Finite Group Databasebeta

← #7711005

Subgroups — #7711005

Order 512.

5238 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59148C214yesmaximal, complemented
2#59144C212yesmaximal, complemented
3#59143C212yesmaximal
4#46018C214yesmaximal, complemented
5#46014C212yesmaximal, complemented
6#46013C212yesmaximal, complemented
7#40025C214yesmaximal, complemented
8#39771C212yesmaximal, complemented
9#39765C212yesmaximal, complemented
10#39746C212yesmaximal, complemented
11#39740C212yesmaximal, complemented
12#39540C214yesmaximal, complemented
13#39511C212yesmaximal, complemented
14#39495C212yesmaximal, complemented
15#38464C214yesmaximal, complemented
16#37537C212yesmaximal, complemented
17#37145C214yesmaximal, complemented
18#36635C211yesmaximal, characteristic, complemented
19C2×#2858C211yesmaximal, characteristic
20#36538C212yesmaximal, complemented
21#36293C214yesmaximal, complemented
22#36271C212yesmaximal, complemented
23#35114C214yesmaximal, complemented
24#34377C212yesmaximal, complemented
25C4×#533C211yesmaximal, characteristic, complemented
26C2×#559C2212yes—
27C2×#557C2212yescomplemented
28C2×#556C2214yescomplemented
29C2×#533C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×#127C2211yescharacteristic
32C22×#124C2212yes—
33C22×#124C2212yes—
34#2864C2212yescomplemented
35#2863C2212yescomplemented
36#2863C2212yescomplemented
37#2862C2211yescharacteristic, complemented
38#2861C2214yescomplemented
39#2860C2214yescomplemented
40#2859C2211yescharacteristic, complemented
41#2858C2212yes—
42#2858C2212yes—
43#2858C2212yes—
44#2858C2212yes—
45#2858C2212yes—
46#2858C2212yes—
47#2858C2212yes—
48#2858C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2855C2212yes—
52#2855C2212yes—
53#2851C2212yes—
54#2820C2214yescomplemented
55#2820C2214yescomplemented
56#2808C2214yescomplemented
57#2808C2214yescomplemented
58#2804C2214yescomplemented
59#2800C2218yescomplemented
60#2796C2218yescomplemented
61#2780C2218yescomplemented
62#2761C2218yescomplemented
63#2751C2218yescomplemented
64#2732C2214yescomplemented
65#2732C2214yescomplemented
66#2727C2214yescomplemented
67#2727C2214yescomplemented
68#2724C2214yescomplemented
69#2715C2218yescomplemented
70#2713C2218yescomplemented
71#2709C2218yes—
72#2707C2218yescomplemented
73#2700C2218yescomplemented
74#2694C2218yescomplemented
75#2694C2218yescomplemented
76#2658C2214yescomplemented
77#2651C2218yescomplemented
78#2640C2214yescomplemented
79#2632C2218yescomplemented
80#2626C2214yes—
81#2626C2214yes—
82#2601C2218yescomplemented
83#2597C2218yescomplemented
84#2592C2214yescomplemented
85#2592C2214yescomplemented
86#2580C2214yescomplemented
87#2568C2212yescomplemented
88#2566C2214yescomplemented
89#2560C2218yescomplemented
90#2558C2218yescomplemented
91#2558C2218yescomplemented
92#2550C2214yescomplemented
93#2548C2212yes—
94#2548C2212yes—
95#2547C2214yescomplemented
96#2546C2214yescomplemented
97#2546C2212yescomplemented
98#2545C2214yescomplemented
99#2545C2214yescomplemented
100#2545C2214yescomplemented
101#2545C2214yescomplemented
102#2545C2214yescomplemented
103#2544C2214yes—
104#2544C2214yes—
105#2531C2218yescomplemented
106#2526C2218yescomplemented
107#2521C2218yescomplemented
108#2513C2214yescomplemented
109#2512C2214yescomplemented
110#2482C2218yes—
111#2480C2218yes—
112#2480C2218yes—
113#2479C2218yescomplemented
114#2479C2218yescomplemented
115#2474C2218yescomplemented
116#2473C2218yes—
117#2458C2218yescomplemented
118#2454C2214yescomplemented
119#2454C2214yescomplemented
120#2452C2214yescomplemented
121#2451C2214yescomplemented
122#2448C2214yescomplemented
123#2448C2214yescomplemented
124#2448C2214yescomplemented
125#2447C2214yescomplemented
126#2447C2214yescomplemented
127#2446C2214yescomplemented
128#2445C2214yes—
129#2445C2214yes—
130#2442C2214yes—
131#2437C2218yes—
132#2435C2214yes—
133#2435C2214yes—
134#2434C2214yes—
135#2405C2218yes—
136#2379C2214yescomplemented
137#2379C2214yescomplemented
138#2367C2214yescomplemented
139#2367C2214yescomplemented
140#2367C2214yescomplemented
141#2366C2212yes—
142#2365C2212yescomplemented
143#2360C2214yes—
144#2342C2218yes—
145#2342C2218yes—
146Q8×C22⋊C4C2214yes—
147D4×C22⋊C4C2214yes—
148D4×C22⋊C4C2214yes—
149#2337C2218yescomplemented
150#2335C2218yescomplemented
151#2326C2214yescomplemented
152#2326C2214yescomplemented
153#2315C2214yes—
154#2312C2214yes—
155C4×C4⋊Q8C2211yescharacteristic, complemented
156C4×C4⋊Q8C2211yescharacteristic, complemented
157C4×C4⋊Q8C2211yescharacteristic, complemented
158C4×C4⋊Q8C2211yescharacteristic, complemented
159C4×C4⋊Q8C2211yescharacteristic, complemented
160C4×C4⋊Q8C2211yescharacteristic, complemented
161C4×#125C2212yescomplemented
162C4×#125C2212yescomplemented
163C4×#125C2212yescomplemented
164C4×#124C2214yescomplemented
165C4×C22⋊Q8C2212yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2212yes—
169C4×C22⋊Q8C2212yes—
170C4×C22⋊Q8C2212yes—
171#2296C2212yes—
172#2295C2212yescomplemented
173#2295C2212yescomplemented
174#2295C2212yescomplemented
175#2295C2212yescomplemented
176#2293C2214yescomplemented
177C2×#390C2212yes—
178C2×#390C2212yes—
179C2×#390C2212yes—
180C2×#390C2212yes—
181#2285C2211yescharacteristic
182#2283C2212yes—
183C42×Q8C2212yescomplemented
184C42×Q8C2212yescomplemented
185C4×#117C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2312yes—
188C23×D4C2312yes—
189C23×D4C2312yes—
190C23×D4C2312yes—
191#559—48no—
192#557—48no—
193#556—416no—
194#533—28no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2311yescharacteristic
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×#127—44no—
207C2×#127C2312yes—
208C2×#127C2312yes—
209C2×#127C2312yes—
210C2×#127C2312yes—
211C2×#126C2318yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#124—216no—
218C2×#124—48no—
219C2×#124C2314yes—
220C2×#124C2314yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#124C2314yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2318yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C22⋊C4C2314yes—
259C22×C22⋊C4C2314yes—
260C22×C22⋊C4C2318yes—
261C22×C22⋊C4C2314yes—
262C22×C22⋊C4C2314yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#400C2318yes—
271#400C2318yes—
272#399C2318yes—
273#399C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#396C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#395C2318yes—
298#395C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2318yes—
323#391C2318yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2318yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2314yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#383C2314yes—
440#382C2312yes—
441#382C2312yes—
442#382C2312yes—
443#382C2312yes—
444#382C2314yes—
445#381C2314yes—
446#381C2318yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2318yes—
451#380C2318yes—
452#380C2312yes—
453#380C2312yes—
454#380C2318yes—
455#380C2312yes—
456#379C2318yes—
457#379C2318yes—
458#379C2318yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489#376C2314yes—
490#376C2314yes—
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2311yescharacteristic
497C43C2311yescharacteristic
498C43C2311yescharacteristic
499C43C2314yes—
500C25C2414yes—
501C22×Q8—28no—
502C22×Q8—44no—
503C22×Q8—44no—
504C22×Q8C2412yes—
505C22×Q8C2412yes—
506C22×Q8C2414yes—
507C22×Q8C2412yes—
508C22×Q8C2412yes—
509C22×Q8C2414yes—
510C22×D4—28no—
511C22×D4—28no—
512C22×D4—44no—
513C22×D4—44no—
514C22×D4—44no—
515C22×D4—44no—
516C22×D4—44no—
517C22×D4—44no—
518C22×D4—44no—
519C22×D4C2414yes—
520C22×D4C2414yes—
521C22×D4C2414yes—
522C22×D4C2414yes—
523C22×D4C2414yes—
524C22×D4C2414yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2414yes—
532C23×C4C2418yes—
533C23×C4C2418yes—
534C23×C4C2411yescharacteristic
535C4⋊Q8—24no—
536C4⋊Q8—24no—
537C4⋊Q8—28no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—42no—
541C4⋊Q8—44no—
542C4⋊Q8—42no—
543C4⋊Q8—48no—
544C4⋊Q8—48no—
545#127—28no—
546#127—44no—
547#127—44no—
548#127—44no—
549#126—416no—
550#126—416no—
551#125—28no—
552#125—44no—
553#125—48no—
554#125—416no—
555#124—216no—
556#124—216no—
557#124—216no—
558#124—216no—
559#124—216no—
560#124—48no—
561#124—48no—
562#124—48no—
563#124—48no—
564#124—48no—
565#124—48no—
566#124—48no—
567#123—416no—
568#123—416no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—44no—
573C22⋊Q8—416no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×D4—48no—
586C4×D4—48no—
587C4×D4—48no—
588C4×D4—48no—
589#117—28no—
590#117—416no—
591#117—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—44no—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C22⋊C4—216no—
637C2×C22⋊C4—216no—
638C2×C22⋊C4—48no—
639C2×C22⋊C4—48no—
640C2×C22⋊C4—416no—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C42—24no—
668C2×C42—24no—
669C2×C42—24no—
670C2×C42—42no—
671C2×C42—42no—
672C2×C42—42no—
673C2×C42#4118yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2418yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744C24—28no—
745C24—28no—
746C24—28no—
747C24—44no—
748C24—44no—
749C24—44no—
750C24—44no—
751C24C2518yes—
752C24C2511yescharacteristic
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—28no—
756C2×Q8—28no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—28no—
761C2×Q8—28no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—42no—
771C2×Q8—816no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—816no—
791C2×D4—816no—
792C2×D4—816no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—28no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—44no—
812C22×C4—48no—
813C22×C4—44no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4C2×#4114yes—
820C22×C4C2×#4114yes—
821C22×C4C2×#4114yes—
822C22×C42−1+414yes—
823C22×C4C2511yescharacteristic
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2518yes—
833C22×C4C2514yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—48no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—42no—
879C4⋊C4—44no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—216no—
895C22⋊C4—216no—
896C22⋊C4—216no—
897C22⋊C4—216no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C42—28no—
915C42—22no—
916C42—22no—
917C42—22no—
918C42—22no—
919C42—22no—
920C42—22no—
921C42—28no—
922C42—28no—
923C42—28no—
924C42—28no—
925C42—22no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—28no—
934C42—41no—
935C42—41no—
936C42—41no—
937C42—41no—
938C42—41no—
939C42—41no—
940C42—41no—
941C42—41no—
942C42—44no—
943C42—48no—
944C42—44no—
945C42—48no—
946C42C2×#4114yes—
947C42C2×#4114yes—
948C42C2×#4114yes—
949C42C2×#4114yes—
950C42H(5,𝔽2)14yes—
951C42H(5,𝔽2)14yes—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—28no—
957C23—28no—
958C23—28no—
959C23—28no—
960C23—28no—
961C23—28no—
962C23—28no—
963C23—416no—
964C23—88no—
965C23—88no—
966C23—88no—
967C23—88no—
968C23—88no—
969C23—88no—
970C23C22×#4112yes—
971C23C2×2−1+412yes—
972C23#58512yes—
973C23C2611yescharacteristic
974Q8—48no—
975Q8—48no—
976Q8—416no—
977Q8—48no—
978Q8—84no—
979Q8—88no—
980D4—416no—
981D4—416no—
982D4—88no—
983D4—88no—
984D4—88no—
985D4—88no—
986C2×C4—28no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—28no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—28no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—24no—
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—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—88no—
1047C2×C4—816no—
1048C2×C4—168no—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C2×H(5,𝔽2)12yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C2×C4C2×H(5,𝔽2)12yes—
1058C2×C4C2×H(5,𝔽2)12yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4#58512yes—
1064C2×C4#58512yes—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—48no—
1072C22—48no—
1073C22—48no—
1074C22—48no—
1075C22—48no—
1076C22—48no—
1077C22—48no—
1078C22—1616no—
1079C22#350714yes—
1080C22C23×#4111yescharacteristic
1081C22C22×H(5,𝔽2)11yescharacteristic
1082C22C22×H(5,𝔽2)11yescharacteristic
1083C22C22×2−1+411yescharacteristic
1084C22C2×#58511yescharacteristic
1085C22C2×#58511yescharacteristic
1086C22C2×#58511yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—22no—
1094C4—22no—
1095C4—22no—
1096C4—22no—
1097C4—44no—
1098C4—41no—
1099C4—44no—
1100C4—44no—
1101C4—48no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—41no—
1108C4#350814yes—
1109C4#356114yes—
1110C2—24no—
1111C2—88no—
1112C2C2×#356111yescharacteristic
1113C2#6274811yescharacteristic
1114C2C2×#350711yescharacteristic
1115C2C2×#350811yescharacteristic
1116C2#6281511yescharacteristic
1117C2#6282411yescharacteristic
1118C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59148C2semidirect
2. #59144C2semidirect
4. #46018C2semidirect
5. #46014C2semidirect
6. #46013C2semidirect
7. #40025C2semidirect
8. #39771C2semidirect
9. #39765C2semidirect
10. #39746C2semidirect
11. #39740C2semidirect
12. #39540C2semidirect
13. #39511C2semidirect
14. #39495C2semidirect
15. #38464C2semidirect
16. #37537C2semidirect
17. #37145C2semidirect
18. #36635C2semidirect
20. #36538C2semidirect
21. #36293C2semidirect
22. #36271C2semidirect
23. #35114C2semidirect
24. #34377C2semidirect
25. C4×#533C2semidirect
27. C2×#557C22semidirect
28. C2×#556C22semidirect
34. #2864C22semidirect
35. #2863C22semidirect
36. #2863C22semidirect
37. #2862C22semidirect
38. #2861C22semidirect
39. #2860C22semidirect
40. #2859C22semidirect
54. #2820C22semidirect
55. #2820C22semidirect
56. #2808C22semidirect
57. #2808C22semidirect
58. #2804C22semidirect
59. #2800C22semidirect
60. #2796C22semidirect
61. #2780C22semidirect
62. #2761C22semidirect
63. #2751C22semidirect
64. #2732C22semidirect
65. #2732C22semidirect
66. #2727C22semidirect
67. #2727C22semidirect
68. #2724C22semidirect
69. #2715C22semidirect
70. #2713C22semidirect
72. #2707C22semidirect
73. #2700C22semidirect
74. #2694C22semidirect
75. #2694C22semidirect
76. #2658C22semidirect
77. #2651C22semidirect
78. #2640C22semidirect
79. #2632C22semidirect
82. #2601C22semidirect
83. #2597C22semidirect
84. #2592C22semidirect
85. #2592C22semidirect
86. #2580C22semidirect
87. #2568C22semidirect
88. #2566C22semidirect
89. #2560C22semidirect
90. #2558C22semidirect
91. #2558C22semidirect
92. #2550C22semidirect
95. #2547C22semidirect
96. #2546C22semidirect
97. #2546C22semidirect
98. #2545C22semidirect
99. #2545C22semidirect
100. #2545C22semidirect
101. #2545C22semidirect
102. #2545C22semidirect
105. #2531C22semidirect
106. #2526C22semidirect
107. #2521C22semidirect
108. #2513C22semidirect
109. #2512C22semidirect
113. #2479C22semidirect
114. #2479C22semidirect
115. #2474C22semidirect
117. #2458C22semidirect
118. #2454C22semidirect
119. #2454C22semidirect
120. #2452C22semidirect
121. #2451C22semidirect
122. #2448C22semidirect
123. #2448C22semidirect
124. #2448C22semidirect
125. #2447C22semidirect
126. #2447C22semidirect
127. #2446C22semidirect
136. #2379C22semidirect
137. #2379C22semidirect
138. #2367C22semidirect
139. #2367C22semidirect
140. #2367C22semidirect
142. #2365C22semidirect
149. #2337C22semidirect
150. #2335C22semidirect
151. #2326C22semidirect
152. #2326C22semidirect
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
162. C4×#125C22semidirect
163. C4×#125C22semidirect
164. C4×#124C22semidirect
172. #2295C22semidirect
173. #2295C22semidirect
174. #2295C22semidirect
175. #2295C22semidirect
176. #2293C22semidirect
183. C42×Q8C22semidirect
184. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#591482
#591442
#591432
#460182
#460142
#460132
#400252
#397712
#397652
#397462
#397402
#395402
#395112
#394952
#384642
#375372
#371452
#366352
C2×#28582
#365382
#362932
#362712
#351142
#343772
C4×#5332