Finite Group Databasebeta

← #6393850

Subgroups — #6393850

Order 512.

3682 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C211yesmaximal, characteristic
2#34194C211yesmaximal, characteristic, complemented
3#34126C211yesmaximal, characteristic, complemented
4#22535C214yesmaximal, complemented
5#22405C218yesmaximal, complemented
6D4×#99C214yesmaximal, complemented
7#21875C211yesmaximal, characteristic, complemented
8#21874C212yesmaximal, complemented
9#21794C211yesmaximal, characteristic, complemented
10#21793C212yesmaximal, complemented
11#21421C211yesmaximal, characteristic, complemented
12#21420C212yesmaximal, complemented
13#21212C211yesmaximal, characteristic, complemented
14C2×#1964C212yesmaximal, complemented
15#3519—22no—
16#3519—21no—
17#3519—21no—
18#3519—21no—
19#3519—22no—
20#3519—22no—
21#3519—21no—
22#3519—21no—
23#3519—21no—
24#3519—21no—
25#3519—22no—
26#3519—21no—
27C2×#555C411yescharacteristic, complemented
28C2×#554C411yescharacteristic, complemented
29C2×#553C412yescomplemented
30C2×#553C2212yes—
31C2×#550C411yescharacteristic, complemented
32C2×#546C412yescomplemented
33C2×#546C2214yes—
34C2×D42C411yescharacteristic, complemented
35C2×D42C2212yes—
36C2×#540C412yescomplemented
37C2×#538C414yescomplemented
38C2×#532C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C22×#121C2212yes—
42C2×#518C412yescomplemented
43C22×C4×D4C2211yescharacteristic
44C2×#410C2214yescomplemented
45C22×#99C2218yescomplemented
46#2357—21no—
47#2354—21no—
48#2353—22no—
49#2352—22no—
50#2349—21no—
51D4×C4⋊C4—21no—
52#2345C2212yescomplemented
53#2345C2212yescomplemented
54#2342C2214yescomplemented
55#2342C2214yescomplemented
56D4×C22⋊C4C2212yes—
57D4×C22⋊C4C2212yes—
58#2319—21no—
59#2318—22no—
60#2293—21no—
61#2290—22no—
62#2285C2211yescharacteristic, complemented
63#2283C2211yescharacteristic, complemented
64#2283C2211yescharacteristic, complemented
65#2280C2212yescomplemented
66#2280C2212yescomplemented
67C2×#380C2212yescomplemented
68#2275—21no—
69C42×D4—21no—
70C4×#117C2211yescharacteristic, complemented
71C2×C4×C22⋊C4C2212yescomplemented
72#1996C2211yescharacteristic, complemented
73#1996C2212yescomplemented
74#1996C2211yescharacteristic, complemented
75#1964C2211yescharacteristic
76#1964C2212yes—
77#1964C2211yescharacteristic
78#1964C2218yescomplemented
79#1964C2214yescomplemented
80#1964C2214yescomplemented
81#1964C2218yescomplemented
82#1964C2212yescomplemented
83#1964C2212yescomplemented
84#1964C2212yescomplemented
85#1964C2212yescomplemented
86#1899C2214yescomplemented
87#1899C2214yescomplemented
88#1898C2218yescomplemented
89#1898C2218yescomplemented
90#1799C2218yescomplemented
91#1799C2214yescomplemented
92#1782C2214yescomplemented
93#1781C2218yescomplemented
94C4×#99C2214yescomplemented
95C4×#99C2218yescomplemented
96C22×#41C2×C412yescomplemented
97C22×#41C2312yes—
98C23×D4C2×C412yes—
99C23×D4C2×C412yescomplemented
100C23×D4C2314yes—
101C23×D4C2311yescharacteristic
102C24×C4C2312yes—
103#555—21no—
104#555—21no—
105#555—22no—
106#555—21no—
107#555—21no—
108#555—22no—
109#554—22no—
110#554—21no—
111#554—21no—
112#554—22no—
113#554—21no—
114#554—21no—
115#553—22no—
116#553—22no—
117#553—22no—
118#553—22no—
119#553—22no—
120#553—22no—
121#553—22no—
122#553—22no—
123#553—22no—
124#553—22no—
125#553—24no—
126#553—24no—
127#553—22no—
128#553—22no—
129#550—21no—
130#550—21no—
131#550—22no—
132#550—21no—
133#550—21no—
134#550—22no—
135#546—22no—
136#546—22no—
137#546—22no—
138#546—22no—
139#546—22no—
140#546—22no—
141#546—22no—
142#546—22no—
143#546—24no—
144#546—24no—
145#546—24no—
146#546—24no—
147#546—24no—
148#546—24no—
149#546—24no—
150#546—24no—
151D42—22no—
152D42—22no—
153D42—24no—
154D42—24no—
155D42—22no—
156D42—22no—
157D42—22no—
158D42—21no—
159D42—21no—
160D42—22no—
161D42—21no—
162D42—21no—
163#540—22no—
164#540—22no—
165#540—22no—
166#540—22no—
167#540—24no—
168#540—24no—
169#538—24no—
170#538—24no—
171#538—24no—
172#538—24no—
173#538—24no—
174#538—24no—
175#538—24no—
176#538—24no—
177#532—21no—
178#532—21no—
179#532—21no—
180#532—21no—
181#532—21no—
182#532—21no—
183#532—21no—
184#532—21no—
185C2×C4⋊Q8C2×C411yescharacteristic, complemented
186C2×#127C2×C412yes—
187C2×#127C2×C411yescharacteristic, complemented
188#529—21no—
189#529—21no—
190#529—21no—
191#529—21no—
192#529—21no—
193#529—21no—
194#529—21no—
195#529—21no—
196C2×#126C2×C412yescomplemented
197C2×#126C2×C414yescomplemented
198C2×#125C2×C411yescharacteristic, complemented
199C2×#125C2×C412yescomplemented
200C2×#124C2×C411yescharacteristic, complemented
201C2×#124C2×C412yescomplemented
202C2×#124C2×C414yescomplemented
203#525—22no—
204#525—22no—
205#525—22no—
206#525—22no—
207#525—22no—
208#525—22no—
209#525—22no—
210#525—22no—
211C2×#123C2×C414yescomplemented
212C2×#123C2×C414yescomplemented
213C2×#123C2×C414yescomplemented
214C2×#123C2312yes—
215C2×C22⋊Q8C2×C412yescomplemented
216C2×C22⋊Q8C2×C414yescomplemented
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—22no—
219C2×#121—22no—
220C2×#121—22no—
221C2×#121—22no—
222C2×#121—22no—
223C2×#121—22no—
224C2×#121—22no—
225C2×#121—22no—
226C2×#121C2×C414yes—
227C2×#121C2×C412yes—
228C2×#121C2×C414yescomplemented
229C2×#121C2×C412yescomplemented
230C2×#121C2×C412yescomplemented
231C2×#121C2×C412yescomplemented
232C2×#121C2×C414yescomplemented
233C2×#121C2×C412yescomplemented
234C2×#121C2×C414yescomplemented
235C2×#121C2311yescharacteristic
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2312yes—
239C2×#120C2×C414yes—
240C2×#120C2×C414yescomplemented
241C2×#120C2314yes—
242#518—24no—
243#518—22no—
244#518—24no—
245#518—22no—
246#518—22no—
247#518—22no—
248C2×C4×Q8C2×C411yescharacteristic, complemented
249C2×C4×D4—22no—
250C2×C4×D4—22no—
251C2×C4×D4C2×C412yes—
252C2×C4×D4C2×C411yescharacteristic
253C2×C4×D4C2×C412yes—
254C2×C4×D4C2×C411yescharacteristic
255C2×C4×D4C2×C411yescharacteristic
256C2×C4×D4C2×C412yes—
257C2×C4×D4C2×C411yescharacteristic
258C2×C4×D4C2×C414yescomplemented
259C2×C4×D4C2×C412yescomplemented
260C2×C4×D4C2×C414yescomplemented
261C2×C4×D4C2×C412yescomplemented
262C2×C4×D4C2×C411yescharacteristic, complemented
263C2×C4×D4C2×C412yescomplemented
264C2×C4×D4D412yes—
265C2×C4×D4D411yescharacteristic
266C2×C4×D4D411yescharacteristic
267C2×C4×D4D411yescharacteristic
268C2×C4×D4D412yes—
269C2×C4×D4D412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D411yescharacteristic
272C2×C4×D4D411yescharacteristic
273C2×C4×D4D411yescharacteristic
274C2×C4×D4D412yes—
275C2×C4×D4D411yescharacteristic
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×#117—22no—
279C2×#117—22no—
280C2×#117C2×C412yescomplemented
281C2×#117C2×C412yescomplemented
282C2×#117C2×C412yescomplemented
283C2×#117C2312yes—
284C2×#117C2312yes—
285C22×C4⋊C4—22no—
286C22×C4⋊C4C2×C412yescomplemented
287C22×C4⋊C4C2311yescharacteristic
288C22×C22⋊C4C2×C414yescomplemented
289C22×C22⋊C4C2×C414yescomplemented
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C42—22no—
294C22×C42C2311yescharacteristic
295#410—48no—
296C2×#99—416no—
297C2×#99C2314yes—
298C2×#99C2318yes—
299C2×#99C2318yes—
300C2×#99C2318yes—
301C2×#99C2318yes—
302C2×#99C2318yes—
303C2×#99C2314yes—
304#390—22no—
305#390—22no—
306#389—22no—
307#389—22no—
308#388—24no—
309#388—24no—
310#388—24no—
311#388—24no—
312#387—24no—
313#387—24no—
314#386—24no—
315#386—24no—
316#385—24no—
317#385—24no—
318#384—21no—
319#383—21no—
320#383—21no—
321#382—21no—
322#382—21no—
323#382—21no—
324#381—22no—
325#381—22no—
326#381C2312yes—
327#381C2312yes—
328#380—22no—
329#380—22no—
330#380—22no—
331#380—22no—
332#380C2312yes—
333#380C2312yes—
334#380C2314yes—
335#380C2314yes—
336#380C2311yescharacteristic
337#380C2312yes—
338#380C2311yescharacteristic
339#379C2314yes—
340#379C2314yes—
341C4×C4⋊C4—22no—
342C4×C4⋊C4—22no—
343C4×C4⋊C4—21no—
344C4×C4⋊C4—21no—
345C4×C4⋊C4—21no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4—21no—
348C4×C4⋊C4—21no—
349C4×C22⋊C4—22no—
350C4×C22⋊C4—22no—
351C4×C22⋊C4—22no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4—24no—
354C4×C22⋊C4—24no—
355C4×C22⋊C4C2312yes—
356C4×C22⋊C4C2312yes—
357C4×C22⋊C4C2314yes—
358C4×C22⋊C4C2314yes—
359C4×C22⋊C4C2311yescharacteristic
360C4×C22⋊C4C2312yes—
361C4×C22⋊C4C2311yescharacteristic
362#376—21no—
363#376—21no—
364#376—21no—
365C2×#95—22no—
366C2×#95—22no—
367C43—21no—
368#342C2314yes—
369#342C2318yes—
370#342C2314yes—
371C25C22×C414yes—
372C25C2412yes—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—44no—
382C2×#41—44no—
383C2×#41—84no—
384C22×Q8C22×C411yescharacteristic
385C22×Q8C22×C412yes—
386C22×D4—24no—
387C22×D4—24no—
388C22×D4—24no—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4—22no—
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—44no—
398C22×D4—48no—
399C22×D4—48no—
400C22×D4—48no—
401C22×D4—84no—
402C22×D4C22×C411yescharacteristic
403C22×D4C22×C414yes—
404C22×D4C22×C412yes—
405C22×D4C22×C411yescharacteristic
406C22×D4C22×C412yes—
407C22×D4C22×C414yes—
408C22×D4C22×C412yes—
409C22×D4C22×C414yes—
410C22×D4C22×C414yes—
411C22×D4C22×C414yes—
412C22×D4C22×C412yes—
413C22×D4C22×C411yescharacteristic
414C22×D4C2×D411yescharacteristic
415C22×D4C2×D411yescharacteristic
416C22×D4C2×D412yes—
417C22×D4C2×D412yes—
418C22×D4C2×D411yescharacteristic
419C22×D4C2×D411yescharacteristic
420C22×D4C2414yes—
421C22×D4C2412yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—84no—
425C23×C4C22×C414yes—
426C23×C4C22×C414yes—
427C23×C4C22×C412yes—
428C23×C4C22×C414yes—
429C23×C4C22×C412yes—
430C23×C4C22×C412yes—
431C23×C4C22×C412yes—
432C23×C4C22×C412yes—
433C23×C4C2×D412yes—
434C23×C4C2×D412yes—
435C23×C4C2×D412yes—
436C23×C4C2×D412yes—
437C23×C4C2×D412yes—
438C23×C4C2×D412yes—
439C23×C4C2×D412yes—
440C23×C4C2×D412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C4⋊Q8—21no—
446C4⋊Q8—21no—
447C4⋊Q8—21no—
448C4⋊Q8—21no—
449#127—22no—
450#127—22no—
451#127—24no—
452#127—21no—
453#127—21no—
454#127—21no—
455#127—21no—
456#126—24no—
457#126—24no—
458#126—24no—
459#126—24no—
460#126—22no—
461#126—22no—
462#126—22no—
463#126—22no—
464#125—24no—
465#125—22no—
466#125—22no—
467#125—21no—
468#125—21no—
469#125—21no—
470#125—21no—
471#124—24no—
472#124—24no—
473#124—24no—
474#124—24no—
475#124—21no—
476#124—21no—
477#124—21no—
478#124—21no—
479#124—22no—
480#124—22no—
481#124—22no—
482#124—22no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496#123—24no—
497#123—24no—
498#123—24no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511#121—24no—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—22no—
516#121—22no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—24no—
521#121—24no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—24no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—22no—
550#121—24no—
551#121—22no—
552#121—22no—
553#121—24no—
554#121—24no—
555#121—24no—
556#121—24no—
557#121—24no—
558#121—24no—
559#121—24no—
560#121—24no—
561#120—24no—
562#120—24no—
563#120—24no—
564#120—24no—
565#120—24no—
566#120—24no—
567#120—24no—
568#120—24no—
569#120—24no—
570#120—24no—
571#120—24no—
572#120—24no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—21no—
576C4×Q8—21no—
577C4×D4—24no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—24no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C411yescharacteristic
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C411yescharacteristic
617C4×D4C22⋊C411yescharacteristic
618C4×D4C22⋊C411yescharacteristic
619C4×D4C22⋊C412yes—
620C4×D4C22⋊C412yes—
621C4×D4C22⋊C412yes—
622C4×D4C22⋊C412yes—
623C4×D4C22⋊C412yes—
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C412yes—
626C4×D4C22⋊C412yes—
627C4×D4C22⋊C411yescharacteristic
628C4×D4C22⋊C411yescharacteristic
629C4×D4C22⋊C411yescharacteristic
630C4×D4C22⋊C411yescharacteristic
631C4×D4C22⋊C412yes—
632C4×D4C22⋊C412yes—
633C4×D4C22⋊C412yes—
634C4×D4C22⋊C411yescharacteristic
635C4×D4C22⋊C411yescharacteristic
636C4×D4C22⋊C412yes—
637C4×D4C22⋊C411yescharacteristic
638C4×D4C22⋊C411yescharacteristic
639C4×D4C22⋊C412yes—
640C4×D4C22⋊C412yes—
641C4×D4C22⋊C412yes—
642C4×D4C22⋊C412yes—
643C4×D4C22⋊C412yes—
644C4×D4C22⋊C412yes—
645C4×D4C22⋊C412yes—
646C4×D4C22⋊C412yes—
647C4×D4C22⋊C411yescharacteristic
648C4×D4C22⋊C411yescharacteristic
649C4×D4C22⋊C412yes—
650C4×D4C22⋊C411yescharacteristic
651C4×D4C22⋊C411yescharacteristic
652C4×D4C22⋊C412yes—
653#117—22no—
654#117—22no—
655#117—22no—
656#117—22no—
657#117—24no—
658#117—22no—
659#117—22no—
660#117—22no—
661#117—22no—
662#117—22no—
663#117—22no—
664#117—24no—
665#117—42no—
666#117—44no—
667#117—84no—
668#117—84no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—24no—
680C2×C4⋊C4—24no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—84no—
683C2×C4⋊C4C22×C411yescharacteristic
684C2×C4⋊C4C22×C412yes—
685C2×C4⋊C4C22×C414yes—
686C2×C4⋊C4C22×C411yescharacteristic
687C2×C4⋊C4C22×C412yes—
688C2×C4⋊C4C22×C412yes—
689C2×C4⋊C4C22×C412yes—
690C2×C4⋊C4C22×C412yes—
691C2×C4⋊C4C22×C414yes—
692C2×C4⋊C4C22×C412yes—
693C2×C4⋊C4C22×C411yescharacteristic
694C2×C4⋊C4C22×C411yescharacteristic
695C2×C4⋊C4C22×C412yes—
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C4⋊C4C2×D412yes—
699C2×C4⋊C4C2×D412yes—
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—28no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4—48no—
719C2×C22⋊C4C22×C412yes—
720C2×C22⋊C4C22×C412yes—
721C2×C22⋊C4C22×C414yes—
722C2×C22⋊C4C22×C414yes—
723C2×C22⋊C4C22×C414yes—
724C2×C22⋊C4C22×C414yes—
725C2×C22⋊C4C22×C414yes—
726C2×C22⋊C4C22×C414yes—
727C2×C22⋊C4C22×C412yes—
728C2×C22⋊C4C22×C412yes—
729C2×C22⋊C4C22×C414yes—
730C2×C22⋊C4C22×C412yes—
731C2×C22⋊C4C22×C412yes—
732C2×C22⋊C4C22×C412yes—
733C2×C22⋊C4C22×C412yes—
734C2×C22⋊C4C2×D412yes—
735C2×C22⋊C4C2×D412yes—
736C2×C22⋊C4C2×D412yes—
737C2×C22⋊C4C2×D412yes—
738C2×C22⋊C4C2×D412yes—
739C2×C22⋊C4C2×D412yes—
740C2×C22⋊C4C2×D412yes—
741C2×C22⋊C4C2×D412yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C42—21no—
750C2×C42—22no—
751C2×C42—22no—
752C2×C42—22no—
753C2×C42—22no—
754C2×C42—21no—
755C2×C42—24no—
756C2×C42—22no—
757C2×C42—24no—
758C2×C42—84no—
759C2×C42C22×C414yes—
760C2×C42C22×C412yes—
761C2×C42C22×C411yescharacteristic
762C2×C42C22×C411yescharacteristic
763C2×C42C22×C411yescharacteristic
764C2×C42C22×C411yescharacteristic
765C2×C42C2×D411yescharacteristic
766C2×C42C2×D411yescharacteristic
767C2×C42C2×D411yescharacteristic
768C2×C42C2×D411yescharacteristic
769C2×C42C2×D411yescharacteristic
770C2×C42C2×D411yescharacteristic
771C2×C42C2×D411yescharacteristic
772C2×C42C2×D411yescharacteristic
773#99—28no—
774#99—216no—
775#99—48no—
776#99—48no—
777#99—48no—
778#99—44no—
779#99—48no—
780#95—21no—
781#95—21no—
782#95—22no—
783#95—24no—
784#95—22no—
785#95—24no—
786#95—21no—
787#95—22no—
788#95—21no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—24no—
793#95—22no—
794#95—24no—
795#95—22no—
796#95—22no—
797#95—22no—
798C24—24no—
799C24—24no—
800C24—24no—
801C24—24no—
802C24—44no—
803C24—48no—
804C24—48no—
805C24—82no—
806C24—84no—
807C24C23×C412yes—
808C24C23×C412yes—
809C24C23×C414yes—
810C24C23×C412yes—
811C24C22×D412yes—
812C24C22×D412yes—
813C24C22×D412yes—
814C24C22×D412yes—
815C24C2511yescharacteristic
816#41—84no—
817#41—84no—
818#41—82no—
819#41—82no—
820#41—82no—
821#41—82no—
822#41—84no—
823#41—84no—
824#41—84no—
825#41—84no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—44no—
831C2×Q8—42no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—24no—
842C2×D4—28no—
843C2×D4—24no—
844C2×D4—28no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—44no—
865C2×D4—42no—
866C2×D4—44no—
867C2×D4—48no—
868C2×D4—48no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—416no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—48no—
877C2×D4—84no—
878C2×D4—84no—
879C2×D4—84no—
880C2×D4—84no—
881C2×D4—84no—
882C2×D4—84no—
883C2×D4—88no—
884C2×D4—88no—
885C2×D4—84no—
886C2×D4—84no—
887C2×D4—84no—
888C2×D4—84no—
889C2×D4C2×C22⋊C412yes—
890C2×D4C2×C22⋊C411yescharacteristic
891C2×D4C2×C22⋊C412yes—
892C2×D4C2×C22⋊C412yes—
893C2×D4C2×C22⋊C411yescharacteristic
894C2×D4C2×C22⋊C411yescharacteristic
895C2×D4C2×C22⋊C412yes—
896C2×D4C2×C22⋊C412yes—
897C2×D4C2×C22⋊C412yes—
898C2×D4C2×C22⋊C411yescharacteristic
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—22no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—24no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—42no—
923C22×C4—48no—
924C22×C4—48no—
925C22×C4—44no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—82no—
930C22×C4—82no—
931C22×C4—82no—
932C22×C4—82no—
933C22×C4—82no—
934C22×C4—82no—
935C22×C4—82no—
936C22×C4—84no—
937C22×C4—84no—
938C22×C4—84no—
939C22×C4—84no—
940C22×C4C2×C22⋊C412yes—
941C22×C4C2×C22⋊C412yes—
942C22×C4C2×C22⋊C412yes—
943C22×C4C2×C22⋊C412yes—
944C22×C4C2×C22⋊C412yes—
945C22×C4C2×C22⋊C412yes—
946C22×C4C2×C22⋊C412yes—
947C22×C4C2×C22⋊C412yes—
948C22×C4C2×C22⋊C412yes—
949C22×C4C2×C22⋊C412yes—
950C22×C4C2×C22⋊C412yes—
951C22×C4C2×C22⋊C412yes—
952C22×C4C2×C22⋊C412yes—
953C22×C4C2×C22⋊C412yes—
954C22×C4C2×C22⋊C412yes—
955C22×C4C2×C22⋊C412yes—
956C22×C4C23×C414yes—
957C22×C4C23×C412yes—
958C22×C4C23×C411yescharacteristic
959C22×C4C23×C411yescharacteristic
960C22×C4C23×C411yescharacteristic
961C22×C4C23×C411yescharacteristic
962C22×C4C23×C412yes—
963C22×C4C23×C412yes—
964C22×C4C23×C411yescharacteristic
965C22×C4C23×C412yes—
966C22×C4C23×C411yescharacteristic
967C22×C4C23×C412yes—
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D412yes—
981C22×C4C22×D412yes—
982C22×C4C22×D412yes—
983C22×C4C22×D412yes—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—82no—
1011C4⋊C4—84no—
1012C4⋊C4—84no—
1013C4⋊C4C2×C22⋊C412yes—
1014C4⋊C4C2×C22⋊C411yescharacteristic
1015C4⋊C4C2×C22⋊C411yescharacteristic
1016C4⋊C4C2×C22⋊C412yes—
1017C4⋊C4C2×C22⋊C411yescharacteristic
1018C4⋊C4C2×C22⋊C411yescharacteristic
1019C4⋊C4C2×C22⋊C412yes—
1020C4⋊C4C2×C22⋊C412yes—
1021C4⋊C4C2×C22⋊C412yes—
1022C4⋊C4C2×C22⋊C412yes—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—24no—
1051C22⋊C4—22no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—22no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—84no—
1059C22⋊C4—84no—
1060C22⋊C4—84no—
1061C22⋊C4C2×C22⋊C412yes—
1062C22⋊C4C2×C22⋊C412yes—
1063C22⋊C4C2×C22⋊C412yes—
1064C22⋊C4C2×C22⋊C412yes—
1065C22⋊C4C2×C22⋊C412yes—
1066C22⋊C4C2×C22⋊C412yes—
1067C22⋊C4C2×C22⋊C412yes—
1068C22⋊C4C2×C22⋊C412yes—
1069C22⋊C4C2×C22⋊C412yes—
1070C22⋊C4C2×C22⋊C412yes—
1071C22⋊C4C2×C22⋊C412yes—
1072C22⋊C4C2×C22⋊C412yes—
1073C22⋊C4C2×C22⋊C412yes—
1074C22⋊C4C2×C22⋊C412yes—
1075C22⋊C4C2×C22⋊C412yes—
1076C22⋊C4C2×C22⋊C412yes—
1077C22⋊C4H(5,𝔽2)14yes—
1078C42—24no—
1079C42—24no—
1080C42—22no—
1081C42—22no—
1082C42—44no—
1083C42—42no—
1084C42—44no—
1085C42—42no—
1086C42—44no—
1087C42—44no—
1088C42—82no—
1089C42—84no—
1090C42—84no—
1091C42C2×C22⋊C411yescharacteristic
1092C42C2×C22⋊C411yescharacteristic
1093C42C2×C22⋊C411yescharacteristic
1094C42C2×C22⋊C411yescharacteristic
1095C42C2×C22⋊C411yescharacteristic
1096C42C2×C22⋊C411yescharacteristic
1097C42C2×C22⋊C411yescharacteristic
1098C42C2×C22⋊C411yescharacteristic
1099C42C2×C22⋊C411yescharacteristic
1100C42C2×C22⋊C411yescharacteristic
1101C42C2×C22⋊C411yescharacteristic
1102C42C2×C22⋊C411yescharacteristic
1103C42C2×C22⋊C411yescharacteristic
1104C42C2×C22⋊C411yescharacteristic
1105C42C2×C22⋊C411yescharacteristic
1106C42C2×C22⋊C411yescharacteristic
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—22no—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—24no—
1120C23—28no—
1121C23—24no—
1122C23—42no—
1123C23—42no—
1124C23—41no—
1125C23—42no—
1126C23—41no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—42no—
1131C23—42no—
1132C23—42no—
1133C23—48no—
1134C23—42no—
1135C23—44no—
1136C23—44no—
1137C23—42no—
1138C23—48no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—88no—
1144C23—88no—
1145C23—1616no—
1146C23C22×C22⋊C412yes—
1147C23C22×C22⋊C412yes—
1148C23C22×C22⋊C412yes—
1149C23C22×C22⋊C412yes—
1150C23C24×C411yescharacteristic
1151C23C23×D411yescharacteristic
1152C23C23×D411yescharacteristic
1153C23C2×H(5,𝔽2)12yes—
1154C23#58512yes—
1155Q8—42no—
1156Q8—42no—
1157Q8—82no—
1158Q8—82no—
1159D4—24no—
1160D4—24no—
1161D4—24no—
1162D4—22no—
1163D4—22no—
1164D4—22no—
1165D4—42no—
1166D4—42no—
1167D4—42no—
1168D4—44no—
1169D4—42no—
1170D4—44no—
1171D4—48no—
1172D4—48no—
1173D4—44no—
1174D4—48no—
1175D4—42no—
1176D4—44no—
1177D4—42no—
1178D4—44no—
1179D4—44no—
1180D4—42no—
1181D4—44no—
1182D4—82no—
1183D4—82no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
1192D4#41014yescomplemented
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—28no—
1217C2×C4—24no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—44no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—44no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—44no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—44no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—44no—
1260C2×C4—44no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—816no—
1270C2×C4—168no—
1271C2×C4C22×C22⋊C411yescharacteristic
1272C2×C4C22×C22⋊C412yes—
1273C2×C4C22×C22⋊C412yes—
1274C2×C4C22×C22⋊C411yescharacteristic
1275C2×C4C22×C22⋊C411yescharacteristic
1276C2×C4C22×C22⋊C411yescharacteristic
1277C2×C4C22×C22⋊C411yescharacteristic
1278C2×C4C22×C22⋊C411yescharacteristic
1279C2×C4C22×C22⋊C411yescharacteristic
1280C2×C4C22×C22⋊C411yescharacteristic
1281C2×C4C22×C22⋊C411yescharacteristic
1282C2×C4C22×C22⋊C411yescharacteristic
1283C2×C4C22×C22⋊C412yes—
1284C2×C4C22×C22⋊C412yes—
1285C2×C4C22×C22⋊C411yescharacteristic
1286C2×C4C22×C22⋊C411yescharacteristic
1287C22—21no—
1288C22—21no—
1289C22—21no—
1290C22—21no—
1291C22—21no—
1292C22—21no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—42no—
1305C22—42no—
1306C22—48no—
1307C22—44no—
1308C22—44no—
1309C22—48no—
1310C22—42no—
1311C22—44no—
1312C22—44no—
1313C22—42no—
1314C22—44no—
1315C22—42no—
1316C22—84no—
1317C22—82no—
1318C22—82no—
1319C22—84no—
1320C22—88no—
1321C22—84no—
1322C22—168no—
1323C22—168no—
1324C22C2×#41014yes—
1325C22C23×C22⋊C411yescharacteristic
1326C22C4×H(5,𝔽2)12yes—
1327C22#348812yes—
1328C22#349811yescharacteristic
1329C22#350011yescharacteristic
1330C4—21no—
1331C4—21no—
1332C4—21no—
1333C4—21no—
1334C4—21no—
1335C4—21no—
1336C4—22no—
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—21no—
1341C4—21no—
1342C4—21no—
1343C4—21no—
1344C4—44no—
1345C4—42no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—82no—
1350C4—82no—
1351C4—84no—
1352C4—84no—
1353C4—82no—
1354C4C2×#41012yes—
1355C4#288312yes—
1356C2—22no—
1357C2—21no—
1358C2—21no—
1359C2—22no—
1360C2—24no—
1361C2—42no—
1362C2—42no—
1363C2—42no—
1364C2—84no—
1365C2—82no—
1366C2#3425811yescharacteristic
1367C2C22×#41011yescharacteristic
1368C2C2×#288311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC2×#3519C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34194C2semidirect
3. #34126C2semidirect
4. #22535C2semidirect
5. #22405C2semidirect
6. D4×#99C2semidirect
7. #21875C2semidirect
8. #21874C2semidirect
9. #21794C2semidirect
10. #21793C2semidirect
11. #21421C2semidirect
12. #21420C2semidirect
13. #21212C2semidirect
14. C2×#1964C2semidirect
27. C2×#555C4semidirect
28. C2×#554C4semidirect
29. C2×#553C4semidirect
31. C2×#550C4semidirect
32. C2×#546C4semidirect
34. C2×D42C4semidirect
36. C2×#540C4semidirect
37. C2×#538C4semidirect
42. C2×#518C4semidirect
44. C2×#410C22semidirect
45. C22×#99C22semidirect
52. #2345C22semidirect
53. #2345C22semidirect
54. #2342C22semidirect
55. #2342C22semidirect
62. #2285C22semidirect
63. #2283C22semidirect
64. #2283C22semidirect
65. #2280C22semidirect
66. #2280C22semidirect
67. C2×#380C22semidirect
70. C4×#117C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. #1996C22semidirect
73. #1996C22semidirect
74. #1996C22semidirect
78. #1964C22semidirect
79. #1964C22semidirect
80. #1964C22semidirect
81. #1964C22semidirect
82. #1964C22semidirect
83. #1964C22semidirect
84. #1964C22semidirect
85. #1964C22semidirect
86. #1899C22semidirect
87. #1899C22semidirect
88. #1898C22semidirect
89. #1898C22semidirect
90. #1799C22semidirect
91. #1799C22semidirect
92. #1782C22semidirect
93. #1781C22semidirect
94. C4×#99C22semidirect
95. C4×#99C22semidirect
96. C22×#41C2×C4semidirect
99. C23×D4C2×C4semidirect
185. C2×C4⋊Q8C2×C4semidirect
187. C2×#127C2×C4semidirect
196. C2×#126C2×C4semidirect
197. C2×#126C2×C4semidirect
198. C2×#125C2×C4semidirect
199. C2×#125C2×C4semidirect
200. C2×#124C2×C4semidirect
201. C2×#124C2×C4semidirect
202. C2×#124C2×C4semidirect
211. C2×#123C2×C4semidirect
212. C2×#123C2×C4semidirect
213. C2×#123C2×C4semidirect
215. C2×C22⋊Q8C2×C4semidirect
216. C2×C22⋊Q8C2×C4semidirect
228. C2×#121C2×C4semidirect
229. C2×#121C2×C4semidirect
230. C2×#121C2×C4semidirect
231. C2×#121C2×C4semidirect
232. C2×#121C2×C4semidirect
233. C2×#121C2×C4semidirect
234. C2×#121C2×C4semidirect
240. C2×#120C2×C4semidirect
248. C2×C4×Q8C2×C4semidirect
258. C2×C4×D4C2×C4semidirect
259. C2×C4×D4C2×C4semidirect
260. C2×C4×D4C2×C4semidirect
261. C2×C4×D4C2×C4semidirect
262. C2×C4×D4C2×C4semidirect
263. C2×C4×D4C2×C4semidirect
280. C2×#117C2×C4semidirect
281. C2×#117C2×C4semidirect
282. C2×#117C2×C4semidirect
286. C22×C4⋊C4C2×C4semidirect
288. C22×C22⋊C4C2×C4semidirect
289. C22×C22⋊C4C2×C4semidirect
1192. D4#410semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
#341942
#341262
#225352
#224052
D4×#992
#218752
#218742
#217942
#217932
#214212
#214202
#212122
C2×#19642