Finite Group Databasebeta

← #7644121

Subgroups — #7644121

Order 512.

5188 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42669C214yesmaximal, complemented
2#42668C214yesmaximal, complemented
3#42664C214yesmaximal, complemented
4#42658C214yesmaximal, complemented
5#42471C214yesmaximal, complemented
6#42468C214yesmaximal, complemented
7#42460C214yesmaximal, complemented
8#42454C214yesmaximal, complemented
9#37465C214yesmaximal, complemented
10#37459C214yesmaximal, complemented
11#36761C214yesmaximal, complemented
12#36759C214yesmaximal, complemented
13#35618C212yesmaximal, complemented
14#35530C212yesmaximal, complemented
15#35518C212yesmaximal, complemented
16#35518C212yesmaximal, complemented
17#35181C211yesmaximal, characteristic, complemented
18#35166C211yesmaximal, characteristic, complemented
19#34633C211yesmaximal, characteristic, complemented
20#34633C211yesmaximal, characteristic, complemented
21#34206C211yesmaximal, characteristic, complemented
22#34206C211yesmaximal, characteristic, complemented
23C2×#2314C211yesmaximal, characteristic, complemented
24C2×#537C2212yes—
25C2×#537C2212yes—
26C2×#532C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#525C2212yes—
29C2×#525C2212yes—
30C2×#520C2212yes—
31C2×#520C2212yes—
32C22×#117C2211yescharacteristic
33#2856C2214yes—
34#2851C2214yes—
35#2837C2218yes—
36#2836C2218yescomplemented
37#2829C2218yescomplemented
38#2828C2218yes—
39#2803C2218yes—
40#2800C2218yescomplemented
41#2797C2218yes—
42#2793C2218yes—
43#2791C2218yescomplemented
44#2786C2218yescomplemented
45#2780C2218yescomplemented
46#2761C2218yescomplemented
47#2753C2218yes—
48#2752C2218yes—
49#2740C2218yescomplemented
50#2711C2218yes—
51#2709C2218yescomplemented
52#2707C2218yescomplemented
53#2701C2218yes—
54#2673C2218yes—
55#2667C2218yescomplemented
56#2661C2218yes—
57#2656C2214yes—
58#2654C2218yescomplemented
59#2651C2218yes—
60#2649C2218yes—
61#2648C2218yescomplemented
62#2646C2214yes—
63#2635C2218yes—
64#2630C2218yescomplemented
65#2621C2212yes—
66#2621C2212yes—
67#2620C2212yes—
68#2620C2212yes—
69#2620C2212yes—
70#2620C2212yes—
71#2619C2212yes—
72#2619C2212yes—
73#2618C2212yes—
74#2618C2212yes—
75#2618C2212yes—
76#2618C2212yes—
77#2617C2212yes—
78#2617C2212yes—
79#2617C2212yes—
80#2617C2212yes—
81#2571C2212yescomplemented
82#2571C2212yescomplemented
83#2570C2214yescomplemented
84#2570C2214yescomplemented
85#2552C2212yescomplemented
86#2552C2212yescomplemented
87#2542C2212yescomplemented
88#2542C2212yescomplemented
89#2541C2212yescomplemented
90#2541C2212yescomplemented
91#2540C2214yescomplemented
92#2540C2214yescomplemented
93#2538C2214yes—
94#2538C2214yes—
95#2537C2214yes—
96#2537C2214yes—
97#2536C2214yes—
98#2536C2214yes—
99#2535C2214yes—
100#2535C2214yes—
101#2522C2218yescomplemented
102#2516C2218yes—
103#2504C2214yescomplemented
104#2503C2214yescomplemented
105#2502C2214yescomplemented
106#2501C2214yescomplemented
107#2500C2214yescomplemented
108#2500C2214yescomplemented
109#2499C2214yescomplemented
110#2499C2214yescomplemented
111#2464C2218yes—
112#2457C2218yescomplemented
113#2444C2218yes—
114#2444C2218yes—
115#2443C2218yes—
116#2443C2218yes—
117#2425C2218yes—
118#2425C2218yes—
119#2424C2218yes—
120#2424C2218yes—
121#2423C2214yescomplemented
122#2423C2214yescomplemented
123#2422C2214yescomplemented
124#2422C2214yescomplemented
125#2421C2214yescomplemented
126#2421C2214yescomplemented
127#2420C2214yescomplemented
128#2420C2214yescomplemented
129#2417C2214yes—
130#2417C2214yes—
131#2416C2214yes—
132#2416C2214yes—
133#2415C2214yes—
134#2415C2214yes—
135#2414C2214yes—
136#2414C2214yes—
137#2392C2214yes—
138#2392C2214yes—
139#2392C2214yes—
140#2392C2214yes—
141#2367C2214yescomplemented
142#2367C2214yescomplemented
143#2366C2212yescomplemented
144#2366C2212yescomplemented
145#2365C2212yescomplemented
146#2365C2212yescomplemented
147#2354C2212yescomplemented
148#2354C2212yescomplemented
149#2352C2214yescomplemented
150#2352C2214yescomplemented
151D4×C4⋊C4C2212yescomplemented
152D4×C4⋊C4C2212yescomplemented
153#2325C2214yes—
154#2325C2214yes—
155#2317C2212yes—
156#2317C2212yes—
157#2314C2214yes—
158#2314C2214yes—
159#2314C2214yes—
160#2314C2214yes—
161#2311C2212yes—
162#2311C2212yes—
163C4×#121C2214yes—
164C4×#121C2214yes—
165#2297C2212yes—
166#2297C2212yes—
167C2×#388C2212yes—
168C2×#388C2212yes—
169C2×#387C2212yes—
170C2×#387C2212yes—
171#2285C2211yescharacteristic
172#2285C2211yescharacteristic
173C2×#384C2211yescharacteristic
174C2×#382C2211yescharacteristic
175C2×#380C2211yescharacteristic
176C2×#380C2211yescharacteristic
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×C4×C4⋊C4C2211yescharacteristic
179C22×#41C2312yes—
180C22×#41C2312yes—
181C24×C4C2311yescharacteristic
182#537—48no—
183#537—48no—
184#532—28no—
185#532—28no—
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2311yescharacteristic
188C2×#127C2311yescharacteristic
189C2×#127C2311yescharacteristic
190C2×#127C2314yes—
191C2×#125C2314yes—
192C2×#124C2312yes—
193C2×#124C2312yes—
194#525—48no—
195#525—48no—
196C2×#123C2314yes—
197C2×#123C2314yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2312yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2312yes—
211C2×#121C2312yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C2312yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#120C2314yes—
225C2×#120C2314yes—
226#520—48no—
227#520—48no—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×#117—28no—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C22⋊C4C2311yescharacteristic
264C22×C22⋊C4C2311yescharacteristic
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C42C2311yescharacteristic
268C22×C42C2312yes—
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2318yes—
298#397C2314yes—
299#397C2314yes—
300#397C2314yes—
301#396C2314yes—
302#396C2318yes—
303#396C2314yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2314yes—
308#396C2314yes—
309#396C2314yes—
310#396C2314yes—
311#396C2314yes—
312#396C2314yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2318yes—
325#394C2318yes—
326#394C2314yes—
327#394C2314yes—
328#394C2314yes—
329#394C2314yes—
330#394C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#392C2314yes—
336#392C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#392C2314yes—
341#392C2314yes—
342#392C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2318yes—
354#390C2318yes—
355#390C2314yes—
356#390C2314yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2318yes—
362#390C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#384C2314yes—
422#384C2314yes—
423#384C2314yes—
424#384C2314yes—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2314yes—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382C2314yes—
431#382C2314yes—
432#382C2312yes—
433#382C2312yes—
434#382C2314yes—
435#382C2314yes—
436#382C2314yes—
437#381C2318yes—
438#381C2318yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451#380C2318yes—
452#380C2318yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#95C2312yes—
476C2×#95C2312yes—
477C2×#95C2312yes—
478C2×#95C2312yes—
479C25C2411yescharacteristic
480C2×#41—28no—
481C2×#41—28no—
482C2×#41—28no—
483C2×#41—28no—
484C2×#41—28no—
485C2×#41—28no—
486C22×Q8C2412yes—
487C22×Q8C2412yes—
488C22×D4C2414yes—
489C22×D4C2414yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C22×D4C2412yes—
493C22×D4C2412yes—
494C22×D4C2412yes—
495C22×D4C2412yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2414yes—
499C22×D4C2414yes—
500C22×D4C2418yes—
501C22×D4C2418yes—
502C23×C4—24no—
503C23×C4—24no—
504C23×C4—24no—
505C23×C4C2411yescharacteristic
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2418yes—
517C23×C4C2418yes—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C4⋊Q8—24no—
522C4⋊Q8—24no—
523#127—24no—
524#127—24no—
525#127—84no—
526#125—84no—
527#124—28no—
528#124—28no—
529#123—48no—
530#123—48no—
531#123—88no—
532#123—88no—
533C22⋊Q8—44no—
534C22⋊Q8—44no—
535C22⋊Q8—44no—
536C22⋊Q8—44no—
537C22⋊Q8—48no—
538C22⋊Q8—48no—
539C22⋊Q8—48no—
540C22⋊Q8—48no—
541#121—28no—
542#121—28no—
543#121—28no—
544#121—28no—
545#121—44no—
546#121—44no—
547#121—44no—
548#121—44no—
549#121—48no—
550#121—48no—
551#121—48no—
552#121—48no—
553#121—416no—
554#121—416no—
555#121—88no—
556#121—88no—
557#120—48no—
558#120—48no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—48no—
569C4×D4—48no—
570C4×D4—48no—
571C4×D4—416no—
572C4×D4—416no—
573C4×D4—84no—
574C4×D4—84no—
575#117—28no—
576#117—28no—
577#117—28no—
578#117—28no—
579#117—28no—
580#117—28no—
581#117—48no—
582#117—48no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—48no—
590C2×C4⋊C4—48no—
591C2×C4⋊C4—82no—
592C2×C4⋊C4—82no—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—82no—
638C2×C22⋊C4—82no—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C42—24no—
678C2×C42—82no—
679C2×C42—82no—
680C2×C42#4118yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2418yes—
686C2×C42C2418yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723C24—22no—
724C24—22no—
725C24—22no—
726C24—41no—
727C24—41no—
728C24—41no—
729C24—41no—
730C24C2512yes—
731C24C2514yes—
732C24C2514yes—
733C24C2511yescharacteristic
734#41—432no—
735#41—432no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—24no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—416no—
828C22×C4C2×#4114yes—
829C22×C4C2×#4114yes—
830C22×C4C2×#4114yes—
831C22×C4H(5,𝔽2)14yes—
832C22×C4H(5,𝔽2)14yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
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—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C42—24no—
933C42—24no—
934C42—28no—
935C42—28no—
936C42—44no—
937C42—44no—
938C42—44no—
939C42—44no—
940C42—48no—
941C42—48no—
942C42C2×#4114yes—
943C42C2×#4114yes—
944C42C2×#4114yes—
945C42C2×#4114yes—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—44no—
972C23—44no—
973C23—44no—
974C23—82no—
975C23—82no—
976C23—82no—
977C23—82no—
978C23C22×#4112yes—
979C23C2×H(5,𝔽2)12yes—
980C23C2×H(5,𝔽2)12yes—
981C23C2611yescharacteristic
982Q8—48no—
983Q8—48no—
984D4—48no—
985D4—48no—
986D4—416no—
987D4—416no—
988D4—48no—
989D4—48no—
990D4—84no—
991D4—84no—
992D4—88no—
993D4—88no—
994D4—88no—
995D4—88no—
996D4—168no—
997D4—168no—
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—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—48no—
1051C2×C4—48no—
1052C2×C4—416no—
1053C2×C4—416no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4—168no—
1059C2×C4—168no—
1060C2×C4#540116yes—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—44no—
1078C22—44no—
1079C22—42no—
1080C22—44no—
1081C22—44no—
1082C22—42no—
1083C22—44no—
1084C22—42no—
1085C22—42no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—42no—
1091C22—44no—
1092C22—42no—
1093C22—44no—
1094C22—44no—
1095C22—42no—
1096C22—44no—
1097C22—44no—
1098C22—88no—
1099C22C2×#54014yes—
1100C22C23×#4111yescharacteristic
1101C22C22×H(5,𝔽2)11yescharacteristic
1102C22C22×H(5,𝔽2)11yescharacteristic
1103C22H(7,𝔽2)11yescharacteristic
1104C22H(7,𝔽2)11yescharacteristic
1105C222−1+611yescharacteristic
1106C222−1+611yescharacteristic
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—22no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—44no—
1119C4—44no—
1120C4—44no—
1121C4—42no—
1122C4—44no—
1123C4—44no—
1124C4C2×#54014yes—
1125C4C2×#54014yes—
1126C2—24no—
1127C2—84no—
1128C2—84no—
1129C2—82no—
1130C2C22×#54011yescharacteristic
1131C2#6284511yescharacteristic
1132C2#6285611yescharacteristic
1133C2#6287811yescharacteristic
1134C2#6287811yescharacteristic
1135C2#6288011yescharacteristic
1136C2#6288811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42669C2semidirect
2. #42668C2semidirect
3. #42664C2semidirect
4. #42658C2semidirect
5. #42471C2semidirect
6. #42468C2semidirect
7. #42460C2semidirect
8. #42454C2semidirect
9. #37465C2semidirect
10. #37459C2semidirect
11. #36761C2semidirect
12. #36759C2semidirect
13. #35618C2semidirect
14. #35530C2semidirect
15. #35518C2semidirect
16. #35518C2semidirect
17. #35181C2semidirect
18. #35166C2semidirect
19. #34633C2semidirect
20. #34633C2semidirect
21. #34206C2semidirect
22. #34206C2semidirect
23. C2×#2314C2semidirect
36. #2836C22semidirect
37. #2829C22semidirect
40. #2800C22semidirect
43. #2791C22semidirect
44. #2786C22semidirect
45. #2780C22semidirect
46. #2761C22semidirect
49. #2740C22semidirect
51. #2709C22semidirect
52. #2707C22semidirect
55. #2667C22semidirect
58. #2654C22semidirect
61. #2648C22semidirect
64. #2630C22semidirect
81. #2571C22semidirect
82. #2571C22semidirect
83. #2570C22semidirect
84. #2570C22semidirect
85. #2552C22semidirect
86. #2552C22semidirect
87. #2542C22semidirect
88. #2542C22semidirect
89. #2541C22semidirect
90. #2541C22semidirect
91. #2540C22semidirect
92. #2540C22semidirect
101. #2522C22semidirect
103. #2504C22semidirect
104. #2503C22semidirect
105. #2502C22semidirect
106. #2501C22semidirect
107. #2500C22semidirect
108. #2500C22semidirect
109. #2499C22semidirect
110. #2499C22semidirect
112. #2457C22semidirect
121. #2423C22semidirect
122. #2423C22semidirect
123. #2422C22semidirect
124. #2422C22semidirect
125. #2421C22semidirect
126. #2421C22semidirect
127. #2420C22semidirect
128. #2420C22semidirect
141. #2367C22semidirect
142. #2367C22semidirect
143. #2366C22semidirect
144. #2366C22semidirect
145. #2365C22semidirect
146. #2365C22semidirect
147. #2354C22semidirect
148. #2354C22semidirect
149. #2352C22semidirect
150. #2352C22semidirect
151. D4×C4⋊C4C22semidirect
152. D4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#426692
#426682
#426642
#426582
#424712
#424682
#424602
#424542
#374652
#374592
#367612
#367592
#356182
#355302
#355182
#351812
#351662
#346332
#342062
C2×#23142