Finite Group Databasebeta

← #7652628

Subgroups — #7652628

Order 512.

4986 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42947C214yesmaximal, complemented
2#42897C214yesmaximal, complemented
3#42536C214yesmaximal, complemented
4#42450C214yesmaximal, complemented
5#40729C218yesmaximal, complemented
6#40141C214yesmaximal, complemented
7#39937C214yesmaximal, complemented
8#39782C214yesmaximal, complemented
9#39145C214yesmaximal, complemented
10#38501C218yesmaximal, complemented
11#35639C211yesmaximal, characteristic, complemented
12#35639C211yesmaximal, characteristic, complemented
13#35629C211yesmaximal, characteristic, complemented
14#35555C211yesmaximal, characteristic, complemented
15#35533C211yesmaximal, characteristic
16#35531C211yesmaximal, characteristic, complemented
17#35266C211yesmaximal, characteristic, complemented
18#35254C211yesmaximal, characteristic, complemented
19#35152C211yesmaximal, characteristic, complemented
20C2×#2566C211yesmaximal, characteristic, complemented
21#34815C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic, complemented
23#34265C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic, complemented
25#34184C211yesmaximal, characteristic, complemented
26C2×#535C2211yescharacteristic
27C2×#535C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35#2860C2214yes—
36#2854C2214yes—
37#2849C2214yes—
38#2837C2218yescomplemented
39#2827C2218yescomplemented
40#2807C2218yescomplemented
41#2783C2218yescomplemented
42#2782C2218yescomplemented
43#2781C2218yescomplemented
44#2777C2218yescomplemented
45#2765C2218yescomplemented
46#2757C2218yescomplemented
47#2750C2218yescomplemented
48#2746C2218yescomplemented
49#2724C2218yescomplemented
50#2711C2218yescomplemented
51#2707C2218yescomplemented
52#2706C2218yescomplemented
53#2705C2218yescomplemented
54#2694C2218yescomplemented
55#2691C2218yescomplemented
56#2664C2218yescomplemented
57#2651C2218yescomplemented
58#2649C2218yescomplemented
59#2644C2214yes—
60#2643C2218yescomplemented
61#2633C2218yescomplemented
62#2630C2218yescomplemented
63#2624C2214yes—
64#2622C2214yes—
65#2594C2218yescomplemented
66#2579C2214yes—
67#2579C2214yes—
68#2573C2218yescomplemented
69#2570C2214yescomplemented
70#2566C2214yes—
71#2566C2214yes—
72#2566C2214yes—
73#2566C2214yes—
74#2558C2218yescomplemented
75#2552C2214yescomplemented
76#2548C2212yes—
77#2545C2212yes—
78#2544C2212yes—
79#2541C2212yes—
80#2514C2214yescomplemented
81#2513C2214yes—
82#2513C2214yescomplemented
83#2512C2214yes—
84#2510C2218yes—
85#2509C2212yescomplemented
86#2508C2212yescomplemented
87#2507C2214yescomplemented
88#2507C2212yescomplemented
89#2506C2214yescomplemented
90#2506C2212yescomplemented
91#2505C2214yes—
92#2504C2212yes—
93#2501C2212yes—
94#2500C2212yes—
95#2500C2212yes—
96#2495C2214yescomplemented
97#2494C2214yescomplemented
98#2487C2214yes—
99#2487C2214yes—
100#2480C2218yes—
101#2473C2214yes—
102#2473C2218yes—
103#2455C2218yescomplemented
104#2454C2214yescomplemented
105#2454C2214yescomplemented
106#2453C2214yescomplemented
107#2453C2214yescomplemented
108#2448C2214yes—
109#2448C2214yes—
110#2448C2212yescomplemented
111#2447C2214yes—
112#2447C2212yescomplemented
113#2446C2212yescomplemented
114#2445C2214yes—
115#2445C2214yes—
116#2445C2214yes—
117#2445C2212yescomplemented
118#2444C2214yes—
119#2443C2214yes—
120#2442C2214yescomplemented
121#2442C2214yescomplemented
122#2441C2214yescomplemented
123#2441C2214yescomplemented
124#2425C2218yescomplemented
125#2424C2218yes—
126#2422C2214yes—
127#2420C2214yes—
128#2419C2218yescomplemented
129#2418C2218yes—
130#2418C2218yes—
131#2416C2214yes—
132#2414C2214yes—
133#2402C2214yescomplemented
134#2395C2214yescomplemented
135C2×#396C2214yes—
136#2367C2214yes—
137#2366C2214yes—
138#2363C2214yes—
139#2361C2218yes—
140#2361C2214yes—
141#2354C2214yescomplemented
142#2351C2214yescomplemented
143#2349C2218yes—
144#2349C2214yescomplemented
145D4×C4⋊C4C2214yescomplemented
146#2334C2218yescomplemented
147#2326C2212yescomplemented
148#2326C2212yescomplemented
149#2325C2218yescomplemented
150#2321C2214yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yescomplemented
155#2317C2212yescomplemented
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163C4×C4⋊Q8C2212yescomplemented
164C4×#127C2212yescomplemented
165C4×#125C2214yescomplemented
166C4×#123C2214yescomplemented
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#390C2211yescharacteristic
178C2×#385C2214yes—
179#2285C2211yescharacteristic
180#2285C2212yescomplemented
181C2×#384C2211yescharacteristic
182C2×#382C2211yescharacteristic
183C2×#382C2212yescomplemented
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#535—28no—
192#535—44no—
193#532—28no—
194C2×C4⋊Q8C2311yescharacteristic
195C2×#127C2311yescharacteristic
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#126C2318yes—
199C2×#125—44no—
200C2×#125C2314yes—
201C2×#125C2314yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#124C2311yescharacteristic
205C2×#124C2311yescharacteristic
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#123C2314yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×#123C2318yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#120C2314yes—
218C2×#120C2314yes—
219#520—44no—
220#520—44no—
221#520—44no—
222C4×#41—28no—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×D4—44no—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2318yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2314yes—
264C22×C42C2312yes—
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#401C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#399C2318yes—
279#399C2314yes—
280#399C2318yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#397C2314yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2314yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2314yes—
321#394C2314yes—
322#394C2318yes—
323#392C2318yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2318yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2312yes—
345#390C2318yes—
346#390C2312yes—
347#390C2318yes—
348#390C2312yes—
349#390C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2314yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#386C2318yes—
406#386C2312yes—
407#386C2312yes—
408#386C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2312yes—
414#386C2318yes—
415#386C2314yes—
416#386C2312yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2318yes—
427#385C2312yes—
428#385C2312yes—
429#385C2312yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2312yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#384C2312yes—
441#384C2314yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#383C2318yes—
449#382C2314yes—
450#382C2312yes—
451#382C2314yes—
452#382C2312yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2318yes—
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#381C2318yes—
460#381C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2318yes—
467#380C2314yes—
468#380C2318yes—
469#380C2318yes—
470#379C2314yes—
471#379C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497C2×#95C2318yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
500C43C2312yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41#4118yes—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2411yescharacteristic
517C22×D4C2414yes—
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2418yes—
521C22×D4C2414yes—
522C22×D4C2414yes—
523C23×C4—44no—
524C23×C4—84no—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2414yes—
535C23×C4C2414yes—
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2418yes—
539C23×C4C2411yescharacteristic
540C4⋊Q8—24no—
541#127—24no—
542#127—28no—
543#127—44no—
544#126—416no—
545#125—48no—
546#125—48no—
547#125—48no—
548#125—88no—
549#124—24no—
550#124—28no—
551#124—24no—
552#124—44no—
553#123—48no—
554#123—88no—
555#123—88no—
556#123—88no—
557#121—216no—
558#121—216no—
559#121—416no—
560#121—44no—
561#121—44no—
562#120—216no—
563#120—48no—
564C4×Q8—28no—
565C4×Q8—44no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×D4—216no—
569C4×D4—28no—
570C4×D4—216no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—44no—
574C4×D4—44no—
575C4×D4—44no—
576C4×D4—48no—
577C4×D4—48no—
578C4×D4—48no—
579C4×D4—88no—
580C4×D4—88no—
581#117—28no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—24no—
586#117—24no—
587#117—24no—
588#117—44no—
589#117—44no—
590#117—44no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4—84no—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C22⋊C4—48no—
646C2×C22⋊C4—44no—
647C2×C22⋊C4—84no—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C42—28no—
682C2×C42—24no—
683C2×C42—24no—
684C2×C42—24no—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2411yescharacteristic
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741C24—24no—
742C24—24no—
743C24—24no—
744C24—44no—
745C24—44no—
746C24C2514yes—
747C24C2512yes—
748C24C2512yes—
749C24C2511yescharacteristic
750#41—232no—
751#41—416no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8C2×#4114yes—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—28no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—216no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—44no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—416no—
785C2×D4C2×#4118yes—
786C2×D4C2×#4114yes—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—28no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—44no—
805C22×C4—42no—
806C22×C4—44no—
807C22×C4—42no—
808C22×C4—44no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—816no—
821C22×C4C2×#4118yes—
822C22×C4C2×#4114yes—
823C22×C4H(5,𝔽2)14yes—
824C22×C42−1+414yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C22⋊C4—28no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—28no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—28no—
899C22⋊C4—216no—
900C22⋊C4—216no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C42—22no—
924C42—24no—
925C42—22no—
926C42—24no—
927C42—28no—
928C42—24no—
929C42—22no—
930C42—22no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—44no—
940C42—44no—
941C42—44no—
942C42—44no—
943C42—48no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—28no—
957C23—24no—
958C23—24no—
959C23—28no—
960C23—416no—
961C23—48no—
962C23—84no—
963C23—88no—
964C23—84no—
965C23C22×#4114yes—
966C23C22×#4112yes—
967C23C2×H(5,𝔽2)12yes—
968C23C2×2−1+412yes—
969C23C2611yescharacteristic
970Q8—28no—
971Q8—44no—
972D4—216no—
973D4—28no—
974D4—416no—
975D4—48no—
976D4—48no—
977D4—48no—
978D4—44no—
979D4—816no—
980D4—164no—
981D4—164no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—216no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—48no—
1032C2×C4—44no—
1033C2×C4—44no—
1034C2×C4—48no—
1035C2×C4—84no—
1036C2×C4—88no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—816no—
1041C2×C4—164no—
1042C2×C4—164no—
1043C2×C4—164no—
1044C2×C4#539116yes—
1045C2×C4C22×#4114yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4#58514yes—
1053C22—24no—
1054C22—22no—
1055C22—22no—
1056C22—24no—
1057C22—28no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—44no—
1062C22—44no—
1063C22—48no—
1064C22—42no—
1065C22—44no—
1066C22—44no—
1067C22—42no—
1068C22—44no—
1069C22—48no—
1070C22—42no—
1071C22—44no—
1072C22—816no—
1073C22C2×#53914yes—
1074C22C23×#4111yescharacteristic
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C2×#58512yes—
1078C22H(7,𝔽2)12yes—
1079C4—24no—
1080C4—24no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—42no—
1091C4—44no—
1092C4—44no—
1093C4—42no—
1094C4—42no—
1095C4—44no—
1096C4—44no—
1097C4—42no—
1098C4C2×#53914yes—
1099C4C2×#53914yes—
1100C2—24no—
1101C2—44no—
1102C2—82no—
1103C2—84no—
1104C2C22×#53911yescharacteristic
1105C2#6283611yescharacteristic
1106C2#6287611yescharacteristic
1107C2#6292612yes—
1108C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35533C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42947C2semidirect
2. #42897C2semidirect
3. #42536C2semidirect
4. #42450C2semidirect
5. #40729C2semidirect
6. #40141C2semidirect
7. #39937C2semidirect
8. #39782C2semidirect
9. #39145C2semidirect
10. #38501C2semidirect
11. #35639C2semidirect
12. #35639C2semidirect
13. #35629C2semidirect
14. #35555C2semidirect
16. #35531C2semidirect
17. #35266C2semidirect
18. #35254C2semidirect
19. #35152C2semidirect
20. C2×#2566C2semidirect
21. #34815C2semidirect
22. #34744C2semidirect
23. #34265C2semidirect
24. #34207C2semidirect
25. #34184C2semidirect
38. #2837C22semidirect
39. #2827C22semidirect
40. #2807C22semidirect
41. #2783C22semidirect
42. #2782C22semidirect
43. #2781C22semidirect
44. #2777C22semidirect
45. #2765C22semidirect
46. #2757C22semidirect
47. #2750C22semidirect
48. #2746C22semidirect
49. #2724C22semidirect
50. #2711C22semidirect
51. #2707C22semidirect
52. #2706C22semidirect
53. #2705C22semidirect
54. #2694C22semidirect
55. #2691C22semidirect
56. #2664C22semidirect
57. #2651C22semidirect
58. #2649C22semidirect
60. #2643C22semidirect
61. #2633C22semidirect
62. #2630C22semidirect
65. #2594C22semidirect
68. #2573C22semidirect
69. #2570C22semidirect
74. #2558C22semidirect
75. #2552C22semidirect
80. #2514C22semidirect
82. #2513C22semidirect
85. #2509C22semidirect
86. #2508C22semidirect
87. #2507C22semidirect
88. #2507C22semidirect
89. #2506C22semidirect
90. #2506C22semidirect
96. #2495C22semidirect
97. #2494C22semidirect
103. #2455C22semidirect
104. #2454C22semidirect
105. #2454C22semidirect
106. #2453C22semidirect
107. #2453C22semidirect
110. #2448C22semidirect
112. #2447C22semidirect
113. #2446C22semidirect
117. #2445C22semidirect
120. #2442C22semidirect
121. #2442C22semidirect
122. #2441C22semidirect
123. #2441C22semidirect
124. #2425C22semidirect
128. #2419C22semidirect
133. #2402C22semidirect
134. #2395C22semidirect
141. #2354C22semidirect
142. #2351C22semidirect
144. #2349C22semidirect
145. D4×C4⋊C4C22semidirect
146. #2334C22semidirect
147. #2326C22semidirect
148. #2326C22semidirect
149. #2325C22semidirect
154. #2317C22semidirect
155. #2317C22semidirect
163. C4×C4⋊Q8C22semidirect
164. C4×#127C22semidirect
165. C4×#125C22semidirect
166. C4×#123C22semidirect
180. #2285C22semidirect
183. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#429472
#428972
#425362
#424502
#407292
#401412
#399372
#397822
#391452
#385012
#356392
#356292
#355552
#355332
#355312
#352662
#352542
#351522
C2×#25662
#348152
#347442
#342652
#342072
#341842