Finite Group Databasebeta

← #7677484

Subgroups — #7677484

Order 512.

7250 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3493C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#59059C214yesmaximal, complemented
4#59055C214yesmaximal, complemented
5#59053C214yesmaximal, complemented
6#59050C214yesmaximal, complemented
7#45217C214yesmaximal, complemented
8#45196C214yesmaximal, complemented
9#45101C214yesmaximal, complemented
10#44897C214yesmaximal, complemented
11#39380C214yesmaximal, complemented
12#37771C214yesmaximal, complemented
13#37770C214yesmaximal, complemented
14#36117C214yesmaximal, complemented
15#35634C212yesmaximal, complemented
16#35621C212yesmaximal, complemented
17#35166C211yesmaximal, characteristic, complemented
18#35153C211yesmaximal, characteristic, complemented
19#35150C211yesmaximal, characteristic, complemented
20#34743C212yesmaximal, complemented
21#34271C211yesmaximal, characteristic, complemented
22#34267C212yesmaximal, complemented
23C2×#2362C211yesmaximal, characteristic, complemented
24#3493—216no—
25C2×#556C2214yes—
26C2×#555C2214yes—
27C2×#553C2214yes—
28C2×#552C2214yes—
29#3461—216no—
30C2×#544C2211yescharacteristic
31C2×#542C2214yescomplemented
32C2×#541C2214yescomplemented
33C2×#539C2214yes—
34C2×#538C2214yes—
35C2×#537C2212yes—
36C2×#537C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#536C2212yes—
39C2×#536C2212yes—
40C2×#533C2214yescomplemented
41C2×#532C2212yes—
42C2×#529C2214yes—
43C2×#529C2214yes—
44C2×#529C2214yescomplemented
45C2×#525C2212yes—
46C2×#525C2212yes—
47C22×C22⋊Q8C2211yescharacteristic
48C2×#520C2212yes—
49C2×C4×#41C2212yes—
50C22×C4×Q8C2211yescharacteristic
51C22×#117C2211yescharacteristic
52#2856C2214yes—
53#2854C2214yes—
54#2854C2214yes—
55#2733C2218yes—
56#2730C2218yes—
57#2730C2218yescomplemented
58#2727C2218yes—
59#2721C2218yes—
60#2721C2218yescomplemented
61#2721C2218yescomplemented
62#2714C2218yes—
63#2705C2218yes—
64#2705C2218yescomplemented
65#2694C2218yes—
66#2673C2218yes—
67#2656C2214yes—
68#2618C2214yes—
69#2617C2214yes—
70#2554C2218yes—
71#2554C2218yes—
72#2552C2214yescomplemented
73#2548C2214yescomplemented
74#2547C2214yescomplemented
75#2546C2214yescomplemented
76#2545C2214yescomplemented
77#2544C2214yescomplemented
78#2542C2214yes—
79#2542C2214yes—
80#2542C2214yes—
81#2542C2214yes—
82#2542C2214yescomplemented
83#2541C2214yescomplemented
84#2540C2214yes—
85#2540C2214yes—
86#2540C2214yes—
87#2540C2214yes—
88#2540C2214yescomplemented
89#2540C2214yescomplemented
90#2539C2218yes—
91#2512C2218yescomplemented
92#2501C2218yes—
93#2490C2218yes—
94#2479C2218yes—
95#2479C2218yescomplemented
96#2479C2218yescomplemented
97#2471C2218yescomplemented
98#2467C2218yescomplemented
99#2456C2218yes—
100#2454C2214yescomplemented
101#2454C2214yescomplemented
102#2448C2218yes—
103#2448C2214yescomplemented
104#2448C2214yescomplemented
105#2441C2218yescomplemented
106#2429C2212yes—
107#2429C2212yes—
108#2429C2214yescomplemented
109#2429C2214yescomplemented
110#2428C2212yes—
111#2428C2212yes—
112#2427C2212yes—
113#2427C2212yes—
114#2426C2218yes—
115#2426C2212yes—
116#2426C2212yes—
117#2426C2214yescomplemented
118#2426C2214yescomplemented
119#2425C2214yes—
120#2425C2218yes—
121#2425C2218yes—
122#2425C2214yes—
123#2424C2214yes—
124#2424C2214yes—
125#2423C2218yescomplemented
126#2417C2214yescomplemented
127#2417C2214yescomplemented
128#2415C2214yes—
129#2415C2214yes—
130#2415C2214yescomplemented
131#2415C2214yescomplemented
132#2414C2214yes—
133#2414C2214yes—
134#2414C2218yes—
135#2392C2214yes—
136#2392C2214yes—
137#2370C2214yescomplemented
138#2370C2214yescomplemented
139#2369C2214yescomplemented
140#2366C2214yescomplemented
141#2365C2214yescomplemented
142#2364C2218yes—
143#2363C2214yescomplemented
144#2362C2214yes—
145#2362C2214yes—
146#2362C2214yes—
147#2362C2214yes—
148#2362C2214yescomplemented
149#2361C2218yes—
150#2361C2214yescomplemented
151#2360C2214yescomplemented
152#2354C2218yescomplemented
153Q8×C4⋊C4C2214yescomplemented
154#2329C2214yes—
155#2324C2214yescomplemented
156#2323C2214yescomplemented
157#2316C2211yescharacteristic
158#2311C2212yes—
159C4×C22⋊Q8C2214yes—
160C4×C22⋊Q8C2214yescomplemented
161C4×#121C2214yes—
162C4×#121C2214yes—
163C4×#121C2214yescomplemented
164#2297C2212yes—
165#2296C2212yes—
166C2×#391C2211yescharacteristic
167C2×#389C2211yescharacteristic
168C2×#388C2212yes—
169C2×#388C2212yes—
170C2×#387C2212yes—
171#2274C2212yes—
172C2×C4×C4⋊C4C2212yes—
173C2×C4×C4⋊C4C2211yescharacteristic
174C2×C4×C22⋊C4C2211yescharacteristic
175C22×#41C2312yes—
176C22×#41C2312yes—
177C23×Q8C2311yescharacteristic
178C24×C4C2311yescharacteristic
179#556—232no—
180#555—232no—
181#553—232no—
182#552—232no—
183#544D4116yescomplemented
184#542—232no—
185#541—232no—
186#539—232no—
187#538—232no—
188#537—28no—
189#537—28no—
190#537—216no—
191#536—216no—
192#536—48no—
193#533—232no—
194#532—48no—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×#127C2314yes—
200C2×#127C2312yes—
201#529—232no—
202#529—232no—
203#529—232no—
204C2×#126C2318yes—
205C2×#126C2318yes—
206C2×#126C2318yes—
207C2×#126C2318yes—
208C2×#125C2314yes—
209C2×#125C2314yes—
210C2×#125C2318yes—
211C2×#125C2314yes—
212C2×#124C2314yes—
213C2×#124C2314yes—
214C2×#124C2314yes—
215C2×#124C2318yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#124C2314yes—
219#525—216no—
220#525—48no—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×#123C2318yes—
224C2×#123C2318yes—
225C2×#123C2314yes—
226C2×#123C2318yes—
227C2×C22⋊Q8—28no—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2318yes—
248C2×#121C2314yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2318yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#120C2314yes—
261C2×#120C2314yes—
262#520—216no—
263C4×#41—216no—
264C2×C4×Q8—28no—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2318yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×#117—28no—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2318yes—
292C2×#117C2318yes—
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C2×#117C2312yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C22⋊C4C2312yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C42C2312yes—
309C22×C42C2312yes—
310C22×C42C2311yescharacteristic
311C22×C42C2314yes—
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314#399C2318yes—
315#399C2318yes—
316#399C2318yes—
317#399C2318yes—
318#399C2318yes—
319#399C2318yes—
320#399C2318yes—
321#399C2318yes—
322#398C2318yes—
323#398C2314yes—
324#398C2314yes—
325#398C2318yes—
326#398C2318yes—
327#397C2318yes—
328#397C2314yes—
329#397C2314yes—
330#397C2318yes—
331#397C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2318yes—
339#396C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2318yes—
350#394C2318yes—
351#392C2318yes—
352#392C2314yes—
353#392C2314yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#391C2314yes—
359#391C2312yes—
360#391C2318yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2312yes—
365#390C2314yes—
366#390C2312yes—
367#390C2318yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2318yes—
373#390C2318yes—
374#390C2314yes—
375#390C2314yes—
376#390C2318yes—
377#390C2318yes—
378#390C2314yes—
379#390C2318yes—
380#390C2314yes—
381#390C2312yes—
382#390C2318yes—
383#390C2318yes—
384#390C2318yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2318yes—
389#389C2318yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2318yes—
396#389C2314yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2314yes—
402#389C2318yes—
403#389C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2314yes—
432#386C2314yes—
433#386C2318yes—
434#386C2314yes—
435#386C2318yes—
436#386C2318yes—
437#386C2314yes—
438#386C2314yes—
439#386C2314yes—
440#385C2318yes—
441#385C2314yes—
442#385C2318yes—
443#385C2314yes—
444#384C2314yes—
445#384C2318yes—
446#384C2318yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2318yes—
452#380C2318yes—
453#380C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2318yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C22⋊C4C2318yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2318yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2318yes—
478C2×#95C2312yes—
479C2×#95C2312yes—
480C2×#95C2311yescharacteristic
481C2×#95C2311yescharacteristic
482C2×#95C2312yes—
483C2×#95C2312yes—
484C25C2411yescharacteristic
485C2×#41—28no—
486C2×#41—28no—
487C2×#41—28no—
488C2×#41—28no—
489C2×#41—28no—
490C2×#41—28no—
491C22×Q8—24no—
492C22×Q8—24no—
493C22×Q8—24no—
494C22×Q8C2414yes—
495C22×Q8C2412yes—
496C22×Q8C2412yes—
497C22×Q8C2414yes—
498C22×D4C2414yes—
499C22×D4C2414yes—
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2414yes—
503C22×D4C2414yes—
504C22×D4C2414yes—
505C22×D4C2414yes—
506C22×D4C2418yes—
507C22×D4C2414yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C23×C4C2414yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2414yes—
523C23×C4C2412yes—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2418yes—
527C23×C4C2414yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2411yescharacteristic
531C4⋊Q8—216no—
532C4⋊Q8—44no—
533C4⋊Q8—48no—
534C4⋊Q8C2×D4132yes—
535#127—48no—
536#127—44no—
537#126—232no—
538#126—232no—
539#126—232no—
540#126—232no—
541#125—216no—
542#125—216no—
543#125—232no—
544#125C2×D4132yes—
545#124—216no—
546#124—216no—
547#124—232no—
548#124—216no—
549#124—44no—
550#124—44no—
551#124—48no—
552#123—232no—
553#123—232no—
554#123—216no—
555#123—232no—
556#123—48no—
557#123—416no—
558C22⋊Q8—232no—
559C22⋊Q8—28no—
560C22⋊Q8—28no—
561C22⋊Q8—216no—
562C22⋊Q8—216no—
563C22⋊Q8—216no—
564C22⋊Q8—216no—
565C22⋊Q8—216no—
566C22⋊Q8—216no—
567C22⋊Q8—216no—
568C22⋊Q8—216no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571C22⋊Q8—48no—
572C22⋊Q8—48no—
573C22⋊Q8C2×D4132yes—
574#121—216no—
575#121—216no—
576#121—232no—
577#121—28no—
578#121—28no—
579#121—216no—
580#121—216no—
581#121—232no—
582#121—216no—
583#121—216no—
584#121—48no—
585#121—48no—
586#121—44no—
587#121—44no—
588#121—48no—
589#121—48no—
590#120—216no—
591#120—48no—
592C4×Q8—216no—
593C4×Q8—216no—
594C4×Q8—216no—
595C4×Q8—216no—
596C4×Q8—28no—
597C4×Q8—28no—
598C4×Q8—216no—
599C4×Q8—48no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—216no—
603C4×D4—216no—
604C4×D4—216no—
605C4×D4—216no—
606C4×D4—232no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—416no—
615#117—28no—
616#117—216no—
617#117—216no—
618#117—216no—
619#117—232no—
620#117—232no—
621#117—216no—
622#117C2×D4116yes—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—28no—
626C2×C4⋊C4—216no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2×D418yes—
629C2×C4⋊C4#4118yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C22⋊C4—28no—
667C2×C22⋊C4—28no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C42—28no—
708C2×C42—24no—
709C2×C42—28no—
710C2×C42—24no—
711C2×C42—216no—
712C2×C42—44no—
713C2×C42C2414yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2418yes—
727C2×C42C2418yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730#95C2411yescharacteristic
731#95C2411yescharacteristic
732#95C2411yescharacteristic
733#95C2411yescharacteristic
734#95C2412yes—
735#95C2418yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—41no—
758C24—41no—
759C24—41no—
760C24—41no—
761C24C2512yes—
762C24C2514yes—
763C24C2514yes—
764C24C2511yescharacteristic
765#41—432no—
766#41—432no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—416no—
779C2×Q8C22×D4116yes—
780C2×D4—28no—
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—28no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—216no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—28no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—48no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—48no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—28no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—216no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—44no—
852C22×C4—42no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—42no—
858C22×C4—48no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—44no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—41no—
865C22×C4—416no—
866C22×C4C22×D418yes—
867C22×C4C22×D414yes—
868C22×C4C2×#4118yes—
869C22×C4C2×#4114yes—
870C22×C4H(5,𝔽2)14yes—
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2514yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2514yes—
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2512yes—
890C4⋊C4—28no—
891C4⋊C4—216no—
892C4⋊C4—216no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—216no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—216no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—216no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4C22×D418yes—
921C4⋊C4C22×D4116yes—
922C4⋊C4C22×D418yes—
923C4⋊C4C22×D4132yes—
924C4⋊C4C22×D4116yes—
925C4⋊C4C2×#41116yes—
926C22⋊C4—28no—
927C22⋊C4—216no—
928C22⋊C4—28no—
929C22⋊C4—216no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—216no—
933C22⋊C4—216no—
934C22⋊C4—216no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—216no—
940C22⋊C4—216no—
941C22⋊C4—216no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4C22×D4116yes—
963C42—24no—
964C42—28no—
965C42—28no—
966C42—28no—
967C42—24no—
968C42—28no—
969C42—28no—
970C42—28no—
971C42—216no—
972C42—24no—
973C42—24no—
974C42—28no—
975C42—28no—
976C42—44no—
977C42—48no—
978C42—48no—
979C42C22×D4116yes—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—44no—
1006C23—44no—
1007C23—44no—
1008C23—82no—
1009C23—82no—
1010C23—82no—
1011C23—82no—
1012C23C23×D412yes—
1013C23C22×#4112yes—
1014C23C2×H(5,𝔽2)12yes—
1015C23C2611yescharacteristic
1016Q8—416no—
1017Q8—416no—
1018Q8—48no—
1019Q8—48no—
1020D4—416no—
1021D4—416no—
1022D4—48no—
1023D4—48no—
1024D4—88no—
1025D4—88no—
1026D4—88no—
1027D4—88no—
1028D4—816no—
1029D4—88no—
1030D4—88no—
1031D4—88no—
1032D4—88no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—24no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—21no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—416no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—48no—
1088C2×C4—48no—
1089C2×C4—48no—
1090C2×C4—416no—
1091C2×C4—416no—
1092C2×C4—88no—
1093C2×C4—816no—
1094C2×C4—82no—
1095C2×C4—84no—
1096C2×C4—82no—
1097C2×C4#550116yes—
1098C2×C4C23×D418yes—
1099C2×C4C23×D418yes—
1100C2×C4C23×D418yes—
1101C2×C4C23×D414yes—
1102C2×C4C22×#4118yes—
1103C2×C4C22×#4114yes—
1104C2×C4C2×H(5,𝔽2)14yes—
1105C2×C4#58512yes—
1106C2×C4#58512yes—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—44no—
1114C22—44no—
1115C22—42no—
1116C22—44no—
1117C22—44no—
1118C22—42no—
1119C22—44no—
1120C22—44no—
1121C22—42no—
1122C22—44no—
1123C22—44no—
1124C22—42no—
1125C22—44no—
1126C22—42no—
1127C22—44no—
1128C22—42no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—42no—
1133C22—44no—
1134C22—88no—
1135C22C2×#55014yes—
1136C22C24×D411yescharacteristic
1137C22C23×#4111yescharacteristic
1138C22C22×H(5,𝔽2)11yescharacteristic
1139C22C2×#58511yescharacteristic
1140C22C2×#58511yescharacteristic
1141C222−1+611yescharacteristic
1142C222−1+611yescharacteristic
1143C4—28no—
1144C4—28no—
1145C4—22no—
1146C4—28no—
1147C4—28no—
1148C4—22no—
1149C4—42no—
1150C4—41no—
1151C4—44no—
1152C4—41no—
1153C4—44no—
1154C4—41no—
1155C4—41no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—42no—
1160C4—44no—
1161C4C2×#55018yes—
1162C2—24no—
1163C2—84no—
1164C2—84no—
1165C2—82no—
1166C2C22×#55011yescharacteristic
1167C2#6278111yescharacteristic
1168C2#6285011yescharacteristic
1169C2#6292711yescharacteristic
1170C2#6296011yescharacteristic
1171C2#6298811yescharacteristic
1172C2#6300211yescharacteristic
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. C2×#3493C2semidirect
2. C2×#3461C2semidirect
3. #59059C2semidirect
4. #59055C2semidirect
5. #59053C2semidirect
6. #59050C2semidirect
7. #45217C2semidirect
8. #45196C2semidirect
9. #45101C2semidirect
10. #44897C2semidirect
11. #39380C2semidirect
12. #37771C2semidirect
13. #37770C2semidirect
14. #36117C2semidirect
15. #35634C2semidirect
16. #35621C2semidirect
17. #35166C2semidirect
18. #35153C2semidirect
19. #35150C2semidirect
20. #34743C2semidirect
21. #34271C2semidirect
22. #34267C2semidirect
23. C2×#2362C2semidirect
31. C2×#542C22semidirect
32. C2×#541C22semidirect
40. C2×#533C22semidirect
44. C2×#529C22semidirect
57. #2730C22semidirect
60. #2721C22semidirect
61. #2721C22semidirect
64. #2705C22semidirect
72. #2552C22semidirect
73. #2548C22semidirect
74. #2547C22semidirect
75. #2546C22semidirect
76. #2545C22semidirect
77. #2544C22semidirect
82. #2542C22semidirect
83. #2541C22semidirect
88. #2540C22semidirect
89. #2540C22semidirect
91. #2512C22semidirect
95. #2479C22semidirect
96. #2479C22semidirect
97. #2471C22semidirect
98. #2467C22semidirect
100. #2454C22semidirect
101. #2454C22semidirect
103. #2448C22semidirect
104. #2448C22semidirect
105. #2441C22semidirect
108. #2429C22semidirect
109. #2429C22semidirect
117. #2426C22semidirect
118. #2426C22semidirect
125. #2423C22semidirect
126. #2417C22semidirect
127. #2417C22semidirect
130. #2415C22semidirect
131. #2415C22semidirect
137. #2370C22semidirect
138. #2370C22semidirect
139. #2369C22semidirect
140. #2366C22semidirect
141. #2365C22semidirect
143. #2363C22semidirect
148. #2362C22semidirect
150. #2361C22semidirect
151. #2360C22semidirect
152. #2354C22semidirect
153. Q8×C4⋊C4C22semidirect
155. #2324C22semidirect
156. #2323C22semidirect
160. C4×C22⋊Q8C22semidirect
163. C4×#121C22semidirect
183. #544D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34932
C2×#34612
#590592
#590552
#590532
#590502
#452172
#451962
#451012
#448972
#393802
#377712
#377702
#361172
#356342
#356212
#351662
#351532
#351502
#347432
#342712
#342672
C2×#23622