Finite Group Databasebeta

← #10586523

Subgroups — #10586523

Order 512.

31425 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63039C214yesmaximal, complemented
2#63038C214yesmaximal, complemented
3#63034C2112yesmaximal, complemented
4#63033C2112yesmaximal, complemented
5#63007C213yesmaximal, complemented
6#63004C213yesmaximal, complemented
7#63001C214yesmaximal, complemented
8#62999C211yesmaximal, characteristic, complemented
9#62999C214yesmaximal, complemented
10Q8×2−1+4C211yesmaximal, characteristic, complemented
11#62953C2112yesmaximal, complemented
12#62952C2112yesmaximal, complemented
13#62926C2118yesmaximal, complemented
14#62913C216yesmaximal, complemented
15#62838C2118yesmaximal, complemented
16#62793C213yesmaximal, complemented
17#62793C213yesmaximal, complemented
18#62788C216yesmaximal, complemented
19C2×Q8×#41C211yesmaximal, characteristic, complemented
20#3565C22172yescomplemented
21#3565C22172yescomplemented
22#3565C22172yescomplemented
23#3559C22172yescomplemented
24#3557C22172yescomplemented
25#3555C22136yescomplemented
26#3555C22136yescomplemented
27#3555C22136yescomplemented
28#3554C22136yescomplemented
29#3554C22172yescomplemented
30#3552C22136yescomplemented
31#3550C22136yescomplemented
32#3548C22136yescomplemented
33#3547C22136yescomplemented
34#3547C22136yescomplemented
35#3547C22136yescomplemented
36#3547C22136yescomplemented
37#3544C22136yescomplemented
38#3541C22172yes—
39#3541C22172yes—
40#3524C22112yes—
41#3524C22112yes—
42#3524C22124yes—
43#3524C22124yescomplemented
44#3523C2216yescomplemented
45#3523C22112yescomplemented
46#3523C22112yescomplemented
47#3523C22118yescomplemented
48#3522C2216yescomplemented
49#3522C22136yescomplemented
50#3522C22112yescomplemented
51#3522C22118yescomplemented
52#3518C22112yes—
53#3518C22112yes—
54#3518C22112yescomplemented
55#3518C22112yescomplemented
56#3518C22136yescomplemented
57#3518C22136yescomplemented
58#3517C22112yes—
59#3517C22112yes—
60#3517C22112yescomplemented
61#3516C2214yes—
62#3516C22136yes—
63#3516C22124yes—
64#3516C22124yescomplemented
65#3515C22136yescomplemented
66#3515C22136yescomplemented
67#3515C22136yescomplemented
68#3512C22136yes—
69#3511C22118yes—
70#3511C22118yes—
71#3511C22136yescomplemented
72#3511C22136yescomplemented
73#3511C22136yescomplemented
74#3509C22136yescomplemented
75#3509C22136yescomplemented
76#3507C22136yescomplemented
77#3507C22118yescomplemented
78#3507C22118yescomplemented
79#3506C22118yes—
80#3506C22118yes—
81#3504C22136yes—
82#3504C22124yescomplemented
83#3503C22118yes—
84#3503C22118yes—
85#3503C22112yescomplemented
86#3503C22112yescomplemented
87#3502C2213yes—
88#3502C2213yes—
89#3502C22112yescomplemented
90#3502C22124yescomplemented
91#3502C22112yescomplemented
92#3502C2216yescomplemented
93#3499C22112yescomplemented
94#3497C2213yes—
95#3497C2213yes—
96#3497C22112yescomplemented
97#3497C2216yescomplemented
98#3493C22118yes—
99#3493C22118yes—
100#3492C22136yes—
101#3487C2211yescharacteristic
102#3487C2213yes—
103#3486C22112yes—
104#3483C22112yes—
105#3483C22112yes—
106#3483C2214yescomplemented
107#3482C22112yes—
108#3482C22112yes—
109#3482C22112yescomplemented
110#3482C22136yescomplemented
111#3482C22112yescomplemented
112#3480C2216yes—
113#3480C22112yes—
114#3480C22112yes—
115#3480C22118yes—
116#3480C22124yes—
117#3480C22112yescomplemented
118Q8×#41C2216yes—
119Q8×#41C2214yes—
120Q8×#41C22118yes—
121Q8×#41C22112yes—
122Q8×#41C2214yes—
123Q8×#41C22112yes—
124Q8×#41C2214yescomplemented
125Q8×#41C2214yescomplemented
126Q8×#41C22112yescomplemented
127C2×Q82C2211yescharacteristic
128C2×Q82C2214yescomplemented
129C2×#557C2213yes—
130C2×#557C22112yescomplemented
131C2×#554C2219yes—
132C2×D4×Q8C2213yes—
133#3461C22136yescomplemented
134#3460C22118yes—
135#3460C22118yes—
136#3444C22118yes—
137#3444C22118yes—
138C2×#533C2219yes—
139C4×2−1+4C2213yes—
140C4×2−1+4C2213yes—
141C4×2−1+4C2216yes—
142C4×2−1+4C22112yescomplemented
143C2×C4×#41C2213yes—
144C22×C4×Q8C2213yes—
145C2×2−1+4C2311yescharacteristic
146C2×2−1+4C2313yes—
147C2×2−1+4C23112yes—
148C22×#41C2311yescharacteristic
149C23×Q8C2313yes—
150#563C231144yes—
151#563C231144yes—
152#562C231144yes—
153#562C231144yes—
154#559C23118yes—
155#559C23136yes—
156#559C23136yes—
157#559C23172yes—
158#559C23118yes—
159#559C23136yes—
160Q82C2314yes—
161Q82C23112yes—
162Q82C2316yes—
163Q82C23112yes—
164Q82C23136yes—
165Q82C23118yes—
166Q82C23112yes—
167Q82C23136yes—
168#557C23112yes—
169#557C23112yes—
170#557C23124yes—
171#557C23118yes—
172#557C23112yes—
173#557C23112yes—
174#557C23136yes—
175#557C23172yes—
176#557C23118yes—
177#557C23136yes—
178#557C23112yes—
179#557C2316yes—
180#557C23124yes—
181#557C23118yes—
182#557C23112yes—
183#557C2314yes—
184#557C23136yes—
185#557C23136yes—
186#557C23172yes—
187#557C23124yes—
188#556C23118yes—
189#556C23136yes—
190#556C23172yes—
191#556C23136yes—
192#556C23136yes—
193#556C23118yes—
194#556C23136yes—
195#556C23136yes—
196#556C23136yes—
197#556C23112yes—
198#556C23136yes—
199#556C23172yes—
200#556C23172yes—
201#556C23172yes—
202#556C23136yes—
203#556C23172yes—
204#555C23136yes—
205#555C23172yes—
206#555C23136yes—
207#555C23136yes—
208#555C23136yes—
209#555C23136yes—
210#555C23136yes—
211#554C23136yes—
212#554C23136yes—
213#554C23172yes—
214#554C23112yes—
215#554C23118yes—
216#554C23136yes—
217#554C23172yes—
218#554C23118yes—
219#554C23136yes—
220#554C23136yes—
221#554C23172yes—
222#554C23136yes—
223#554C23172yes—
224#554C23136yes—
225#554C23172yes—
226#554C23136yes—
227#553C23112yes—
228#553C23136yes—
229#553C23172yes—
230#553C23136yes—
231#553C23172yes—
232#553C23136yes—
233#553C23136yes—
234#553C23136yes—
235#553C23172yes—
236#553C23172yes—
237#553C23172yes—
238#553C23172yes—
239#552C23136yes—
240#552C23172yes—
241#552C23136yes—
242#552C23112yes—
243#552C23136yes—
244#552C23136yes—
245#552C23172yes—
246#552C23136yes—
247#552C23172yes—
248#552C23172yes—
249#552C23172yes—
250#552C23172yes—
251#552C23172yes—
252#552C23172yes—
253#550C2314yes—
254#550C23112yes—
255#550C23112yes—
256#550C2316yes—
257#550C23118yes—
258#550C23112yes—
259#550C2314yes—
260#550C23112yes—
261#550C23136yes—
262#550C23136yes—
263D4×Q8C23112yes—
264D4×Q8C23136yes—
265D4×Q8C2314yes—
266D4×Q8C2316yes—
267D4×Q8C23136yes—
268D4×Q8C23118yes—
269D4×Q8C23112yes—
270D4×Q8C23136yes—
271D4×Q8C23112yes—
272D4×Q8C23112yes—
273D4×Q8C23136yes—
274D4×Q8C23124yes—
275D4×Q8C23136yes—
276#548C2314yes—
277#548C2314yes—
278#548C23112yes—
279#548C23112yes—
280#548C23112yes—
281#548C23112yes—
282#548C23136yes—
283#548C23124yes—
284#548C2314yes—
285#548C2314yes—
286#548C23112yes—
287#548C23136yes—
288#548C23136yes—
289#548C23172yes—
290#548C23124yes—
291#548C23124yes—
292#548C23172yes—
293#547C23136yes—
294#547C23136yes—
295#547C23136yes—
296#547C23136yes—
297#547C23172yes—
298#547C23136yes—
299#547C23172yes—
300#547C23136yes—
301#547C23172yes—
302#544C23118yes—
303#544C23118yes—
304#544C23136yes—
305#544C23172yes—
306#544C23172yes—
307#544C23172yes—
308#544C23172yes—
309#542C23172yes—
310#542C23136yes—
311#542C23136yes—
312#542C23112yes—
313#542C23136yes—
314#542C23172yes—
315#542C23172yes—
316#542C23172yes—
317#542C23172yes—
318#542C23172yes—
319#542C231144yes—
320#542C23172yes—
321#542C231144yes—
322#541C23112yes—
323#541C23136yes—
324#541C23172yes—
325#541C23172yes—
326#541C23172yes—
327#541C23172yes—
328#541C23172yes—
329#540C23136yes—
330#540C23172yes—
331#540C23136yes—
332#540C23172yes—
333#539C23172yes—
334#539C23172yes—
335#539C231144yes—
336#539C231144yes—
337#538C23172yes—
338#538C23172yes—
339#537C23118yes—
340#537C23118yes—
341#537C23136yes—
342#537C23172yes—
343#537C23172yes—
344#536C23136yes—
345#536C23136yes—
346#536C23172yes—
347#536C23172yes—
348#535C2316yes—
349#535C23118yes—
350#533C23136yes—
351#533C23136yes—
352#533C23136yes—
353#533C23136yes—
354#533C23118yes—
355#533C23118yes—
356#533C23118yes—
357#533C23118yes—
358#533C23118yes—
359#533C23118yes—
360#533C23136yes—
361#533C23136yes—
362#533C23172yes—
363#533C23136yes—
364#533C23136yes—
365#533C23172yes—
366#533C23136yes—
367#533C23136yes—
368#532C23118yes—
369#532C23118yes—
370#532C23118yes—
371#532C23118yes—
372#532C23118yes—
373#532C23118yes—
374#532C23136yes—
375#532C23136yes—
376#532C23172yes—
377#532C23136yes—
378#532C23136yes—
379C2×C4⋊Q8C2319yes—
380C2×C4⋊Q8C2319yes—
381C2×C4⋊Q8C23136yes—
382C2×C4⋊Q8C23136yes—
383#529C23112yes—
384#529C23112yes—
385#529C23136yes—
386#529C23136yes—
387#529C23136yes—
388#529C23118yes—
389#529C23118yes—
390#529C23136yes—
391#529C23136yes—
392#529C23136yes—
393#529C23136yes—
394#529C23118yes—
395#529C23118yes—
396#529C23136yes—
397#529C23172yes—
398#529C23136yes—
399#529C23136yes—
400#529C23172yes—
401#529C23136yes—
402#529C23136yes—
403#529C23172yes—
404#529C23172yes—
405C2×#125C23118yes—
406C2×#125C23172yes—
407#525C2316yes—
408#525C23118yes—
409#525C23136yes—
410#525C23136yes—
411#525C23136yes—
412#525C23136yes—
413C2×C22⋊Q8C23118yes—
414C2×C22⋊Q8C23118yes—
415#520C23118yes—
416#520C23136yes—
417#520C23118yes—
418#520C23112yes—
419#520C23124yes—
420#520C23112yes—
421#520C2314yes—
422#520C23136yes—
423#520C23136yes—
424#520C23136yes—
425#520C23124yes—
426#519C2311yescharacteristic
427#519C2313yes—
428#519C23112yes—
429#519C23112yes—
430#519C23124yes—
431#519C2314yes—
432#519C23112yes—
433#519C23136yes—
434#519C23124yes—
435C4×#41C23112yes—
436C4×#41C23112yes—
437C4×#41C23112yes—
438C4×#41C23112yes—
439C4×#41C23118yes—
440C4×#41C23118yes—
441C4×#41C23136yes—
442C4×#41C23124yes—
443C4×#41C23112yes—
444C4×#41C23112yes—
445C4×#41C23136yes—
446C4×#41C23136yes—
447C4×#41C23112yes—
448C4×#41C23136yes—
449C4×#41C23136yes—
450C4×#41C23136yes—
451C2×C4×Q8C2311yescharacteristic
452C2×C4×Q8C2316yes—
453C2×C4×Q8C2319yes—
454C2×C4×Q8C23118yes—
455C2×C4×Q8C2313yes—
456C2×C4×Q8C2319yes—
457C2×C4×Q8C2316yes—
458C2×C4×Q8C23118yes—
459C2×C4×Q8C2313yes—
460C2×C4×Q8C2313yes—
461C2×C4×Q8C23112yes—
462C2×C4×Q8C23124yes—
463C2×C4×Q8C23112yes—
464C2×C4×Q8C23136yes—
465C2×C4×Q8C23112yes—
466C2×C4×Q8C2316yes—
467C2×C4×D4C2319yes—
468C2×C4×D4C2319yes—
469C2×#117C2319yes—
470C22×C4⋊C4C2319yes—
471C22×C42C2319yes—
4722−1+4—28no—
4732−1+4—224no—
4742−1+4—448no—
475C2×#41—28no—
476C2×#41C2414yes—
477C2×#41C2414yes—
478C2×#41C2416yes—
479C2×#41C24118yes—
480C2×#41C24112yes—
481C2×#41C2414yes—
482C2×#41C2414yes—
483C2×#41C24136yes—
484C2×#41C24136yes—
485C2×#41C24136yes—
486C2×#41C24136yes—
487C2×#41C24136yes—
488C2×#41C24124yes—
489C22×Q8—412no—
490C22×Q8C2411yescharacteristic
491C22×Q8C24112yes—
492C22×Q8C2414yes—
493C22×Q8C2414yes—
494C22×Q8C2416yes—
495C22×Q8C2419yes—
496C22×Q8C24118yes—
497C22×Q8C24136yes—
498C22×Q8C2416yes—
499C22×Q8C24124yes—
500C22×Q8C2411yescharacteristic
501C22×D4C2413yes—
502C23×C4C2413yes—
503C23×C4C2419yes—
504C23×C4C2419yes—
505C4⋊Q8C24118yes—
506C4⋊Q8C24136yes—
507C4⋊Q8C24136yes—
508C4⋊Q8C24118yes—
509C4⋊Q8C24136yes—
510C4⋊Q8C24136yes—
511C4⋊Q8C24136yes—
512C4⋊Q8C24172yes—
513C4⋊Q8C24136yes—
514C4⋊Q8C24136yes—
515C4⋊Q8C24172yes—
516C4⋊Q8C24172yes—
517C4⋊Q8C24118yes—
518C4⋊Q8C24118yes—
519C4⋊Q8C24136yes—
520C4⋊Q8C24118yes—
521C4⋊Q8C24118yes—
522C4⋊Q8C24112yes—
523C4⋊Q8C24112yes—
524C4⋊Q8C24172yes—
525C4⋊Q8C24172yes—
526#127C24118yes—
527#127C24112yes—
528#127C24136yes—
529#127C24118yes—
530#126C24124yes—
531#126C24112yes—
532#126C24112yes—
533#126C24124yes—
534#126C24172yes—
535#126C24136yes—
536#126C24172yes—
537#126C24136yes—
538#126C24172yes—
539#126C241144yes—
540#126C24172yes—
541#126C24172yes—
542#126C241144yes—
543#126C24172yes—
544#125C24118yes—
545#125C24172yes—
546#125C24136yes—
547#125C24172yes—
548#125C24172yes—
549#125C24172yes—
550#125C241144yes—
551#125C24112yes—
552#125C24112yes—
553#125C24112yes—
554#125C24118yes—
555#125C24136yes—
556#125C24136yes—
557#125C24136yes—
558#125C24136yes—
559#125C24136yes—
560#125C24172yes—
561#125C24124yes—
562#125C24172yes—
563#125C24172yes—
564#125C24172yes—
565#124C24118yes—
566#124C24118yes—
567#124C24112yes—
568#124C24112yes—
569#124C24112yes—
570#124C24136yes—
571#124C24112yes—
572#124C24136yes—
573#124C24136yes—
574#124C24136yes—
575#124C24136yes—
576#124C24172yes—
577#124C24172yes—
578#124C241144yes—
579#124C24172yes—
580#124C24172yes—
581#123C2414yes—
582#123C24112yes—
583#123C24136yes—
584#123C24136yes—
585#123C24172yes—
586#123C24136yes—
587#123C24172yes—
588#123C24136yes—
589#123C24124yes—
590#123C24172yes—
591#123C24172yes—
592#123C24172yes—
593#123C241144yes—
594#123C241144yes—
595#123C24172yes—
596#123C24172yes—
597C22⋊Q8C24172yes—
598C22⋊Q8C24172yes—
599C22⋊Q8C24172yes—
600C22⋊Q8C24172yes—
601C22⋊Q8C24112yes—
602C22⋊Q8C24112yes—
603C22⋊Q8C2416yes—
604C22⋊Q8C24118yes—
605C22⋊Q8C24118yes—
606C22⋊Q8C2416yes—
607C22⋊Q8C24136yes—
608C22⋊Q8C24136yes—
609C22⋊Q8C24136yes—
610C22⋊Q8C24136yes—
611C22⋊Q8C24136yes—
612C22⋊Q8C24136yes—
613C22⋊Q8C24112yes—
614C22⋊Q8C24136yes—
615C22⋊Q8C24172yes—
616C22⋊Q8C24136yes—
617C22⋊Q8C24136yes—
618C22⋊Q8C24172yes—
619C22⋊Q8C24112yes—
620C22⋊Q8C24136yes—
621C22⋊Q8C24136yes—
622C22⋊Q8C24112yes—
623C22⋊Q8C24124yes—
624C22⋊Q8C24172yes—
625C22⋊Q8C24172yes—
626C22⋊Q8C24172yes—
627C22⋊Q8C24172yes—
628C22⋊Q8C24172yes—
629C22⋊Q8C24172yes—
630C22⋊Q8C24172yes—
631C22⋊Q8C241144yes—
632C22⋊Q8C24172yes—
633#121C24112yes—
634#121C24112yes—
635#121C2416yes—
636#121C24118yes—
637#121C24118yes—
638#121C2416yes—
639#121C24136yes—
640#121C24136yes—
641#121C24136yes—
642#121C24136yes—
643#121C24136yes—
644#121C24136yes—
645#121C24112yes—
646#121C24112yes—
647#121C24136yes—
648#121C24136yes—
649#121C24136yes—
650#121C24136yes—
651#121C24172yes—
652#121C24172yes—
653#121C24112yes—
654#121C24136yes—
655#121C24172yes—
656#121C24172yes—
657#121C241144yes—
658#121C24172yes—
659#120C24112yes—
660#120C24136yes—
661C4×Q8C2411yescharacteristic
662C4×Q8C2413yes—
663C4×Q8C2411yescharacteristic
664C4×Q8C2413yes—
665C4×Q8C2416yes—
666C4×Q8C24118yes—
667C4×Q8C24112yes—
668C4×Q8C24112yes—
669C4×Q8C2414yes—
670C4×Q8C24118yes—
671C4×Q8C2414yes—
672C4×Q8C24112yes—
673C4×Q8C24118yes—
674C4×Q8C24118yes—
675C4×Q8C24136yes—
676C4×Q8C24118yes—
677C4×Q8C24118yes—
678C4×Q8C24118yes—
679C4×Q8C24112yes—
680C4×Q8C24136yes—
681C4×Q8C24118yes—
682C4×Q8C24118yes—
683C4×Q8C24136yes—
684C4×Q8C24136yes—
685C4×Q8C24112yes—
686C4×Q8C24112yes—
687C4×Q8C24112yes—
688C4×Q8C24136yes—
689C4×Q8C24172yes—
690C4×Q8C24124yes—
691C4×Q8C24136yes—
692C4×Q8C24136yes—
693C4×Q8C24172yes—
694C4×Q8C24136yes—
695C4×Q8C24124yes—
696C4×Q8C24112yes—
697C4×Q8C2414yes—
698C4×Q8C2414yes—
699C4×Q8C24112yes—
700C4×Q8C24136yes—
701C4×Q8C24136yes—
702C4×Q8C24136yes—
703C4×Q8C24118yes—
704C4×Q8C24118yes—
705C4×Q8C24136yes—
706C4×Q8C24136yes—
707C4×Q8C24136yes—
708C4×Q8C24124yes—
709C4×Q8C24172yes—
710C4×Q8C24124yes—
711C4×D4C24136yes—
712C4×D4C24136yes—
713C4×D4C24136yes—
714C4×D4C24136yes—
715C4×D4C24112yes—
716C4×D4C24112yes—
717C4×D4C24112yes—
718C4×D4C24112yes—
719C4×D4C24124yes—
720C4×D4C24112yes—
721C4×D4C24136yes—
722C4×D4C24136yes—
723C4×D4C24112yes—
724C4×D4C24136yes—
725C4×D4C24136yes—
726C4×D4C24118yes—
727C4×D4C24112yes—
728C4×D4C24118yes—
729C4×D4C24136yes—
730C4×D4C24172yes—
731C4×D4C24136yes—
732C4×D4C24172yes—
733C4×D4C24136yes—
734C4×D4C24136yes—
735C4×D4C24136yes—
736C4×D4C24172yes—
737C4×D4C24136yes—
738C4×D4C24118yes—
739C4×D4C24118yes—
740C4×D4C24136yes—
741C4×D4C24172yes—
742C4×D4C24136yes—
743C4×D4C24136yes—
744C4×D4C24136yes—
745C4×D4C24136yes—
746C4×D4C24136yes—
747C4×D4C24136yes—
748C4×D4C24172yes—
749C4×D4C24136yes—
750C4×D4C24136yes—
751C4×D4C24172yes—
752#117C24136yes—
753#117C24136yes—
754#117C24112yes—
755#117C2416yes—
756#117C24118yes—
757#117C24112yes—
758#117C24112yes—
759#117C24124yes—
760#117C24136yes—
761#117C24136yes—
762#117C24136yes—
763#117C24172yes—
764#117C24136yes—
765#117C24136yes—
766#117C24172yes—
767#117C24172yes—
768#117C24136yes—
769#117C24136yes—
770#117C24172yes—
771#117C24136yes—
772#117C24136yes—
773#117C24136yes—
774#117C24136yes—
775#117C24172yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C24118yes—
778C2×C4⋊C4C24118yes—
779C2×C4⋊C4C2419yes—
780C2×C4⋊C4C24118yes—
781C2×C4⋊C4C24136yes—
782C2×C4⋊C4C2419yes—
783C2×C4⋊C4C2419yes—
784C2×C4⋊C4C24112yes—
785C2×C4⋊C4C24172yes—
786C2×C4⋊C4C24136yes—
787C2×C4⋊C4C24172yes—
788C2×C4⋊C4C24136yes—
789C2×C4⋊C4C24136yes—
790C2×C4⋊C4C24118yes—
791C2×C4⋊C4C24172yes—
792C2×C22⋊C4C24118yes—
793C2×C42C2419yes—
794C2×C42C2419yes—
795C2×C42C2419yes—
796C2×C42C2413yes—
797C2×C42C24118yes—
798C2×C42C24172yes—
799C2×C42C24136yes—
800C2×C42C24136yes—
801C2×C42C24118yes—
802C2×C42C24118yes—
803C2×C42C24118yes—
804C24C2513yes—
805#41—216no—
806#41—216no—
807#41—248no—
808#41—216no—
809#41—216no—
810#41—224no—
811#41—272no—
812#41—472no—
813#41—472no—
814#41—472no—
815#41—836no—
816#41—836no—
817#41—824no—
818C2×Q8—248no—
819C2×Q8—216no—
820C2×Q8—24no—
821C2×Q8—224no—
822C2×Q8—216no—
823C2×Q8—418no—
824C2×Q8—436no—
825C2×Q8—472no—
826C2×Q8—86no—
827C2×Q8—824no—
828C2×Q82−1+418yescomplemented
829C2×Q8C25118yes—
830C2×Q8C2516yes—
831C2×Q8C2513yes—
832C2×Q8C25118yes—
833C2×Q8C25112yes—
834C2×Q8C25118yes—
835C2×Q8C25124yes—
836C2×Q8C25112yes—
837C2×Q8C25136yes—
838C2×Q8C25136yes—
839C2×Q8C2514yes—
840C2×Q8C2511yescharacteristic
841C2×D4—212no—
842C2×D4C2514yes—
843C2×D4C25112yes—
844C2×D4C25112yes—
845C2×D4C2516yes—
846C2×D4C25118yes—
847C2×D4C25112yes—
848C2×D4C25112yes—
849C2×D4C25136yes—
850C2×D4C25136yes—
851C2×D4C25112yes—
852C2×D4C25136yes—
853C2×D4C25136yes—
854C2×D4C25112yes—
855C22×C4—212no—
856C22×C4—418no—
857C22×C4—89no—
858C22×C4C2511yescharacteristic
859C22×C4C2516yes—
860C22×C4C2516yes—
861C22×C4C2513yes—
862C22×C4C25136yes—
863C22×C4C25112yes—
864C22×C4C25112yes—
865C22×C4C25112yes—
866C22×C4C25118yes—
867C22×C4C2513yes—
868C22×C4C25124yes—
869C22×C4C2519yes—
870C22×C4C2519yes—
871C22×C4C25118yes—
872C22×C4C25118yes—
873C22×C4C25118yes—
874C22×C4C25136yes—
875C22×C4C25172yes—
876C22×C4C25136yes—
877C22×C4C2513yes—
878C4⋊C4C2513yes—
879C4⋊C4C2513yes—
880C4⋊C4C2516yes—
881C4⋊C4C2516yes—
882C4⋊C4C25112yes—
883C4⋊C4C25118yes—
884C4⋊C4C25136yes—
885C4⋊C4C25118yes—
886C4⋊C4C25112yes—
887C4⋊C4C25136yes—
888C4⋊C4C25136yes—
889C4⋊C4C25136yes—
890C4⋊C4C25136yes—
891C4⋊C4C25118yes—
892C4⋊C4C25118yes—
893C4⋊C4C25112yes—
894C4⋊C4C25172yes—
895C4⋊C4C25172yes—
896C4⋊C4C25136yes—
897C4⋊C4C25136yes—
898C4⋊C4C25136yes—
899C4⋊C4C25172yes—
900C4⋊C4C25136yes—
901C4⋊C4C2514yes—
902C4⋊C4C2516yes—
903C4⋊C4C25112yes—
904C4⋊C4C25112yes—
905C4⋊C4C25112yes—
906C4⋊C4C2514yes—
907C4⋊C4C25112yes—
908C4⋊C4C25112yes—
909C4⋊C4C25136yes—
910C4⋊C4C25136yes—
911C4⋊C4C25112yes—
912C4⋊C4C25112yes—
913C4⋊C4C25124yes—
914C4⋊C4C25124yes—
915C4⋊C4C25136yes—
916C22⋊C4C25172yes—
917C22⋊C4C2514yes—
918C22⋊C4C25112yes—
919C22⋊C4C25112yes—
920C22⋊C4C25112yes—
921C22⋊C4C25136yes—
922C22⋊C4C2514yes—
923C22⋊C4C25112yes—
924C22⋊C4C2514yes—
925C22⋊C4C25112yes—
926C22⋊C4C25112yes—
927C22⋊C4C25136yes—
928C22⋊C4C25136yes—
929C22⋊C4C25112yes—
930C22⋊C4C25124yes—
931C22⋊C4C25136yes—
932C22⋊C4C25172yes—
933C22⋊C4C25136yes—
934C22⋊C4C25112yes—
935C22⋊C4C25112yes—
936C22⋊C4C25172yes—
937C22⋊C4C25136yes—
938C22⋊C4C25124yes—
939C42C2513yes—
940C42C2513yes—
941C42C25118yes—
942C42C25118yes—
943C42C2513yes—
944C42C2513yes—
945C42C25124yes—
946C42C25118yes—
947C42C25118yes—
948C42C25112yes—
949C42C25118yes—
950C42C25118yes—
951C42C25112yes—
952C42C25112yes—
953C42C25136yes—
954C42C25136yes—
955C42C25172yes—
956C42C25136yes—
957C23—26no—
958C23—43no—
959C23—43no—
960C23C2616yes—
961C23C2614yes—
962C23C26112yes—
963C23C2611yescharacteristic
964Q8—236no—
965Q8—212no—
966Q8—26no—
967Q8—236no—
968Q8—224no—
969Q8—418no—
970Q8—436no—
971Q8—424no—
972Q8—436no—
973Q8—412no—
974Q8C2×2−1+4116yes—
975Q8#58514yes—
976D4—28no—
977D4—224no—
978D4—224no—
979D4—212no—
980D4—236no—
981D4—224no—
982D4—412no—
983D4—436no—
984D4—436no—
985D4—412no—
986D4—412no—
987D4—436no—
988D4—436no—
989C2×C4—22no—
990C2×C4—212no—
991C2×C4—212no—
992C2×C4—272no—
993C2×C4—224no—
994C2×C4—26no—
995C2×C4—236no—
996C2×C4—224no—
997C2×C4—224no—
998C2×C4—49no—
999C2×C4—418no—
1000C2×C4—43no—
1001C2×C4—49no—
1002C2×C4—418no—
1003C2×C4—418no—
1004C2×C4—472no—
1005C2×C4—436no—
1006C2×C4—424no—
1007C2×C4—436no—
1008C2×C4C2×2−1+4112yes—
1009C2×C4C2611yescharacteristic
1010C2×C4C2611yescharacteristic
1011C2×C4C2613yes—
1012C2×C4C26112yes—
1013C2×C4C2614yes—
1014C2×C4C2614yes—
1015C2×C4C26112yes—
1016C2×C4C2613yes—
1017C2×C4C26118yes—
1018C2×C4C26118yes—
1019C2×C4C26112yes—
1020C2×C4C2613yes—
1021C2×C4C2614yes—
1022C2×C4C2616yes—
1023C2×C4C2613yes—
1024C22—21no—
1025C22—21no—
1026C22—24no—
1027C22—212no—
1028C22—26no—
1029C22—26no—
1030C22—24no—
1031C22—212no—
1032C22—24no—
1033C22—26no—
1034C22—212no—
1035C22—412no—
1036C22C22×2−1+412yes—
1037C22C2711yescharacteristic
1038C4—21no—
1039C4—21no—
1040C4—212no—
1041C4—24no—
1042C4—24no—
1043C4—212no—
1044C4—218no—
1045C4—23no—
1046C4—23no—
1047C4—24no—
1048C4—23no—
1049C4—218no—
1050C4—212no—
1051C4C22×2−1+4112yes—
1052C4C2×#58516yes—
1053C2—22no—
1054C2—44no—
1055C2—412no—
1056C2—46no—
1057C2C23×2−1+411yescharacteristic
1058C2C22×#58511yescharacteristic
1059C2#6310311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC22C27
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63039C2semidirect
2. #63038C2semidirect
3. #63034C2semidirect
4. #63033C2semidirect
5. #63007C2semidirect
6. #63004C2semidirect
7. #63001C2semidirect
8. #62999C2semidirect
9. #62999C2semidirect
10. Q8×2−1+4C2semidirect
11. #62953C2semidirect
12. #62952C2semidirect
13. #62926C2semidirect
14. #62913C2semidirect
15. #62838C2semidirect
16. #62793C2semidirect
17. #62793C2semidirect
18. #62788C2semidirect
19. C2×Q8×#41C2semidirect
20. #3565C22semidirect
21. #3565C22semidirect
22. #3565C22semidirect
23. #3559C22semidirect
24. #3557C22semidirect
25. #3555C22semidirect
26. #3555C22semidirect
27. #3555C22semidirect
28. #3554C22semidirect
29. #3554C22semidirect
30. #3552C22semidirect
31. #3550C22semidirect
32. #3548C22semidirect
33. #3547C22semidirect
34. #3547C22semidirect
35. #3547C22semidirect
36. #3547C22semidirect
37. #3544C22semidirect
43. #3524C22semidirect
44. #3523C22semidirect
45. #3523C22semidirect
46. #3523C22semidirect
47. #3523C22semidirect
48. #3522C22semidirect
49. #3522C22semidirect
50. #3522C22semidirect
51. #3522C22semidirect
54. #3518C22semidirect
55. #3518C22semidirect
56. #3518C22semidirect
57. #3518C22semidirect
60. #3517C22semidirect
64. #3516C22semidirect
65. #3515C22semidirect
66. #3515C22semidirect
67. #3515C22semidirect
71. #3511C22semidirect
72. #3511C22semidirect
73. #3511C22semidirect
74. #3509C22semidirect
75. #3509C22semidirect
76. #3507C22semidirect
77. #3507C22semidirect
78. #3507C22semidirect
82. #3504C22semidirect
85. #3503C22semidirect
86. #3503C22semidirect
89. #3502C22semidirect
90. #3502C22semidirect
91. #3502C22semidirect
92. #3502C22semidirect
93. #3499C22semidirect
96. #3497C22semidirect
97. #3497C22semidirect
106. #3483C22semidirect
109. #3482C22semidirect
110. #3482C22semidirect
111. #3482C22semidirect
117. #3480C22semidirect
124. Q8×#41C22semidirect
125. Q8×#41C22semidirect
126. Q8×#41C22semidirect
128. C2×Q82C22semidirect
130. C2×#557C22semidirect
133. #3461C22semidirect
142. C4×2−1+4C22semidirect
828. C2×Q82−1+4semidirect

Maximal subgroups

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

subgroupindex
#630392
#630382
#630342
#630332
#630072
#630042
#630012
#629992
Q8×2−1+42
#629532
#629522
#629262
#629132
#628382
#627932
#627882
C2×Q8×#412