Finite Group Databasebeta

← #8095104

Subgroups — #8095104

Order 512.

5849 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53144C214yesmaximal, complemented
2#53032C212yesmaximal, complemented
3#53005C214yesmaximal, complemented
4#53005C212yesmaximal, complemented
5#52990C212yesmaximal, complemented
6#52958C212yesmaximal, complemented
7#52925C214yesmaximal, complemented
8#52914C214yesmaximal, complemented
9#46073C212yesmaximal, complemented
10#46043C214yesmaximal, complemented
11#46004C212yesmaximal, complemented
12#45667C214yesmaximal, complemented
13#45667C212yesmaximal, complemented
14#45568C214yesmaximal, complemented
15#45539C214yesmaximal, complemented
16#45494C212yesmaximal, complemented
17#35644C212yesmaximal, complemented
18#35628C212yesmaximal, complemented
19#35542C212yesmaximal, complemented
20#35312C212yesmaximal, complemented
21#35305C212yesmaximal, complemented
22#35242C212yesmaximal, complemented
23#34946C211yesmaximal, characteristic, complemented
24#34736C211yesmaximal, characteristic
25C2×#2409C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C24×Q8C2211yescharacteristic, complemented
28C2×#544C2212yescomplemented
29C2×#536C2212yes—
30C2×#536C2212yes—
31C2×#533C2211yescharacteristic, complemented
32C2×#525C2212yes—
33C22×C22⋊Q8C2212yes—
34C22×C4×D4C2211yescharacteristic
35#2862C2214yescomplemented
36#2861C2214yescomplemented
37#2849C2218yescomplemented
38#2848C2214yescomplemented
39#2848C2214yescomplemented
40#2844C2218yescomplemented
41#2844C2214yescomplemented
42#2840C2214yescomplemented
43#2835C2214yescomplemented
44#2835C2214yescomplemented
45#2835C2218yescomplemented
46#2832C2218yescomplemented
47#2832C2218yescomplemented
48#2832C2218yescomplemented
49#2832C2218yescomplemented
50#2832C2214yescomplemented
51#2824C2218yescomplemented
52#2824C2214yescomplemented
53#2811C2214yescomplemented
54#2804C2214yes—
55#2804C2218yescomplemented
56#2785C2214yescomplemented
57#2785C2218yescomplemented
58#2782C2218yes—
59#2782C2218yescomplemented
60#2782C2218yescomplemented
61#2763C2214yescomplemented
62#2763C2218yescomplemented
63#2763C2214yescomplemented
64#2763C2218yescomplemented
65#2763C2218yescomplemented
66#2763C2218yescomplemented
67#2763C2218yescomplemented
68#2753C2218yescomplemented
69#2753C2218yescomplemented
70#2753C2218yescomplemented
71#2736C2218yescomplemented
72#2736C2214yescomplemented
73#2712C2218yescomplemented
74#2712C2214yescomplemented
75#2684C2214yes—
76#2684C2218yes—
77#2642C2214yescomplemented
78#2640C2214yescomplemented
79#2616C2214yescomplemented
80#2616C2214yescomplemented
81#2614C2218yescomplemented
82#2592C2214yescomplemented
83#2592C2214yescomplemented
84#2568C2214yescomplemented
85#2568C2214yescomplemented
86#2563C2211yescharacteristic
87#2563C2211yescharacteristic, complemented
88#2563C2214yescomplemented
89#2562C2212yes—
90#2562C2212yescomplemented
91#2562C2214yescomplemented
92#2562C2214yescomplemented
93#2561C2218yes—
94#2561C2212yes—
95#2561C2212yescomplemented
96#2547C2211yescharacteristic
97#2547C2214yescomplemented
98#2547C2211yescharacteristic, complemented
99#2503C2218yescomplemented
100#2503C2212yescomplemented
101#2492C2214yescomplemented
102#2492C2214yescomplemented
103#2492C2214yescomplemented
104#2492C2214yescomplemented
105#2492C2214yescomplemented
106#2492C2214yescomplemented
107#2492C2214yescomplemented
108#2492C2214yescomplemented
109#2492C2214yescomplemented
110#2491C2214yescomplemented
111#2490C2214yescomplemented
112#2489C2214yescomplemented
113#2489C2214yescomplemented
114#2489C2214yescomplemented
115#2489C2214yescomplemented
116#2489C2214yescomplemented
117#2489C2214yescomplemented
118#2489C2214yescomplemented
119#2489C2214yescomplemented
120#2489C2214yescomplemented
121#2488C2218yescomplemented
122#2488C2218yescomplemented
123#2488C2218yescomplemented
124#2488C2218yescomplemented
125#2488C2218yescomplemented
126#2472C2218yescomplemented
127#2436C2214yescomplemented
128#2436C2214yescomplemented
129#2435C2212yes—
130#2435C2214yescomplemented
131#2434C2214yescomplemented
132#2434C2214yescomplemented
133#2434C2214yescomplemented
134#2432C2214yescomplemented
135#2432C2214yescomplemented
136#2409C2211yescharacteristic
137#2409C2212yes—
138#2409C2212yes—
139#2409C2212yes—
140#2409C2212yes—
141#2409C2211yescharacteristic
142#2409C2212yescomplemented
143#2409C2214yescomplemented
144#2409C2214yescomplemented
145#2409C2212yescomplemented
146#2409C2214yescomplemented
147#2409C2214yescomplemented
148#2409C2212yescomplemented
149#2409C2212yescomplemented
150#2408C2211yescharacteristic
151#2408C2211yescharacteristic
152#2407C2212yes—
153#2407C2212yes—
154#2406C2212yes—
155#2406C2218yes—
156#2405C2218yes—
157#2405C2212yes—
158#2404C2212yes—
159#2403C2212yes—
160#2398C2212yes—
161#2398C2212yescomplemented
162#2388C2212yes—
163#2388C2212yes—
164C2×#395C2212yescomplemented
165C2×#393C2212yes—
166#2379C2214yes—
167#2379C2218yescomplemented
168#2375C2214yes—
169#2311C2212yes—
170#2311C2212yes—
171#2310C2212yescomplemented
172#2310C2212yescomplemented
173C4×#124C2212yes—
174C4×#124C2212yescomplemented
175C4×#120C2212yes—
176C4×#120C2212yes—
177#2297C2212yes—
178C2×#391C2212yescomplemented
179C2×#386C2212yes—
180C2×#385C2212yescomplemented
181#2280C2211yescharacteristic
182#2280C2212yes—
183#2280C2212yescomplemented
184C2×#380C2211yescharacteristic, complemented
185#2274C2212yescomplemented
186C4×#117C2211yescharacteristic, complemented
187C22×#41—44no—
188C22×#41—48no—
189C22×#41C2312yes—
190C22×#41C2312yes—
191C22×#41C2312yes—
192C22×#41C2312yes—
193C23×Q8—44no—
194C23×Q8—48no—
195C23×Q8C2312yes—
196C23×Q8C2312yes—
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200C23×Q8C2312yes—
201C23×Q8C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C23×D4C2312yes—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C24×C4C2312yes—
208C24×C4C2312yes—
209#544—48no—
210#536—48no—
211#536—48no—
212#533—44no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2314yes—
225C2×#124C2318yes—
226C2×#124C2312yes—
227#525—48no—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×#123C2314yes—
231C2×C22⋊Q8—48no—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#120C2312yes—
248C2×#120C2314yes—
249C2×#120C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×D4—44no—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2314yes—
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2314yes—
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2312yes—
273C22×C42C2311yescharacteristic
274#400C2314yes—
275#400C2314yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#397C2318yes—
291#397C2312yes—
292#397C2312yes—
293#397C2318yes—
294#397C2312yes—
295#397C2312yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#395C2314yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2314yes—
307#395C2314yes—
308#395C2318yes—
309#395C2318yes—
310#395C2312yes—
311#395C2318yes—
312#395C2312yes—
313#395C2314yes—
314#394C2314yes—
315#394C2314yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2314yes—
322#394C2312yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2314yes—
327#394C2312yes—
328#393C2312yes—
329#393C2312yes—
330#393C2318yes—
331#393C2318yes—
332#393C2312yes—
333#393C2312yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#393C2314yes—
339#393C2318yes—
340#393C2318yes—
341#393C2314yes—
342#393C2318yes—
343#393C2318yes—
344#393C2318yes—
345#393C2318yes—
346#393C2312yes—
347#393C2314yes—
348#393C2314yes—
349#393C2312yes—
350#392C2314yes—
351#392C2312yes—
352#392C2314yes—
353#392C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2312yes—
365#391C2312yes—
366#391C2318yes—
367#391C2314yes—
368#391C2314yes—
369#391C2318yes—
370#391C2312yes—
371#391C2318yes—
372#391C2318yes—
373#391C2318yes—
374#391C2318yes—
375#391C2318yes—
376#391C2314yes—
377#391C2314yes—
378#391C2312yes—
379#390C2312yes—
380#390C2318yes—
381#390C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2312yes—
385#390C2312yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2314yes—
414#386C2312yes—
415#386C2314yes—
416#386C2314yes—
417#386C2312yes—
418#386C2314yes—
419#386C2314yes—
420#386C2314yes—
421#386C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2312yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2312yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#382C2312yes—
441#382C2312yes—
442#382C2318yes—
443#382C2318yes—
444#382C2318yes—
445#382C2318yes—
446#382C2318yes—
447#382C2318yes—
448#382C2318yes—
449#381C2318yes—
450#381C2318yes—
451#381C2314yes—
452#381C2314yes—
453#381C2312yes—
454#380C2312yes—
455#380C2312yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468#380C2312yes—
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2312yes—
472#380C2312yes—
473#379C2312yes—
474#379C2314yes—
475#379C2314yes—
476#379C2312yes—
477#379C2318yes—
478#379C2318yes—
479#379C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498#376C2312yes—
499C2×#95C2312yes—
500C2×#95C2314yes—
501C2×#95C2314yes—
502C43C2312yes—
503C25C2411yescharacteristic
504C25C2411yescharacteristic
505C25C2412yes—
506C2×#41—28no—
507C2×#41—28no—
508C2×#41—28no—
509C2×#41—44no—
510C2×#41—48no—
511C2×#41—44no—
512C2×#41—48no—
513C2×#41—44no—
514C2×#41—44no—
515C2×#41—44no—
516C2×#41—464no—
517C22×Q8—28no—
518C22×Q8—28no—
519C22×Q8—28no—
520C22×Q8—44no—
521C22×Q8—48no—
522C22×Q8—44no—
523C22×Q8—44no—
524C22×Q8—48no—
525C22×Q8—48no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8—48no—
529C22×Q8—48no—
530C22×Q8—42no—
531C22×Q8—44no—
532C22×Q8—464no—
533C22×Q8C2414yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2418yes—
539C22×Q8C2414yes—
540C22×Q8C2414yes—
541C22×Q8C2412yes—
542C22×D4—24no—
543C22×D4—42no—
544C22×D4—44no—
545C22×D4—42no—
546C22×D4—42no—
547C22×D4—48no—
548C22×D4—44no—
549C22×D4C2414yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2411yescharacteristic
554C22×D4C2414yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C23×C4—24no—
560C23×C4—24no—
561C23×C4—28no—
562C23×C4—28no—
563C23×C4—44no—
564C23×C4—48no—
565C23×C4—48no—
566C23×C4—44no—
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2414yes—
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2414yes—
579C23×C4C2411yescharacteristic
580C23×C4C2414yes—
581C23×C4C2411yescharacteristic
582C23×C4C2412yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2411yescharacteristic
587C4⋊Q8—42no—
588C4⋊Q8—42no—
589C4⋊Q8—48no—
590C4⋊Q8—48no—
591C4⋊Q8—48no—
592C4⋊Q8—48no—
593#125—44no—
594#125—48no—
595#125—48no—
596#124—28no—
597#124—48no—
598#124—48no—
599#124—416no—
600#124—44no—
601#123—48no—
602#123—416no—
603#123—416no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606C22⋊Q8—416no—
607C22⋊Q8—48no—
608C22⋊Q8—48no—
609C22⋊Q8—48no—
610C22⋊Q8—48no—
611C22⋊Q8—44no—
612C22⋊Q8—44no—
613C22⋊Q8—48no—
614C22⋊Q8—48no—
615C22⋊Q8—48no—
616C22⋊Q8—48no—
617#121—44no—
618#121—44no—
619#120—28no—
620#120—48no—
621#120—44no—
622C4×Q8—44no—
623C4×Q8—44no—
624C4×D4—42no—
625C4×D4—42no—
626C4×D4—42no—
627C4×D4—42no—
628C4×D4—42no—
629C4×D4—42no—
630C4×D4—42no—
631C4×D4—42no—
632C4×D4—48no—
633C4×D4—48no—
634#117—28no—
635#117—28no—
636#117—28no—
637C2×C4⋊C4—28no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—48no—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C22⋊C4—44no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—48no—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2411yescharacteristic
681C2×C22⋊C4C2411yescharacteristic
682C2×C22⋊C4C2411yescharacteristic
683C2×C22⋊C4C2411yescharacteristic
684C2×C22⋊C4C2411yescharacteristic
685C2×C22⋊C4C2411yescharacteristic
686C2×C22⋊C4C2411yescharacteristic
687C2×C22⋊C4C2411yescharacteristic
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C42—24no—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2418yes—
724C2×C42C2414yes—
725C2×C42C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2412yes—
733#95C2414yes—
734#95C2412yes—
735#95C2418yes—
736#95C2418yes—
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—24no—
768C24—22no—
769C24—24no—
770C24—22no—
771C24—24no—
772C24—42no—
773C24—44no—
774C24—42no—
775C24—41no—
776C24—42no—
777C24—42no—
778C24—44no—
779C24C2511yescharacteristic
780C24C2514yes—
781C24C2511yescharacteristic
782C24C2511yescharacteristic
783C24C2511yescharacteristic
784C24C2511yescharacteristic
785#41—432no—
786#41—432no—
787#41—432no—
788#41—432no—
789C2×Q8—28no—
790C2×Q8—28no—
791C2×Q8—28no—
792C2×Q8—28no—
793C2×Q8—24no—
794C2×Q8—28no—
795C2×Q8—28no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—48no—
802C2×Q8—48no—
803C2×Q8—42no—
804C2×Q8—44no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—44no—
809C2×Q8—48no—
810C2×Q8—48no—
811C2×Q8—48no—
812C2×Q8—432no—
813C2×Q8—432no—
814C2×Q8—432no—
815C2×Q8—432no—
816C2×Q8—432no—
817C2×Q8—416no—
818C2×Q8—432no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—41no—
838C2×D4—42no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—416no—
848C2×D4—432no—
849C2×D4—416no—
850C2×D42−1+414yes—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—28no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—22no—
860C22×C4—28no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—22no—
881C22×C4—44no—
882C22×C4—42no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—41no—
891C22×C4—44no—
892C22×C4—42no—
893C22×C4—44no—
894C22×C4—432no—
895C22×C4—432no—
896C22×C4—416no—
897C22×C4—416no—
898C22×C4H(5,𝔽2)14yes—
899C22×C4H(5,𝔽2)18yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2511yescharacteristic
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2518yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2518yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2514yes—
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—48no—
945C4⋊C4—48no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—24no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—44no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—42no—
980C22⋊C4—44no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—44no—
987C22⋊C4—48no—
988C42—22no—
989C42—22no—
990C42—22no—
991C42—22no—
992C42—28no—
993C42—28no—
994C42—28no—
995C42—24no—
996C42—44no—
997C42—48no—
998C42—42no—
999C42—48no—
1000C23—21no—
1001C23—21no—
1002C23—22no—
1003C23—28no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—24no—
1018C23—24no—
1019C23—21no—
1020C23—24no—
1021C23—24no—
1022C23—21no—
1023C23—24no—
1024C23—21no—
1025C23—22no—
1026C23—24no—
1027C23—24no—
1028C23—48no—
1029C23—48no—
1030C23—44no—
1031C23—48no—
1032C23—44no—
1033C23—44no—
1034C23—48no—
1035C23—44no—
1036C23—82no—
1037C23—84no—
1038C23—84no—
1039C23—88no—
1040C23—84no—
1041C23—88no—
1042C23C2×H(5,𝔽2)12yes—
1043C23C2×H(5,𝔽2)14yes—
1044C23C2×2−1+412yes—
1045C23C2×2−1+412yes—
1046C23#58512yes—
1047C23C2611yescharacteristic
1048Q8—416no—
1049Q8—416no—
1050Q8—48no—
1051Q8—416no—
1052Q8—416no—
1053Q8—48no—
1054Q8—84no—
1055Q8—84no—
1056Q8—168no—
1057D4—44no—
1058D4—44no—
1059D4—44no—
1060D4—44no—
1061D4—48no—
1062D4—416no—
1063D4—416no—
1064D4—48no—
1065D4—88no—
1066D4—88no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—28no—
1087C2×C4—28no—
1088C2×C4—28no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—21no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—28no—
1100C2×C4—24no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—28no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—44no—
1112C2×C4—48no—
1113C2×C4—416no—
1114C2×C4—416no—
1115C2×C4—416no—
1116C2×C4—44no—
1117C2×C4—416no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—44no—
1121C2×C4—44no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—416no—
1128C2×C4—82no—
1129C2×C4—88no—
1130C2×C4H(3,𝔽4)116yes—
1131C2×C4C2×H(5,𝔽2)12yes—
1132C2×C4C2×H(5,𝔽2)12yes—
1133C2×C4C2×H(5,𝔽2)14yes—
1134C2×C4C2×H(5,𝔽2)14yes—
1135C2×C4C2×2−1+412yes—
1136C22—22no—
1137C22—22no—
1138C22—24no—
1139C22—24no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—416no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—42no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—42no—
1155C22—42no—
1156C22—41no—
1157C22—44no—
1158C22—44no—
1159C22—41no—
1160C22—44no—
1161C22—42no—
1162C22—44no—
1163C22—44no—
1164C22—41no—
1165C22—44no—
1166C22—42no—
1167C22—44no—
1168C22—88no—
1169C22—816no—
1170C22C2×H(3,𝔽4)14yes—
1171C22C22×H(5,𝔽2)11yescharacteristic
1172C22C22×H(5,𝔽2)12yes—
1173C22C22×2−1+411yescharacteristic
1174C22C2×#58511yescharacteristic
1175C222−1+612yes—
1176C4—22no—
1177C4—41no—
1178C4—44no—
1179C4—41no—
1180C4—41no—
1181C4—44no—
1182C4—44no—
1183C4—44no—
1184C4—41no—
1185C4—41no—
1186C4—44no—
1187C4—41no—
1188C4—41no—
1189C4—48no—
1190C4—48no—
1191C4—44no—
1192C4—44no—
1193C4C2×H(3,𝔽4)14yes—
1194C4C2×H(3,𝔽4)14yes—
1195C2—24no—
1196C2—42no—
1197C2—42no—
1198C2—42no—
1199C2—81no—
1200C2—84no—
1201C2C22×H(3,𝔽4)11yescharacteristic
1202C2#6281911yescharacteristic
1203C2#6288611yescharacteristic
1204C2#6294212yes—
1205C2#6295412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34736C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53144C2semidirect
2. #53032C2semidirect
3. #53005C2semidirect
4. #53005C2semidirect
5. #52990C2semidirect
6. #52958C2semidirect
7. #52925C2semidirect
8. #52914C2semidirect
9. #46073C2semidirect
10. #46043C2semidirect
11. #46004C2semidirect
12. #45667C2semidirect
13. #45667C2semidirect
14. #45568C2semidirect
15. #45539C2semidirect
16. #45494C2semidirect
17. #35644C2semidirect
18. #35628C2semidirect
19. #35542C2semidirect
20. #35312C2semidirect
21. #35305C2semidirect
22. #35242C2semidirect
23. #34946C2semidirect
25. C2×#2409C2semidirect
27. C24×Q8C22semidirect
28. C2×#544C22semidirect
31. C2×#533C22semidirect
35. #2862C22semidirect
36. #2861C22semidirect
37. #2849C22semidirect
38. #2848C22semidirect
39. #2848C22semidirect
40. #2844C22semidirect
41. #2844C22semidirect
42. #2840C22semidirect
43. #2835C22semidirect
44. #2835C22semidirect
45. #2835C22semidirect
46. #2832C22semidirect
47. #2832C22semidirect
48. #2832C22semidirect
49. #2832C22semidirect
50. #2832C22semidirect
51. #2824C22semidirect
52. #2824C22semidirect
53. #2811C22semidirect
55. #2804C22semidirect
56. #2785C22semidirect
57. #2785C22semidirect
59. #2782C22semidirect
60. #2782C22semidirect
61. #2763C22semidirect
62. #2763C22semidirect
63. #2763C22semidirect
64. #2763C22semidirect
65. #2763C22semidirect
66. #2763C22semidirect
67. #2763C22semidirect
68. #2753C22semidirect
69. #2753C22semidirect
70. #2753C22semidirect
71. #2736C22semidirect
72. #2736C22semidirect
73. #2712C22semidirect
74. #2712C22semidirect
77. #2642C22semidirect
78. #2640C22semidirect
79. #2616C22semidirect
80. #2616C22semidirect
81. #2614C22semidirect
82. #2592C22semidirect
83. #2592C22semidirect
84. #2568C22semidirect
85. #2568C22semidirect
87. #2563C22semidirect
88. #2563C22semidirect
90. #2562C22semidirect
91. #2562C22semidirect
92. #2562C22semidirect
95. #2561C22semidirect
97. #2547C22semidirect
98. #2547C22semidirect
99. #2503C22semidirect
100. #2503C22semidirect
101. #2492C22semidirect
102. #2492C22semidirect
103. #2492C22semidirect
104. #2492C22semidirect
105. #2492C22semidirect
106. #2492C22semidirect
107. #2492C22semidirect
108. #2492C22semidirect
109. #2492C22semidirect
110. #2491C22semidirect
111. #2490C22semidirect
112. #2489C22semidirect
113. #2489C22semidirect
114. #2489C22semidirect
115. #2489C22semidirect
116. #2489C22semidirect
117. #2489C22semidirect
118. #2489C22semidirect
119. #2489C22semidirect
120. #2489C22semidirect
121. #2488C22semidirect
122. #2488C22semidirect
123. #2488C22semidirect
124. #2488C22semidirect
125. #2488C22semidirect
126. #2472C22semidirect
127. #2436C22semidirect
128. #2436C22semidirect
130. #2435C22semidirect
131. #2434C22semidirect
132. #2434C22semidirect
133. #2434C22semidirect
134. #2432C22semidirect
135. #2432C22semidirect
142. #2409C22semidirect
143. #2409C22semidirect
144. #2409C22semidirect
145. #2409C22semidirect
146. #2409C22semidirect
147. #2409C22semidirect
148. #2409C22semidirect
149. #2409C22semidirect
161. #2398C22semidirect
164. C2×#395C22semidirect
167. #2379C22semidirect
171. #2310C22semidirect
172. #2310C22semidirect
174. C4×#124C22semidirect
178. C2×#391C22semidirect
180. C2×#385C22semidirect
183. #2280C22semidirect
184. C2×#380C22semidirect
185. #2274C22semidirect
186. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531442
#530322
#530052
#529902
#529582
#529252
#529142
#460732
#460432
#460042
#456672
#455682
#455392
#454942
#356442
#356282
#355422
#353122
#353052
#352422
#349462
#347362
C2×#24092