Finite Group Databasebeta

← #10581112

Subgroups — #10581112

Order 512.

5939 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62837C211yesmaximal, characteristic, complemented
2#62829C211yesmaximal, characteristic
3#62585C214yesmaximal, complemented
4#62577C214yesmaximal, complemented
5#62505C214yesmaximal, complemented
6#62448C214yesmaximal, complemented
7#62388C214yesmaximal, complemented
8#62337C214yesmaximal, complemented
9#62281C214yesmaximal, complemented
10#62271C212yesmaximal, complemented
11#62268C212yesmaximal, complemented
12#61525C218yesmaximal, complemented
13#61520C218yesmaximal, complemented
14#61020C212yesmaximal, complemented
15#61018C212yesmaximal, complemented
16#60950C212yesmaximal, complemented
17#60726C212yesmaximal, complemented
18#60720C212yesmaximal, complemented
19C2×#3181C212yesmaximal, complemented
20#60207C211yesmaximal, characteristic, complemented
21#3566—24no—
22#3564—22no—
23#3563—22no—
24#3563—22no—
25#3560—22no—
26#3557C2212yes—
27#3556C2212yescomplemented
28#3555—24no—
29#3551C2212yes—
30#3550C2212yescomplemented
31#3538C2212yes—
32#3538C2211yescharacteristic
33#3538C2212yescomplemented
34#3537C2211yescharacteristic
35#3536C2212yes—
36#3523C2218yescomplemented
37#3516C2214yes—
38#3515C2214yes—
39#3514C2214yes—
40#3513—24no—
41#3513C2214yes—
42#3512C2212yes—
43#3510C2212yes—
44#3509C2214yescomplemented
45#3509C2212yescomplemented
46#3509C2212yescomplemented
47#3507—22no—
48#3503C2214yescomplemented
49#3502—22no—
50#3495—24no—
51#3493—22no—
52#3491—22no—
53#3444C2211yescharacteristic
54C2×#533C2212yescomplemented
55C2×#529C2212yes—
56#3400C2218yescomplemented
57#3398C2218yescomplemented
58#3390C2218yescomplemented
59#3388C2218yescomplemented
60#3377C2218yescomplemented
61#3374C2218yescomplemented
62#3372C2218yescomplemented
63#3371C2218yescomplemented
64#3350C2218yescomplemented
65#3349C2218yescomplemented
66#3344C2218yescomplemented
67#3343C2218yescomplemented
68#3337C2218yes—
69#3336C2218yescomplemented
70#3320C2218yes—
71#3320C2218yescomplemented
72#3313C2218yescomplemented
73#3312C2218yescomplemented
74#3312C2218yescomplemented
75#3312C2218yescomplemented
76#3311C2218yescomplemented
77#3310C2218yes—
78#3300C2218yescomplemented
79#3299C2218yescomplemented
80#3298C2218yescomplemented
81#3296C2218yescomplemented
82D4×Q16C2218yescomplemented
83D4×SD16C2218yes—
84#3270C2218yescomplemented
85#3270C2218yescomplemented
86#3266C2218yescomplemented
87#3266C2218yescomplemented
88#3261C2214yescomplemented
89#3260C2214yes—
90#3258C2218yescomplemented
91#3252C2218yescomplemented
92#3240C2214yescomplemented
93#3240C2214yescomplemented
94#3238C2214yescomplemented
95#3237C2214yescomplemented
96#3236C2214yescomplemented
97#3236C2214yescomplemented
98#3218C2214yescomplemented
99#3218C2214yescomplemented
100#3218C2214yescomplemented
101#3216C2214yescomplemented
102#3215C2214yescomplemented
103#3215C2214yescomplemented
104#3202C2214yescomplemented
105#3201C2218yescomplemented
106#3200C2214yes—
107#3195C2214yescomplemented
108#3193C2214yes—
109#3181C2214yescomplemented
110#3181C2214yescomplemented
111#3181C2218yescomplemented
112#3181C2214yescomplemented
113#3181C2214yescomplemented
114#3181C2218yescomplemented
115#3181C2214yescomplemented
116#3181C2214yescomplemented
117#3178C2218yescomplemented
118#3178C2218yescomplemented
119#3177C2214yescomplemented
120#3177C2214yescomplemented
121#3174C2214yes—
122#3174C2214yescomplemented
123#3172C2214yescomplemented
124#3172C2214yescomplemented
125#3172C2214yescomplemented
126#3172C2214yescomplemented
127#3166C2212yescomplemented
128#3162C2212yescomplemented
129C2×#501C2212yescomplemented
130#3152C2212yescomplemented
131C2×#497C2212yescomplemented
132C2×#497C2212yescomplemented
133#3140C2212yescomplemented
134#3139C2212yescomplemented
135#3135C2212yescomplemented
136C2×#491C2212yescomplemented
137C2×#491C2212yescomplemented
138C2×#489C2212yescomplemented
139#3127C2214yescomplemented
140#3127C2214yescomplemented
141#3126C2214yescomplemented
142#3123C2214yescomplemented
143#3121C2218yescomplemented
144#3120C2218yescomplemented
145#3108C2218yescomplemented
146#3104C2214yescomplemented
147#3101C2214yescomplemented
148#3063C2218yescomplemented
149#3059C2214yescomplemented
150#3057C2214yes—
151C2×#467C2214yescomplemented
152C2×#465C2214yes—
153#2970C2214yescomplemented
154#2970C2214yescomplemented
155#2968C2218yescomplemented
156#2961C2212yescomplemented
157#2950C2214yescomplemented
158#2949C2214yescomplemented
159#2947C2218yescomplemented
160C2×#441C2214yescomplemented
161C2×#440C2214yescomplemented
162#2932C2212yescomplemented
163#2929C2212yes—
164#2929C2212yescomplemented
165#2923C2211yescharacteristic, complemented
166#2923C2211yescharacteristic, complemented
167#2920C2211yescharacteristic, complemented
168#2875C2211yescharacteristic, complemented
169#2875C2211yescharacteristic, complemented
170C22×#97C2211yescharacteristic, complemented
171C2×#137C2318yes—
172C22×Q16C2314yes—
173C22×Q16C2314yes—
174C22×SD16C2314yes—
175C22×SD16C2314yes—
176C2×#131C2312yes—
177C2×#131C2312yes—
178C23×C8C2312yes—
179#564—24no—
180#563—22no—
181#563—24no—
182#563—22no—
183#563—22no—
184#563—24no—
185#563—22no—
186#563—24no—
187#562—24no—
188#560—22no—
189#560—22no—
190#559—22no—
191#559—24no—
192#559C2314yes—
193Q82—22no—
194Q82—24no—
195#557—24no—
196#557—28no—
197#557—24no—
198#557—24no—
199#557—24no—
200#557C2318yes—
201#557C2318yes—
202#557C2314yes—
203#556—24no—
204#556—28no—
205#556—24no—
206#556—24no—
207#556—24no—
208#556—24no—
209#556C2314yes—
210#556C2318yes—
211#555—22no—
212#555—24no—
213#554—24no—
214#554—24no—
215#554—24no—
216#554—24no—
217#554C2314yes—
218#554C2314yes—
219#553—24no—
220#553—24no—
221#553—24no—
222#553—24no—
223#553—24no—
224#553C2314yes—
225#553C2314yes—
226#552—24no—
227#552—24no—
228#552—28no—
229#552—28no—
230#552—24no—
231#552—24no—
232#552—24no—
233#552—24no—
234#552—24no—
235#552—24no—
236#552—24no—
237#552—24no—
238#552—24no—
239#552—24no—
240#552C2314yes—
241#552C2318yes—
242#552C2318yes—
243#552C2314yes—
244#551—24no—
245#551—22no—
246#551—24no—
247#551—24no—
248#551—24no—
249#551—22no—
250#551—24no—
251#551—24no—
252#551—24no—
253#551—24no—
254D4×Q8C2318yes—
255D4×Q8C2318yes—
256D4×Q8C2318yes—
257D4×Q8C2314yes—
258#548C2314yes—
259#548C2314yes—
260#547—24no—
261#547C2314yes—
262#546—24no—
263#546—24no—
264#546—24no—
265#546C2314yes—
266#546C2314yes—
267D42—22no—
268D42C2314yes—
269#544—22no—
270#544—24no—
271#544—24no—
272#544—24no—
273#544—24no—
274#544—24no—
275#543—22no—
276#542—24no—
277#542—24no—
278#542—28no—
279#542—24no—
280#542C2314yes—
281#542C2314yes—
282#541—28no—
283#541—28no—
284#541—24no—
285#541—28no—
286#541—24no—
287#541—24no—
288#541—24no—
289#541C2314yes—
290#541C2314yes—
291#541C2312yes—
292#541C2314yes—
293#541C2312yes—
294#541C2314yes—
295#540—24no—
296#540C2312yes—
297#540C2312yes—
298#539—24no—
299#539—22no—
300#539—24no—
301#539—22no—
302#539—24no—
303#539—24no—
304#539—24no—
305#539—24no—
306#538—24no—
307#538—22no—
308#538—22no—
309#538—24no—
310#538—24no—
311#538—24no—
312#537—22no—
313#537C2314yes—
314#536—24no—
315#536C2314yes—
316#536C2314yes—
317#536C2312yes—
318#535C2312yes—
319#534—22no—
320#533—28no—
321#533—22no—
322#533—22no—
323#533—22no—
324#533—22no—
325#533D412yes—
326#533C2314yes—
327#533C2314yes—
328#533C2314yes—
329#533C2314yes—
330#533C2314yes—
331#533C2314yes—
332#533C2312yes—
333#533C2312yes—
334#533C2312yes—
335#533C2311yescharacteristic
336#532D412yes—
337#532C2312yes—
338#532C2311yescharacteristic
339C2×C4⋊Q8C2312yes—
340C2×C4⋊Q8C2312yes—
341C2×C4⋊Q8C2312yes—
342C2×C4⋊Q8C2312yes—
343#529—24no—
344#529—24no—
345#529—28no—
346#529—22no—
347#529—22no—
348#529—22no—
349#529—22no—
350#529D412yes—
351#529D412yes—
352#529D414yes—
353#529C2314yes—
354#529C2314yes—
355#529C2314yes—
356#529C2314yes—
357#529C2314yes—
358#529C2314yes—
359#529C2314yes—
360C2×#126—22no—
361C2×#125—22no—
362C2×#125C2312yes—
363C2×#125C2312yes—
364C2×#124C2312yes—
365C2×#124C2312yes—
366#525—24no—
367#525D414yes—
368#525C2311yescharacteristic
369#525C2311yescharacteristic
370C2×#123—22no—
371C2×#123—24no—
372C2×C22⋊Q8—22no—
373C2×C22⋊Q8C2312yes—
374C2×C22⋊Q8C2314yes—
375C2×#121C2312yes—
376#520—24no—
377#520—24no—
378#520C2314yes—
379#519—24no—
380#519C2314yes—
381#519C2314yes—
382#519C2312yes—
383#518—24no—
384#518C2312yes—
385C4×#41C2314yes—
386C4×#41C2311yescharacteristic
387C4×#41C2311yescharacteristic
388C2×C4×Q8—22no—
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2314yes—
391C2×C4×D4—22no—
392C2×C4×D4C2312yes—
393C2×#117—22no—
394C2×#117—22no—
395C22×C42C2311yescharacteristic
396#501C2318yes—
397#501C2318yes—
398#501C2314yes—
399#501C2314yes—
400#501C2314yes—
401#501C2314yes—
402#499C2314yes—
403#499C2314yes—
404#497C2318yes—
405#497C2318yes—
406#497C2314yes—
407#497C2314yes—
408#497C2314yes—
409#497C2314yes—
410#494C2314yes—
411#492C2314yes—
412#491C2314yes—
413#491C2318yes—
414#491C2314yes—
415#491C2314yes—
416#491C2314yes—
417#491C2314yes—
418#491C2314yes—
419#491C2314yes—
420#490C2314yes—
421#489C2318yes—
422#489C2314yes—
423#489C2314yes—
424#489C2314yes—
425#489C2314yes—
426#488C2318yes—
427#487C2318yes—
428#485C2318yes—
429#485C2318yes—
430#485C2318yes—
431#485C2318yes—
432#484C2318yes—
433#484C2318yes—
434#483C2318yes—
435#483C2318yes—
436#483C2318yes—
437#482C2318yes—
438#482C2318yes—
439#480C2318yes—
440#479C2318yes—
441#479C2318yes—
442#479C2318yes—
443#479C2318yes—
444#479C2318yes—
445#479C2318yes—
446#478C2318yes—
447#478C2318yes—
448#477C2318yes—
449#477C2318yes—
450#476C2318yes—
451#475C2318yes—
452#470C2318yes—
453#470C2318yes—
454#470C2318yes—
455#470C2318yes—
456#468C2318yes—
457#468C2318yes—
458#468C2318yes—
459#468C2318yes—
460#467C2318yes—
461#467C2318yes—
462#467C2318yes—
463#467C2318yes—
464#467C2318yes—
465#467C2318yes—
466#465C2318yes—
467#465C2318yes—
468#465C2318yes—
469#465C2318yes—
470#465C2318yes—
471#465C2318yes—
472#464C2318yes—
473#464C2318yes—
474#464C2318yes—
475#464C2318yes—
476#462C2318yes—
477#462C2318yes—
478#462C2318yes—
479#462C2318yes—
480#461C2318yes—
481#461C2318yes—
482#461C2318yes—
483#460C2318yes—
484#452C2318yes—
485#452C2318yes—
486#451C2318yes—
487#451C2318yes—
488#451C2318yes—
489#451C2318yes—
490#451C2318yes—
491#450C2318yes—
492#450C2318yes—
493#448C2318yes—
494#448C2318yes—
495#448C2318yes—
496#446C2318yes—
497#446C2318yes—
498#441C2318yes—
499#441C2318yes—
500#441C2318yes—
501#441C2318yes—
502#441C2318yes—
503#441C2318yes—
504#440C2318yes—
505#440C2318yes—
506#440C2318yes—
507#440C2318yes—
508#440C2318yes—
509#440C2318yes—
510C4×Q16C2318yes—
511C4×Q16C2318yes—
512C4×Q16C2318yes—
513C4×Q16C2318yes—
514C4×SD16C2318yes—
515C4×SD16C2318yes—
516C4×SD16C2318yes—
517C4×SD16C2318yes—
518#435C2318yes—
519#435C2318yes—
520#435C2318yes—
521#435C2318yes—
522C8×D4C2318yes—
523C8×D4C2318yes—
524#433C2314yes—
525#433C2314yes—
526#432C2314yes—
527#432C2314yes—
528#432C2314yes—
529#431C2314yes—
530#428C2318yes—
531#427C2314yes—
532#427C2314yes—
533C2×#107C2314yes—
534C2×#106C2314yes—
535#424C2312yes—
536#424C2312yes—
537#423C2312yes—
538#419C2314yes—
539#419C2314yes—
540#419C2314yes—
541#418C2314yes—
542#416C2318yes—
543C2×#103C2314yes—
544C2×#103C2314yes—
545C2×#103C2314yes—
546C2×#103C2318yes—
547C2×#102C2314yes—
548#408C2312yes—
549#408C2312yes—
550#407C2312yes—
551#405C2312yes—
552#405C2314yes—
553#405C2312yes—
554#405C2314yes—
555C4×M16C2312yes—
556C4×M16C2312yes—
557C4×M16C2311yescharacteristic
558C4×M16C2311yescharacteristic
559C2×#97C2311yescharacteristic
560C2×#97C2312yes—
561C2×#97C2312yes—
562C2×#97C2311yescharacteristic
563C2×#97C2312yes—
564C2×#97C2314yes—
565C2×#97C2312yes—
566C2×#97C2312yes—
567C2×#41—24no—
568C2×#41C2×D414yes—
569C2×#41C2414yes—
570C2×#41C2411yescharacteristic
571C2×#41C2411yescharacteristic
572C22×Q8—22no—
573C22×Q8C2412yes—
574C22×Q8C2414yes—
575C22×Q8C2412yes—
576C22×Q8C2414yes—
577C22×Q8C2414yes—
578C22×D4—22no—
579C22×D4—24no—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C23×C4—22no—
583C23×C4C2×D412yes—
584C23×C4C2411yescharacteristic
585#137—416no—
586C2×Q16—48no—
587C2×Q16—48no—
588C2×Q16C2418yes—
589C2×Q16C2418yes—
590C2×Q16C2418yes—
591C2×Q16C2418yes—
592C2×SD16—48no—
593C2×SD16—48no—
594C2×SD16C2418yes—
595C2×SD16C2418yes—
596C2×SD16C2418yes—
597C2×SD16C2418yes—
598#131—44no—
599#131—44no—
600C2×M16C2414yes—
601C2×M16C2412yes—
602C2×M16C2412yes—
603C2×M16C2414yes—
604C22×C8—44no—
605C22×C8C2412yes—
606C22×C8C2414yes—
607C22×C8C2414yes—
608C22×C8C2412yes—
609C22×C8C2414yes—
610C22×C8C2414yes—
611C4⋊Q8—28no—
612C4⋊Q8—22no—
613C4⋊Q8—24no—
614C4⋊Q8—24no—
615C4⋊Q8—24no—
616C4⋊Q8—28no—
617C4⋊Q8—24no—
618C4⋊Q8—28no—
619C4⋊Q8—28no—
620C4⋊Q8—22no—
621C4⋊Q8—22no—
622C4⋊Q8—22no—
623C4⋊Q8—22no—
624C4⋊Q8—24no—
625C4⋊Q8—24no—
626C4⋊Q8C2×D412yes—
627C4⋊Q8C2×D411yescharacteristic
628C4⋊Q8C2414yes—
629C4⋊Q8C2414yes—
630C4⋊Q8C2414yes—
631C4⋊Q8C2414yes—
632C4⋊Q8C2412yes—
633C4⋊Q8C2414yes—
634C4⋊Q8C2414yes—
635C4⋊Q8C2414yes—
636#127—22no—
637#127C2×D411yescharacteristic
638#127C2412yes—
639#126—24no—
640#126—24no—
641#126—24no—
642#126—24no—
643#126—24no—
644#126—24no—
645#126—24no—
646#126—28no—
647#126—28no—
648#126—24no—
649#126—24no—
650#126—28no—
651#126—28no—
652#126—24no—
653#126—28no—
654#126—28no—
655#126—28no—
656#126—28no—
657#126—24no—
658#126—24no—
659#126—24no—
660#126—24no—
661#126—24no—
662#126—24no—
663#126C2×D414yes—
664#126C2×D414yes—
665#125—24no—
666#125—24no—
667#125—28no—
668#125—28no—
669#125—28no—
670#125—24no—
671#125—24no—
672#125—24no—
673#125—24no—
674#125—28no—
675#125—28no—
676#125—24no—
677#125—28no—
678#125—28no—
679#125—28no—
680#125—28no—
681#125—28no—
682#125—28no—
683#125—24no—
684#125—24no—
685#125—24no—
686#125—24no—
687#125—22no—
688#125—22no—
689#125—24no—
690#125—24no—
691#125—24no—
692#125C2×D412yes—
693#125C2×D414yes—
694#125C2414yes—
695#125C2414yes—
696#125C2412yes—
697#125C2412yes—
698#125C2414yes—
699#125C2414yes—
700#124—22no—
701#124—24no—
702#124—28no—
703#124—22no—
704#124—24no—
705#124—24no—
706#124—24no—
707#124—24no—
708#124—24no—
709#124—24no—
710#124—22no—
711#124—22no—
712#124—24no—
713#124C2×D411yescharacteristic
714#124C2×D411yescharacteristic
715#124C2×D414yes—
716#124C2414yes—
717#124C2414yes—
718#124C2414yes—
719#123—24no—
720#123—28no—
721#123—28no—
722#123—22no—
723#123—24no—
724#123—24no—
725#123—22no—
726#123—24no—
727#123—24no—
728#123—24no—
729#123—24no—
730#123—24no—
731#123—24no—
732#123—24no—
733#123—24no—
734#123—24no—
735#123—24no—
736#123—24no—
737#123—24no—
738#123—24no—
739#123—24no—
740#123—24no—
741#123—24no—
742#123—24no—
743#123—24no—
744#123—24no—
745#123—24no—
746#123—24no—
747#123C2×D414yes—
748#123C2×D414yes—
749#123C2×D412yes—
750#123C2×D412yes—
751C22⋊Q8—24no—
752C22⋊Q8—24no—
753C22⋊Q8—24no—
754C22⋊Q8—24no—
755C22⋊Q8—24no—
756C22⋊Q8—24no—
757C22⋊Q8—24no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—24no—
761C22⋊Q8—24no—
762C22⋊Q8—24no—
763C22⋊Q8—24no—
764C22⋊Q8—24no—
765C22⋊Q8—24no—
766C22⋊Q8—24no—
767C22⋊Q8—24no—
768C22⋊Q8—24no—
769C22⋊Q8—24no—
770C22⋊Q8—24no—
771C22⋊Q8—24no—
772C22⋊Q8—24no—
773C22⋊Q8—24no—
774C22⋊Q8—24no—
775C22⋊Q8—24no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—24no—
779C22⋊Q8—24no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—28no—
783C22⋊Q8—28no—
784C22⋊Q8C2×D414yes—
785C22⋊Q8C2×D414yes—
786C22⋊Q8C2×D412yes—
787C22⋊Q8C2×D412yes—
788C22⋊Q8C2414yes—
789C22⋊Q8C2414yes—
790C22⋊Q8C2418yes—
791C22⋊Q8C2418yes—
792C22⋊Q8C2414yes—
793C22⋊Q8C2414yes—
794C22⋊Q8C2418yes—
795C22⋊Q8C2418yes—
796#121—24no—
797#121—24no—
798#121—24no—
799#121—24no—
800#121—24no—
801#121—24no—
802#121—24no—
803#121—22no—
804#121—22no—
805#121—24no—
806#121—24no—
807#121—24no—
808#121—24no—
809#121—24no—
810#121—24no—
811#121C2×D414yes—
812#121C2×D414yes—
813#121C2×D412yes—
814#121C2×D412yes—
815#121C2414yes—
816#121C2414yes—
817#121C2414yes—
818#121C2414yes—
819#120—24no—
820#120—22no—
821#120—22no—
822#120—24no—
823#120—24no—
824#120—24no—
825#120C2×D412yes—
826#120C2×D412yes—
827C4×Q8—28no—
828C4×Q8—28no—
829C4×Q8—28no—
830C4×Q8—24no—
831C4×Q8—28no—
832C4×Q8—28no—
833C4×Q8—24no—
834C4×Q8—24no—
835C4×Q8—24no—
836C4×Q8—24no—
837C4×Q8—24no—
838C4×Q8—22no—
839C4×Q8—22no—
840C4×Q8—24no—
841C4×Q8—24no—
842C4×Q8—24no—
843C4×Q8—24no—
844C4×Q8—24no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8C2×D414yes—
848C4×Q8C2×D412yes—
849C4×Q8C2×D412yes—
850C4×Q8C2418yes—
851C4×Q8C2414yes—
852C4×Q8C2414yes—
853C4×Q8C2418yes—
854C4×Q8C2414yes—
855C4×Q8C2418yes—
856C4×Q8C2418yes—
857C4×Q8C2414yes—
858C4×Q8C2414yes—
859C4×D4—24no—
860C4×D4—24no—
861C4×D4—28no—
862C4×D4—28no—
863C4×D4—28no—
864C4×D4—24no—
865C4×D4—24no—
866C4×D4—24no—
867C4×D4—24no—
868C4×D4—24no—
869C4×D4—24no—
870C4×D4—24no—
871C4×D4—24no—
872C4×D4—24no—
873C4×D4—24no—
874C4×D4—24no—
875C4×D4—24no—
876C4×D4—24no—
877C4×D4—24no—
878C4×D4—22no—
879C4×D4—22no—
880C4×D4—24no—
881C4×D4C2×D414yes—
882C4×D4C2×D414yes—
883C4×D4C2×D414yes—
884C4×D4C2×D414yes—
885C4×D4C2×D414yes—
886C4×D4C2×D412yes—
887C4×D4C2×D412yes—
888C4×D4C2414yes—
889C4×D4C2414yes—
890C4×D4C2414yes—
891C4×D4C2414yes—
892C4×D4C2414yes—
893C4×D4C2414yes—
894C4×D4C2414yes—
895#117—24no—
896#117—24no—
897#117—24no—
898#117—24no—
899#117—24no—
900#117—24no—
901#117—24no—
902#117—24no—
903#117—28no—
904#117—28no—
905#117—28no—
906#117—28no—
907#117—24no—
908#117—24no—
909#117—24no—
910#117—24no—
911#117—24no—
912#117—24no—
913#117—24no—
914#117—24no—
915#117—24no—
916#117C2×D414yes—
917#117C2×D414yes—
918#117C2×D414yes—
919#117C2412yes—
920#117C2412yes—
921#117C2414yes—
922#117C2414yes—
923#117C2412yes—
924#117C2412yes—
925#117C2411yescharacteristic
926#117C2411yescharacteristic
927C2×C4⋊C4—22no—
928C2×C4⋊C4—22no—
929C2×C4⋊C4—22no—
930C2×C4⋊C4—22no—
931C2×C4⋊C4—22no—
932C2×C4⋊C4—22no—
933C2×C4⋊C4—24no—
934C2×C4⋊C4—24no—
935C2×C4⋊C4—22no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—24no—
938C2×C4⋊C4—24no—
939C2×C4⋊C4—24no—
940C2×C4⋊C4—24no—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C22⋊C4—24no—
946C2×C22⋊C4—22no—
947C2×C22⋊C4—22no—
948C2×C22⋊C4—22no—
949C2×C22⋊C4—22no—
950C2×C22⋊C4—22no—
951C2×C22⋊C4—24no—
952C2×C22⋊C4—24no—
953C2×C22⋊C4—24no—
954C2×C22⋊C4—24no—
955C2×C42—22no—
956C2×C42—24no—
957C2×C42C2×D412yes—
958C2×C42C2×D412yes—
959C2×C42C2×D412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966#107C2418yes—
967#107C2418yes—
968#107C2418yes—
969#107C2418yes—
970#106C2418yes—
971#106C2418yes—
972#106C2418yes—
973#106C2418yes—
974C4⋊C8C2418yes—
975C4⋊C8C2418yes—
976C4⋊C8C2418yes—
977#103C2418yes—
978#103C2418yes—
979#103C2418yes—
980#103C2418yes—
981#103C2418yes—
982#103C2418yes—
983#103C2418yes—
984#103C2418yes—
985#103C2418yes—
986#103C2418yes—
987#103C2418yes—
988#103C2418yes—
989#102C2418yes—
990#102C2418yes—
991#102C2418yes—
992#102C2418yes—
993C22⋊C8C2418yes—
994C22⋊C8C2418yes—
995C22⋊C8C2418yes—
996#97C2411yescharacteristic
997#97C2411yescharacteristic
998#97C2412yes—
999#97C2412yes—
1000#97C2412yes—
1001#97C2414yes—
1002#97C2414yes—
1003#97C2412yes—
1004#97C2412yes—
1005#97C2414yes—
1006#97C2414yes—
1007C4×C8C2412yes—
1008C4×C8C2412yes—
1009C4×C8C2414yes—
1010C4×C8C2414yes—
1011C24—22no—
1012C24—22no—
1013C24C22×D411yescharacteristic
1014#41—42no—
1015#41—42no—
1016#41—48no—
1017#41—48no—
1018#41—88no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—48no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—48no—
1035C2×Q8C22×D414yes—
1036C2×Q8C22×D411yescharacteristic
1037C2×Q8C22×D411yescharacteristic
1038C2×Q8C2514yes—
1039C2×Q8C2518yes—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—88no—
1051C2×D4—84no—
1052C2×D4C22×D414yes—
1053C2×D4C22×D414yes—
1054C2×D4C22×D414yes—
1055C2×D4C22×D411yescharacteristic
1056C2×D4C22×D412yes—
1057C2×D4C22×D412yes—
1058C2×D4C22×D411yescharacteristic
1059C2×D4C2514yes—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—84no—
1077C22×C4C22×D412yes—
1078C22×C4C22×D412yes—
1079C22×C4C22×D412yes—
1080C22×C4C22×D412yes—
1081C22×C4C22×D411yescharacteristic
1082C22×C4C22×D412yes—
1083C22×C4C22×D412yes—
1084C22×C4C22×D412yes—
1085C22×C4C22×D414yes—
1086C22×C4C22×D414yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091Q16—216no—
1092Q16—48no—
1093Q16—48no—
1094Q16—48no—
1095SD16—216no—
1096SD16—48no—
1097SD16—48no—
1098SD16—48no—
1099M16—28no—
1100M16—44no—
1101M16—42no—
1102M16—42no—
1103C2×C8—24no—
1104C2×C8—28no—
1105C2×C8—28no—
1106C2×C8—44no—
1107C2×C8—42no—
1108C2×C8—44no—
1109C2×C8C2512yes—
1110C2×C8C2514yes—
1111C2×C8C2514yes—
1112C2×C8C2514yes—
1113C2×C8C2512yes—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—22no—
1140C4⋊C4—22no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4C22×D414yes—
1153C4⋊C4C22×D414yes—
1154C4⋊C4C22×D414yes—
1155C4⋊C4C22×D414yes—
1156C4⋊C4C22×D414yes—
1157C4⋊C4C22×D414yes—
1158C4⋊C4C22×D414yes—
1159C4⋊C4C22×D414yes—
1160C4⋊C4C22×D412yes—
1161C4⋊C4C22×D412yes—
1162C4⋊C4C2518yes—
1163C4⋊C4C2514yes—
1164C4⋊C4C2514yes—
1165C22⋊C4—24no—
1166C22⋊C4—22no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—22no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4C22×D414yes—
1192C22⋊C4C22×D414yes—
1193C22⋊C4C22×D414yes—
1194C22⋊C4C22×D414yes—
1195C22⋊C4C22×D414yes—
1196C22⋊C4C22×D414yes—
1197C22⋊C4C22×D414yes—
1198C22⋊C4C22×D414yes—
1199C22⋊C4C22×D412yes—
1200C22⋊C4C22×D412yes—
1201C42—24no—
1202C42—24no—
1203C42—28no—
1204C42—28no—
1205C42—24no—
1206C42—24no—
1207C42—28no—
1208C42—28no—
1209C42—22no—
1210C42—22no—
1211C42—24no—
1212C42—24no—
1213C42C22×D411yescharacteristic
1214C42C22×D412yes—
1215C42C22×D412yes—
1216C42C22×D412yes—
1217C42C22×D412yes—
1218C42C22×D412yes—
1219C42C22×D411yescharacteristic
1220C42C22×D414yes—
1221C42C22×D414yes—
1222C42C2511yescharacteristic
1223C42C2512yes—
1224C42C2512yes—
1225C42C2511yescharacteristic
1226C42C2512yes—
1227C23—24no—
1228C23—24no—
1229C23—41no—
1230C23—44no—
1231C23—82no—
1232C23—82no—
1233C23—82no—
1234C23—84no—
1235C23C23×D411yescharacteristic
1236C23C23×D412yes—
1237C23C23×D412yes—
1238C23C23×D412yes—
1239Q8—28no—
1240Q8—28no—
1241Q8—28no—
1242Q8—41no—
1243Q8—41no—
1244Q8—44no—
1245Q8—48no—
1246Q8—48no—
1247Q8—82no—
1248Q8—84no—
1249Q8—84no—
1250Q8—82no—
1251Q8—84no—
1252Q8—84no—
1253D4—28no—
1254D4—28no—
1255D4—28no—
1256D4—41no—
1257D4—41no—
1258D4—42no—
1259D4—42no—
1260D4—44no—
1261D4—48no—
1262D4—82no—
1263D4—82no—
1264D4—84no—
1265D4—84no—
1266D4—84no—
1267D4—84no—
1268D4—84no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—28no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—28no—
1279C2×C4—24no—
1280C2×C4—42no—
1281C2×C4—41no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—44no—
1289C2×C4—48no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—84no—
1295C2×C4—82no—
1296C2×C4—82no—
1297C2×C4—82no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4C23×D412yes—
1303C2×C4C23×D412yes—
1304C2×C4C23×D412yes—
1305C2×C4C23×D414yes—
1306C2×C4C23×D414yes—
1307C2×C4C23×D412yes—
1308C2×C4C23×D412yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D411yescharacteristic
1311C2×C4C23×D412yes—
1312C2×C4C2611yescharacteristic
1313C8—22no—
1314C8—24no—
1315C8—24no—
1316C8—24no—
1317C8#58514yes—
1318C22—22no—
1319C22—22no—
1320C22—21no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—24no—
1325C22—24no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—164no—
1331C22—322no—
1332C22#358614yes—
1333C22C24×D411yescharacteristic
1334C4—21no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—24no—
1343C4—24no—
1344C4—44no—
1345C4—48no—
1346C4—44no—
1347C4—48no—
1348C4—44no—
1349C4C2×#58512yes—
1350C2—24no—
1351C2—42no—
1352C2—41no—
1353C2—42no—
1354C2—84no—
1355C2#6281211yescharacteristic
1356C2C2×#358612yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62829C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62837C2semidirect
3. #62585C2semidirect
4. #62577C2semidirect
5. #62505C2semidirect
6. #62448C2semidirect
7. #62388C2semidirect
8. #62337C2semidirect
9. #62281C2semidirect
10. #62271C2semidirect
11. #62268C2semidirect
12. #61525C2semidirect
13. #61520C2semidirect
14. #61020C2semidirect
15. #61018C2semidirect
16. #60950C2semidirect
17. #60726C2semidirect
18. #60720C2semidirect
19. C2×#3181C2semidirect
20. #60207C2semidirect
27. #3556C22semidirect
30. #3550C22semidirect
33. #3538C22semidirect
36. #3523C22semidirect
44. #3509C22semidirect
45. #3509C22semidirect
46. #3509C22semidirect
48. #3503C22semidirect
54. C2×#533C22semidirect
56. #3400C22semidirect
57. #3398C22semidirect
58. #3390C22semidirect
59. #3388C22semidirect
60. #3377C22semidirect
61. #3374C22semidirect
62. #3372C22semidirect
63. #3371C22semidirect
64. #3350C22semidirect
65. #3349C22semidirect
66. #3344C22semidirect
67. #3343C22semidirect
69. #3336C22semidirect
71. #3320C22semidirect
72. #3313C22semidirect
73. #3312C22semidirect
74. #3312C22semidirect
75. #3312C22semidirect
76. #3311C22semidirect
78. #3300C22semidirect
79. #3299C22semidirect
80. #3298C22semidirect
81. #3296C22semidirect
82. D4×Q16C22semidirect
84. #3270C22semidirect
85. #3270C22semidirect
86. #3266C22semidirect
87. #3266C22semidirect
88. #3261C22semidirect
90. #3258C22semidirect
91. #3252C22semidirect
92. #3240C22semidirect
93. #3240C22semidirect
94. #3238C22semidirect
95. #3237C22semidirect
96. #3236C22semidirect
97. #3236C22semidirect
98. #3218C22semidirect
99. #3218C22semidirect
100. #3218C22semidirect
101. #3216C22semidirect
102. #3215C22semidirect
103. #3215C22semidirect
104. #3202C22semidirect
105. #3201C22semidirect
107. #3195C22semidirect
109. #3181C22semidirect
110. #3181C22semidirect
111. #3181C22semidirect
112. #3181C22semidirect
113. #3181C22semidirect
114. #3181C22semidirect
115. #3181C22semidirect
116. #3181C22semidirect
117. #3178C22semidirect
118. #3178C22semidirect
119. #3177C22semidirect
120. #3177C22semidirect
122. #3174C22semidirect
123. #3172C22semidirect
124. #3172C22semidirect
125. #3172C22semidirect
126. #3172C22semidirect
127. #3166C22semidirect
128. #3162C22semidirect
129. C2×#501C22semidirect
130. #3152C22semidirect
131. C2×#497C22semidirect
132. C2×#497C22semidirect
133. #3140C22semidirect
134. #3139C22semidirect
135. #3135C22semidirect
136. C2×#491C22semidirect
137. C2×#491C22semidirect
138. C2×#489C22semidirect
139. #3127C22semidirect
140. #3127C22semidirect
141. #3126C22semidirect
142. #3123C22semidirect
143. #3121C22semidirect
144. #3120C22semidirect
145. #3108C22semidirect
146. #3104C22semidirect
147. #3101C22semidirect
148. #3063C22semidirect
149. #3059C22semidirect
151. C2×#467C22semidirect
153. #2970C22semidirect
154. #2970C22semidirect
155. #2968C22semidirect
156. #2961C22semidirect
157. #2950C22semidirect
158. #2949C22semidirect
159. #2947C22semidirect
160. C2×#441C22semidirect
161. C2×#440C22semidirect
162. #2932C22semidirect
164. #2929C22semidirect
165. #2923C22semidirect
166. #2923C22semidirect
167. #2920C22semidirect
168. #2875C22semidirect
169. #2875C22semidirect
170. C22×#97C22semidirect

Maximal subgroups

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

subgroupindex
#628372
#628292
#625852
#625772
#625052
#624482
#623882
#623372
#622812
#622712
#622682
#615252
#615202
#610202
#610182
#609502
#607262
#607202
C2×#31812
#602072