Finite Group Databasebeta

← #7645854

Subgroups — #7645854

Order 512.

6670 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3491C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#42179C218yesmaximal, complemented
4#42178C218yesmaximal, complemented
5#39947C218yesmaximal, complemented
6#39945C218yesmaximal, complemented
7#37538C212yesmaximal, complemented
8#37441C212yesmaximal, complemented
9#37233C212yesmaximal, complemented
10#37118C212yesmaximal, complemented
11#36970C211yesmaximal, characteristic, complemented
12#36969C211yesmaximal, characteristic, complemented
13#36967C211yesmaximal, characteristic
14#36966C211yesmaximal, characteristic, complemented
15#35452C212yesmaximal, complemented
16#35451C212yesmaximal, complemented
17#35247C212yesmaximal, complemented
18#35145C212yesmaximal, complemented
19#35094C212yesmaximal, complemented
20#35092C212yesmaximal, complemented
21#35062C212yesmaximal, complemented
22#34972C212yesmaximal, complemented
23#34048C211yesmaximal, characteristic, complemented
24#3491—216no—
25C2×#556—216no—
26C2×#556C2218yescomplemented
27C2×#556C2218yescomplemented
28C2×#552C2214yescomplemented
29C2×#552C2214yescomplemented
30C2×#551C2214yescomplemented
31C2×#551C2214yescomplemented
32C2×#543C2211yescharacteristic
33C2×#539C2212yes—
34C2×#539C2212yes—
35C2×#534C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic, complemented
37C2×#529C2212yes—
38C2×#529C2212yes—
39C22×#126C2211yescharacteristic
40C22×#126C2211yescharacteristic
41C22×#126C2211yescharacteristic, complemented
42C22×#126C2211yescharacteristic, complemented
43C22×#124C2211yescharacteristic
44C22×#124C2211yescharacteristic
45C22×#123C2212yes—
46C22×C22⋊Q8C2211yescharacteristic
47C22×C22⋊Q8C2211yescharacteristic, complemented
48C2×#518C2212yes—
49C22×C4×Q8C2211yescharacteristic, complemented
50C22×C4×Q8C2211yescharacteristic, complemented
51C22×C4×Q8C2211yescharacteristic, complemented
52C22×C4×D4C2211yescharacteristic
53C22×#117C2211yescharacteristic
54C22×#117C2211yescharacteristic, complemented
55#2860C2218yescomplemented
56#2855C2212yescomplemented
57#2855C2212yescomplemented
58#2854C2212yes—
59#2854C2212yes—
60#2853C2214yescomplemented
61#2849C2214yescomplemented
62#2823C2218yescomplemented
63#2814C2218yescomplemented
64#2723C2218yescomplemented
65#2720C2218yescomplemented
66#2718C2218yescomplemented
67#2716C2218yescomplemented
68#2713C2218yescomplemented
69#2710C2218yes—
70#2700C2218yescomplemented
71#2698C2218yescomplemented
72#2696C2218yescomplemented
73#2692C2218yescomplemented
74#2689C2218yescomplemented
75#2685C2218yescomplemented
76#2677C2218yescomplemented
77#2674C2218yescomplemented
78#2674C2218yescomplemented
79#2670C2218yes—
80#2664C2214yescomplemented
81#2664C2214yescomplemented
82#2663C2218yescomplemented
83#2662C2214yescomplemented
84#2662C2214yescomplemented
85#2637C2214yescomplemented
86#2637C2218yescomplemented
87#2636C2214yescomplemented
88#2630C2218yes—
89#2627C2212yescomplemented
90#2627C2214yescomplemented
91#2626C2212yescomplemented
92#2626C2214yescomplemented
93#2623C2214yescomplemented
94#2618C2212yes—
95#2617C2212yes—
96#2614C2214yescomplemented
97#2604C2214yescomplemented
98#2604C2218yescomplemented
99#2603C2214yescomplemented
100#2602C2218yes—
101#2601C2218yescomplemented
102#2601C2218yescomplemented
103#2592C2214yescomplemented
104#2591C2212yes—
105#2584C2214yescomplemented
106#2583C2214yescomplemented
107#2583C2212yescomplemented
108#2582C2214yescomplemented
109#2579C2214yescomplemented
110#2579C2214yescomplemented
111#2565C2214yescomplemented
112#2561C2214yescomplemented
113#2561C2212yescomplemented
114#2545C2214yescomplemented
115#2539C2212yes—
116#2538C2214yescomplemented
117#2534C2214yescomplemented
118#2534C2214yescomplemented
119#2503C2212yescomplemented
120#2501C2212yes—
121#2486C2214yescomplemented
122#2483C2212yes—
123#2483C2212yes—
124#2483C2212yes—
125#2480C2218yescomplemented
126#2479C2218yescomplemented
127#2478C2218yescomplemented
128#2477C2218yescomplemented
129#2475C2218yescomplemented
130#2474C2218yescomplemented
131#2472C2218yescomplemented
132#2471C2218yescomplemented
133#2469C2218yescomplemented
134#2468C2218yescomplemented
135#2466C2218yescomplemented
136#2465C2218yescomplemented
137#2462C2218yescomplemented
138#2461C2218yes—
139#2459C2218yes—
140#2458C2218yescomplemented
141#2436C2212yes—
142#2434C2212yescomplemented
143#2413C2214yescomplemented
144#2413C2214yescomplemented
145#2413C2214yescomplemented
146#2411C2214yescomplemented
147#2409C2214yescomplemented
148#2405C2212yes—
149#2405C2212yes—
150#2405C2212yes—
151#2405C2212yes—
152#2403C2212yes—
153#2396C2218yescomplemented
154#2323C2218yescomplemented
155#2322C2214yescomplemented
156#2322C2214yescomplemented
157#2321C2214yescomplemented
158#2321C2214yescomplemented
159#2314C2218yescomplemented
160#2313C2212yescomplemented
161#2313C2212yescomplemented
162#2312C2211yescharacteristic
163#2312C2211yescharacteristic
164#2312C2212yes—
165C4×C4⋊Q8C2214yescomplemented
166C4×#124C2214yescomplemented
167C4×#123C2214yescomplemented
168C4×#123C2214yescomplemented
169#2298C2218yescomplemented
170#2285C2212yescomplemented
171#2280C2212yes—
172C4×#117C2212yescomplemented
173C23×Q8C2311yescharacteristic
174C23×Q8C2311yescharacteristic
175C23×Q8C2311yescharacteristic
176C23×D4C2311yescharacteristic
177C23×D4C2312yes—
178C24×C4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180#556—264no—
181#556—264no—
182#552—232no—
183#552—232no—
184#551—232no—
185#551—232no—
186#543—28no—
187#539—216no—
188#539—216no—
189#534—28no—
190C2×C4⋊Q8—28no—
191C2×C4⋊Q8C2318yes—
192C2×C4⋊Q8C2314yes—
193#529—216no—
194#529—216no—
195C2×#126—28no—
196C2×#126—28no—
197C2×#126—28no—
198C2×#126—28no—
199C2×#126C2314yes—
200C2×#126C2314yes—
201C2×#126C2314yes—
202C2×#126C2314yes—
203C2×#126C2314yes—
204C2×#126C2314yes—
205C2×#126C2318yes—
206C2×#126C2318yes—
207C2×#126C2314yes—
208C2×#126C2314yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#124—28no—
214C2×#124—28no—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2318yes—
218C2×#124C2318yes—
219C2×#124C2314yes—
220C2×#123—216no—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×C22⋊Q8—28no—
233C2×C22⋊Q8—28no—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2318yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#120C2314yes—
247C2×#120C2314yes—
248C2×#120C2314yes—
249#518—216no—
250C2×C4×Q8—28no—
251C2×C4×Q8—28no—
252C2×C4×Q8—28no—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2318yes—
260C2×C4×D4—28no—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×#117—28no—
270C2×#117D4116yescomplemented
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2318yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313#400C2314yes—
314#400C2318yes—
315#400C2318yes—
316#400C2314yes—
317#399C2318yes—
318#399C2314yes—
319#399C2318yes—
320#399C2314yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2314yes—
327#398C2318yes—
328#398C2318yes—
329#398C2314yes—
330#397C2314yes—
331#397C2318yes—
332#397C2318yes—
333#397C2318yes—
334#397C2314yes—
335#397C2318yes—
336#397C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#395C2314yes—
346#395C2318yes—
347#395C2318yes—
348#395C2318yes—
349#395C2318yes—
350#395C2314yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2314yes—
355#394C2318yes—
356#394C2318yes—
357#394C2314yes—
358#394C2318yes—
359#394C2318yes—
360#393C2314yes—
361#393C2318yes—
362#393C2318yes—
363#393C2318yes—
364#393C2318yes—
365#393C2314yes—
366#392C2318yes—
367#392C2314yes—
368#392C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2318yes—
373#391C2314yes—
374#391C2314yes—
375#390C2318yes—
376#390C2318yes—
377#390C2314yes—
378#390C2314yes—
379#390C2318yes—
380#390C2314yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2318yes—
389#389C2314yes—
390#389C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#386C2314yes—
424#386C2314yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2318yes—
431#386C2314yes—
432#386C2318yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#385C2314yes—
445#385C2314yes—
446#385C2314yes—
447#384C2314yes—
448#384C2314yes—
449#382C2314yes—
450#382C2314yes—
451#381C2314yes—
452#381C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#381C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2318yes—
464#379C2314yes—
465#379C2314yes—
466#379C2314yes—
467#379C2312yes—
468#379C2312yes—
469#379C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2318yes—
483#376C2314yes—
484C43C2314yes—
485C25C2411yescharacteristic
486C25C2411yescharacteristic
487C25C2412yes—
488C22×Q8—24no—
489C22×Q8—24no—
490C22×Q8—24no—
491C22×Q8—44no—
492C22×Q8—44no—
493C22×Q8—44no—
494C22×Q8C2414yes—
495C22×Q8C2414yes—
496C22×Q8C2414yes—
497C22×Q8C2412yes—
498C22×Q8C2412yes—
499C22×D4—24no—
500C22×D4—28no—
501C22×D4—44no—
502C22×D4—48no—
503C22×D4C2414yes—
504C22×D4C2414yes—
505C22×D4C2414yes—
506C22×D4C2412yes—
507C22×D4C2412yes—
508C22×D4C2418yes—
509C23×C4—24no—
510C23×C4—44no—
511C23×C4—44no—
512C23×C4C2×D418yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—232no—
535C4⋊Q8—48no—
536#126—216no—
537#126—216no—
538#126—232no—
539#126—232no—
540#126—216no—
541#126—216no—
542#126—216no—
543#126—216no—
544#126—216no—
545#126—216no—
546#125—216no—
547#125—216no—
548#125—28no—
549#125—28no—
550#124—232no—
551#124—232no—
552#124—28no—
553#124—28no—
554#124—48no—
555#123—216no—
556#123—216no—
557#123—216no—
558#123—216no—
559#123—216no—
560#123—216no—
561#123—216no—
562#123—48no—
563#123—48no—
564#123—48no—
565#123—48no—
566C22⋊Q8—216no—
567C22⋊Q8—216no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—232no—
571C22⋊Q8—216no—
572C22⋊Q8—216no—
573C22⋊Q8—216no—
574C22⋊Q8—216no—
575C22⋊Q8—416no—
576#121—28no—
577#121—28no—
578#120—216no—
579#120—48no—
580#120—48no—
581C4×Q8—232no—
582C4×Q8—216no—
583C4×Q8—216no—
584C4×Q8—216no—
585C4×Q8—216no—
586C4×Q8—28no—
587C4×Q8—28no—
588C4×D4—216no—
589C4×D4—216no—
590C4×D4—216no—
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—216no—
594C4×D4—28no—
595C4×D4—28no—
596#117—232no—
597#117—216no—
598#117—216no—
599#117—216no—
600#117—48no—
601#117C2×D4132yes—
602#117C2×D4132yes—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4C2×D418yes—
616C2×C4⋊C4C2×D418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—28no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—28no—
665C2×C22⋊C4—28no—
666C2×C22⋊C4—216no—
667C2×C22⋊C4C2×D418yes—
668C2×C22⋊C4C2×D418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C42—24no—
707C2×C42—24no—
708C2×C42—24no—
709C2×C42—24no—
710C2×C42—24no—
711C2×C42C2×D418yes—
712C2×C42C2×D418yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750C24—24no—
751C24—22no—
752C24—24no—
753C24—24no—
754C24—42no—
755C24—42no—
756C24—42no—
757C24—42no—
758C24—44no—
759C24—44no—
760C24—44no—
761C24C22×D414yes—
762C24C2512yes—
763C24C2514yes—
764C24C2512yes—
765C24C2511yescharacteristic
766C2×Q8—28no—
767C2×Q8—28no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—28no—
772C2×Q8—28no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—48no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—416no—
779C2×Q8—416no—
780C2×Q8—416no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—28no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—28no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—416no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4—48no—
798C2×D4—432no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—416no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—48no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—48no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—416no—
835C22×C4C22×D414yes—
836C22×C4C22×D414yes—
837C22×C4C22×D414yes—
838C22×C4C22×D414yes—
839C22×C4C22×D414yes—
840C22×C4C22×D414yes—
841C22×C4C22×D418yes—
842C22×C4C22×D418yes—
843C22×C4C2518yes—
844C22×C4C2518yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2512yes—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—216no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4C22×D4116yes—
899C4⋊C4C22×D4116yes—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4C22×D4116yes—
936C22⋊C4C22×D4116yes—
937C42—28no—
938C42—28no—
939C42—28no—
940C42—28no—
941C42—28no—
942C42—28no—
943C42—28no—
944C42—48no—
945C42—48no—
946C42—44no—
947C42—44no—
948C42C22×D418yes—
949C42C22×D418yes—
950C42C22×D418yes—
951C42C22×D418yes—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—28no—
958C23—22no—
959C23—24no—
960C23—28no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—28no—
967C23—44no—
968C23—44no—
969C23—44no—
970C23—44no—
971C23—48no—
972C23—44no—
973C23—88no—
974C23—88no—
975C23—84no—
976C23—84no—
977C23—168no—
978C23C23×D414yes—
979C23C23×D412yes—
980C23#58514yes—
981C23C2611yescharacteristic
982Q8—416no—
983Q8—416no—
984Q8—416no—
985Q8—84no—
986Q8—84no—
987D4—416no—
988D4—416no—
989D4—416no—
990D4—84no—
991D4—84no—
992D4—168no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—28no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—28no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—44no—
1033C2×C4—44no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—416no—
1037C2×C4—44no—
1038C2×C4—48no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—44no—
1044C2×C4—88no—
1045C2×C4—88no—
1046C2×C4—84no—
1047C2×C4—84no—
1048C2×C4C23×D414yes—
1049C2×C4C23×D414yes—
1050C2×C4C23×D414yes—
1051C2×C4C23×D414yes—
1052C2×C4C23×D412yes—
1053C2×C4C23×D412yes—
1054C2×C4C23×D414yes—
1055C2×C4#58514yes—
1056C22—22no—
1057C22—22no—
1058C22—28no—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—48no—
1063C22—44no—
1064C22—42no—
1065C22—44no—
1066C22—42no—
1067C22—42no—
1068C22—44no—
1069C22—48no—
1070C22—48no—
1071C22—48no—
1072C22—88no—
1073C22—88no—
1074C22—168no—
1075C22#344914yes—
1076C22C24×D411yescharacteristic
1077C22C2×#58512yes—
1078C22C2×#58512yes—
1079C222−1+612yes—
1080C4—24no—
1081C4—24no—
1082C4—24no—
1083C4—24no—
1084C4—24no—
1085C4—24no—
1086C4—22no—
1087C4—22no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—42no—
1092C4—44no—
1093C4—42no—
1094C4—44no—
1095C4—42no—
1096C4—42no—
1097C4—48no—
1098C4—48no—
1099C2—24no—
1100C2—44no—
1101C2—82no—
1102C2—84no—
1103C2C2×#344911yescharacteristic
1104C2#6281111yescharacteristic
1105C2#6285911yescharacteristic
1106C2#6296414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36967C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3491C2semidirect
2. C22×#556C2semidirect
3. #42179C2semidirect
4. #42178C2semidirect
5. #39947C2semidirect
6. #39945C2semidirect
7. #37538C2semidirect
8. #37441C2semidirect
9. #37233C2semidirect
10. #37118C2semidirect
11. #36970C2semidirect
12. #36969C2semidirect
14. #36966C2semidirect
15. #35452C2semidirect
16. #35451C2semidirect
17. #35247C2semidirect
18. #35145C2semidirect
19. #35094C2semidirect
20. #35092C2semidirect
21. #35062C2semidirect
22. #34972C2semidirect
23. #34048C2semidirect
26. C2×#556C22semidirect
27. C2×#556C22semidirect
28. C2×#552C22semidirect
29. C2×#552C22semidirect
30. C2×#551C22semidirect
31. C2×#551C22semidirect
36. C22×C4⋊Q8C22semidirect
41. C22×#126C22semidirect
42. C22×#126C22semidirect
47. C22×C22⋊Q8C22semidirect
49. C22×C4×Q8C22semidirect
50. C22×C4×Q8C22semidirect
51. C22×C4×Q8C22semidirect
54. C22×#117C22semidirect
55. #2860C22semidirect
56. #2855C22semidirect
57. #2855C22semidirect
60. #2853C22semidirect
61. #2849C22semidirect
62. #2823C22semidirect
63. #2814C22semidirect
64. #2723C22semidirect
65. #2720C22semidirect
66. #2718C22semidirect
67. #2716C22semidirect
68. #2713C22semidirect
70. #2700C22semidirect
71. #2698C22semidirect
72. #2696C22semidirect
73. #2692C22semidirect
74. #2689C22semidirect
75. #2685C22semidirect
76. #2677C22semidirect
77. #2674C22semidirect
78. #2674C22semidirect
80. #2664C22semidirect
81. #2664C22semidirect
82. #2663C22semidirect
83. #2662C22semidirect
84. #2662C22semidirect
85. #2637C22semidirect
86. #2637C22semidirect
87. #2636C22semidirect
89. #2627C22semidirect
90. #2627C22semidirect
91. #2626C22semidirect
92. #2626C22semidirect
93. #2623C22semidirect
96. #2614C22semidirect
97. #2604C22semidirect
98. #2604C22semidirect
99. #2603C22semidirect
101. #2601C22semidirect
102. #2601C22semidirect
103. #2592C22semidirect
105. #2584C22semidirect
106. #2583C22semidirect
107. #2583C22semidirect
108. #2582C22semidirect
109. #2579C22semidirect
110. #2579C22semidirect
111. #2565C22semidirect
112. #2561C22semidirect
113. #2561C22semidirect
114. #2545C22semidirect
116. #2538C22semidirect
117. #2534C22semidirect
118. #2534C22semidirect
119. #2503C22semidirect
121. #2486C22semidirect
125. #2480C22semidirect
126. #2479C22semidirect
127. #2478C22semidirect
128. #2477C22semidirect
129. #2475C22semidirect
130. #2474C22semidirect
131. #2472C22semidirect
132. #2471C22semidirect
133. #2469C22semidirect
134. #2468C22semidirect
135. #2466C22semidirect
136. #2465C22semidirect
137. #2462C22semidirect
140. #2458C22semidirect
142. #2434C22semidirect
143. #2413C22semidirect
144. #2413C22semidirect
145. #2413C22semidirect
146. #2411C22semidirect
147. #2409C22semidirect
153. #2396C22semidirect
154. #2323C22semidirect
155. #2322C22semidirect
156. #2322C22semidirect
157. #2321C22semidirect
158. #2321C22semidirect
159. #2314C22semidirect
160. #2313C22semidirect
161. #2313C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#124C22semidirect
167. C4×#123C22semidirect
168. C4×#123C22semidirect
169. #2298C22semidirect
170. #2285C22semidirect
172. C4×#117C22semidirect
270. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34912
C22×#5562
#421792
#421782
#399472
#399452
#375382
#374412
#372332
#371182
#369702
#369692
#369672
#369662
#354522
#354512
#352472
#351452
#350942
#350922
#350622
#349722
#340482