Finite Group Databasebeta

← #7674358

Subgroups — #7674358

Order 512.

4704 conjugacy classes of subgroups.

The subgroup lattice has 1077 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45147C214yesmaximal, complemented
2#45145C214yesmaximal, complemented
3#44958C214yesmaximal, complemented
4#44956C214yesmaximal, complemented
5#39547C214yesmaximal, complemented
6#39546C214yesmaximal, complemented
7#37979C218yesmaximal, complemented
8#37977C218yesmaximal, complemented
9#37939C214yesmaximal, complemented
10#37938C214yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35627C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35555C211yesmaximal, characteristic, complemented
15#35286C211yesmaximal, characteristic, complemented
16#35280C211yesmaximal, characteristic, complemented
17#35227C211yesmaximal, characteristic
18#35157C211yesmaximal, characteristic
19#34634C211yesmaximal, characteristic, complemented
20#34215C211yesmaximal, characteristic, complemented
21#34189C211yesmaximal, characteristic, complemented
22#34179C211yesmaximal, characteristic, complemented
23#34178C211yesmaximal, characteristic, complemented
24#34065C211yesmaximal, characteristic
25C2×#2317C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C2×#525C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32#2859C2214yescomplemented
33#2857C2214yescomplemented
34#2853C2214yes—
35#2849C2214yes—
36#2777C2218yescomplemented
37#2772C2218yescomplemented
38#2766C2218yescomplemented
39#2766C2218yescomplemented
40#2765C2218yes—
41#2764C2218yes—
42#2761C2218yes—
43#2758C2218yescomplemented
44#2743C2218yes—
45#2739C2218yes—
46#2738C2218yes—
47#2738C2218yescomplemented
48#2719C2218yescomplemented
49#2707C2218yes—
50#2698C2218yescomplemented
51#2687C2218yes—
52#2647C2214yescomplemented
53#2629C2212yes—
54#2629C2212yes—
55#2629C2214yescomplemented
56#2628C2212yes—
57#2628C2212yes—
58#2627C2214yes—
59#2626C2214yes—
60#2623C2214yes—
61#2622C2214yes—
62#2612C2218yescomplemented
63#2611C2218yes—
64#2606C2218yescomplemented
65#2601C2218yes—
66#2590C2218yescomplemented
67#2582C2214yescomplemented
68#2571C2214yescomplemented
69#2571C2214yescomplemented
70#2570C2214yescomplemented
71#2570C2214yescomplemented
72#2558C2218yes—
73#2556C2218yescomplemented
74#2553C2218yes—
75#2552C2214yescomplemented
76#2552C2214yescomplemented
77#2538C2214yescomplemented
78#2533C2218yescomplemented
79#2530C2218yescomplemented
80#2529C2218yescomplemented
81#2527C2218yes—
82#2519C2218yescomplemented
83#2515C2218yes—
84#2514C2214yescomplemented
85#2513C2214yescomplemented
86#2512C2214yescomplemented
87#2511C2214yescomplemented
88#2510C2218yes—
89#2509C2214yescomplemented
90#2508C2214yescomplemented
91#2507C2214yescomplemented
92#2506C2214yescomplemented
93#2505C2218yes—
94#2504C2212yes—
95#2503C2212yes—
96#2502C2212yes—
97#2501C2212yes—
98#2500C2212yes—
99#2500C2212yes—
100#2499C2212yes—
101#2499C2212yes—
102#2497C2214yescomplemented
103#2496C2214yescomplemented
104#2495C2214yescomplemented
105#2494C2214yescomplemented
106#2487C2214yes—
107#2486C2214yes—
108#2485C2214yes—
109#2485C2214yes—
110#2481C2218yes—
111#2477C2218yes—
112#2475C2218yes—
113#2473C2218yes—
114#2442C2218yes—
115#2417C2218yes—
116#2396C2214yes—
117#2396C2214yes—
118#2368C2218yes—
119#2357C2214yescomplemented
120#2356C2214yescomplemented
121#2355C2214yescomplemented
122#2355C2214yescomplemented
123#2353C2218yes—
124#2347C2214yes—
125#2347C2214yes—
126#2346C2214yes—
127#2346C2214yes—
128#2345C2214yes—
129#2345C2214yes—
130#2344C2214yes—
131#2344C2214yes—
132#2331C2214yescomplemented
133#2324C2212yes—
134#2324C2212yes—
135#2323C2212yes—
136#2323C2212yes—
137#2322C2214yes—
138#2321C2214yes—
139#2317C2212yes—
140#2317C2212yes—
141#2317C2214yes—
142#2317C2212yes—
143#2317C2212yes—
144#2317C2214yes—
145#2317C2211yescharacteristic
146#2317C2211yescharacteristic
147#2317C2211yescharacteristic
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2211yescharacteristic
151#2316C2211yescharacteristic
152#2316C2211yescharacteristic
153#2314C2214yescomplemented
154#2313C2214yes—
155#2312C2214yes—
156#2311C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160C4×#125C2214yescomplemented
161#2297C2211yescharacteristic
162#2296C2211yescharacteristic
163#2296C2211yescharacteristic
164#2296C2211yescharacteristic
165#2293C2212yes—
166#2293C2212yes—
167C2×#389C2214yes—
168#2290C2212yes—
169#2290C2212yes—
170C2×#385C2214yes—
171#2285C2211yescharacteristic
172C2×#384C2211yescharacteristic
173C2×#384C2211yescharacteristic
174#2283C2214yes—
175#2283C2214yescomplemented
176C2×#382C2211yescharacteristic
177C2×#382C2211yescharacteristic
178#2280C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2214yes—
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C24×C4C2311yescharacteristic
189C24×C4C2312yes—
190#533—28no—
191C2×C4⋊Q8C2312yes—
192C2×#126C2318yes—
193C2×#125C2312yes—
194C2×#125C2318yes—
195C2×#125C2318yes—
196#525—28no—
197C2×#123C2312yes—
198C2×#123C2318yes—
199C2×C22⋊Q8C2311yescharacteristic
200C2×C22⋊Q8C2311yescharacteristic
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2318yes—
203C2×#121C2311yescharacteristic
204C2×#121C2311yescharacteristic
205C2×#120C2312yes—
206C4×#41—28no—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C2×#117—28no—
214C2×#117—28no—
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2312yes—
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2318yes—
234C22×C4⋊C4—28no—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C42C2312yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253#401C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2314yes—
265#400C2318yes—
266#399C2314yes—
267#399C2318yes—
268#399C2314yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#398C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#398C2314yes—
280#398C2318yes—
281#398C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#396C2314yes—
289#396C2318yes—
290#396C2314yes—
291#396C2314yes—
292#396C2314yes—
293#396C2318yes—
294#396C2318yes—
295#395C2314yes—
296#395C2314yes—
297#394C2318yes—
298#394C2318yes—
299#393C2314yes—
300#393C2314yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2318yes—
307#391C2318yes—
308#391C2318yes—
309#390C2312yes—
310#390C2312yes—
311#390C2312yes—
312#390C2312yes—
313#390C2314yes—
314#390C2314yes—
315#390C2312yes—
316#389C2314yes—
317#389C2314yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2318yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2318yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2318yes—
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#387C2314yes—
375#387C2314yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#386C2314yes—
384#386C2314yes—
385#386C2314yes—
386#386C2314yes—
387#386C2314yes—
388#386C2314yes—
389#386C2314yes—
390#386C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2314yes—
396#385C2314yes—
397#385C2314yes—
398#385C2314yes—
399#385C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2318yes—
403#385C2314yes—
404#385C2314yes—
405#384C2312yes—
406#384C2312yes—
407#384C2314yes—
408#384C2312yes—
409#384C2314yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#384C2312yes—
414#384C2312yes—
415#384C2312yes—
416#383C2318yes—
417#383C2318yes—
418#383C2318yes—
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#382C2312yes—
423#382C2314yes—
424#382C2312yes—
425#382C2318yes—
426#382C2318yes—
427#382C2312yes—
428#382C2314yes—
429#382C2312yes—
430#382C2312yes—
431#382C2318yes—
432#382C2312yes—
433#381C2312yes—
434#381C2312yes—
435#381C2318yes—
436#381C2318yes—
437#381C2318yes—
438#381C2312yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2318yes—
452#380C2318yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#379C2312yes—
457#379C2312yes—
458#379C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492#376C2312yes—
493#376C2318yes—
494#376C2318yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C43C2312yes—
498C25C2411yescharacteristic
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2414yes—
504C22×D4C2412yes—
505C22×D4C2411yescharacteristic
506C22×D4C2412yes—
507C22×D4C2412yes—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—28no—
511C23×C4—84no—
512C23×C4#4118yes—
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2412yes—
528C23×C4C2411yescharacteristic
529C4⋊Q8—28no—
530#126—88no—
531#125—28no—
532#125—88no—
533#125—88no—
534#123—28no—
535#123—88no—
536C22⋊Q8—24no—
537C22⋊Q8—24no—
538C22⋊Q8—216no—
539C22⋊Q8—88no—
540#121—24no—
541#121—24no—
542#120—28no—
543C4×Q8—28no—
544C4×Q8—216no—
545C4×D4—216no—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—28no—
549#117—28no—
550#117—28no—
551#117—28no—
552#117—28no—
553#117—24no—
554#117—24no—
555#117—24no—
556#117—24no—
557#117—24no—
558#117—24no—
559#117—24no—
560#117—24no—
561#117—24no—
562#117—24no—
563#117—24no—
564#117—28no—
565#117—28no—
566#117—28no—
567#117—88no—
568C2×C4⋊C4—28no—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—28no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—28no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—84no—
579C2×C4⋊C4—84no—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C22⋊C4—28no—
629C2×C22⋊C4—28no—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C42—24no—
661C2×C42—28no—
662C2×C42—28no—
663C2×C42#4118yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2414yes—
677C2×C42C2418yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2418yes—
713#95C2414yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724C24—22no—
725C24—22no—
726C24—42no—
727C24—42no—
728C24C2×#4114yes—
729C24C2512yes—
730C24C2511yescharacteristic
731C24C2511yescharacteristic
732C24C2511yescharacteristic
733#41—416no—
734C2×Q8—22no—
735C2×Q8—22no—
736C2×Q8—28no—
737C2×Q8—22no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—44no—
749C2×D4—44no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—232no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—24no—
762C22×C4—28no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—48no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—48no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—816no—
785C22×C4C2×#4114yes—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2×#4114yes—
789C22×C4C2×#4114yes—
790C22×C4C2×#4118yes—
791C22×C4C2×#4114yes—
792C22×C4C2×#4114yes—
793C22×C42−1+414yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—28no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C42—28no—
894C42—28no—
895C42—24no—
896C42—22no—
897C42—22no—
898C42—24no—
899C42—28no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—44no—
907C42—48no—
908C42—48no—
909C42—48no—
910C42—48no—
911C42—44no—
912C42C2×#4114yes—
913C42C2×#4114yes—
914C42C2×#4118yes—
915C23—22no—
916C23—22no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—28no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—24no—
931C23—44no—
932C23—44no—
933C23—48no—
934C23—48no—
935C23C22×#4112yes—
936C23C22×#4112yes—
937C23C22×#4112yes—
938C23C22×#4112yes—
939C23C2×2−1+412yes—
940C23C2611yescharacteristic
941Q8—44no—
942Q8—88no—
943D4—48no—
944D4—44no—
945D4—84no—
946D4—84no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—28no—
956C2×C4—28no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—28no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—416no—
1002C2×C4—48no—
1003C2×C4—88no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4—84no—
1007C2×C4—84no—
1008C2×C4—88no—
1009C2×C4#552116yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4114yes—
1013C2×C4C22×#4114yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4112yes—
1016C2×C4C22×#4112yes—
1017C2×C4C22×#4112yes—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C22—22no—
1021C22—24no—
1022C22—22no—
1023C22—24no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—416no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—44no—
1037C22—42no—
1038C22—44no—
1039C22—42no—
1040C22C2×#55214yes—
1041C22C23×#4111yescharacteristic
1042C22C23×#4111yescharacteristic
1043C22C22×2−1+411yescharacteristic
1044C22H(7,𝔽2)12yes—
1045C222−1+612yes—
1046C4—24no—
1047C4—24no—
1048C4—22no—
1049C4—22no—
1050C4—44no—
1051C4—44no—
1052C4—44no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4—42no—
1061C4—44no—
1062C4—44no—
1063C4—44no—
1064C4—42no—
1065C4C2×#55214yes—
1066C4C2×#55214yes—
1067C2—24no—
1068C2—42no—
1069C2—42no—
1070C2—82no—
1071C2C22×#55211yescharacteristic
1072C2#6285511yescharacteristic
1073C2#6285612yes—
1074C2#6286011yescharacteristic
1075C2#6287712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45147C2semidirect
2. #45145C2semidirect
3. #44958C2semidirect
4. #44956C2semidirect
5. #39547C2semidirect
6. #39546C2semidirect
7. #37979C2semidirect
8. #37977C2semidirect
9. #37939C2semidirect
10. #37938C2semidirect
11. #35629C2semidirect
12. #35627C2semidirect
13. #35557C2semidirect
14. #35555C2semidirect
15. #35286C2semidirect
16. #35280C2semidirect
19. #34634C2semidirect
20. #34215C2semidirect
21. #34189C2semidirect
22. #34179C2semidirect
23. #34178C2semidirect
25. C2×#2317C2semidirect
32. #2859C22semidirect
33. #2857C22semidirect
36. #2777C22semidirect
37. #2772C22semidirect
38. #2766C22semidirect
39. #2766C22semidirect
43. #2758C22semidirect
47. #2738C22semidirect
48. #2719C22semidirect
50. #2698C22semidirect
52. #2647C22semidirect
55. #2629C22semidirect
62. #2612C22semidirect
64. #2606C22semidirect
66. #2590C22semidirect
67. #2582C22semidirect
68. #2571C22semidirect
69. #2571C22semidirect
70. #2570C22semidirect
71. #2570C22semidirect
73. #2556C22semidirect
75. #2552C22semidirect
76. #2552C22semidirect
77. #2538C22semidirect
78. #2533C22semidirect
79. #2530C22semidirect
80. #2529C22semidirect
82. #2519C22semidirect
84. #2514C22semidirect
85. #2513C22semidirect
86. #2512C22semidirect
87. #2511C22semidirect
89. #2509C22semidirect
90. #2508C22semidirect
91. #2507C22semidirect
92. #2506C22semidirect
102. #2497C22semidirect
103. #2496C22semidirect
104. #2495C22semidirect
105. #2494C22semidirect
119. #2357C22semidirect
120. #2356C22semidirect
121. #2355C22semidirect
122. #2355C22semidirect
132. #2331C22semidirect
153. #2314C22semidirect
160. C4×#125C22semidirect
175. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#451472
#451452
#449582
#449562
#395472
#395462
#379792
#379772
#379392
#379382
#356292
#356272
#355572
#355552
#352862
#352802
#352272
#351572
#346342
#342152
#341892
#341792
#341782
#340652
C2×#23172