321#390C2314yes—
322#390C2314yes—
323#390C2318yes—
324#390C2312yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2312yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2318yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2314yes—
360#388C2314yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#387C2314yes—
366#387C2314yes—
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#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2314yes—
391#386C2314yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2314yes—
396#386C2314yes—
397#386C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2318yes—
406#385C2314yes—
407#385C2314yes—
408#384C2312yes—
409#384C2314yes—
410#384C2314yes—
411#384C2314yes—
412#384C2312yes—
413#384C2312yes—
414#384C2314yes—
415#384C2314yes—
416#383C2312yes—
417#383C2312yes—
418#383C2312yes—
419#383C2312yes—
420#382C2312yes—
421#382C2314yes—
422#382C2312yes—
423#382C2312yes—
424#382C2312yes—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2314yes—
428#381C2312yes—
429#381C2312yes—
430#381C2314yes—
431#381C2314yes—
432#381C2318yes—
433#380C2318yes—
434#380C2318yes—
435#380C2318yes—
436#380C2318yes—
437#380C2318yes—
438#380C2314yes—
439#380C2312yes—
440#380C2311yescharacteristic
441#380C2312yes—
442#380C2311yescharacteristic
443#380C2312yes—
444#380C2312yes—
445#380C2318yes—
446#380C2312yes—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2314yes—
474#376C2312yes—
475#376C2314yes—
476#376C2312yes—
477#376C2314yes—
478#376C2312yes—
479#376C2312yes—
480#376C2311yescharacteristic
481#376C2311yescharacteristic
482C2×#95C2312yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C2×#95C2312yes—
486C43C2312yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—28no—
490C2×#41—42no—
491C2×#41—48no—
492C22×Q8—28no—
493C22×Q8—48no—
494C22×Q8C2414yes—
495C22×Q8C2412yes—
496C22×Q8C2411yescharacteristic
497C22×Q8C2414yes—
498C22×Q8C2414yes—
499C22×D4C2412yes—
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2411yescharacteristic
503C22×D4C2418yes—
504C22×D4C2412yes—
505C22×D4C2414yes—
506C23×C4C2412yes—
507C23×C4C2414yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2414yes—
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2418yes—
516C23×C4C2411yescharacteristic
517C4⋊Q8—28no—
518C4⋊Q8—28no—
519C4⋊Q8—28no—
520C4⋊Q8—28no—
521C4⋊Q8—24no—
522C4⋊Q8—28no—
523C4⋊Q8—216no—
524C4⋊Q8—48no—
525#127—28no—
526#127—24no—
527#126—416no—
528#125—28no—
529#125—416no—
530#124—28no—
531#124—216no—
532#124—44no—
533#124—48no—
534#123—416no—
535#123—416no—
536#123—416no—
537C22⋊Q8—416no—
538C22⋊Q8—416no—
539C22⋊Q8—48no—
540C22⋊Q8—48no—
541C22⋊Q8—48no—
542C22⋊Q8—416no—
543#121—28no—
544#121—28no—
545#121—48no—
546C4×Q8—24no—
547C4×Q8—24no—
548C4×Q8—48no—
549C4×Q8—48no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×Q8—416no—
553C4×D4—28no—
554C4×D4—28no—
555C4×D4—28no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—48no—
561C4×D4—44no—
562C4×D4—48no—
563C4×D4—416no—
564#117—24no—
565#117—28no—
566#117—28no—
567#117—44no—
568#117—416no—
569#117—416no—
570C2×C4⋊C4—28no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C42—28no—
640C2×C42—216no—
641C2×C42#4118yes—
642C2×C42C2414yes—
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2412yes—
646C2×C42C2414yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2412yes—
654C2×C42C2418yes—
655C2×C42C2418yes—
656C2×C42C2418yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664#95C2411yescharacteristic
665#95C2412yes—
666#95C2411yescharacteristic
667#95C2412yes—
668#95C2412yes—
669#95C2412yes—
670#95C2414yes—
671#95C2412yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2418yes—
677#95C2411yescharacteristic
678#95C2411yescharacteristic
679#95C2412yes—
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688#95C2414yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2412yes—
698#95C2412yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710C24C2514yes—
711C24C2511yescharacteristic
712C24C2512yes—
713#41—416no—
714#41—816no—
715C2×Q8—22no—
716C2×Q8—24no—
717C2×Q8—28no—
718C2×Q8—28no—
719C2×Q8—28no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—22no—
724C2×Q8—22no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—48no—
728C2×Q8—816no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—22no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—28no—
738C2×D4—24no—
739C2×D4—22no—
740C2×D4—24no—
741C2×D4—42no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D42−1+414yes—
747C22×C4—24no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—42no—
761C22×C4—44no—
762C22×C4—42no—
763C22×C4—48no—
764C22×C4—44no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—48no—
771C22×C4C2×#4114yes—
772C22×C4C2×#4114yes—
773C22×C4C2×#4114yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2512yes—
784C22×C4C2518yes—
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—216no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—216no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C22⋊C4—24no—
837C22⋊C4—28no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—216no—
845C22⋊C4—216no—
846C22⋊C4—48no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—28no—
866C42—28no—
867C42—28no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—28no—
872C42—24no—
873C42—24no—
874C42—42no—
875C42—42no—
876C42—48no—
877C42—48no—
878C42—48no—
879C42C2×#4114yes—
880C42C2×#4114yes—
881C42C2×#4114yes—
882C42C2×#4114yes—
883C42H(5,𝔽2)18yes—
884C23—22no—
885C23—22no—
886C23—24no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—24no—
892C23—24no—
893C23—28no—
894C23—24no—
895C23—24no—
896C23—28no—
897C23C22×#4112yes—
898C23C2×2−1+414yes—
899C23C2611yescharacteristic
900Q8—416no—
901Q8—44no—
902Q8—416no—
903Q8—48no—
904Q8—88no—
905D4—28no—
906D4—48no—
907D4—48no—
908D4—48no—
909D4—84no—
910D4—816no—
911D4—88no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—28no—
922C2×C4—28no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—44no—
960C2×C4—416no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—84no—
964C2×C4—88no—
965C2×C4—88no—
966C2×C4—88no—
967C2×C4—816no—
968C2×C4C22×#4112yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4112yes—
973C2×C4C22×#4112yes—
974C2×C4C2×H(5,𝔽2)14yes—
975C2×C4C2×H(5,𝔽2)14yes—
976C2×C4C2×H(5,𝔽2)14yes—
977C2×C4C2×2−1+412yes—
978C2×C4#58512yes—
979C22—22no—
980C22—22no—
981C22—24no—
982C22—22no—
983C22—28no—
984C22—42no—
985C22—42no—
986C22—44no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22—48no—
993C22—48no—
994C22C23×#4111yescharacteristic
995C22C22×H(5,𝔽2)12yes—
996C22C22×2−1+411yescharacteristic
997C22C2×#58511yescharacteristic
998C222−1+612yes—
999C4—22no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—24no—
1004C4—24no—
1005C4—42no—
1006C4—44no—
1007C4—48no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4—44no—
1018C4#349514yes—
1019C4#350814yes—
1020C2—42no—
1021C2—44no—
1022C2—84no—
1023C2C2×#350811yescharacteristic
1024C2C2×#349511yescharacteristic
1025C2#6286011yescharacteristic
1026C2#6292512yes—
1027C2#6294212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35190C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51057C2semidirect
2. #51055C2semidirect
3. #51054C2semidirect
4. #45083C2semidirect
5. #45056C2semidirect
6. #44995C2semidirect
7. #44979C2semidirect
8. #44947C2semidirect
9. #44905C2semidirect
10. #39771C2semidirect
11. #39769C2semidirect
12. #37750C2semidirect
13. #37749C2semidirect
14. #37384C2semidirect
15. #36134C2semidirect
16. #36115C2semidirect
17. #35326C2semidirect
18. #35317C2semidirect
19. #35279C2semidirect
21. #34625C2semidirect
22. #34393C2semidirect
23. #34371C2semidirect
24. #34123C2semidirect

Maximal subgroups

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

subgroupindex
#510572
#510552
#510542
#450832
#450562
#449952
#449792
#449472
#449052
#397712
#397692
#377502
#377492
#373842
#361342
#361152
#353262
#353172
#352792
#351902
#346252
#343932
#343712
#341232