Finite Group Databasebeta

← #10578462

Subgroups — #10578462

Order 512.

5883 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62837C212yesmaximal, complemented
2#62385C214yesmaximal, complemented
3#62382C214yesmaximal, complemented
4#62380C214yesmaximal, complemented
5#62375C212yesmaximal, complemented
6#62374C212yesmaximal, complemented
7#62369C214yesmaximal, complemented
8#62366C214yesmaximal, complemented
9#62364C214yesmaximal, complemented
10#62361C212yesmaximal, complemented
11#62360C212yesmaximal, complemented
12#61411C212yesmaximal, complemented
13#61408C212yesmaximal, complemented
14#61373C212yesmaximal, complemented
15#61372C212yesmaximal, complemented
16#61330C214yesmaximal, complemented
17#61328C214yesmaximal, complemented
18#60936C214yesmaximal, complemented
19#60918C212yesmaximal, complemented
20#60708C214yesmaximal, complemented
21#60673C211yesmaximal, characteristic
22C2×#3170C211yesmaximal, characteristic, complemented
23C2×#2960C211yesmaximal, characteristic, complemented
24#3563—24no—
25#3563—24no—
26#3556C2214yes—
27#3555—24no—
28#3555C2218yes—
29#3550C2214yes—
30#3538—24no—
31#3523—24no—
32#3523C2218yes—
33#3509—24no—
34#3509—22no—
35#3509C2214yes—
36#3507C2214yes—
37#3507C2214yes—
38#3503—22no—
39#3503C2214yes—
40#3502C2214yes—
41#3502C2214yes—
42#3495—24no—
43#3495C2218yes—
44#3444C2212yes—
45C2×#533C2212yes—
46C2×#533C2211yescharacteristic
47#3402C2218yescomplemented
48#3400C2218yescomplemented
49#3398C2218yescomplemented
50#3398C2218yescomplemented
51#3396C2214yescomplemented
52#3395C2214yescomplemented
53#3395C2214yescomplemented
54#3395C2214yescomplemented
55#3393C2214yescomplemented
56#3393C2214yescomplemented
57#3393C2218yescomplemented
58#3390C2218yescomplemented
59#3387C2218yescomplemented
60#3386C2218yescomplemented
61#3385C2218yescomplemented
62#3383C2214yescomplemented
63#3383C2214yescomplemented
64#3383C2218yescomplemented
65Q8×Q16C2214yescomplemented
66Q8×Q16C2214yescomplemented
67#3380C2214yescomplemented
68Q8×D8C2214yescomplemented
69#3377C22116yescomplemented
70#3375C2218yescomplemented
71#3374C2218yescomplemented
72#3374C2218yescomplemented
73#3372C2218yescomplemented
74#3369C2218yescomplemented
75#3367C2218yescomplemented
76#3365C2218yescomplemented
77#3364C22116yescomplemented
78#3364C2218yescomplemented
79#3363C2218yescomplemented
80#3363C2218yescomplemented
81#3360C2218yescomplemented
82#3359C2218yescomplemented
83#3262C2218yes—
84#3261C2218yes—
85#3258C22116yes—
86#3255C2214yes—
87#3254C2214yes—
88#3252C2218yes—
89#3250C2218yes—
90#3249C2218yes—
91#3249C2214yes—
92#3248C22116yes—
93#3248C2218yes—
94#3246C2214yes—
95#3181C22116yes—
96#3178C22116yes—
97#3177C2218yes—
98#3175C2218yes—
99#3170C2212yes—
100#3170C2212yes—
101#3170C2212yes—
102#3170C2212yes—
103#3170C2212yes—
104#3170C2212yes—
105#3170C2212yes—
106#3170C2212yes—
107#3170C2211yescharacteristic
108#3170C2211yescharacteristic
109#3170C2218yes—
110#3169C2211yescharacteristic
111#3169C2211yescharacteristic
112#3168C2212yes—
113#3168C2212yes—
114#3168C2212yes—
115#3168C2212yes—
116#3168C2218yes—
117#3167C2212yes—
118#3167C2212yes—
119#3164C2214yes—
120#3160C2211yescharacteristic
121C2×#500C2211yescharacteristic
122#3156C2214yes—
123#3147C2211yescharacteristic
124C2×#494C2211yescharacteristic
125#3137C2218yes—
126#3131C2212yes—
127C2×#487C2212yes—
128#3083C2218yes—
129#3082C2218yes—
130#3079C2214yes—
131#3078C2214yes—
132#3056C2218yes—
133#3050C2212yes—
134#3050C2212yes—
135C2×#467C2212yes—
136C2×#467C2212yes—
137#3046C2218yes—
138#3044C2218yes—
139#3039C2214yes—
140#3037C2214yes—
141#2960C2212yes—
142#2960C2212yes—
143#2960C2212yes—
144#2960C2212yes—
145#2960C2212yes—
146#2960C2212yes—
147#2960C2212yes—
148#2960C2212yes—
149C2×#446C2212yes—
150C2×#446C2212yes—
151C2×C8×Q8C2212yes—
152C2×C8×Q8C2212yes—
153#2951C2214yes—
154#2950C2214yes—
155#2947C2218yes—
156C4×#135C2212yes—
157C4×#135C2212yes—
158C2×C4×Q16C2212yes—
159C2×C4×Q16C2212yes—
160C2×#424C2212yes—
161C2×#423C2211yescharacteristic
162C2×#405C2212yes—
163C22×C4×C8C2211yescharacteristic
164C2×#137C2318yes—
165C2×#135C2312yes—
166C2×#135C2312yes—
167C22×Q16C2312yes—
168C22×Q16C2312yes—
169C22×M16C2312yes—
170C23×C8C2311yescharacteristic
171C23×C8C2311yescharacteristic
172#564—28no—
173#563—28no—
174#563—216no—
175#559C2318yes—
176Q82—24no—
177Q82C2318yes—
178Q82C2318yes—
179#557—24no—
180#557—24no—
181#557—24no—
182#557—28no—
183#557—28no—
184#557—28no—
185#557C2318yes—
186#557C2318yes—
187#557C2318yes—
188#557C2318yes—
189#557C23116yes—
190#557C2318yes—
191#556—24no—
192#556—24no—
193#556—28no—
194#556—28no—
195#556—28no—
196#556C2318yes—
197#556C2318yes—
198#556C23116yes—
199#554—24no—
200#554—28no—
201#554—28no—
202#554C2318yes—
203#552—28no—
204#552—28no—
205#552—28no—
206#552—28no—
207#552—28no—
208#552—28no—
209#552—216no—
210#552—216no—
211#552—28no—
212#552—28no—
213#551—216no—
214D4×Q8—28no—
215D4×Q8—24no—
216D4×Q8—28no—
217D4×Q8C2318yes—
218#544—28no—
219#544—28no—
220#544—28no—
221#544—24no—
222#544—28no—
223#544C2318yes—
224#542—28no—
225#542C23116yes—
226#541—28no—
227#541—28no—
228#541—216no—
229#541—28no—
230#541—28no—
231#541—28no—
232#541—216no—
233#541C23116yes—
234#539—28no—
235#539—28no—
236#536—24no—
237#536—28no—
238#536C2318yes—
239#533—24no—
240#533—24no—
241#533—24no—
242#533—28no—
243#533—22no—
244#533—22no—
245#533—22no—
246#533—22no—
247#533D412yes—
248#533D412yes—
249#533D412yes—
250#533D412yes—
251#533C2312yes—
252#533C2312yes—
253#533C2314yes—
254#533C2314yes—
255#533C2314yes—
256#533C2314yes—
257#533C23116yes—
258#533C2312yes—
259#533C2312yes—
260#533C2312yes—
261#533C2312yes—
262#533C2312yes—
263#532C2312yes—
264#532C2312yes—
265#532C2312yes—
266C2×C4⋊Q8—24no—
267C2×C4⋊Q8D411yescharacteristic
268C2×C4⋊Q8D411yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271#529—28no—
272#529—22no—
273#529—22no—
274#529—22no—
275#529—22no—
276#529C2314yes—
277#529C2314yes—
278#529C23116yes—
279C2×#125—22no—
280C2×#125D412yes—
281#525—22no—
282#525—22no—
283#525C2314yes—
284C2×C22⋊Q8—22no—
285C2×C22⋊Q8D412yes—
286C2×C22⋊Q8D412yes—
287C2×C22⋊Q8C2314yes—
288#520—24no—
289#520C2318yes—
290#519—24no—
291#519—28no—
292#519C2318yes—
293C4×#41—22no—
294C4×#41—22no—
295C4×#41C2314yes—
296C2×C4×Q8—22no—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×#117—22no—
301C2×#117C2312yes—
302C22×C42C2311yescharacteristic
303#501C23116yes—
304#500C2312yes—
305#500C2318yes—
306#500C2312yes—
307#500C2311yescharacteristic
308#500C2311yescharacteristic
309#500C2312yes—
310#500C2312yes—
311#499C2318yes—
312#499C2312yes—
313#499C2312yes—
314#498C2312yes—
315#497C23116yes—
316#495C2312yes—
317#495C2318yes—
318#495C2312yes—
319#494C2312yes—
320#494C2312yes—
321#494C2318yes—
322#494C2311yescharacteristic
323#494C2312yes—
324#494C2312yes—
325#493C2311yescharacteristic
326#492C2312yes—
327#491C23116yes—
328#489C23116yes—
329#488C23116yes—
330#488C2314yes—
331#488C2314yes—
332#487C2314yes—
333#487C23116yes—
334#487C2314yes—
335#487C2312yes—
336#487C2314yes—
337#487C2314yes—
338#487C2312yes—
339#486C2312yes—
340#486C2312yes—
341#479C23116yes—
342#479C23116yes—
343#479C23116yes—
344#479C23116yes—
345#478C23116yes—
346#477C2318yes—
347#477C2318yes—
348#477C23116yes—
349#477C23116yes—
350#476C2318yes—
351#475C2318yes—
352#475C2318yes—
353#475C23116yes—
354#474C2318yes—
355#474C23116yes—
356#470C23116yes—
357#468C23116yes—
358#467C2314yes—
359#467C2312yes—
360#467C2312yes—
361#467C2312yes—
362#467C2312yes—
363#467C2314yes—
364#467C2314yes—
365#467C2314yes—
366#467C2314yes—
367#467C2314yes—
368#467C2314yes—
369#467C2314yes—
370#467C23116yes—
371#466C2312yes—
372#466C2312yes—
373#466C2312yes—
374#466C2312yes—
375#465C2314yes—
376#465C2314yes—
377#465C2314yes—
378#465C2314yes—
379#465C23116yes—
380#464C23116yes—
381#464C23116yes—
382#464C23116yes—
383#464C23116yes—
384#463C23116yes—
385#462C2318yes—
386#462C2318yes—
387#462C23116yes—
388#462C23116yes—
389#462C2318yes—
390#462C23116yes—
391#461C2318yes—
392#461C23116yes—
393#461C2318yes—
394#460C2318yes—
395#446C2314yes—
396#446C2314yes—
397#446C2314yes—
398#446C2314yes—
399#446C2314yes—
400#446C2314yes—
401#446C2314yes—
402#446C2314yes—
403C8×Q8C2314yes—
404C8×Q8C2314yes—
405C8×Q8C2314yes—
406C8×Q8C2314yes—
407C8×Q8C2314yes—
408C8×Q8C2314yes—
409C8×Q8C2314yes—
410C8×Q8C2314yes—
411#441C23116yes—
412#441C23116yes—
413#440C23116yes—
414#440C23116yes—
415C4×Q16C2312yes—
416C4×Q16C23116yes—
417C4×Q16C2314yes—
418C4×Q16C2314yes—
419C4×Q16C2312yes—
420C4×Q16C2314yes—
421C4×Q16C2314yes—
422C4×Q16C2312yes—
423C4×Q16C2318yes—
424C4×Q16C2318yes—
425C4×Q16C2314yes—
426C4×Q16C2314yes—
427C4×Q16C2318yes—
428C4×Q16C2312yes—
429C4×Q16C2314yes—
430C4×Q16C2314yes—
431C4×SD16C2314yes—
432C4×SD16C23116yes—
433C4×SD16C2314yes—
434C4×SD16C2314yes—
435C4×SD16C2314yes—
436C4×D8C2312yes—
437C4×D8C2312yes—
438C4×D8C2312yes—
439C4×D8C2318yes—
440C4×D8C2312yes—
441#428C2318yes—
442#427C2312yes—
443#427C2312yes—
444C2×#107C2312yes—
445C2×#107C2312yes—
446#424C2314yes—
447#424C2314yes—
448#424C2314yes—
449#424C2314yes—
450#423C2312yes—
451#423C2312yes—
452#423C2312yes—
453#423C2312yes—
454C2×C4⋊C8C2312yes—
455C2×C4⋊C8C2312yes—
456C2×C4⋊C8C2314yes—
457C2×C4⋊C8C2314yes—
458#419C2318yes—
459#417C2318yes—
460#416C2314yes—
461#416C2314yes—
462C2×#103C2314yes—
463C2×#103C2314yes—
464#405C2314yes—
465#405C2314yes—
466#405C2314yes—
467#405C2314yes—
468C2×#97C2314yes—
469C2×C4×C8C2311yescharacteristic
470C2×C4×C8C2311yescharacteristic
471C2×C4×C8C2311yescharacteristic
472C2×C4×C8C2311yescharacteristic
473C2×C4×C8C2311yescharacteristic
474C2×C4×C8C2311yescharacteristic
475C2×C4×C8C2311yescharacteristic
476C2×C4×C8C2311yescharacteristic
477C2×C4×C8C2311yescharacteristic
478C2×C4×C8C2311yescharacteristic
479C2×C4×C8C2311yescharacteristic
480C2×C4×C8C2311yescharacteristic
481C2×C4×C8C2314yes—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41C2414yes—
485C22×Q8—28no—
486C22×Q8—22no—
487C22×Q8C2×D412yes—
488C22×Q8C2×D412yes—
489C22×Q8C2414yes—
490C23×C4C2×D411yescharacteristic
491C23×C4C2×D411yescharacteristic
492C23×C4C2411yescharacteristic
493#137—416no—
494#135—28no—
495#135—44no—
496C2×Q16—28no—
497C2×Q16—44no—
498C2×Q16C2414yes—
499C2×Q16C2414yes—
500C2×Q16C2412yes—
501C2×Q16C2414yes—
502C2×Q16C2414yes—
503C2×Q16C2412yes—
504C2×Q16C24116yes—
505C2×SD16C2414yes—
506C2×SD16C2414yes—
507C2×SD16C24116yes—
508C2×D8C2412yes—
509C2×D8C2412yes—
510C2×M16—44no—
511C2×M16C2414yes—
512C2×M16C2414yes—
513C22×C8—24no—
514C22×C8—42no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2414yes—
527C22×C8C2411yescharacteristic
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—216no—
531C4⋊Q8—28no—
532C4⋊Q8—28no—
533C4⋊Q8—28no—
534C4⋊Q8—216no—
535C4⋊Q8—216no—
536C4⋊Q8—22no—
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8C2×D412yes—
541C4⋊Q8C2×D412yes—
542C4⋊Q8C2×D412yes—
543C4⋊Q8C2×D412yes—
544C4⋊Q8C2×D412yes—
545C4⋊Q8C2×D412yes—
546C4⋊Q8C2×D412yes—
547C4⋊Q8C2×D412yes—
548C4⋊Q8C2414yes—
549C4⋊Q8C2414yes—
550C4⋊Q8C2412yes—
551C4⋊Q8C24116yes—
552C4⋊Q8C2414yes—
553C4⋊Q8C2414yes—
554C4⋊Q8C2412yes—
555C4⋊Q8C2412yes—
556C4⋊Q8C24116yes—
557#127C2412yes—
558#126—216no—
559#126—216no—
560#126—216no—
561#126—216no—
562#126—216no—
563#126—216no—
564#126—216no—
565#126—24no—
566#126—24no—
567#126—216no—
568#125—28no—
569#125—216no—
570#125—28no—
571#125—28no—
572#125—28no—
573#125—216no—
574#125—216no—
575#125—216no—
576#125—216no—
577#125—216no—
578#125—216no—
579#125—216no—
580#125—216no—
581#125—24no—
582#125—24no—
583#125—24no—
584#125—24no—
585#125—22no—
586#125—22no—
587#125—216no—
588#125C2×D414yes—
589#125C2×D414yes—
590#125C2×D414yes—
591#125C2×D414yes—
592#125C2414yes—
593#125C24116yes—
594#124—28no—
595#124—216no—
596#124—22no—
597#124—22no—
598#124C2414yes—
599#124C24116yes—
600#123—24no—
601#123—24no—
602#123—24no—
603#123—216no—
604#123—216no—
605#123—216no—
606#123—216no—
607C22⋊Q8—28no—
608C22⋊Q8—28no—
609C22⋊Q8—28no—
610C22⋊Q8—216no—
611C22⋊Q8—24no—
612C22⋊Q8—24no—
613C22⋊Q8—24no—
614C22⋊Q8—24no—
615C22⋊Q8—24no—
616C22⋊Q8—24no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—216no—
622C22⋊Q8—28no—
623C22⋊Q8—28no—
624C22⋊Q8—28no—
625C22⋊Q8—216no—
626C22⋊Q8—216no—
627C22⋊Q8—216no—
628C22⋊Q8—216no—
629C22⋊Q8C2×D414yes—
630C22⋊Q8C2×D414yes—
631C22⋊Q8C2×D414yes—
632C22⋊Q8C2×D414yes—
633C22⋊Q8C2×D414yes—
634C22⋊Q8C2×D414yes—
635C22⋊Q8C2×D414yes—
636C22⋊Q8C2×D414yes—
637C22⋊Q8C2418yes—
638C22⋊Q8C2418yes—
639C22⋊Q8C2414yes—
640C22⋊Q8C2414yes—
641#121—22no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121C2414yes—
646#121C2414yes—
647#120—24no—
648C4×Q8—28no—
649C4×Q8—28no—
650C4×Q8—28no—
651C4×Q8—28no—
652C4×Q8—28no—
653C4×Q8—28no—
654C4×Q8—216no—
655C4×Q8—28no—
656C4×Q8—28no—
657C4×Q8—28no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×Q8—22no—
667C4×Q8—22no—
668C4×Q8—216no—
669C4×Q8C2×D414yes—
670C4×Q8C2×D414yes—
671C4×Q8C2×D414yes—
672C4×Q8C2×D414yes—
673C4×Q8C2418yes—
674C4×Q8C2418yes—
675C4×Q8C2414yes—
676C4×Q8C2414yes—
677C4×Q8C24116yes—
678C4×Q8C24116yes—
679C4×Q8C24116yes—
680C4×Q8C2414yes—
681C4×Q8C2414yes—
682C4×Q8C2414yes—
683C4×Q8C2414yes—
684C4×D4—24no—
685C4×D4—24no—
686C4×D4—24no—
687C4×D4—24no—
688C4×D4—24no—
689C4×D4—24no—
690C4×D4—216no—
691C4×D4—28no—
692C4×D4—216no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4C2414yes—
698C4×D4C2414yes—
699C4×D4C24116yes—
700#117—24no—
701#117—24no—
702#117—24no—
703#117—24no—
704#117—22no—
705#117—22no—
706#117—216no—
707#117—216no—
708#117—28no—
709#117—28no—
710#117—28no—
711#117—216no—
712#117—24no—
713#117—24no—
714#117—24no—
715#117—216no—
716#117C2×D414yes—
717#117C2×D414yes—
718#117C2414yes—
719#117C2414yes—
720#117C2414yes—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—24no—
725C2×C4⋊C4—24no—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—28no—
728C2×C4⋊C4C2×D412yes—
729C2×C4⋊C4C2×D412yes—
730C2×C4⋊C4C2×D412yes—
731C2×C4⋊C4C2×D414yes—
732C2×C4⋊C4C2×D414yes—
733C2×C4⋊C4C2×D412yes—
734C2×C4⋊C4C2414yes—
735C2×C22⋊C4—24no—
736C2×C22⋊C4C2×D414yes—
737C2×C42—24no—
738C2×C42—24no—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2414yes—
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#107C2414yes—
753#107C2414yes—
754#107C2414yes—
755#107C2414yes—
756#107C2412yes—
757#107C2412yes—
758#107C2412yes—
759#107C2412yes—
760#107C24116yes—
761#106C2414yes—
762#106C2414yes—
763#106C24116yes—
764C4⋊C8C2414yes—
765C4⋊C8C2414yes—
766C4⋊C8C2414yes—
767C4⋊C8C2414yes—
768C4⋊C8C2418yes—
769C4⋊C8C2418yes—
770C4⋊C8C2418yes—
771C4⋊C8C2418yes—
772#103C2418yes—
773#103C2418yes—
774#103C2418yes—
775#103C2418yes—
776#103C2414yes—
777#103C2414yes—
778#103C2414yes—
779#103C2414yes—
780#103C24116yes—
781#103C24116yes—
782#103C24116yes—
783#102C2414yes—
784#102C2414yes—
785#102C2414yes—
786#102C2414yes—
787#102C24116yes—
788#97C2418yes—
789#97C2418yes—
790C4×C8C2411yescharacteristic
791C4×C8C2411yescharacteristic
792C4×C8C2411yescharacteristic
793C4×C8C2411yescharacteristic
794C4×C8C2411yescharacteristic
795C4×C8C2411yescharacteristic
796C4×C8C2411yescharacteristic
797C4×C8C2411yescharacteristic
798C4×C8C2411yescharacteristic
799C4×C8C2411yescharacteristic
800C4×C8C2411yescharacteristic
801C4×C8C2411yescharacteristic
802C4×C8C2411yescharacteristic
803C4×C8C2411yescharacteristic
804C4×C8C2411yescharacteristic
805C4×C8C2411yescharacteristic
806C4×C8C2418yes—
807C4×C8C2418yes—
808C24C22×D411yescharacteristic
809#41—28no—
810#41—28no—
811#41—48no—
812#41—84no—
813C2×Q8—28no—
814C2×Q8—24no—
815C2×Q8—22no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—216no—
819C2×Q8—22no—
820C2×Q8—28no—
821C2×Q8—28no—
822C2×Q8—44no—
823C2×Q8—84no—
824C2×Q8—816no—
825C2×Q8C22×D414yes—
826C2×Q8C22×D414yes—
827C2×Q8C22×D414yes—
828C2×Q8C22×D414yes—
829C2×Q8C2518yes—
830C2×Q8C2514yes—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4C2514yes—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—216no—
846C22×C4—42no—
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D414yes—
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D414yes—
863C22×C4C22×D411yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867Q16—28no—
868Q16—28no—
869Q16—24no—
870Q16—44no—
871Q16—44no—
872Q16—42no—
873Q16—416no—
874SD16—28no—
875SD16—44no—
876SD16—416no—
877D8—24no—
878D8—42no—
879M16—28no—
880M16—44no—
881C2×C8—22no—
882C2×C8—22no—
883C2×C8—22no—
884C2×C8—22no—
885C2×C8—22no—
886C2×C8—22no—
887C2×C8—22no—
888C2×C8—41no—
889C2×C8—41no—
890C2×C8—41no—
891C2×C8—41no—
892C2×C8—44no—
893C2×C82−1+414yes—
894C2×C8C2511yescharacteristic
895C2×C8C2511yescharacteristic
896C2×C8C2511yescharacteristic
897C2×C8C2511yescharacteristic
898C2×C8C2511yescharacteristic
899C2×C8C2511yescharacteristic
900C2×C8C2518yes—
901C2×C8C2511yescharacteristic
902C2×C8C2511yescharacteristic
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—216no—
911C4⋊C4—216no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—216no—
927C4⋊C4—216no—
928C4⋊C4—216no—
929C4⋊C4—216no—
930C4⋊C4—216no—
931C4⋊C4—216no—
932C4⋊C4C22×D414yes—
933C4⋊C4C22×D414yes—
934C4⋊C4C22×D414yes—
935C4⋊C4C22×D414yes—
936C4⋊C4C22×D418yes—
937C4⋊C4C22×D414yes—
938C4⋊C4C22×D414yes—
939C4⋊C4C22×D414yes—
940C4⋊C4C22×D418yes—
941C4⋊C4C22×D418yes—
942C4⋊C4C22×D418yes—
943C4⋊C4C22×D414yes—
944C4⋊C4C2514yes—
945C4⋊C4C2518yes—
946C4⋊C4C2514yes—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—216no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—216no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—216no—
961C22⋊C4C22×D418yes—
962C22⋊C4C22×D418yes—
963C42—28no—
964C42—24no—
965C42—24no—
966C42—28no—
967C42—24no—
968C42—216no—
969C42—216no—
970C42—216no—
971C42C22×D411yescharacteristic
972C42C22×D411yescharacteristic
973C42C22×D411yescharacteristic
974C42C22×D411yescharacteristic
975C42C22×D411yescharacteristic
976C42C22×D411yescharacteristic
977C42C22×D411yescharacteristic
978C42C22×D411yescharacteristic
979C42C22×D411yescharacteristic
980C42C22×D411yescharacteristic
981C42C22×D411yescharacteristic
982C42C22×D411yescharacteristic
983C42C22×D418yes—
984C42C2511yescharacteristic
985C42C2511yescharacteristic
986C42C2511yescharacteristic
987C42C2511yescharacteristic
988C42C2518yes—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—41no—
993C23C23×D411yescharacteristic
994C23C23×D411yescharacteristic
995C23C23×D411yescharacteristic
996Q8—28no—
997Q8—28no—
998Q8—28no—
999Q8—24no—
1000Q8—28no—
1001Q8—28no—
1002Q8—24no—
1003Q8—44no—
1004Q8—48no—
1005Q8—48no—
1006Q8—44no—
1007Q8—84no—
1008Q8—816no—
1009Q8—82no—
1010D4—24no—
1011D4—24no—
1012D4—48no—
1013D4—48no—
1014D4—44no—
1015D4—82no—
1016D4—84no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—44no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—816no—
1047C2×C4—84no—
1048C2×C4#57814yes—
1049C2×C4C23×D411yescharacteristic
1050C2×C4C23×D418yes—
1051C2×C4C23×D418yes—
1052C2×C4C23×D411yescharacteristic
1053C2×C4C23×D411yescharacteristic
1054C2×C4C23×D411yescharacteristic
1055C2×C4C23×D411yescharacteristic
1056C2×C4C23×D411yescharacteristic
1057C2×C4C23×D411yescharacteristic
1058C2×C4C23×D411yescharacteristic
1059C2×C4C23×D411yescharacteristic
1060C2×C4C23×D411yescharacteristic
1061C2×C4C23×D411yescharacteristic
1062C2×C4C2×2−1+412yes—
1063C2×C4#58512yes—
1064C2×C4C2611yescharacteristic
1065C8—21no—
1066C8—21no—
1067C8—21no—
1068C8—21no—
1069C8—21no—
1070C8—21no—
1071C8—28no—
1072C8C2×2−1+412yes—
1073C8C2×2−1+412yes—
1074C22—21no—
1075C22—21no—
1076C22—21no—
1077C22—21no—
1078C22—21no—
1079C22—21no—
1080C22—21no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22#349712yes—
1086C22C2×#57812yes—
1087C22C24×D411yescharacteristic
1088C4—21no—
1089C4—21no—
1090C4—21no—
1091C4—21no—
1092C4—28no—
1093C4—21no—
1094C4—21no—
1095C4—21no—
1096C4—28no—
1097C4—44no—
1098C4—48no—
1099C4—44no—
1100C4—44no—
1101C4—48no—
1102C4#349712yes—
1103C4C2×#57812yes—
1104C4C2×#57812yes—
1105C4#358412yes—
1106C4C22×2−1+411yescharacteristic
1107C4C2×#58511yescharacteristic
1108C2—22no—
1109C2—22no—
1110C2—41no—
1111C2—84no—
1112C2C2×#349711yescharacteristic
1113C2C22×#57811yescharacteristic
1114C2C2×#358411yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#60673C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62837C2semidirect
2. #62385C2semidirect
3. #62382C2semidirect
4. #62380C2semidirect
5. #62375C2semidirect
6. #62374C2semidirect
7. #62369C2semidirect
8. #62366C2semidirect
9. #62364C2semidirect
10. #62361C2semidirect
11. #62360C2semidirect
12. #61411C2semidirect
13. #61408C2semidirect
14. #61373C2semidirect
15. #61372C2semidirect
16. #61330C2semidirect
17. #61328C2semidirect
18. #60936C2semidirect
19. #60918C2semidirect
20. #60708C2semidirect
22. C2×#3170C2semidirect
23. C2×#2960C2semidirect
47. #3402C22semidirect
48. #3400C22semidirect
49. #3398C22semidirect
50. #3398C22semidirect
51. #3396C22semidirect
52. #3395C22semidirect
53. #3395C22semidirect
54. #3395C22semidirect
55. #3393C22semidirect
56. #3393C22semidirect
57. #3393C22semidirect
58. #3390C22semidirect
59. #3387C22semidirect
60. #3386C22semidirect
61. #3385C22semidirect
62. #3383C22semidirect
63. #3383C22semidirect
64. #3383C22semidirect
65. Q8×Q16C22semidirect
66. Q8×Q16C22semidirect
67. #3380C22semidirect
68. Q8×D8C22semidirect
69. #3377C22semidirect
70. #3375C22semidirect
71. #3374C22semidirect
72. #3374C22semidirect
73. #3372C22semidirect
74. #3369C22semidirect
75. #3367C22semidirect
76. #3365C22semidirect
77. #3364C22semidirect
78. #3364C22semidirect
79. #3363C22semidirect
80. #3363C22semidirect
81. #3360C22semidirect
82. #3359C22semidirect

Maximal subgroups

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

subgroupindex
#628372
#623852
#623822
#623802
#623752
#623742
#623692
#623662
#623642
#623612
#623602
#614112
#614082
#613732
#613722
#613302
#613282
#609362
#609182
#607082
#606732
C2×#31702
C2×#29602