Finite Group Databasebeta

← #7647864

Subgroups — #7647864

Order 512.

5008 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41967C218yesmaximal, complemented
2#40657C214yesmaximal, complemented
3#40650C214yesmaximal, complemented
4#39500C212yesmaximal, complemented
5#39374C212yesmaximal, complemented
6#39188C212yesmaximal, complemented
7#39185C212yesmaximal, complemented
8#37858C214yesmaximal, complemented
9#37669C214yesmaximal, complemented
10#37636C212yesmaximal, complemented
11#37626C212yesmaximal, complemented
12#37366C214yesmaximal, complemented
13#37334C214yesmaximal, complemented
14#35546C214yesmaximal, complemented
15#35268C214yesmaximal, complemented
16#35237C211yesmaximal, characteristic, complemented
17#35198C212yesmaximal, complemented
18#35192C211yesmaximal, characteristic, complemented
19#35185C212yesmaximal, complemented
20#34977C211yesmaximal, characteristic, complemented
21#34935C211yesmaximal, characteristic, complemented
22#34226C211yesmaximal, characteristic, complemented
23#34125C211yesmaximal, characteristic, complemented
24#34058C211yesmaximal, characteristic, complemented
25C2×#542C2214yescomplemented
26C2×#532C2211yescharacteristic
27C2×#525C2212yes—
28C2×C4×#41C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2864C2212yescomplemented
31#2864C2214yescomplemented
32#2862C2212yescomplemented
33#2860C2214yes—
34#2860C2214yescomplemented
35#2858C2214yes—
36#2847C2214yes—
37#2832C2218yescomplemented
38#2828C2218yescomplemented
39#2808C2218yescomplemented
40#2803C2218yes—
41#2796C2218yescomplemented
42#2777C2218yescomplemented
43#2743C2218yes—
44#2737C2218yes—
45#2733C2218yes—
46#2714C2218yes—
47#2710C2218yes—
48#2705C2218yes—
49#2696C2218yes—
50#2689C2218yescomplemented
51#2685C2218yes—
52#2684C2218yes—
53#2678C2218yes—
54#2670C2218yes—
55#2665C2214yes—
56#2662C2218yescomplemented
57#2650C2218yescomplemented
58#2635C2218yescomplemented
59#2632C2218yescomplemented
60#2631C2214yes—
61#2628C2214yescomplemented
62#2628C2214yescomplemented
63#2624C2214yes—
64#2624C2214yescomplemented
65#2624C2214yescomplemented
66#2624C2214yescomplemented
67#2619C2214yes—
68#2619C2214yescomplemented
69#2610C2214yescomplemented
70#2605C2214yescomplemented
71#2578C2218yescomplemented
72#2572C2218yescomplemented
73#2571C2212yescomplemented
74#2567C2211yescharacteristic, complemented
75#2563C2212yes—
76#2563C2211yescharacteristic, complemented
77#2551C2212yescomplemented
78#2548C2211yescharacteristic, complemented
79#2541C2212yes—
80#2541C2211yescharacteristic, complemented
81#2538C2212yes—
82#2537C2212yes—
83#2536C2212yes—
84#2535C2212yes—
85#2535C2212yes—
86#2535C2212yes—
87#2534C2214yes—
88#2521C2218yescomplemented
89#2521C2218yescomplemented
90#2518C2218yescomplemented
91#2516C2218yescomplemented
92#2516C2218yescomplemented
93#2513C2214yes—
94#2509C2214yescomplemented
95#2504C2212yes—
96#2500C2212yes—
97#2496C2214yescomplemented
98#2495C2214yescomplemented
99#2495C2214yescomplemented
100#2491C2214yes—
101#2491C2214yescomplemented
102#2491C2214yescomplemented
103#2488C2218yescomplemented
104#2486C2212yes—
105#2469C2218yescomplemented
106#2467C2218yescomplemented
107#2467C2218yescomplemented
108#2461C2218yescomplemented
109#2459C2218yescomplemented
110#2459C2218yescomplemented
111#2459C2218yescomplemented
112#2457C2218yescomplemented
113#2452C2214yescomplemented
114#2445C2214yes—
115#2444C2218yescomplemented
116#2439C2214yes—
117#2439C2214yes—
118#2433C2212yes—
119#2431C2212yes—
120#2428C2214yes—
121#2428C2214yescomplemented
122#2427C2218yescomplemented
123#2426C2214yescomplemented
124#2421C2214yescomplemented
125#2420C2214yescomplemented
126#2420C2214yescomplemented
127#2414C2214yes—
128#2408C2212yes—
129#2404C2214yes—
130#2392C2214yes—
131#2388C2214yes—
132#2367C2214yescomplemented
133#2363C2214yes—
134#2357C2212yes—
135#2357C2212yes—
136#2357C2211yescharacteristic, complemented
137#2357C2212yescomplemented
138#2357C2211yescharacteristic, complemented
139#2351C2211yescharacteristic, complemented
140#2351C2211yescharacteristic, complemented
141#2349C2212yescomplemented
142#2347C2212yes—
143#2347C2214yescomplemented
144#2341C2212yes—
145#2341C2212yes—
146#2339C2212yes—
147#2331C2214yescomplemented
148#2328C2214yes—
149#2324C2214yes—
150#2324C2214yescomplemented
151#2323C2214yescomplemented
152#2319C2212yes—
153#2319C2212yes—
154#2319C2214yes—
155#2319C2212yescomplemented
156#2316C2212yes—
157#2314C2214yescomplemented
158#2312C2212yes—
159#2312C2212yes—
160#2309C2212yes—
161C4×C4⋊Q8C2212yescomplemented
162C4×#127C2212yescomplemented
163C4×#127C2212yescomplemented
164C4×#124C2212yescomplemented
165C4×#121C2214yes—
166C4×#121C2214yescomplemented
167#2293C2212yes—
168#2293C2212yes—
169#2293C2212yes—
170#2293C2212yes—
171#2293C2214yes—
172#2293C2212yescomplemented
173#2285C2211yescharacteristic
174#2283C2211yescharacteristic
175#2283C2212yescomplemented
176#2280C2214yes—
177#2280C2212yes—
178#2275C2212yescomplemented
179C42×Q8C2212yescomplemented
180C4×#117C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C4×#117C2212yescomplemented
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×D4C2311yescharacteristic
186C24×C4C2312yes—
187#542—416no—
188#532—28no—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×#127C2311yescharacteristic
193C2×#127C2312yes—
194C2×#127C2314yes—
195C2×#126C2318yes—
196C2×#126C2318yes—
197C2×#124C2312yes—
198C2×#124C2312yes—
199C2×#124C2318yes—
200C2×#124C2318yes—
201C2×#124C2318yes—
202#525—48no—
203C2×#123C2314yes—
204C2×#123C2318yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2318yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#120C2314yes—
216C2×#120C2318yes—
217C4×#41—28no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×D4—28no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2318yes—
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4C2312yes—
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#399C2318yes—
257#399C2318yes—
258#399C2318yes—
259#398C2314yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2314yes—
266#397C2314yes—
267#397C2314yes—
268#397C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2314yes—
273#395C2318yes—
274#395C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#393C2318yes—
291#393C2314yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2318yes—
296#392C2314yes—
297#392C2318yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#392C2314yes—
302#392C2314yes—
303#392C2318yes—
304#392C2314yes—
305#391C2314yes—
306#391C2312yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#390C2312yes—
311#390C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C2318yes—
315#390C2314yes—
316#390C2314yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2314yes—
322#390C2314yes—
323#390C2318yes—
324#390C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2312yes—
330#390C2314yes—
331#390C2314yes—
332#390C2318yes—
333#390C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2318yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#385C2318yes—
402#385C2318yes—
403#384C2312yes—
404#384C2312yes—
405#383C2314yes—
406#383C2318yes—
407#383C2312yes—
408#382C2314yes—
409#382C2312yes—
410#382C2314yes—
411#382C2314yes—
412#382C2312yes—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2312yes—
416#382C2312yes—
417#381C2314yes—
418#381C2318yes—
419#381C2314yes—
420#381C2314yes—
421#381C2312yes—
422#381C2312yes—
423#381C2312yes—
424#381C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2312yes—
435#380C2312yes—
436#380C2312yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#379C2314yes—
441#379C2314yes—
442#379C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2314yes—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478#376C2311yescharacteristic
479#376C2312yes—
480#376C2311yescharacteristic
481#376C2312yes—
482C2×#95C2314yes—
483C43C2312yes—
484C43C2312yes—
485C43C2314yes—
486C25C2412yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—28no—
490C2×#41—42no—
491C2×#41—84no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2412yes—
494C22×Q8C2418yes—
495C22×D4—24no—
496C22×D4—44no—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2411yescharacteristic
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2414yes—
505C22×D4C2418yes—
506C22×D4C2418yes—
507C22×D4C2418yes—
508C22×D4C2418yes—
509C23×C4—28no—
510C23×C4—44no—
511C23×C4—44no—
512C23×C4C2412yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2414yes—
520C23×C4C2414yes—
521C23×C4C2418yes—
522C23×C4C2411yescharacteristic
523C4⋊Q8—24no—
524C4⋊Q8—48no—
525C4⋊Q8—48no—
526#127—24no—
527#127—44no—
528#127—48no—
529#126—416no—
530#126—88no—
531#124—28no—
532#124—28no—
533#124—416no—
534#124—88no—
535#124—88no—
536#123—416no—
537#123—48no—
538C22⋊Q8—216no—
539C22⋊Q8—416no—
540#121—28no—
541#121—28no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—48no—
546#121—48no—
547#121—88no—
548#120—48no—
549#120—88no—
550C4×Q8—28no—
551C4×Q8—24no—
552C4×Q8—24no—
553C4×Q8—44no—
554C4×Q8—84no—
555C4×D4—28no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—28no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—416no—
568C4×D4—84no—
569C4×D4—88no—
570#117—24no—
571#117—28no—
572#117—44no—
573#117—48no—
574#117—48no—
575#117—48no—
576#117—44no—
577#117—44no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C22⋊C4—28no—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C42—28no—
651C2×C42#4118yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2418yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#95C2411yescharacteristic
677#95C2414yes—
678#95C2418yes—
679#95C2412yes—
680#95C2411yescharacteristic
681#95C2411yescharacteristic
682#95C2412yes—
683#95C2411yescharacteristic
684#95C2414yes—
685#95C2414yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2418yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2412yes—
700#95C2412yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713C24—24no—
714C24—44no—
715C24—42no—
716C24—44no—
717C24—42no—
718C24C2514yes—
719C24C2512yes—
720C24C2514yes—
721C24C2511yescharacteristic
722#41—416no—
723#41—816no—
724C2×Q8—22no—
725C2×Q8—24no—
726C2×Q8—22no—
727C2×Q8—44no—
728C2×Q8—48no—
729C2×Q8—48no—
730C2×Q8—48no—
731C2×Q8H(5,𝔽2)14yes—
732C2×D4—24no—
733C2×D4—28no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—22no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—28no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—22no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—416no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—24no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—48no—
784C22×C4—42no—
785C22×C4—44no—
786C22×C4—42no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—816no—
791C22×C4C2×#4114yes—
792C22×C4C2×#4114yes—
793C22×C4C2×#4114yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2518yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C22⋊C4—24no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—216no—
853C22⋊C4—216no—
854C22⋊C4—44no—
855C22⋊C4—42no—
856C22⋊C4—44no—
857C22⋊C4—42no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—44no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—28no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—28no—
895C42—44no—
896C42—44no—
897C42—42no—
898C42—44no—
899C42—44no—
900C42—42no—
901C42—48no—
902C42—44no—
903C42—44no—
904C42C2×#4114yes—
905C42C2×#4114yes—
906C42C2×#4114yes—
907C42C2×#4114yes—
908C23—21no—
909C23—22no—
910C23—21no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—22no—
918C23—24no—
919C23—24no—
920C23—28no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—28no—
929C23—48no—
930C23—84no—
931C23—84no—
932C23—88no—
933C23—88no—
934C23C22×#4112yes—
935C23C2611yescharacteristic
936Q8—28no—
937Q8—48no—
938Q8—168no—
939D4—48no—
940D4—48no—
941D4—48no—
942D4—48no—
943D4—48no—
944D4—48no—
945D4—44no—
946D4—88no—
947D4—816no—
948D4—816no—
949D4—168no—
950D4—168no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—24no—
995C2×C4—28no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—416no—
1000C2×C4—84no—
1001C2×C4—88no—
1002C2×C4—88no—
1003C2×C4—84no—
1004C2×C4—168no—
1005C2×C4C22×#4112yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C2×H(5,𝔽2)14yes—
1012C2×C4C2×H(5,𝔽2)12yes—
1013C2×C4#58514yes—
1014C2×C4#58512yes—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—42no—
1019C22—42no—
1020C22—44no—
1021C22—42no—
1022C22—44no—
1023C22—44no—
1024C22—42no—
1025C22—44no—
1026C22—48no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—48no—
1032C22—44no—
1033C22—44no—
1034C22—42no—
1035C22—44no—
1036C22—44no—
1037C22—816no—
1038C22C23×#4111yescharacteristic
1039C22C22×H(5,𝔽2)11yescharacteristic
1040C22C2×#58511yescharacteristic
1041C22C2×#58512yes—
1042C22H(7,𝔽2)12yes—
1043C4—22no—
1044C4—24no—
1045C4—22no—
1046C4—22no—
1047C4—22no—
1048C4—44no—
1049C4—42no—
1050C4—44no—
1051C4—42no—
1052C4—42no—
1053C4—48no—
1054C4—44no—
1055C4—44no—
1056C4—42no—
1057C4—42no—
1058C4—44no—
1059C4—44no—
1060C4—42no—
1061C4#345514yes—
1062C4#349414yes—
1063C2—42no—
1064C2—82no—
1065C2—84no—
1066C2—84no—
1067C2C2×#345511yescharacteristic
1068C2C2×#349411yescharacteristic
1069C2#6285511yescharacteristic
1070C2#6292312yes—
1071C2#6293812yes—
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. #41967C2semidirect
2. #40657C2semidirect
3. #40650C2semidirect
4. #39500C2semidirect
5. #39374C2semidirect
6. #39188C2semidirect
7. #39185C2semidirect
8. #37858C2semidirect
9. #37669C2semidirect
10. #37636C2semidirect
11. #37626C2semidirect
12. #37366C2semidirect
13. #37334C2semidirect
14. #35546C2semidirect
15. #35268C2semidirect
16. #35237C2semidirect
17. #35198C2semidirect
18. #35192C2semidirect
19. #35185C2semidirect
20. #34977C2semidirect
21. #34935C2semidirect
22. #34226C2semidirect
23. #34125C2semidirect
24. #34058C2semidirect
25. C2×#542C22semidirect
30. #2864C22semidirect
31. #2864C22semidirect
32. #2862C22semidirect
34. #2860C22semidirect
37. #2832C22semidirect
38. #2828C22semidirect
39. #2808C22semidirect
41. #2796C22semidirect
42. #2777C22semidirect
50. #2689C22semidirect
56. #2662C22semidirect
57. #2650C22semidirect
58. #2635C22semidirect
59. #2632C22semidirect
61. #2628C22semidirect
62. #2628C22semidirect
64. #2624C22semidirect
65. #2624C22semidirect
66. #2624C22semidirect
68. #2619C22semidirect
69. #2610C22semidirect
70. #2605C22semidirect
71. #2578C22semidirect
72. #2572C22semidirect
73. #2571C22semidirect
74. #2567C22semidirect
76. #2563C22semidirect
77. #2551C22semidirect
78. #2548C22semidirect
80. #2541C22semidirect
88. #2521C22semidirect
89. #2521C22semidirect
90. #2518C22semidirect
91. #2516C22semidirect
92. #2516C22semidirect
94. #2509C22semidirect
97. #2496C22semidirect
98. #2495C22semidirect
99. #2495C22semidirect
101. #2491C22semidirect
102. #2491C22semidirect
103. #2488C22semidirect
105. #2469C22semidirect
106. #2467C22semidirect
107. #2467C22semidirect
108. #2461C22semidirect
109. #2459C22semidirect
110. #2459C22semidirect
111. #2459C22semidirect
112. #2457C22semidirect
113. #2452C22semidirect
115. #2444C22semidirect
121. #2428C22semidirect
122. #2427C22semidirect
123. #2426C22semidirect
124. #2421C22semidirect
125. #2420C22semidirect
126. #2420C22semidirect
132. #2367C22semidirect
136. #2357C22semidirect
137. #2357C22semidirect
138. #2357C22semidirect
139. #2351C22semidirect
140. #2351C22semidirect
141. #2349C22semidirect
143. #2347C22semidirect
147. #2331C22semidirect
150. #2324C22semidirect
151. #2323C22semidirect
155. #2319C22semidirect
157. #2314C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×#127C22semidirect
163. C4×#127C22semidirect
164. C4×#124C22semidirect
166. C4×#121C22semidirect
172. #2293C22semidirect
175. #2283C22semidirect
178. #2275C22semidirect
179. C42×Q8C22semidirect
182. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#419672
#406572
#406502
#395002
#393742
#391882
#391852
#378582
#376692
#376362
#376262
#373662
#373342
#355462
#352682
#352372
#351982
#351922
#351852
#349772
#349352
#342262
#341252
#340582