Finite Group Databasebeta

← #7683758

Subgroups — #7683758

Order 512.

5684 conjugacy classes of subgroups.

The subgroup lattice has 1109 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59461C214yesmaximal, complemented
2#59458C214yesmaximal, complemented
3#59323C214yesmaximal, complemented
4#59314C214yesmaximal, complemented
5#59150C218yesmaximal, complemented
6#45086C214yesmaximal, complemented
7#44951C214yesmaximal, complemented
8#44940C214yesmaximal, complemented
9#44908C214yesmaximal, complemented
10#43121C218yesmaximal, complemented
11#35576C211yesmaximal, characteristic, complemented
12#35574C211yesmaximal, characteristic, complemented
13#35555C211yesmaximal, characteristic, complemented
14#35532C211yesmaximal, characteristic, complemented
15#35529C211yesmaximal, characteristic, complemented
16#35515C211yesmaximal, characteristic, complemented
17C2×#2542C211yesmaximal, characteristic, complemented
18#34815C211yesmaximal, characteristic, complemented
19#34745C211yesmaximal, characteristic, complemented
20#34275C211yesmaximal, characteristic
21#34269C211yesmaximal, characteristic
22#34265C211yesmaximal, characteristic
23#34248C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34183C211yesmaximal, characteristic, complemented
26C2×#554C2218yescomplemented
27C2×#544C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2214yes—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#518C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2807C2218yescomplemented
39#2780C2218yescomplemented
40#2780C2218yescomplemented
41#2768C2218yescomplemented
42#2748C2218yescomplemented
43#2742C2218yescomplemented
44#2732C2218yescomplemented
45#2729C2218yescomplemented
46#2720C2218yescomplemented
47#2720C2218yescomplemented
48#2692C2218yescomplemented
49#2692C2218yescomplemented
50#2589C2218yescomplemented
51#2583C2214yes—
52#2583C2218yescomplemented
53#2580C2214yes—
54#2580C2218yescomplemented
55#2579C2214yes—
56#2570C2214yescomplemented
57#2567C2212yescomplemented
58#2566C2212yes—
59#2566C2212yes—
60#2566C2212yescomplemented
61#2565C2212yescomplemented
62#2564C2218yescomplemented
63#2563C2212yes—
64#2556C2218yescomplemented
65#2552C2214yescomplemented
66#2551C2214yescomplemented
67#2551C2214yescomplemented
68#2550C2214yescomplemented
69#2550C2214yescomplemented
70#2549C2218yescomplemented
71#2542C2214yes—
72#2542C2214yes—
73#2542C2214yes—
74#2542C2214yes—
75#2542C2212yes—
76#2542C2212yescomplemented
77#2538C2214yes—
78#2522C2218yescomplemented
79#2522C2218yescomplemented
80#2509C2212yescomplemented
81#2508C2212yescomplemented
82#2507C2214yescomplemented
83#2507C2212yescomplemented
84#2506C2212yescomplemented
85#2506C2214yescomplemented
86#2505C2214yes—
87#2487C2218yescomplemented
88#2473C2214yes—
89#2473C2218yes—
90#2465C2218yescomplemented
91#2454C2214yes—
92#2454C2214yes—
93#2454C2218yescomplemented
94#2454C2212yescomplemented
95#2453C2212yescomplemented
96#2452C2214yes—
97#2452C2214yes—
98#2452C2218yescomplemented
99#2452C2212yescomplemented
100#2452C2214yescomplemented
101#2451C2214yescomplemented
102#2451C2212yescomplemented
103#2450C2214yes—
104#2450C2218yescomplemented
105#2449C2214yes—
106#2449C2218yes—
107#2449C2218yescomplemented
108#2449C2218yescomplemented
109#2449C2218yescomplemented
110#2441C2214yescomplemented
111#2440C2218yescomplemented
112#2440C2214yescomplemented
113#2440C2214yescomplemented
114#2439C2214yescomplemented
115#2437C2218yes—
116#2437C2218yes—
117#2434C2214yes—
118#2423C2218yescomplemented
119#2409C2214yes—
120#2402C2214yescomplemented
121#2396C2214yescomplemented
122C2×#399C2214yes—
123#2368C2218yescomplemented
124#2367C2214yes—
125#2367C2214yes—
126#2366C2214yes—
127#2366C2214yes—
128#2363C2214yes—
129#2363C2214yes—
130#2361C2214yes—
131#2361C2214yes—
132#2360C2218yes—
133#2358C2218yes—
134#2358C2218yes—
135#2355C2214yescomplemented
136Q8×C4⋊C4C2214yescomplemented
137Q8×C4⋊C4C2214yescomplemented
138#2349C2214yes—
139#2349C2214yes—
140D4×C4⋊C4C2218yes—
141D4×C4⋊C4C2214yes—
142D4×C4⋊C4C2214yes—
143D4×C4⋊C4C2214yescomplemented
144#2330C2214yescomplemented
145#2328C2212yes—
146#2326C2212yes—
147#2324C2214yes—
148#2321C2214yes—
149#2317C2211yescharacteristic
150#2317C2211yescharacteristic
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yescomplemented
155#2317C2212yescomplemented
156#2316C2211yescharacteristic
157#2315C2214yes—
158#2311C2211yescharacteristic
159#2309C2211yescharacteristic
160C4×C4⋊Q8C2214yescomplemented
161C4×#127C2212yes—
162C4×#125C2214yescomplemented
163C4×#124C2212yes—
164C4×C22⋊Q8C2214yescomplemented
165C4×#121C2214yes—
166C4×#120C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#390C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#385C2214yes—
178#2285C2211yescharacteristic
179#2285C2212yescomplemented
180C2×#384C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#384C2212yescomplemented
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2312yes—
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#554—432no—
192#544—44no—
193#535Q8116yescomplemented
194#533—28no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2318yes—
202C2×#127C2312yes—
203C2×#125C2314yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#125C2318yes—
208C2×#124C2312yes—
209C2×C22⋊Q8—416no—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×#121C2314yes—
222C2×#120C2314yes—
223#520—44no—
224#520—44no—
225#518—28no—
226#518—44no—
227C4×#41—28no—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2318yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×D4—44no—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2318yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2318yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2318yes—
271C22×C4⋊C4C2314yes—
272C22×C22⋊C4C2314yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C22⋊C4C2314yes—
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280C22×C42C2311yescharacteristic
281#400C2314yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#399C2314yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2318yes—
294#399C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2318yes—
306#398C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2314yes—
313#396C2318yes—
314#396C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2314yes—
321#393C2318yes—
322#393C2318yes—
323#393C2318yes—
324#393C2314yes—
325#391C2318yes—
326#391C2311yescharacteristic
327#391C2312yes—
328#391C2311yescharacteristic
329#391C2314yes—
330#391C2312yes—
331#391C2318yes—
332#391C2318yes—
333#390C2311yescharacteristic
334#390C2318yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2312yes—
341#390C2311yescharacteristic
342#390C2312yes—
343#390C2318yes—
344#390C2318yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2318yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2312yes—
364#389C2312yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2312yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2318yes—
406#386C2318yes—
407#386C2312yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2312yes—
413#385C2312yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2318yes—
422#385C2312yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2318yes—
432#385C2312yes—
433#385C2312yes—
434#385C2312yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#384C2312yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2314yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#384C2318yes—
450#384C2314yes—
451#384C2312yes—
452#384C2311yescharacteristic
453#382C2314yes—
454#382C2311yescharacteristic
455#382C2312yes—
456#382C2312yes—
457#382C2311yescharacteristic
458#382C2312yes—
459#382C2312yes—
460#382C2312yes—
461#380C2318yes—
462#380C2318yes—
463#380C2314yes—
464#380C2318yes—
465#380C2318yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#380C2314yes—
470#379C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2318yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500#376C2312yes—
501C2×#95C2318yes—
502C2×#95C2312yes—
503C43C2312yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41C2×Q818yes—
508C22×Q8—44no—
509C22×Q8—48no—
510C22×Q8C2414yes—
511C22×Q8C2411yescharacteristic
512C22×Q8C2418yes—
513C22×Q8C2414yes—
514C22×D4—24no—
515C22×D4—24no—
516C22×D4C2×Q818yes—
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2411yescharacteristic
521C22×D4C2418yes—
522C23×C4—48no—
523C23×C4—44no—
524C23×C4C2411yescharacteristic
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2418yes—
534C23×C4C2418yes—
535C23×C4C2414yes—
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2411yescharacteristic
540C4⋊Q8—28no—
541C4⋊Q8—48no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—416no—
546#127C2×Q8116yescomplemented
547#125—28no—
548#125—216no—
549#125—44no—
550#125—44no—
551#125—416no—
552#124C2×Q8116yescomplemented
553C22⋊Q8—232no—
554C22⋊Q8—216no—
555C22⋊Q8—216no—
556C22⋊Q8—48no—
557C22⋊Q8—416no—
558C22⋊Q8—416no—
559C22⋊Q8—416no—
560C22⋊Q8—416no—
561C22⋊Q8—416no—
562C22⋊Q8—416no—
563C22⋊Q8—416no—
564#121C2×Q8132yescomplemented
565#120C2×Q8132yes—
566C4×Q8—28no—
567C4×Q8—216no—
568C4×Q8—44no—
569C4×Q8—44no—
570C4×Q8—416no—
571C4×D4—28no—
572C4×D4—216no—
573C4×D4—216no—
574C4×D4—216no—
575C4×D4—416no—
576C4×D4—48no—
577C4×D4—48no—
578C4×D4—44no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—416no—
585C4×D4—416no—
586C4×D4—48no—
587C4×D4—48no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—28no—
594#117—44no—
595#117—44no—
596#117C2×Q818yes—
597#117#4118yes—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—28no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4—48no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—416no—
607C2×C4⋊C4—416no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C22⋊C4—216no—
664C2×C22⋊C4—48no—
665C2×C22⋊C4—48no—
666C2×C22⋊C4—48no—
667C2×C22⋊C4—44no—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2412yes—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—24no—
697C2×C42—28no—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753C24—24no—
754C24—24no—
755C24—44no—
756C24—44no—
757C24C22×Q818yes—
758C24C2514yes—
759C24C2512yes—
760C24C2511yescharacteristic
761#41—232no—
762C2×Q8—22no—
763C2×Q8—28no—
764C2×Q8—22no—
765C2×Q8—28no—
766C2×Q8—216no—
767C2×Q8—44no—
768C2×Q8—48no—
769C2×Q8—48no—
770C2×Q8—48no—
771C2×Q8—44no—
772C2×Q8—816no—
773C2×Q8C22×Q814yes—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—232no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—22no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4C22×Q818yes—
786C2×D4C22×Q818yes—
787C2×D4C22×Q818yes—
788C2×D4C22×Q814yes—
789C2×D4C22×Q8132yes—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—28no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—216no—
805C22×C4—216no—
806C22×C4—42no—
807C22×C4—44no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—816no—
826C22×C4C22×Q818yes—
827C22×C4C22×Q814yes—
828C22×C4C2×#4114yes—
829C22×C4H(5,𝔽2)14yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—216no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—216no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4C22×Q818yes—
904C4⋊C4C2×#4118yes—
905C4⋊C4H(5,𝔽2)18yes—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—216no—
912C22⋊C4—28no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4C22×Q818yes—
930C22⋊C4C22×Q8132yes—
931C22⋊C4C2×#4118yes—
932C42—22no—
933C42—22no—
934C42—28no—
935C42—24no—
936C42—24no—
937C42—22no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—44no—
948C42—44no—
949C42—44no—
950C42—48no—
951C42—48no—
952C42C22×Q818yes—
953C42C2×#4118yes—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—28no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—28no—
964C23—216no—
965C23—416no—
966C23—84no—
967C23—88no—
968C23—84no—
969C23C23×Q818yes—
970C23C23×Q814yes—
971C23C23×Q812yes—
972C23C22×#4112yes—
973C23C2×H(5,𝔽2)12yes—
974C23C2611yescharacteristic
975Q8—28no—
976Q8—416no—
977Q8—816no—
978Q8—164no—
979D4—216no—
980D4—216no—
981D4—216no—
982D4—28no—
983D4—432no—
984C2×C4—28no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—216no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—416no—
1032C2×C4—48no—
1033C2×C4—48no—
1034C2×C4—44no—
1035C2×C4—816no—
1036C2×C4—816no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—164no—
1041C2×C4—164no—
1042C2×C4—164no—
1043C2×C4—164no—
1044C2×C4#554116yescomplemented
1045C2×C4C23×Q818yes—
1046C2×C4C23×Q814yes—
1047C2×C4C23×Q812yes—
1048C2×C4C23×Q812yes—
1049C2×C4C22×#4118yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C2×H(5,𝔽2)14yes—
1053C2×C4C2×H(5,𝔽2)14yes—
1054C2×C4C2×H(5,𝔽2)14yes—
1055C2×C4C2×H(5,𝔽2)12yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C22—24no—
1058C22—24no—
1059C22—22no—
1060C22—22no—
1061C22—28no—
1062C22—216no—
1063C22—24no—
1064C22—28no—
1065C22—44no—
1066C22—48no—
1067C22—44no—
1068C22—42no—
1069C22—44no—
1070C22—42no—
1071C22—816no—
1072C22C2×#55414yes—
1073C22C24×Q811yescharacteristic
1074C22C23×#4111yescharacteristic
1075C22C22×H(5,𝔽2)12yes—
1076C22C22×H(5,𝔽2)11yescharacteristic
1077C222−1+612yes—
1078C4—28no—
1079C4—24no—
1080C4—28no—
1081C4—24no—
1082C4—24no—
1083C4—24no—
1084C4—42no—
1085C4—42no—
1086C4—44no—
1087C4—44no—
1088C4—44no—
1089C4—44no—
1090C4—44no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4C2×#55414yes—
1099C4C2×#55414yes—
1100C2—24no—
1101C2—44no—
1102C2—48no—
1103C2C22×#55411yescharacteristic
1104C2#6283211yescharacteristic
1105C2#6288711yescharacteristic
1106C2Q8×H(5,𝔽2)12yes—
1107C2#6298512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59461C2semidirect
2. #59458C2semidirect
3. #59323C2semidirect
4. #59314C2semidirect
5. #59150C2semidirect
6. #45086C2semidirect
7. #44951C2semidirect
8. #44940C2semidirect
9. #44908C2semidirect
10. #43121C2semidirect
11. #35576C2semidirect
12. #35574C2semidirect
13. #35555C2semidirect
14. #35532C2semidirect
15. #35529C2semidirect
16. #35515C2semidirect
17. C2×#2542C2semidirect
18. #34815C2semidirect
19. #34745C2semidirect
23. #34248C2semidirect
24. #34214C2semidirect
25. #34183C2semidirect
26. C2×#554C22semidirect
38. #2807C22semidirect
39. #2780C22semidirect
40. #2780C22semidirect
41. #2768C22semidirect
42. #2748C22semidirect
43. #2742C22semidirect
44. #2732C22semidirect
45. #2729C22semidirect
46. #2720C22semidirect
47. #2720C22semidirect
48. #2692C22semidirect
49. #2692C22semidirect
50. #2589C22semidirect
52. #2583C22semidirect
54. #2580C22semidirect
56. #2570C22semidirect
57. #2567C22semidirect
60. #2566C22semidirect
61. #2565C22semidirect
62. #2564C22semidirect
64. #2556C22semidirect
65. #2552C22semidirect
66. #2551C22semidirect
67. #2551C22semidirect
68. #2550C22semidirect
69. #2550C22semidirect
70. #2549C22semidirect
76. #2542C22semidirect
78. #2522C22semidirect
79. #2522C22semidirect
80. #2509C22semidirect
81. #2508C22semidirect
82. #2507C22semidirect
83. #2507C22semidirect
84. #2506C22semidirect
85. #2506C22semidirect
87. #2487C22semidirect
90. #2465C22semidirect
93. #2454C22semidirect
94. #2454C22semidirect
95. #2453C22semidirect
98. #2452C22semidirect
99. #2452C22semidirect
100. #2452C22semidirect
101. #2451C22semidirect
102. #2451C22semidirect
104. #2450C22semidirect
107. #2449C22semidirect
108. #2449C22semidirect
109. #2449C22semidirect
110. #2441C22semidirect
111. #2440C22semidirect
112. #2440C22semidirect
113. #2440C22semidirect
114. #2439C22semidirect
118. #2423C22semidirect
120. #2402C22semidirect
121. #2396C22semidirect
123. #2368C22semidirect
135. #2355C22semidirect
136. Q8×C4⋊C4C22semidirect
137. Q8×C4⋊C4C22semidirect
143. D4×C4⋊C4C22semidirect
144. #2330C22semidirect
154. #2317C22semidirect
155. #2317C22semidirect
160. C4×C4⋊Q8C22semidirect
162. C4×#125C22semidirect
164. C4×C22⋊Q8C22semidirect
179. #2285C22semidirect
182. C2×#384C22semidirect
193. #535Q8semidirect
546. #127C2×Q8semidirect
552. #124C2×Q8semidirect
564. #121C2×Q8semidirect
1044. C2×C4#554semidirect

Maximal subgroups

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

subgroupindex
#594612
#594582
#593232
#593142
#591502
#450862
#449512
#449402
#449082
#431212
#355762
#355742
#355552
#355322
#355292
#355152
C2×#25422
#348152
#347452
#342752
#342692
#342652
#342482
#342142
#341832