Finite Group Databasebeta

← #6393849

Subgroups — #6393849

Order 512.

3400 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3494C211yesmaximal, characteristic
2#34180C211yesmaximal, characteristic, complemented
3#34109C211yesmaximal, characteristic, complemented
4#22535C214yesmaximal, complemented
5#22406C214yesmaximal, complemented
6#22405C218yesmaximal, complemented
7#21875C212yesmaximal, complemented
8#21874C211yesmaximal, characteristic, complemented
9#21794C212yesmaximal, complemented
10#21793C211yesmaximal, characteristic, complemented
11#21421C212yesmaximal, complemented
12#21420C211yesmaximal, characteristic, complemented
13#21212C212yesmaximal, complemented
14C2×#1964C211yesmaximal, characteristic, complemented
15#3494—22no—
16#3494—21no—
17#3494—22no—
18#3494—22no—
19#3494—21no—
20#3494—21no—
21#3494—21no—
22#3494—21no—
23#3494—21no—
24#3494—21no—
25#3494—21no—
26#3494—22no—
27C2×#555C412yescomplemented
28C2×#553C412yescomplemented
29C2×#553C2212yes—
30C2×#551C414yescomplemented
31C2×#547C2212yes—
32C2×#546C2214yes—
33C2×#544C411yescharacteristic, complemented
34C2×#542C412yescomplemented
35C2×#540C412yescomplemented
36C2×#535C411yescharacteristic, complemented
37C2×#532C2212yes—
38C2×#529C2212yes—
39C2×#525C2211yescharacteristic
40C22×#121C2211yescharacteristic
41C2×#520C411yescharacteristic, complemented
42C2×#518C411yescharacteristic, complemented
43C22×#117C2211yescharacteristic
44C2×#410C2218yescomplemented
45C22×#99C2214yes—
46#2347—21no—
47#2347—21no—
48#2346—21no—
49#2346—21no—
50#2345C2212yescomplemented
51#2345C2212yescomplemented
52#2344C2212yescomplemented
53#2344C2212yescomplemented
54#2343—22no—
55#2343—22no—
56#2342C2214yes—
57#2342C2214yes—
58#2317—21no—
59#2314—22no—
60#2298—22no—
61#2296—21no—
62#2285C2212yescomplemented
63#2283C2212yescomplemented
64#2283C2212yescomplemented
65#2280C2211yescharacteristic
66#2280C2211yescharacteristic
67C2×#380C2211yescharacteristic
68#2274—21no—
69C4×#117—21no—
70C4×#117C2212yescomplemented
71C2×C4×C22⋊C4C2211yescharacteristic
72#1996C2212yescomplemented
73#1996C2211yescharacteristic, complemented
74#1996C2211yescharacteristic, complemented
75#1964C2214yes—
76#1964C2214yes—
77#1964C2212yes—
78#1964C2212yes—
79#1964C2212yes—
80#1964C2212yes—
81#1964C2218yescomplemented
82#1964C2218yescomplemented
83#1964C2211yescharacteristic, complemented
84#1964C2212yescomplemented
85#1964C2211yescharacteristic, complemented
86#1899C2218yescomplemented
87#1899C2218yescomplemented
88#1898C2214yes—
89#1898C2214yes—
90#1799C2214yescomplemented
91#1799C2218yescomplemented
92#1782C2218yescomplemented
93#1781C2214yes—
94C4×#99C2218yescomplemented
95C4×#99C2214yescomplemented
96C22×#41C2×C411yescharacteristic
97C22×#41C2314yes—
98C23×D4C2×C411yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101#555—22no—
102#555—22no—
103#555—22no—
104#555—22no—
105#555—24no—
106#555—24no—
107#553—22no—
108#553—22no—
109#553—22no—
110#553—22no—
111#553—24no—
112#553—24no—
113#553—22no—
114#553—22no—
115#553—24no—
116#553—24no—
117#553—22no—
118#553—22no—
119#551—24no—
120#551—24no—
121#551—24no—
122#551—24no—
123#551—24no—
124#551—24no—
125#551—24no—
126#551—24no—
127#547—22no—
128#547—22no—
129#547—24no—
130#547—24no—
131#547—22no—
132#547—22no—
133#546—24no—
134#546—24no—
135#546—24no—
136#546—24no—
137#546—24no—
138#546—24no—
139#546—24no—
140#546—24no—
141#544—22no—
142#544—22no—
143#544—21no—
144#544—21no—
145#544—21no—
146#544—21no—
147#542—22no—
148#542—22no—
149#542—22no—
150#542—22no—
151#542—22no—
152#542—22no—
153#542—22no—
154#542—22no—
155#540—22no—
156#540—22no—
157#540—22no—
158#540—22no—
159#540—22no—
160#540—22no—
161#540—22no—
162#540—22no—
163#535—22no—
164#535—22no—
165#535—21no—
166#535—21no—
167#535—21no—
168#535—21no—
169#532—22no—
170#532—22no—
171#532—22no—
172#532—22no—
173#532—22no—
174#532—22no—
175#532—22no—
176#532—22no—
177C2×C4⋊Q8C2×C412yescomplemented
178C2×C4⋊Q8C2×C412yescomplemented
179C2×#127C2×C412yescomplemented
180#529—22no—
181#529—22no—
182#529—22no—
183#529—22no—
184#529—22no—
185#529—22no—
186#529—22no—
187#529—22no—
188C2×#126C2×C414yescomplemented
189C2×#126C2×C414yescomplemented
190C2×#125C2×C412yescomplemented
191C2×#125C2×C412yescomplemented
192C2×#124C2×C414yes—
193C2×#124C2×C412yescomplemented
194C2×#124C2×C414yescomplemented
195#525—21no—
196#525—21no—
197#525—21no—
198#525—21no—
199#525—21no—
200#525—21no—
201#525—21no—
202#525—21no—
203C2×#123C2×C412yes—
204C2×#123C2×C414yes—
205C2×#123C2×C414yescomplemented
206C2×#123C2×C414yescomplemented
207C2×#123C2314yes—
208C2×C22⋊Q8C2×C411yescharacteristic
209C2×C22⋊Q8C2×C414yes—
210C2×C22⋊Q8C2×C414yescomplemented
211C2×C22⋊Q8C2311yescharacteristic
212C2×#121—21no—
213C2×#121—21no—
214C2×#121—21no—
215C2×#121—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121C2×C412yes—
221C2×#121C2×C412yes—
222C2×#121C2×C411yescharacteristic
223C2×#121C2×C414yes—
224C2×#121C2×C414yes—
225C2×#121C2×C412yescomplemented
226C2×#121C2×C412yescomplemented
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2311yescharacteristic
230C2×#121C2314yes—
231C2×#120C2×C414yes—
232C2×#120C2312yes—
233#520—22no—
234#520—22no—
235#520—21no—
236#520—21no—
237#520—21no—
238#520—21no—
239#518—22no—
240#518—22no—
241#518—21no—
242#518—21no—
243#518—21no—
244#518—21no—
245C2×C4×Q8C2×C412yescomplemented
246C2×C4×D4C2×C414yes—
247C2×C4×D4C2×C412yes—
248C2×C4×D4C2×C412yescomplemented
249C2×C4×D4C2×C412yescomplemented
250C2×C4×D4C2×C412yescomplemented
251C2×C4×D4C2×C412yescomplemented
252C2×C4×D4C2×C412yescomplemented
253C2×C4×D4C2×C414yescomplemented
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×#117—21no—
257C2×#117—21no—
258C2×#117C2×C411yescharacteristic
259C2×#117C2×C411yescharacteristic
260C2×#117C2×C411yescharacteristic
261C2×#117C2×C412yes—
262C2×#117C2×C412yes—
263C2×#117C2×C411yescharacteristic
264C2×#117C2×C411yescharacteristic
265C2×#117C2×C412yescomplemented
266C2×#117C2×C414yescomplemented
267C2×#117D412yes—
268C2×#117D411yescharacteristic
269C2×#117D412yes—
270C2×#117D412yes—
271C2×#117D411yescharacteristic
272C2×#117D411yescharacteristic
273C2×#117D411yescharacteristic
274C2×#117D411yescharacteristic
275C2×#117D411yescharacteristic
276C2×#117D411yescharacteristic
277C2×#117D411yescharacteristic
278C2×#117D412yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×C411yescharacteristic
283C22×C4⋊C4C2×C412yescomplemented
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C22⋊C4C2×C414yes—
287C22×C22⋊C4C2×C412yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C42—21no—
292C22×C42C2312yes—
293#410—416no—
294C2×#99—48no—
295C2×#99C2318yes—
296C2×#99C2314yes—
297C2×#99C2318yes—
298C2×#99C2318yes—
299C2×#99C2318yes—
300C2×#99C2314yes—
301C2×#99C2318yes—
302#389—22no—
303#389—22no—
304#389—22no—
305#389—22no—
306#388—24no—
307#388—24no—
308#388—24no—
309#388—24no—
310#387—24no—
311#387—24no—
312#387—24no—
313#387—24no—
314#385—24no—
315#385—24no—
316#384—22no—
317#383—22no—
318#383—22no—
319#382—22no—
320#382—22no—
321#382—22no—
322#381—21no—
323#381—21no—
324#381C2314yes—
325#381C2314yes—
326#380—21no—
327#380—21no—
328#380—21no—
329#380—21no—
330#380C2314yes—
331#380C2314yes—
332#380C2312yes—
333#380C2312yes—
334#380C2312yes—
335#380C2311yescharacteristic
336#380C2311yescharacteristic
337#379C2312yes—
338#379C2312yes—
339C4×C4⋊C4—22no—
340C4×C4⋊C4—22no—
341C4×C4⋊C4—22no—
342C4×C4⋊C4—22no—
343C4×C4⋊C4—22no—
344C4×C4⋊C4—22no—
345C4×C4⋊C4—22no—
346C4×C4⋊C4—22no—
347C4×C4⋊C4—22no—
348C4×C4⋊C4—22no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—21no—
352C4×C22⋊C4—21no—
353C4×C22⋊C4—24no—
354C4×C22⋊C4—24no—
355C4×C22⋊C4C2314yes—
356C4×C22⋊C4C2314yes—
357C4×C22⋊C4C2312yes—
358C4×C22⋊C4C2312yes—
359C4×C22⋊C4C2311yescharacteristic
360C4×C22⋊C4C2311yescharacteristic
361C4×C22⋊C4C2312yes—
362#376—22no—
363#376—22no—
364#376—22no—
365C2×#95—21no—
366C2×#95—21no—
367C43—22no—
368#342C2318yes—
369#342C2314yes—
370#342C2314yes—
371C25C22×C412yes—
372C25C2411yescharacteristic
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—24no—
378C2×#41—24no—
379C2×#41—24no—
380C2×#41—24no—
381C2×#41—48no—
382C2×#41—48no—
383C2×#41—44no—
384C22×Q8C22×C411yescharacteristic
385C22×Q8C22×C414yes—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—44no—
395C22×D4—44no—
396C22×D4—44no—
397C22×D4C22×C412yes—
398C22×D4C22×C412yes—
399C22×D4C22×C412yes—
400C22×D4C22×C411yescharacteristic
401C22×D4C22×C414yes—
402C22×D4C22×C414yes—
403C22×D4C22×C412yes—
404C22×D4C22×C414yes—
405C22×D4C2412yes—
406C22×D4C2414yes—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4C22×C411yescharacteristic
411C23×C4C22×C412yes—
412C23×C4C22×C414yes—
413C23×C4C22×C412yes—
414C23×C4C22×C414yes—
415C23×C4C22×C414yes—
416C23×C4C22×C411yescharacteristic
417C23×C4C22×C411yescharacteristic
418C23×C4C22×C411yescharacteristic
419C23×C4C2×D411yescharacteristic
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D411yescharacteristic
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D411yescharacteristic
425C23×C4C2×D411yescharacteristic
426C23×C4C2×D411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C4⋊Q8—24no—
432C4⋊Q8—22no—
433C4⋊Q8—22no—
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438#127—22no—
439#127—22no—
440#127—22no—
441#127—22no—
442#126—24no—
443#126—24no—
444#126—24no—
445#126—24no—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—24no—
450#125—24no—
451#125—22no—
452#125—22no—
453#125—22no—
454#125—22no—
455#125—22no—
456#125—22no—
457#124—24no—
458#124—24no—
459#124—24no—
460#124—24no—
461#124—22no—
462#124—22no—
463#124—22no—
464#124—22no—
465#124—24no—
466#124—24no—
467#124—24no—
468#124—24no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—24no—
474#123—24no—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—24no—
530#121—24no—
531#121—24no—
532#121—24no—
533#121—24no—
534#121—22no—
535#121—22no—
536#121—24no—
537#121—22no—
538#121—22no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—24no—
547#120—22no—
548#120—22no—
549#120—22no—
550#120—22no—
551#120—24no—
552#120—24no—
553#120—24no—
554#120—24no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—24no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—24no—
602#117—22no—
603#117—22no—
604#117—24no—
605#117—24no—
606#117—24no—
607#117—24no—
608#117—28no—
609#117—44no—
610#117—44no—
611#117—44no—
612#117—48no—
613#117C22⋊C412yes—
614#117C22⋊C412yes—
615#117C22⋊C411yescharacteristic
616#117C22⋊C411yescharacteristic
617#117C22⋊C411yescharacteristic
618#117C22⋊C411yescharacteristic
619#117C22⋊C412yes—
620#117C22⋊C412yes—
621#117C22⋊C411yescharacteristic
622#117C22⋊C411yescharacteristic
623#117C22⋊C411yescharacteristic
624#117C22⋊C411yescharacteristic
625#117C22⋊C412yes—
626#117C22⋊C412yes—
627#117C22⋊C412yes—
628#117C22⋊C412yes—
629#117C22⋊C412yes—
630#117C22⋊C412yes—
631#117C22⋊C412yes—
632#117C22⋊C412yes—
633#117C22⋊C412yes—
634#117C22⋊C412yes—
635#117C22⋊C412yes—
636#117C22⋊C412yes—
637#117C22⋊C412yes—
638#117C22⋊C412yes—
639#117C22⋊C412yes—
640#117C22⋊C412yes—
641#117C22⋊C411yescharacteristic
642#117C22⋊C411yescharacteristic
643#117C22⋊C411yescharacteristic
644#117C22⋊C411yescharacteristic
645#117C22⋊C412yes—
646#117C22⋊C412yes—
647#117C22⋊C411yescharacteristic
648#117C22⋊C411yescharacteristic
649#117C22⋊C411yescharacteristic
650#117C22⋊C411yescharacteristic
651#117C22⋊C412yes—
652#117C22⋊C412yes—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—24no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—24no—
666C2×C4⋊C4—24no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—24no—
669C2×C4⋊C4—44no—
670C2×C4⋊C4C22×C412yes—
671C2×C4⋊C4C22×C412yes—
672C2×C4⋊C4C22×C414yes—
673C2×C4⋊C4C22×C411yescharacteristic
674C2×C4⋊C4C22×C411yescharacteristic
675C2×C4⋊C4C22×C412yes—
676C2×C4⋊C4C22×C414yes—
677C2×C4⋊C4C22×C414yes—
678C2×C4⋊C4C22×C414yes—
679C2×C4⋊C4C22×C412yes—
680C2×C4⋊C4C22×C411yescharacteristic
681C2×C4⋊C4C22×C411yescharacteristic
682C2×C4⋊C4C22×C411yescharacteristic
683C2×C4⋊C4C22×C411yescharacteristic
684C2×C4⋊C4C22×C412yes—
685C2×C4⋊C4C22×C412yes—
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D412yes—
689C2×C4⋊C4C2×D412yes—
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D412yes—
695C2×C4⋊C4C2×D412yes—
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—42no—
714C2×C22⋊C4—44no—
715C2×C22⋊C4C22×C412yes—
716C2×C22⋊C4C22×C414yes—
717C2×C22⋊C4C22×C414yes—
718C2×C22⋊C4C22×C414yes—
719C2×C22⋊C4C22×C414yes—
720C2×C22⋊C4C22×C414yes—
721C2×C22⋊C4C22×C414yes—
722C2×C22⋊C4C22×C412yes—
723C2×C22⋊C4C22×C412yes—
724C2×C22⋊C4C22×C414yes—
725C2×C22⋊C4C22×C412yes—
726C2×C22⋊C4C22×C412yes—
727C2×C22⋊C4C22×C412yes—
728C2×C22⋊C4C22×C412yes—
729C2×C22⋊C4C22×C412yes—
730C2×C22⋊C4C2×D412yes—
731C2×C22⋊C4C2×D412yes—
732C2×C22⋊C4C2×D412yes—
733C2×C22⋊C4C2×D412yes—
734C2×C22⋊C4C2×D412yes—
735C2×C22⋊C4C2×D412yes—
736C2×C22⋊C4C2×D412yes—
737C2×C22⋊C4C2×D412yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C42—22no—
746C2×C42—22no—
747C2×C42—24no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—22no—
751C2×C42—24no—
752C2×C42—24no—
753C2×C42—24no—
754C2×C42—44no—
755C2×C42C22×C412yes—
756C2×C42C22×C414yes—
757C2×C42C22×C412yes—
758C2×C42C22×C412yes—
759C2×C42C22×C412yes—
760C2×C42C22×C412yes—
761C2×C42C2×D412yes—
762C2×C42C2×D412yes—
763C2×C42C2×D412yes—
764C2×C42C2×D412yes—
765C2×C42C2×D412yes—
766C2×C42C2×D412yes—
767C2×C42C2×D412yes—
768C2×C42C2×D412yes—
769#99—216no—
770#99—28no—
771#99—48no—
772#99—44no—
773#99—48no—
774#99—48no—
775#99—48no—
776#95—21no—
777#95—22no—
778#95—21no—
779#95—22no—
780#95—22no—
781#95—21no—
782#95—24no—
783#95—24no—
784#95—22no—
785#95—24no—
786#95—24no—
787#95—21no—
788#95—24no—
789#95—24no—
790#95—22no—
791#95—22no—
792#95—24no—
793#95—24no—
794C24—22no—
795C24—22no—
796C24—22no—
797C24—22no—
798C24—42no—
799C24—44no—
800C24—44no—
801C24—81no—
802C24—82no—
803C24C23×C411yescharacteristic
804C24C23×C414yes—
805C24C23×C412yes—
806C24C23×C411yescharacteristic
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C24C22×D411yescharacteristic
810C24C22×D411yescharacteristic
811C24C2511yescharacteristic
812#41—44no—
813#41—44no—
814#41—44no—
815#41—44no—
816#41—88no—
817#41—88no—
818#41—84no—
819#41—84no—
820#41—84no—
821#41—84no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—48no—
827C2×Q8—42no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—24no—
841C2×D4—24no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—42no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—84no—
863C2×D4—82no—
864C2×D4—84no—
865C2×D4—84no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—82no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—22no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—82no—
910C22×C4—82no—
911C22×C4—84no—
912C22×C4—82no—
913C22×C4—82no—
914C22×C4C2×C22⋊C411yescharacteristic
915C22×C4C2×C22⋊C411yescharacteristic
916C22×C4C2×C22⋊C411yescharacteristic
917C22×C4C2×C22⋊C411yescharacteristic
918C22×C4C2×C22⋊C411yescharacteristic
919C22×C4C2×C22⋊C411yescharacteristic
920C22×C4C2×C22⋊C411yescharacteristic
921C22×C4C2×C22⋊C411yescharacteristic
922C22×C4C2×C22⋊C411yescharacteristic
923C22×C4C2×C22⋊C411yescharacteristic
924C22×C4C2×C22⋊C411yescharacteristic
925C22×C4C2×C22⋊C411yescharacteristic
926C22×C4C2×C22⋊C411yescharacteristic
927C22×C4C2×C22⋊C411yescharacteristic
928C22×C4C2×C22⋊C411yescharacteristic
929C22×C4C2×C22⋊C411yescharacteristic
930C22×C4C23×C412yes—
931C22×C4C23×C414yes—
932C22×C4C23×C411yescharacteristic
933C22×C4C23×C412yes—
934C22×C4C23×C412yes—
935C22×C4C23×C411yescharacteristic
936C22×C4C23×C412yes—
937C22×C4C23×C412yes—
938C22×C4C23×C411yescharacteristic
939C22×C4C23×C412yes—
940C22×C4C23×C412yes—
941C22×C4C23×C411yescharacteristic
942C22×C4C22×D412yes—
943C22×C4C22×D412yes—
944C22×C4C22×D412yes—
945C22×C4C22×D412yes—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D412yes—
955C22×C4C22×D412yes—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—48no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—84no—
985C4⋊C4—84no—
986C4⋊C4—84no—
987C4⋊C4C2×C22⋊C412yes—
988C4⋊C4C2×C22⋊C411yescharacteristic
989C4⋊C4C2×C22⋊C411yescharacteristic
990C4⋊C4C2×C22⋊C412yes—
991C4⋊C4C2×C22⋊C411yescharacteristic
992C4⋊C4C2×C22⋊C411yescharacteristic
993C4⋊C4C2×C22⋊C412yes—
994C4⋊C4C2×C22⋊C411yescharacteristic
995C4⋊C4C2×C22⋊C411yescharacteristic
996C4⋊C4C2×C22⋊C412yes—
997C4⋊C4C2×C22⋊C411yescharacteristic
998C4⋊C4C2×C22⋊C411yescharacteristic
999C4⋊C4C2×C22⋊C412yes—
1000C4⋊C4C2×C22⋊C412yes—
1001C4⋊C4C2×C22⋊C412yes—
1002C4⋊C4C2×C22⋊C412yes—
1003C4⋊C4C2×C22⋊C412yes—
1004C4⋊C4C2×C22⋊C412yes—
1005C4⋊C4C2×C22⋊C412yes—
1006C4⋊C4C2×C22⋊C412yes—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—24no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—22no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—22no—
1038C22⋊C4—24no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—82no—
1043C22⋊C4—82no—
1044C22⋊C4—82no—
1045C22⋊C4C2×C22⋊C412yes—
1046C22⋊C4C2×C22⋊C412yes—
1047C22⋊C4C2×C22⋊C412yes—
1048C22⋊C4C2×C22⋊C412yes—
1049C22⋊C4C2×C22⋊C412yes—
1050C22⋊C4C2×C22⋊C412yes—
1051C22⋊C4C2×C22⋊C412yes—
1052C22⋊C4C2×C22⋊C412yes—
1053C22⋊C4C2×C22⋊C412yes—
1054C22⋊C4C2×C22⋊C412yes—
1055C22⋊C4C2×C22⋊C412yes—
1056C22⋊C4C2×C22⋊C412yes—
1057C22⋊C4C2×C22⋊C412yes—
1058C22⋊C4C2×C22⋊C412yes—
1059C22⋊C4C2×C22⋊C412yes—
1060C22⋊C4C2×C22⋊C412yes—
1061C22⋊C4H(5,𝔽2)14yes—
1062C42—24no—
1063C42—24no—
1064C42—22no—
1065C42—22no—
1066C42—48no—
1067C42—42no—
1068C42—42no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—84no—
1073C42—84no—
1074C42—84no—
1075C42C2×C22⋊C412yes—
1076C42C2×C22⋊C412yes—
1077C42C2×C22⋊C412yes—
1078C42C2×C22⋊C412yes—
1079C42C2×C22⋊C412yes—
1080C42C2×C22⋊C412yes—
1081C42C2×C22⋊C412yes—
1082C42C2×C22⋊C412yes—
1083C42C2×C22⋊C412yes—
1084C42C2×C22⋊C412yes—
1085C42C2×C22⋊C412yes—
1086C42C2×C22⋊C412yes—
1087C42C2×C22⋊C412yes—
1088C42C2×C22⋊C412yes—
1089C42C2×C22⋊C412yes—
1090C42C2×C22⋊C412yes—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—22no—
1100C23—21no—
1101C23—21no—
1102C23—24no—
1103C23—22no—
1104C23—24no—
1105C23—28no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—44no—
1118C23—42no—
1119C23—44no—
1120C23—44no—
1121C23—42no—
1122C23—44no—
1123C23—82no—
1124C23—82no—
1125C23—82no—
1126C23—82no—
1127C23—84no—
1128C23—84no—
1129C23—168no—
1130C23C22×C22⋊C411yescharacteristic
1131C23C22×C22⋊C411yescharacteristic
1132C23C22×C22⋊C411yescharacteristic
1133C23C22×C22⋊C411yescharacteristic
1134C23C24×C411yescharacteristic
1135C23C23×D411yescharacteristic
1136C23C23×D411yescharacteristic
1137C23C2×H(5,𝔽2)12yes—
1138C23#58512yes—
1139Q8—42no—
1140Q8—42no—
1141Q8—84no—
1142Q8—84no—
1143D4—44no—
1144D4—44no—
1145D4—42no—
1146D4—44no—
1147D4—44no—
1148D4—48no—
1149D4—44no—
1150D4—44no—
1151D4—42no—
1152D4—44no—
1153D4—42no—
1154D4—44no—
1155D4—44no—
1156D4—42no—
1157D4—84no—
1158D4—84no—
1159D4—84no—
1160D4—84no—
1161D4—84no—
1162D4—84no—
1163D4—82no—
1164D4—82no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—28no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—44no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—44no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—44no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—42no—
1227C2×C4—44no—
1228C2×C4—42no—
1229C2×C4—44no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—44no—
1233C2×C4—42no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—82no—
1241C2×C4—82no—
1242C2×C4—88no—
1243C2×C4—164no—
1244C2×C4#41014yescomplemented
1245C2×C4C22×C22⋊C412yes—
1246C2×C4C22×C22⋊C412yes—
1247C2×C4C22×C22⋊C411yescharacteristic
1248C2×C4C22×C22⋊C411yescharacteristic
1249C2×C4C22×C22⋊C411yescharacteristic
1250C2×C4C22×C22⋊C411yescharacteristic
1251C2×C4C22×C22⋊C412yes—
1252C2×C4C22×C22⋊C412yes—
1253C2×C4C22×C22⋊C412yes—
1254C2×C4C22×C22⋊C412yes—
1255C2×C4C22×C22⋊C412yes—
1256C2×C4C22×C22⋊C412yes—
1257C2×C4C22×C22⋊C411yescharacteristic
1258C2×C4C22×C22⋊C411yescharacteristic
1259C2×C4C22×C22⋊C411yescharacteristic
1260C2×C4C22×C22⋊C411yescharacteristic
1261C22—21no—
1262C22—21no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—21no—
1272C22—21no—
1273C22—21no—
1274C22—21no—
1275C22—21no—
1276C22—21no—
1277C22—21no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—44no—
1287C22—42no—
1288C22—42no—
1289C22—44no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—82no—
1294C22—84no—
1295C22—88no—
1296C22—164no—
1297C22—164no—
1298C22C2×#41012yes—
1299C22C23×C22⋊C411yescharacteristic
1300C22C4×H(5,𝔽2)12yes—
1301C22#348812yes—
1302C22#349811yescharacteristic
1303C22#350011yescharacteristic
1304C4—21no—
1305C4—21no—
1306C4—21no—
1307C4—21no—
1308C4—21no—
1309C4—21no—
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—44no—
1319C4—42no—
1320C4—42no—
1321C4—44no—
1322C4—42no—
1323C4—84no—
1324C4—82no—
1325C4—82no—
1326C4—82no—
1327C4—84no—
1328C4C2×#41012yes—
1329C4C2×#41012yes—
1330C2—22no—
1331C2—21no—
1332C2—21no—
1333C2—22no—
1334C2—22no—
1335C2—41no—
1336C2—41no—
1337C2—41no—
1338C2—82no—
1339C2—84no—
1340C2#3425811yescharacteristic
1341C2C22×#41011yescharacteristic
1342C2#6007011yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC2×#3494C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34180C2semidirect
3. #34109C2semidirect
4. #22535C2semidirect
5. #22406C2semidirect
6. #22405C2semidirect
7. #21875C2semidirect
8. #21874C2semidirect
9. #21794C2semidirect
10. #21793C2semidirect
11. #21421C2semidirect
12. #21420C2semidirect
13. #21212C2semidirect
14. C2×#1964C2semidirect
27. C2×#555C4semidirect
28. C2×#553C4semidirect
30. C2×#551C4semidirect
33. C2×#544C4semidirect
34. C2×#542C4semidirect
35. C2×#540C4semidirect
36. C2×#535C4semidirect
41. C2×#520C4semidirect
42. C2×#518C4semidirect
44. C2×#410C22semidirect
50. #2345C22semidirect
51. #2345C22semidirect
52. #2344C22semidirect
53. #2344C22semidirect
62. #2285C22semidirect
63. #2283C22semidirect
64. #2283C22semidirect
70. C4×#117C22semidirect
72. #1996C22semidirect
73. #1996C22semidirect
74. #1996C22semidirect
81. #1964C22semidirect
82. #1964C22semidirect
83. #1964C22semidirect
84. #1964C22semidirect
85. #1964C22semidirect
86. #1899C22semidirect
87. #1899C22semidirect
90. #1799C22semidirect
91. #1799C22semidirect
92. #1782C22semidirect
94. C4×#99C22semidirect
95. C4×#99C22semidirect
177. C2×C4⋊Q8C2×C4semidirect
178. C2×C4⋊Q8C2×C4semidirect
179. C2×#127C2×C4semidirect
188. C2×#126C2×C4semidirect
189. C2×#126C2×C4semidirect
190. C2×#125C2×C4semidirect
191. C2×#125C2×C4semidirect
193. C2×#124C2×C4semidirect
194. C2×#124C2×C4semidirect
205. C2×#123C2×C4semidirect
206. C2×#123C2×C4semidirect
210. C2×C22⋊Q8C2×C4semidirect
225. C2×#121C2×C4semidirect
226. C2×#121C2×C4semidirect
245. C2×C4×Q8C2×C4semidirect
248. C2×C4×D4C2×C4semidirect
249. C2×C4×D4C2×C4semidirect
250. C2×C4×D4C2×C4semidirect
251. C2×C4×D4C2×C4semidirect
252. C2×C4×D4C2×C4semidirect
253. C2×C4×D4C2×C4semidirect
265. C2×#117C2×C4semidirect
266. C2×#117C2×C4semidirect
283. C22×C4⋊C4C2×C4semidirect
1244. C2×C4#410semidirect

Maximal subgroups

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

subgroupindex
C2×#34942
#341802
#341092
#225352
#224062
#224052
#218752
#218742
#217942
#217932
#214212
#214202
#212122
C2×#19642