Finite Group Databasebeta

← #7643383

Subgroups — #7643383

Order 512.

5336 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39730C214yesmaximal, complemented
2#39346C214yesmaximal, complemented
3#39142C214yesmaximal, complemented
4#38936C214yesmaximal, complemented
5#38062C214yesmaximal, complemented
6#38061C214yesmaximal, complemented
7#37670C214yesmaximal, complemented
8#37669C214yesmaximal, complemented
9#37289C212yesmaximal, complemented
10#37286C212yesmaximal, complemented
11#37284C212yesmaximal, complemented
12#37283C212yesmaximal, complemented
13#36624C212yesmaximal, complemented
14#35549C214yesmaximal, complemented
15#35546C214yesmaximal, complemented
16#35294C211yesmaximal, characteristic, complemented
17#35293C211yesmaximal, characteristic, complemented
18#35291C212yesmaximal, complemented
19#35288C212yesmaximal, complemented
20#35278C212yesmaximal, complemented
21#35277C212yesmaximal, complemented
22#34226C212yesmaximal, complemented
23#34012C211yesmaximal, characteristic, complemented
24C2×#542C2214yes—
25C2×#540C2214yes—
26C2×#532C2212yes—
27C2×#525C2214yes—
28C23×C42C2211yescharacteristic
29#2868C2211yescharacteristic, complemented
30#2867C2211yescharacteristic, complemented
31#2862C2211yescharacteristic, complemented
32#2859C2212yescomplemented
33#2859C2211yescharacteristic, complemented
34#2858C2212yescomplemented
35#2857C2212yes—
36#2857C2212yes—
37#2856C2212yes—
38#2856C2212yes—
39#2854C2214yes—
40#2854C2214yes—
41#2850C2214yes—
42#2850C2214yes—
43#2847C2214yes—
44#2847C2214yes—
45#2795C2214yescomplemented
46#2785C2214yescomplemented
47#2782C2214yescomplemented
48#2781C2218yescomplemented
49#2778C2218yes—
50#2760C2214yes—
51#2756C2218yes—
52#2752C2214yes—
53#2749C2218yes—
54#2718C2218yescomplemented
55#2708C2218yes—
56#2706C2218yes—
57#2705C2218yes—
58#2696C2218yes—
59#2693C2218yes—
60#2686C2218yes—
61#2680C2214yescomplemented
62#2678C2218yes—
63#2670C2214yes—
64#2668C2214yes—
65#2645C2214yescomplemented
66#2644C2214yescomplemented
67#2641C2214yescomplemented
68#2640C2214yescomplemented
69#2629C2212yes—
70#2628C2212yes—
71#2625C2214yes—
72#2624C2214yes—
73#2620C2214yes—
74#2619C2214yes—
75#2619C2212yes—
76#2619C2212yes—
77#2578C2218yescomplemented
78#2576C2218yescomplemented
79#2572C2218yescomplemented
80#2570C2214yescomplemented
81#2553C2218yescomplemented
82#2550C2214yescomplemented
83#2544C2214yescomplemented
84#2544C2214yescomplemented
85#2518C2218yescomplemented
86#2518C2218yescomplemented
87#2514C2214yescomplemented
88#2513C2214yescomplemented
89#2512C2214yescomplemented
90#2512C2214yescomplemented
91#2510C2218yescomplemented
92#2509C2214yescomplemented
93#2508C2214yescomplemented
94#2495C2214yes—
95#2494C2214yes—
96#2491C2214yes—
97#2491C2214yes—
98#2490C2214yes—
99#2489C2214yes—
100#2488C2218yescomplemented
101#2467C2218yes—
102#2459C2218yes—
103#2457C2218yes—
104#2457C2218yes—
105#2454C2214yescomplemented
106#2453C2214yescomplemented
107#2452C2214yescomplemented
108#2452C2214yescomplemented
109#2448C2214yescomplemented
110#2447C2214yescomplemented
111#2445C2214yescomplemented
112#2445C2214yescomplemented
113#2445C2214yescomplemented
114#2445C2214yescomplemented
115#2444C2218yes—
116#2441C2214yes—
117#2439C2214yes—
118#2431C2214yes—
119#2431C2214yes—
120#2428C2214yes—
121#2428C2214yes—
122#2428C2214yes—
123#2428C2214yes—
124#2427C2218yes—
125#2427C2214yes—
126#2426C2214yes—
127#2425C2218yes—
128#2422C2214yes—
129#2422C2214yes—
130#2421C2214yes—
131#2420C2218yes—
132#2420C2214yes—
133#2367C2214yescomplemented
134#2367C2214yescomplemented
135#2363C2214yes—
136#2363C2214yes—
137#2357C2214yescomplemented
138#2349C2214yescomplemented
139#2341C2214yes—
140#2339C2214yes—
141#2331C2212yescomplemented
142#2330C2212yescomplemented
143#2328C2214yescomplemented
144#2328C2212yescomplemented
145#2328C2212yescomplemented
146#2326C2214yescomplemented
147#2324C2214yes—
148#2324C2214yes—
149#2324C2214yes—
150#2323C2214yes—
151#2320C2214yescomplemented
152#2319C2214yescomplemented
153#2319C2214yescomplemented
154C4×C4⋊Q8C2212yescomplemented
155C4×C4⋊Q8C2212yescomplemented
156C4×#127C2212yescomplemented
157C4×#127C2212yescomplemented
158C4×#121C2214yes—
159C4×#121C2214yes—
160C4×#121C2214yes—
161C4×#121C2214yes—
162#2297C2214yes—
163#2285C2212yes—
164#2285C2212yes—
165#2285C2211yescharacteristic
166#2285C2211yescharacteristic
167#2285C2212yes—
168#2283C2212yes—
169#2283C2212yes—
170#2283C2212yes—
171#2283C2212yes—
172#2283C2212yes—
173#2283C2212yes—
174#2280C2212yes—
175#2280C2212yes—
176#2280C2211yescharacteristic
177#2280C2211yescharacteristic
178#2275C2214yescomplemented
179C4×#117C2211yescharacteristic
180C4×#117C2212yes—
181C4×#117C2212yes—
182C4×#117C2211yescharacteristic
183C22×#41C2314yes—
184C24×C4C2312yes—
185C24×C4C2311yescharacteristic
186#542—416no—
187#540—416no—
188#532—216no—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2314yes—
192C2×#127C2312yes—
193C2×#127C2312yes—
194C2×#127C2312yes—
195C2×#127C2314yes—
196C2×#127C2314yes—
197C2×#126C2318yes—
198C2×#125C2312yes—
199C2×#125C2314yes—
200C2×#124C2314yes—
201C2×#124C2314yes—
202C2×#124C2314yes—
203C2×#124C2318yes—
204#525—416no—
205C2×#123C2318yes—
206C2×#123C2318yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2318yes—
221C2×#121C2318yes—
222C2×#120C2318yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2318yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2314yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C22×C42—28no—
245C22×C42C2312yes—
246C22×C42C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252#401C2318yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#399C2318yes—
259#399C2314yes—
260#398C2318yes—
261#398C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#395C2314yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2314yes—
279#394C2318yes—
280#394C2318yes—
281#394C2314yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2314yes—
291#392C2314yes—
292#392C2318yes—
293#392C2314yes—
294#392C2318yes—
295#392C2318yes—
296#391C2314yes—
297#391C2314yes—
298#391C2318yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2318yes—
312#390C2318yes—
313#390C2314yes—
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2318yes—
332#389C2314yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#384C2312yes—
381#384C2312yes—
382#384C2314yes—
383#384C2312yes—
384#384C2311yescharacteristic
385#384C2312yes—
386#384C2311yescharacteristic
387#383C2312yes—
388#383C2318yes—
389#383C2312yes—
390#383C2312yes—
391#383C2312yes—
392#382C2314yes—
393#382C2314yes—
394#382C2318yes—
395#382C2312yes—
396#382C2312yes—
397#382C2312yes—
398#382C2312yes—
399#382C2312yes—
400#382C2312yes—
401#382C2312yes—
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2312yes—
405#381C2318yes—
406#381C2318yes—
407#381C2312yes—
408#381C2312yes—
409#381C2312yes—
410#381C2312yes—
411#381C2312yes—
412#381C2311yescharacteristic
413#381C2311yescharacteristic
414#380C2318yes—
415#380C2318yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2312yes—
423#380C2312yes—
424#380C2312yes—
425#380C2312yes—
426#380C2312yes—
427#380C2312yes—
428#380C2312yes—
429#380C2312yes—
430#380C2312yes—
431#380C2312yes—
432#380C2312yes—
433#380C2312yes—
434#379C2311yescharacteristic
435#379C2311yescharacteristic
436#379C2312yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
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—
472#376C2312yes—
473#376C2312yes—
474#376C2312yes—
475#376C2312yes—
476#376C2311yescharacteristic
477#376C2311yescharacteristic
478#376C2312yes—
479C2×#95C2318yes—
480C43C2312yes—
481C43C2311yescharacteristic
482C43C2311yescharacteristic
483C25C2411yescharacteristic
484C2×#41—216no—
485C2×#41—48no—
486C2×#41—48no—
487C22×Q8C2414yes—
488C22×Q8C2414yes—
489C22×D4C2414yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2418yes—
493C22×D4C2418yes—
494C22×D4C2418yes—
495C22×D4C2414yes—
496C22×D4C2418yes—
497C22×D4C2414yes—
498C23×C4—28no—
499C23×C4—24no—
500C23×C4—28no—
501C23×C4—44no—
502C23×C4—42no—
503C23×C4—42no—
504C23×C4C2412yes—
505C23×C4C2412yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2418yes—
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C23×C4C2418yes—
516C23×C4C2418yes—
517C4⋊Q8—28no—
518C4⋊Q8—44no—
519C4⋊Q8—48no—
520#127—28no—
521#127—44no—
522#127—44no—
523#127—48no—
524#127—48no—
525#126—416no—
526#125—44no—
527#125—48no—
528#124—216no—
529#124—48no—
530#124—48no—
531#124—416no—
532#123—416no—
533#123—416no—
534#123—416no—
535#123—416no—
536C22⋊Q8—216no—
537C22⋊Q8—416no—
538C22⋊Q8—48no—
539#121—216no—
540#121—216no—
541#121—216no—
542#121—216no—
543#121—416no—
544#121—416no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—48no—
549#120—416no—
550C4×Q8—48no—
551C4×Q8—48no—
552C4×D4—216no—
553C4×D4—216no—
554C4×D4—48no—
555C4×D4—48no—
556C4×D4—48no—
557C4×D4—48no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—416no—
561C4×D4—416no—
562#117—28no—
563#117—28no—
564#117—42no—
565#117—42no—
566#117—44no—
567#117—44no—
568#117—42no—
569#117—42no—
570#117—48no—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2411yescharacteristic
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2411yescharacteristic
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C42—24no—
638C2×C42—28no—
639C2×C42—28no—
640C2×C42—28no—
641C2×C42—28no—
642C2×C42—28no—
643C2×C42#4118yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2412yes—
657C2×C42C2411yescharacteristic
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2418yes—
666C2×C42C2418yes—
667C2×C42C2418yes—
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671#95C2412yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2412yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2412yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712C24—22no—
713C24—24no—
714C24—42no—
715C24—41no—
716C24—41no—
717C24C2518yes—
718C24C2511yescharacteristic
719C24C2512yes—
720#41—832no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—28no—
724C2×Q8—48no—
725C2×Q8—44no—
726C2×D4—216no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—44no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—216no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—432no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—416no—
789C22×C4C2×#4114yes—
790C22×C4C2×#4118yes—
791C22×C4H(5,𝔽2)18yes—
792C22×C4C2511yescharacteristic
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2518yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2518yes—
804C22×C4C2518yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2511yescharacteristic
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—216no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—42no—
826C4⋊C4—41no—
827C4⋊C4—42no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—41no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—44no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4—216no—
848C22⋊C4—216no—
849C22⋊C4—216no—
850C22⋊C4—216no—
851C22⋊C4—216no—
852C22⋊C4—42no—
853C22⋊C4—41no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—42no—
859C22⋊C4—41no—
860C22⋊C4—41no—
861C22⋊C4—41no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C42—22no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—22no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—24no—
898C42—22no—
899C42—48no—
900C42—48no—
901C42—48no—
902C42C2×#4114yes—
903C42C2×#4118yes—
904C42C2×#4114yes—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—21no—
910C23—21no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—28no—
916C23—28no—
917C23—28no—
918C23—28no—
919C23—28no—
920C23—28no—
921C23—28no—
922C23—48no—
923C23—44no—
924C23—44no—
925C23—48no—
926C23—44no—
927C23C22×#4112yes—
928C23C2×H(5,𝔽2)14yes—
929C23C2611yescharacteristic
930Q8—416no—
931Q8—164no—
932D4—416no—
933D4—416no—
934D4—416no—
935D4—816no—
936D4—816no—
937D4—816no—
938D4—164no—
939D4—168no—
940D4—164no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—28no—
948C2×C4—216no—
949C2×C4—216no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—28no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—28no—
964C2×C4—28no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—28no—
985C2×C4—28no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—48no—
994C2×C4—48no—
995C2×C4—44no—
996C2×C4—48no—
997C2×C4—48no—
998C2×C4—816no—
999C2×C4—168no—
1000C2×C4—168no—
1001C2×C4C22×#4112yes—
1002C2×C4C22×#4114yes—
1003C2×C4C22×#4112yes—
1004C2×C4C22×#4114yes—
1005C2×C4C2×H(5,𝔽2)14yes—
1006C2×C4C2×H(5,𝔽2)14yes—
1007C2×C4#58512yes—
1008C2×C4#58512yes—
1009C2×C4#58514yes—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—22no—
1015C22—416no—
1016C22—42no—
1017C22—41no—
1018C22—42no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—42no—
1023C22—48no—
1024C22—48no—
1025C22—48no—
1026C22—48no—
1027C22—48no—
1028C22—48no—
1029C22—48no—
1030C22C23×#4111yescharacteristic
1031C22C22×H(5,𝔽2)12yes—
1032C22C2×#58512yes—
1033C22C2×#58511yescharacteristic
1034C22C2×#58511yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—22no—
1038C4—42no—
1039C4—48no—
1040C4—42no—
1041C4—48no—
1042C4—41no—
1043C4—41no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—48no—
1048C4—42no—
1049C4—42no—
1050C4—41no—
1051C4—41no—
1052C4—42no—
1053C4#345514yes—
1054C4#349418yes—
1055C2—42no—
1056C2—44no—
1057C2—88no—
1058C2C2×#345511yescharacteristic
1059C2C2×#349412yes—
1060C2#6283411yescharacteristic
1061C2#6283612yes—
1062C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39730C2semidirect
2. #39346C2semidirect
3. #39142C2semidirect
4. #38936C2semidirect
5. #38062C2semidirect
6. #38061C2semidirect
7. #37670C2semidirect
8. #37669C2semidirect
9. #37289C2semidirect
10. #37286C2semidirect
11. #37284C2semidirect
12. #37283C2semidirect
13. #36624C2semidirect
14. #35549C2semidirect
15. #35546C2semidirect
16. #35294C2semidirect
17. #35293C2semidirect
18. #35291C2semidirect
19. #35288C2semidirect
20. #35278C2semidirect
21. #35277C2semidirect
22. #34226C2semidirect
23. #34012C2semidirect
29. #2868C22semidirect
30. #2867C22semidirect
31. #2862C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2858C22semidirect
45. #2795C22semidirect
46. #2785C22semidirect
47. #2782C22semidirect
48. #2781C22semidirect
54. #2718C22semidirect
61. #2680C22semidirect
65. #2645C22semidirect
66. #2644C22semidirect
67. #2641C22semidirect
68. #2640C22semidirect
77. #2578C22semidirect
78. #2576C22semidirect
79. #2572C22semidirect
80. #2570C22semidirect
81. #2553C22semidirect
82. #2550C22semidirect
83. #2544C22semidirect
84. #2544C22semidirect
85. #2518C22semidirect
86. #2518C22semidirect
87. #2514C22semidirect
88. #2513C22semidirect
89. #2512C22semidirect
90. #2512C22semidirect
91. #2510C22semidirect
92. #2509C22semidirect
93. #2508C22semidirect
100. #2488C22semidirect
105. #2454C22semidirect
106. #2453C22semidirect
107. #2452C22semidirect
108. #2452C22semidirect
109. #2448C22semidirect
110. #2447C22semidirect
111. #2445C22semidirect
112. #2445C22semidirect
113. #2445C22semidirect
114. #2445C22semidirect
133. #2367C22semidirect
134. #2367C22semidirect
137. #2357C22semidirect
138. #2349C22semidirect
141. #2331C22semidirect
142. #2330C22semidirect
143. #2328C22semidirect
144. #2328C22semidirect
145. #2328C22semidirect
146. #2326C22semidirect
151. #2320C22semidirect
152. #2319C22semidirect
153. #2319C22semidirect
154. C4×C4⋊Q8C22semidirect
155. C4×C4⋊Q8C22semidirect
156. C4×#127C22semidirect
157. C4×#127C22semidirect
178. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#397302
#393462
#391422
#389362
#380622
#380612
#376702
#376692
#372892
#372862
#372842
#372832
#366242
#355492
#355462
#352942
#352932
#352912
#352882
#352782
#352772
#342262
#340122