Finite Group Databasebeta

← #7709987

Subgroups — #7709987

Order 512.

5058 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59655C212yesmaximal, complemented
2#59461C214yesmaximal, complemented
3#59429C212yesmaximal, complemented
4#46154C214yesmaximal, complemented
5#46152C212yesmaximal, complemented
6#46005C212yesmaximal, complemented
7#39752C212yesmaximal, complemented
8#39700C214yesmaximal, complemented
9#39675C214yesmaximal, complemented
10#39652C214yesmaximal, complemented
11#39633C212yesmaximal, complemented
12#39617C212yesmaximal, complemented
13#39367C212yesmaximal
14#37688C214yesmaximal, complemented
15#37561C212yesmaximal, complemented
16#36749C214yesmaximal, complemented
17#36645C211yesmaximal, characteristic, complemented
18#36635C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C212yesmaximal, complemented
20#36190C214yesmaximal, complemented
21#36154C212yesmaximal
22#35014C212yesmaximal, complemented
23#35002C212yesmaximal, complemented
24#34377C212yesmaximal
25C2×C4×#124C211yesmaximal, characteristic
26C2×Q82C2212yescomplemented
27C2×#554C2212yes—
28C2×#543C2214yes—
29C2×#533C2212yes—
30C22×#124C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33#2868C2211yescharacteristic, complemented
34#2868C2211yescharacteristic, complemented
35#2864C2212yescomplemented
36#2863C2212yescomplemented
37#2863C2212yescomplemented
38#2862C2211yescharacteristic, complemented
39#2862C2212yescomplemented
40#2859C2211yescharacteristic, complemented
41#2859C2212yescomplemented
42#2859C2212yescomplemented
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2214yes—
50#2855C2212yes—
51#2855C2212yes—
52#2851C2212yes—
53#2848C2214yes—
54#2845C2214yescomplemented
55#2844C2214yescomplemented
56#2809C2214yescomplemented
57#2806C2214yescomplemented
58#2799C2218yescomplemented
59#2790C2218yescomplemented
60#2790C2218yescomplemented
61#2788C2218yescomplemented
62#2768C2218yescomplemented
63#2742C2218yescomplemented
64#2732C2214yes—
65#2729C2218yescomplemented
66#2729C2218yescomplemented
67#2720C2218yescomplemented
68#2720C2218yescomplemented
69#2704C2218yescomplemented
70#2692C2218yes—
71#2683C2214yes—
72#2677C2218yescomplemented
73#2677C2218yescomplemented
74#2666C2218yescomplemented
75#2660C2214yescomplemented
76#2659C2214yes—
77#2659C2214yes—
78#2647C2214yescomplemented
79#2646C2214yes—
80#2626C2214yes—
81#2589C2218yescomplemented
82#2587C2218yescomplemented
83#2582C2212yescomplemented
84#2582C2214yescomplemented
85#2581C2214yescomplemented
86#2574C2218yescomplemented
87#2570C2214yescomplemented
88#2569C2218yes—
89#2567C2212yescomplemented
90#2567C2214yescomplemented
91#2565C2214yescomplemented
92#2563C2212yes—
93#2550C2214yescomplemented
94#2549C2218yescomplemented
95#2549C2218yescomplemented
96#2542C2214yes—
97#2538C2212yes—
98#2538C2214yes—
99#2522C2218yescomplemented
100#2505C2218yescomplemented
101#2502C2214yescomplemented
102#2497C2214yescomplemented
103#2497C2214yescomplemented
104#2497C2214yescomplemented
105#2492C2214yescomplemented
106#2492C2214yescomplemented
107#2487C2214yes—
108#2465C2218yescomplemented
109#2465C2218yescomplemented
110#2454C2214yes—
111#2453C2214yescomplemented
112#2452C2214yes—
113#2452C2214yes—
114#2451C2218yescomplemented
115#2451C2214yescomplemented
116#2451C2214yescomplemented
117#2450C2218yes—
118#2442C2214yes—
119#2440C2218yes—
120#2440C2214yes—
121#2440C2214yescomplemented
122#2440C2214yescomplemented
123#2440C2214yescomplemented
124#2440C2214yescomplemented
125#2440C2214yescomplemented
126#2438C2218yes—
127#2437C2218yes—
128#2437C2218yes—
129#2429C2218yescomplemented
130#2429C2214yescomplemented
131#2423C2218yescomplemented
132#2423C2214yescomplemented
133#2423C2214yescomplemented
134#2417C2214yes—
135#2379C2214yes—
136#2379C2214yes—
137#2368C2218yescomplemented
138#2367C2214yes—
139#2367C2214yes—
140#2360C2214yescomplemented
141Q8×C4⋊C4C2212yescomplemented
142Q8×C4⋊C4C2214yescomplemented
143#2349C2214yes—
144D4×C4⋊C4C2212yes—
145#2345C2214yescomplemented
146#2342C2218yes—
147Q8×C22⋊C4C2214yes—
148D4×C22⋊C4C2214yes—
149#2337C2218yes—
150#2329C2214yes—
151#2326C2214yes—
152#2326C2214yes—
153#2315C2214yes—
154#2312C2214yes—
155C4×C4⋊Q8C2211yescharacteristic, complemented
156C4×C4⋊Q8C2212yescomplemented
157C4×C4⋊Q8C2212yescomplemented
158C4×C4⋊Q8C2211yescharacteristic, complemented
159C4×C4⋊Q8C2212yescomplemented
160C4×C4⋊Q8C2212yescomplemented
161C4×#125C2212yescomplemented
162C4×#124C2212yes—
163C4×#124C2212yes—
164C4×#124C2212yes—
165C4×#124C2212yes—
166C4×#124C2212yes—
167C4×#124C2212yes—
168C4×#124C2212yes—
169C4×#124C2212yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2212yes—
172C4×C22⋊Q8C2214yes—
173#2295C2212yescomplemented
174#2295C2212yescomplemented
175C2×#391C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#388C2212yes—
178C2×#388C2212yes—
179#2285C2212yes—
180#2285C2212yes—
181#2283C2212yes—
182C2×#382C2211yescharacteristic
183C2×#380C2214yes—
184C2×C4×C22⋊C4C2212yes—
185C2×C4×C22⋊C4C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C24×C4C2312yes—
190Q82—48no—
191#554—48no—
192#543—416no—
193#533—48no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2318yes—
205C2×#125C2312yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#124Q8116yescomplemented
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C4×Q8—44no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×D4—44no—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×#117C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2318yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#399C2318yes—
272#399C2318yes—
273#399C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#393C2318yes—
303#393C2318yes—
304#393C2318yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2314yes—
313#391C2318yes—
314#391C2318yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2318yes—
320#391C2318yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2318yes—
327#391C2312yes—
328#391C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2318yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#386C2318yes—
401#386C2318yes—
402#385C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#384C2312yes—
419#384C2312yes—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#384C2318yes—
426#384C2312yes—
427#384C2312yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#383C2314yes—
432#382C2312yes—
433#382C2314yes—
434#382C2312yes—
435#382C2314yes—
436#382C2312yes—
437#382C2312yes—
438#382C2314yes—
439#382C2312yes—
440#382C2312yes—
441#382C2312yes—
442#381C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2312yes—
446#380C2314yes—
447#380C2314yes—
448#380C2318yes—
449#380C2318yes—
450#380C2312yes—
451#380C2318yes—
452#380C2312yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2318yes—
458#380C2318yes—
459#380C2314yes—
460#379C2318yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485#376C2314yes—
486C2×#95C2312yes—
487C2×#95C2312yes—
488C2×#95C2318yes—
489C2×#95C2312yes—
490C2×#95C2312yes—
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2311yescharacteristic
497C43C2311yescharacteristic
498C43C2311yescharacteristic
499C25C2412yes—
500C22×Q8—42no—
501C22×Q8—42no—
502C22×Q8C2×Q818yes—
503C22×Q8C2412yes—
504C22×Q8C2412yes—
505C22×Q8C2412yes—
506C22×Q8C2414yes—
507C22×Q8C2414yes—
508C22×Q8C2418yes—
509C22×Q8C2412yes—
510C22×D4—42no—
511C22×D4—42no—
512C22×D4C2×Q818yes—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C23×C4—28no—
516C23×C4—44no—
517C23×C4—44no—
518C23×C4C2414yes—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2414yes—
527C23×C4C2418yes—
528C23×C4C2418yes—
529C23×C4C2412yes—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C4⋊Q8—28no—
533C4⋊Q8—42no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—48no—
539C4⋊Q8—48no—
540C4⋊Q8—42no—
541C4⋊Q8—44no—
542C4⋊Q8—416no—
543#125—44no—
544#125—48no—
545#125—48no—
546#124C2×Q8116yes—
547#124C2×Q8116yes—
548#124C2×Q8116yes—
549#124C2×Q8116yes—
550C22⋊Q8—216no—
551C22⋊Q8—28no—
552C22⋊Q8—28no—
553C22⋊Q8—48no—
554C22⋊Q8—416no—
555C22⋊Q8—416no—
556C22⋊Q8—416no—
557C22⋊Q8—416no—
558C22⋊Q8—416no—
559C22⋊Q8—416no—
560C22⋊Q8—416no—
561C22⋊Q8—48no—
562C22⋊Q8—48no—
563C4×Q8—28no—
564C4×Q8—28no—
565C4×Q8—44no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×Q8—48no—
569C4×Q8—44no—
570C4×Q8—48no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×D4—28no—
575C4×D4—44no—
576C4×D4—44no—
577C4×D4—48no—
578C4×D4—48no—
579C4×D4—44no—
580#117—48no—
581C2×C4⋊C4—48no—
582C2×C4⋊C4—42no—
583C2×C4⋊C4—42no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—48no—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C22⋊C4—28no—
634C2×C22⋊C4—44no—
635C2×C22⋊C4—44no—
636C2×C22⋊C4—416no—
637C2×C22⋊C4C2×Q8116yes—
638C2×C22⋊C4C2×Q8116yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—44no—
662C2×C42—42no—
663C2×C42—42no—
664C2×C42—42no—
665C2×C42C2×Q818yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2414yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2418yes—
687C2×C42C2418yes—
688C2×C42C2414yes—
689C2×C42C2418yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737C24—24no—
738C24—24no—
739C24—42no—
740C24—42no—
741C24—42no—
742C24—42no—
743C24C22×Q818yes—
744C24C2514yes—
745C24C2511yescharacteristic
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—28no—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—44no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—44no—
760C2×Q8—44no—
761C2×Q8—44no—
762C2×Q8—48no—
763C2×Q8—48no—
764C2×Q8—48no—
765C2×Q8—416no—
766C2×Q8C22×Q818yes—
767C2×Q8C22×Q818yes—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—416no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4C22×Q818yes—
774C2×D4C22×Q818yes—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—22no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—22no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—42no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—42no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—816no—
812C22×C4C22×Q814yes—
813C22×C4C22×Q814yes—
814C22×C4C22×Q814yes—
815C22×C4C22×Q818yes—
816C22×C4H(5,𝔽2)14yes—
817C22×C42−1+414yes—
818C22×C4C2511yescharacteristic
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2514yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—216no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—48no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—42no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4C22×Q8116yes—
904C22⋊C4C22×Q8116yes—
905C22⋊C4C22×Q8116yes—
906C22⋊C4C22×Q8116yes—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—22no—
914C42—28no—
915C42—28no—
916C42—22no—
917C42—22no—
918C42—22no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—22no—
926C42—28no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—41no—
931C42—41no—
932C42—41no—
933C42—44no—
934C42—48no—
935C42—48no—
936C42—48no—
937C42C22×Q814yes—
938C42C22×Q814yes—
939C42C22×Q814yes—
940C42C22×Q814yes—
941C42H(5,𝔽2)14yes—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—216no—
953C23—48no—
954C23—48no—
955C23—84no—
956C23—84no—
957C23—84no—
958C23—84no—
959C23C23×Q818yes—
960C23C23×Q812yes—
961C23C2×H(5,𝔽2)12yes—
962C23C2×2−1+412yes—
963C23C2611yescharacteristic
964Q8—216no—
965Q8—48no—
966Q8—48no—
967Q8—84no—
968Q8—88no—
969Q8—88no—
970Q8—168no—
971D4—216no—
972D4—48no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—24no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—28no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—24no—
1018C2×C4—21no—
1019C2×C4—28no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—44no—
1029C2×C4—48no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—44no—
1033C2×C4—416no—
1034C2×C4—88no—
1035C2×C4—84no—
1036C2×C4—84no—
1037C2×C4—168no—
1038C2×C4—168no—
1039C2×C4C23×Q812yes—
1040C2×C4C23×Q812yes—
1041C2×C4C23×Q812yes—
1042C2×C4C23×Q812yes—
1043C2×C4C23×Q812yes—
1044C2×C4C23×Q818yes—
1045C2×C4C23×Q812yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4C2×H(5,𝔽2)12yes—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4C2×2−1+412yes—
1053C2×C4#58512yes—
1054C2×C4#58512yes—
1055C2×C4#58512yes—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—28no—
1063C22—28no—
1064C22—28no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—816no—
1070C22#350314yes—
1071C22C24×Q811yescharacteristic
1072C22C22×H(5,𝔽2)11yescharacteristic
1073C22C22×H(5,𝔽2)11yescharacteristic
1074C22C22×2−1+411yescharacteristic
1075C22C2×#58511yescharacteristic
1076C22C2×#58511yescharacteristic
1077C22C2×#58511yescharacteristic
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—28no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—44no—
1090C4—44no—
1091C4—44no—
1092C4—41no—
1093C4—44no—
1094C4—48no—
1095C4—41no—
1096C4—44no—
1097C4—44no—
1098C4—48no—
1099C4#350114yes—
1100C4#356114yes—
1101C2—24no—
1102C2—48no—
1103C2C2×#356111yescharacteristic
1104C2#6275211yescharacteristic
1105C2C2×#350111yescharacteristic
1106C2C2×#350311yescharacteristic
1107C2#6281311yescharacteristic
1108C2#6282211yescharacteristic
1109C2#6283411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59655C2semidirect
2. #59461C2semidirect
3. #59429C2semidirect
4. #46154C2semidirect
5. #46152C2semidirect
6. #46005C2semidirect
7. #39752C2semidirect
8. #39700C2semidirect
9. #39675C2semidirect
10. #39652C2semidirect
11. #39633C2semidirect
12. #39617C2semidirect
14. #37688C2semidirect
15. #37561C2semidirect
16. #36749C2semidirect
17. #36645C2semidirect
18. #36635C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36190C2semidirect
22. #35014C2semidirect
23. #35002C2semidirect
26. C2×Q82C22semidirect
33. #2868C22semidirect
34. #2868C22semidirect
35. #2864C22semidirect
36. #2863C22semidirect
37. #2863C22semidirect
38. #2862C22semidirect
39. #2862C22semidirect
40. #2859C22semidirect
41. #2859C22semidirect
42. #2859C22semidirect
54. #2845C22semidirect
55. #2844C22semidirect
56. #2809C22semidirect
57. #2806C22semidirect
58. #2799C22semidirect
59. #2790C22semidirect
60. #2790C22semidirect
61. #2788C22semidirect
62. #2768C22semidirect
63. #2742C22semidirect
65. #2729C22semidirect
66. #2729C22semidirect
67. #2720C22semidirect
68. #2720C22semidirect
69. #2704C22semidirect
72. #2677C22semidirect
73. #2677C22semidirect
74. #2666C22semidirect
75. #2660C22semidirect
78. #2647C22semidirect
81. #2589C22semidirect
82. #2587C22semidirect
83. #2582C22semidirect
84. #2582C22semidirect
85. #2581C22semidirect
86. #2574C22semidirect
87. #2570C22semidirect
89. #2567C22semidirect
90. #2567C22semidirect
91. #2565C22semidirect
93. #2550C22semidirect
94. #2549C22semidirect
95. #2549C22semidirect
99. #2522C22semidirect
100. #2505C22semidirect
101. #2502C22semidirect
102. #2497C22semidirect
103. #2497C22semidirect
104. #2497C22semidirect
105. #2492C22semidirect
106. #2492C22semidirect
108. #2465C22semidirect
109. #2465C22semidirect
111. #2453C22semidirect
114. #2451C22semidirect
115. #2451C22semidirect
116. #2451C22semidirect
121. #2440C22semidirect
122. #2440C22semidirect
123. #2440C22semidirect
124. #2440C22semidirect
125. #2440C22semidirect
129. #2429C22semidirect
130. #2429C22semidirect
131. #2423C22semidirect
132. #2423C22semidirect
133. #2423C22semidirect
137. #2368C22semidirect
140. #2360C22semidirect
141. Q8×C4⋊C4C22semidirect
142. Q8×C4⋊C4C22semidirect
145. #2345C22semidirect
155. C4×C4⋊Q8C22semidirect
156. C4×C4⋊Q8C22semidirect
157. C4×C4⋊Q8C22semidirect
158. C4×C4⋊Q8C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×#125C22semidirect
173. #2295C22semidirect
174. #2295C22semidirect
208. C2×#124Q8semidirect

Maximal subgroups

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

subgroupindex
#596552
#594612
#594292
#461542
#461522
#460052
#397522
#397002
#396752
#396522
#396332
#396172
#393672
#376882
#375612
#367492
#366452
#366352
Q8×C22⋊Q82
#361902
#361542
#350142
#350022
#343772
C2×C4×#1242