Finite Group Databasebeta

← #6356894

Subgroups — #6356894

Order 512.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62544C211yesmaximal, characteristic, complemented
2#62130C211yesmaximal, characteristic, complemented
3#61997C211yesmaximal, characteristic
4#60335C211yesmaximal, characteristic, complemented
5#19586C211yesmaximal, characteristic, complemented
6#19577C211yesmaximal, characteristic, complemented
7#19544C211yesmaximal, characteristic, complemented
8#19541C211yesmaximal, characteristic, complemented
9#19533C211yesmaximal, characteristic, complemented
10#19520C211yesmaximal, characteristic, complemented
11#19479C211yesmaximal, characteristic, complemented
12#19472C211yesmaximal, characteristic, complemented
13#19418C211yesmaximal, characteristic, complemented
14#19409C211yesmaximal, characteristic, complemented
15#19403C211yesmaximal, characteristic, complemented
16#19400C211yesmaximal, characteristic, complemented
17#19382C211yesmaximal, characteristic, complemented
18#19375C211yesmaximal, characteristic, complemented
19#19366C211yesmaximal, characteristic, complemented
20#19324C211yesmaximal, characteristic, complemented
21#19308C211yesmaximal, characteristic, complemented
22#19260C211yesmaximal, characteristic, complemented
23#19246C211yesmaximal, characteristic, complemented
24#19242C211yesmaximal, characteristic, complemented
25#19218C211yesmaximal, characteristic, complemented
26#19185C211yesmaximal, characteristic, complemented
27#19176C211yesmaximal, characteristic, complemented
28#19123C211yesmaximal, characteristic, complemented
29#17841C211yesmaximal, characteristic, complemented
30#17778C211yesmaximal, characteristic, complemented
31#17771C211yesmaximal, characteristic, complemented
32#3509C2211yescharacteristic
33#3508C2211yescharacteristic
34#3482C2211yescharacteristic
35#3394—21no—
36#3390—21no—
37#3377—21no—
38#3371—21no—
39#3371—21no—
40#3365—21no—
41#3349—21no—
42#3343—21no—
43#3336—21no—
44#3332—21no—
45#3323—21no—
46#3323—21no—
47#3323—21no—
48#3323—21no—
49#3317—21no—
50#3317—21no—
51#3313—21no—
52#3312—21no—
53#3311—21no—
54#3311—21no—
55#3300—21no—
56#3278—21no—
57#3275—21no—
58#3275—21no—
59#3255C2211yescharacteristic
60#3252C2211yescharacteristic, complemented
61#3251C2211yescharacteristic
62#3251C2211yescharacteristic
63#3249C2211yescharacteristic
64#3248C2211yescharacteristic, complemented
65#3238C2211yescharacteristic, complemented
66#3237C2211yescharacteristic
67#3233C2211yescharacteristic, complemented
68#3231C2211yescharacteristic
69#3228C2211yescharacteristic
70#3227C2211yescharacteristic
71#3212C2211yescharacteristic
72#3212C2211yescharacteristic
73#3210C2211yescharacteristic
74#3210C2211yescharacteristic
75#3208C2211yescharacteristic
76#3208C2211yescharacteristic
77#3185C2211yescharacteristic
78#3182C2211yescharacteristic
79#3167C2211yescharacteristic
80#3141C2211yescharacteristic
81#3138C2211yescharacteristic
82#3131C2211yescharacteristic
83#3116C2211yescharacteristic
84#3113C2211yescharacteristic, complemented
85#3107C2211yescharacteristic
86#3104C2211yescharacteristic, complemented
87#3103C2211yescharacteristic
88#3103C2211yescharacteristic
89#3078C2211yescharacteristic, complemented
90#3076C2211yescharacteristic
91C2×#477C2211yescharacteristic, complemented
92#3038C2211yescharacteristic
93#3037C2211yescharacteristic
94#3037C2211yescharacteristic
95#2994—21no—
96#2994C2211yescharacteristic, complemented
97#2993—21no—
98#2993C2211yescharacteristic, complemented
99#2991C2211yescharacteristic
100#2990—21no—
101#2990C2211yescharacteristic
102#2990C2211yescharacteristic
103#2988C2211yescharacteristic
104#2985—21no—
105#2985C2211yescharacteristic
106#2984C2211yescharacteristic, complemented
107#2982C2211yescharacteristic, complemented
108#2971C2211yescharacteristic
109#2969—21no—
110#2969C2211yescharacteristic, complemented
111#2966—21no—
112#2966C2211yescharacteristic, complemented
113#2965—21no—
114#2965C2211yescharacteristic
115Q8×M16C2211yescharacteristic, complemented
116#2962—21no—
117#2962C2211yescharacteristic
118C2×C8×Q8C2211yescharacteristic, complemented
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1703C2211yescharacteristic, complemented
123#1702C2211yescharacteristic
124#1702C2211yescharacteristic
125#1701C2211yescharacteristic
126#1701C2211yescharacteristic
127#1700C2211yescharacteristic, complemented
128#1699C2211yescharacteristic, complemented
129#1698C2211yescharacteristic
130#1698C2211yescharacteristic
131#1698C2211yescharacteristic
132#1698C2211yescharacteristic
133#1697C2211yescharacteristic
134#1697C2211yescharacteristic
135#1694C2211yescharacteristic, complemented
136#1694C2211yescharacteristic, complemented
137#1692C2211yescharacteristic, complemented
138#1691C2211yescharacteristic, complemented
139#1690C2211yescharacteristic, complemented
140#1689C2211yescharacteristic, complemented
141#1686C2211yescharacteristic
142#1686C2211yescharacteristic
143#1684C2211yescharacteristic, complemented
144#1684C2211yescharacteristic, complemented
145#1684C2211yescharacteristic, complemented
146#1683C2211yescharacteristic, complemented
147#1682C2211yescharacteristic
148#1682C2211yescharacteristic
149#1682C2211yescharacteristic
150#1682C2211yescharacteristic
151#1680C2211yescharacteristic, complemented
152#1680C2211yescharacteristic, complemented
153#1680C2211yescharacteristic, complemented
154#1680C2211yescharacteristic, complemented
155#1680C2211yescharacteristic, complemented
156#1679C2211yescharacteristic, complemented
157#1678C2211yescharacteristic
158#1678C2211yescharacteristic
159#1678C2211yescharacteristic
160#1678C2211yescharacteristic
161#1678C2211yescharacteristic
162#1678C2211yescharacteristic
163#1678C2211yescharacteristic
164#1678C2211yescharacteristic
165#1677C2211yescharacteristic
166#1677C2211yescharacteristic
167#1674C2211yescharacteristic, complemented
168#1673C2211yescharacteristic, complemented
169#1672C2211yescharacteristic, complemented
170#1672C2211yescharacteristic, complemented
171#1672C2211yescharacteristic, complemented
172#1672C2211yescharacteristic, complemented
173#1672C2211yescharacteristic, complemented
174#1671C2211yescharacteristic, complemented
175#1670C2211yescharacteristic, complemented
176#1670C2211yescharacteristic, complemented
177#1666C2211yescharacteristic
178#1666C2211yescharacteristic
179#1666C2211yescharacteristic
180#1666C2211yescharacteristic
181#1665C2211yescharacteristic
182#1665C2211yescharacteristic
183#1574C2211yescharacteristic, complemented
184#1574C2211yescharacteristic, complemented
185#1572C2211yescharacteristic
186#1572C2211yescharacteristic, complemented
187#1570C2211yescharacteristic
188#1570C2211yescharacteristic, complemented
189#1569C2211yescharacteristic
190#1569C2211yescharacteristic, complemented
191#1566C2211yescharacteristic, complemented
192#1565C2211yescharacteristic
193#1565C2211yescharacteristic, complemented
194#1564C2211yescharacteristic, complemented
195#1561C2211yescharacteristic, complemented
196#1559C2211yescharacteristic
197#1559C2211yescharacteristic, complemented
198#1557C2211yescharacteristic
199#1557C2211yescharacteristic
200#1555C2211yescharacteristic
201#1554C2211yescharacteristic
202#1554C2211yescharacteristic, complemented
203#1553C2211yescharacteristic
204#1553C2211yescharacteristic
205#1552C2211yescharacteristic
206#1552C2211yescharacteristic
207#1550C2211yescharacteristic
208#1550C2211yescharacteristic, complemented
209#1548C2211yescharacteristic, complemented
210#1548C2211yescharacteristic, complemented
211#1547C2211yescharacteristic
212#1547C2211yescharacteristic
213#1544C2211yescharacteristic, complemented
214#1542C2211yescharacteristic
215#1542C2211yescharacteristic, complemented
216#1540C2211yescharacteristic
217#1540C2211yescharacteristic
218C2×#331C2211yescharacteristic
219C2×#137—21no—
220C2×#137—21no—
221C2×AGL(1,ℤ/8)—21no—
222#559—21no—
223#559—21no—
224#557—21no—
225#557—21no—
226#557D411yescharacteristic
227#556—21no—
228#556—21no—
229#556—21no—
230#556D411yescharacteristic
231#552—21no—
232#552—21no—
233#552—21no—
234#552—21no—
235#552—21no—
236#552—21no—
237#552D411yescharacteristic
238#552D411yescharacteristic
239#550—21no—
240#550—21no—
241D4×Q8D411yescharacteristic
242#548D411yescharacteristic
243#548D411yescharacteristic
244#547—21no—
245#547D411yescharacteristic
246#546—21no—
247#546—21no—
248#546—21no—
249#546—21no—
250#541—21no—
251#541—21no—
252#540—21no—
253#540—21no—
254#536—21no—
255#535—21no—
256#533—21no—
257#533C2311yescharacteristic
258#533C2311yescharacteristic
259#533C2311yescharacteristic
260#533C2311yescharacteristic
261#533C2311yescharacteristic
262#533C2311yescharacteristic
263#533C2311yescharacteristic
264#532C2311yescharacteristic
265#532C2311yescharacteristic
266#532C2311yescharacteristic
267#532C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×#127C2311yescharacteristic
270#529—21no—
271#529—21no—
272#529C2311yescharacteristic
273#529C2311yescharacteristic
274#519—21no—
275#518—21no—
276C4×#41—21no—
277C4×#41C2311yescharacteristic
278C4×#41C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281#501—21no—
282#501—21no—
283#500C2311yescharacteristic
284#499—21no—
285#498C2311yescharacteristic
286#498C2311yescharacteristic
287#495—21no—
288#495—21no—
289#494C2311yescharacteristic
290#492—21no—
291#492C2311yescharacteristic
292#492C2311yescharacteristic
293#491—21no—
294#490—21no—
295#490—21no—
296#489—21no—
297#489—21no—
298#489—21no—
299#488—21no—
300#488—21no—
301#488—21no—
302#488—21no—
303#488—21no—
304#487C2311yescharacteristic
305#487C2311yescharacteristic
306#487C2311yescharacteristic
307#487C2311yescharacteristic
308#486—21no—
309#486C2311yescharacteristic
310#486C2311yescharacteristic
311#486C2311yescharacteristic
312#486C2311yescharacteristic
313#486C2311yescharacteristic
314#486C2311yescharacteristic
315#485—21no—
316#485—21no—
317#485—21no—
318#485—21no—
319#485—21no—
320#485—21no—
321#485—21no—
322#484—21no—
323#483—21no—
324#483—21no—
325#482—21no—
326#482—21no—
327#482—21no—
328#481—21no—
329#481—21no—
330#481—21no—
331#481—21no—
332#480—21no—
333#479—21no—
334#479—21no—
335#479—21no—
336#479—21no—
337#479—21no—
338#479—21no—
339#479—21no—
340#478—21no—
341#478—21no—
342#478—21no—
343#478—21no—
344#478—21no—
345#477—21no—
346#477—21no—
347#477—21no—
348#477C2311yescharacteristic
349#477C2311yescharacteristic
350#477C2311yescharacteristic
351#477C2311yescharacteristic
352#477C2311yescharacteristic
353#477C2311yescharacteristic
354#476—21no—
355#476—21no—
356#476C2311yescharacteristic
357#476C2311yescharacteristic
358#475—21no—
359#475C2311yescharacteristic
360#475C2311yescharacteristic
361#475C2311yescharacteristic
362#475C2311yescharacteristic
363#475C2311yescharacteristic
364#475C2311yescharacteristic
365#474C2311yescharacteristic
366#474C2311yescharacteristic
367#470—21no—
368#470—21no—
369#470—21no—
370#470—21no—
371#470—21no—
372#469—21no—
373#469—21no—
374#468—21no—
375#468—21no—
376#468—21no—
377#468—21no—
378#468—21no—
379#467—21no—
380#467—21no—
381#467—21no—
382#465—21no—
383#465—21no—
384#465—21no—
385#464—21no—
386#464—21no—
387#464—21no—
388#464—21no—
389#464—21no—
390#464—21no—
391#464—21no—
392#464—21no—
393#464—21no—
394#464—21no—
395#463—21no—
396#463—21no—
397#462—21no—
398#462—21no—
399#462C2311yescharacteristic
400#462C2311yescharacteristic
401#462C2311yescharacteristic
402#462C2311yescharacteristic
403#462C2311yescharacteristic
404#462C2311yescharacteristic
405#461C2311yescharacteristic
406#461C2311yescharacteristic
407#460—21no—
408#460—21no—
409#460—21no—
410#460C2311yescharacteristic
411#460C2311yescharacteristic
412#460C2311yescharacteristic
413#460C2311yescharacteristic
414#460C2311yescharacteristic
415#460C2311yescharacteristic
416#459—21no—
417#459C2311yescharacteristic
418#459C2311yescharacteristic
419#452—21no—
420#452—21no—
421#452—21no—
422#452—21no—
423#452—21no—
424#452—21no—
425#452—21no—
426#452—21no—
427#451—21no—
428#451—21no—
429#450—21no—
430#450—21no—
431#450—21no—
432#450—21no—
433#449—21no—
434#449—21no—
435#448—21no—
436#448—21no—
437#446—21no—
438#446—21no—
439#446—21no—
440#446—21no—
441#446—21no—
442#446—21no—
443#446—21no—
444#446—21no—
445#446—21no—
446#446—21no—
447#446D411yescharacteristic
448#446D411yescharacteristic
449#446C2311yescharacteristic
450#446C2311yescharacteristic
451#446C2311yescharacteristic
452#446C2311yescharacteristic
453C8×Q8—21no—
454C8×Q8—21no—
455C8×Q8—21no—
456C8×Q8—21no—
457C8×Q8—21no—
458C8×Q8C2311yescharacteristic
459C8×Q8C2311yescharacteristic
460C8×Q8C2311yescharacteristic
461C8×Q8C2311yescharacteristic
462C8×Q8C2311yescharacteristic
463C8×Q8C2311yescharacteristic
464C8×Q8C2311yescharacteristic
465C8×Q8C2311yescharacteristic
466#441—21no—
467#441—21no—
468#441—21no—
469#441—21no—
470#441—21no—
471#440—21no—
472#440—21no—
473#440—21no—
474C4×Q16—21no—
475C4×Q16—21no—
476C4×Q16—21no—
477C4×SD16—21no—
478C4×SD16—21no—
479C4×SD16—21no—
480C4×SD16—21no—
481C4×SD16—21no—
482C4×SD16—21no—
483C4×SD16—21no—
484#436—21no—
485#436—21no—
486#436—21no—
487#436—21no—
488#436—21no—
489#436—21no—
490#436—21no—
491#436D411yescharacteristic
492#436D411yescharacteristic
493#436C2311yescharacteristic
494#436C2311yescharacteristic
495#435—21no—
496#435—21no—
497#435—21no—
498#435—21no—
499#435—21no—
500#435—21no—
501#435—21no—
502#435—21no—
503#435D411yescharacteristic
504#435D411yescharacteristic
505#435D411yescharacteristic
506#435D411yescharacteristic
507C8×D4—21no—
508C8×D4—21no—
509C8×D4—21no—
510C8×D4—21no—
511C8×D4—21no—
512C8×D4—21no—
513C8×D4C2311yescharacteristic
514C8×D4C2311yescharacteristic
515#433—21no—
516#433—21no—
517#433—21no—
518#433—21no—
519#433—21no—
520#433—21no—
521#432—21no—
522#432—21no—
523#432C2311yescharacteristic
524#432C2311yescharacteristic
525#432C2311yescharacteristic
526#432C2311yescharacteristic
527#431—21no—
528#431—21no—
529#431—21no—
530#431—21no—
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#431C2311yescharacteristic
536#431C2311yescharacteristic
537#431C2311yescharacteristic
538#431C2311yescharacteristic
539#428—21no—
540#427—21no—
541C2×#107—21no—
542#424—21no—
543#424—21no—
544#424—21no—
545#423—21no—
546#423C2311yescharacteristic
547#423C2311yescharacteristic
548#423C2311yescharacteristic
549#423C2311yescharacteristic
550#423C2311yescharacteristic
551C2×C4⋊C8—21no—
552C2×C4⋊C8—21no—
553C2×C4⋊C8C2311yescharacteristic
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557#419—21no—
558#418—21no—
559#418—21no—
560#418—21no—
561#417—21no—
562#417—21no—
563#417—21no—
564#417—21no—
565#416—21no—
566#416—21no—
567#416—21no—
568C2×#103—21no—
569#405—21no—
570#405—21no—
571#405—21no—
572C4×M16—21no—
573C4×M16—21no—
574C4×M16C2311yescharacteristic
575C4×M16C2311yescharacteristic
576C2×C4×C8—21no—
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#334C2311yescharacteristic
585#334C2311yescharacteristic
586#334C2311yescharacteristic
587#334C2311yescharacteristic
588#334C2311yescharacteristic
589#334C2311yescharacteristic
590#334C2311yescharacteristic
591#334C2311yescharacteristic
592#334C2311yescharacteristic
593#334C2311yescharacteristic
594#333C2311yescharacteristic
595#333C2311yescharacteristic
596#333C2311yescharacteristic
597#333C2311yescharacteristic
598#333C2311yescharacteristic
599#333C2311yescharacteristic
600#333C2311yescharacteristic
601#333C2311yescharacteristic
602#332C2311yescharacteristic
603#332C2311yescharacteristic
604#332C2311yescharacteristic
605#332C2311yescharacteristic
606#332C2311yescharacteristic
607#332C2311yescharacteristic
608#332C2311yescharacteristic
609#332C2311yescharacteristic
610#332C2311yescharacteristic
611#332C2311yescharacteristic
612#332C2311yescharacteristic
613#332C2311yescharacteristic
614#332C2311yescharacteristic
615#332C2311yescharacteristic
616#332C2311yescharacteristic
617#332C2311yescharacteristic
618#331C2311yescharacteristic
619#331C2311yescharacteristic
620#331C2311yescharacteristic
621#331C2311yescharacteristic
622#331C2311yescharacteristic
623#331C2311yescharacteristic
624#331C2311yescharacteristic
625#331C2311yescharacteristic
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41C2×D411yescharacteristic
632C2×#41#4111yescharacteristic
633C22×Q8—21no—
634C22×Q8C2×D411yescharacteristic
635C22×Q8C2×D411yescharacteristic
636C22×D4—21no—
637C22×D4—21no—
638C22×D4—21no—
639#137—82no—
640#137—82no—
641AGL(1,ℤ/8)—82no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—21no—
647C2×Q16—21no—
648C2×Q16—21no—
649C2×Q16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×SD16—21no—
659C2×SD16—21no—
660C2×SD16—21no—
661C2×SD16—21no—
662C2×D8—21no—
663C2×D8—21no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16—21no—
668C2×M16—21no—
669C2×M16—21no—
670C2×M16—21no—
671C2×M16C2×D411yescharacteristic
672C2×M16C2×D411yescharacteristic
673C2×M16C2×D411yescharacteristic
674C2×M16C2×D411yescharacteristic
675C22×C8—21no—
676C22×C8—21no—
677C22×C8—21no—
678C22×C8—21no—
679C22×C8—21no—
680C22×C8—21no—
681C22×C8C2×D411yescharacteristic
682C22×C8C2×D411yescharacteristic
683C4⋊Q8—21no—
684C4⋊Q8—21no—
685C4⋊Q8—21no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8—41no—
689C4⋊Q8C2×D411yescharacteristic
690C4⋊Q8C2×D411yescharacteristic
691C4⋊Q8C2411yescharacteristic
692C4⋊Q8C2411yescharacteristic
693C4⋊Q8C2411yescharacteristic
694C4⋊Q8C2411yescharacteristic
695C4⋊Q8C2411yescharacteristic
696C4⋊Q8C2411yescharacteristic
697#127—21no—
698#127—21no—
699#127—21no—
700#127—41no—
701#127C2411yescharacteristic
702#127C2411yescharacteristic
703#126—21no—
704#126—21no—
705#126—21no—
706#126—21no—
707#126—21no—
708#126—21no—
709#126—41no—
710#126—41no—
711#126—41no—
712#126—41no—
713#125—21no—
714#125—21no—
715#125—21no—
716#125—21no—
717#125—21no—
718#125—21no—
719#125—21no—
720#125—21no—
721#125—21no—
722#125—21no—
723#125—21no—
724#125—41no—
725#125—41no—
726#125—41no—
727#125—41no—
728#125C2×D411yescharacteristic
729#125C2×D411yescharacteristic
730#124—21no—
731#124—21no—
732#124—21no—
733#124—21no—
734#124—21no—
735#124—21no—
736#124—41no—
737#124—41no—
738#124C2×D411yescharacteristic
739#124C2×D411yescharacteristic
740#123—21no—
741#123—21no—
742#123—21no—
743#123—21no—
744#123—21no—
745#123—21no—
746#123—41no—
747#123—41no—
748#123—41no—
749#123—41no—
750#123—41no—
751#123—41no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—21no—
763C22⋊Q8—21no—
764C22⋊Q8—21no—
765C22⋊Q8—21no—
766C22⋊Q8—21no—
767C22⋊Q8—21no—
768C22⋊Q8—21no—
769C22⋊Q8—21no—
770C22⋊Q8—21no—
771C22⋊Q8C2×D411yescharacteristic
772C22⋊Q8C2×D411yescharacteristic
773C22⋊Q8C2×D411yescharacteristic
774C22⋊Q8C2×D411yescharacteristic
775#121—21no—
776#121—21no—
777#121—21no—
778#121—21no—
779#121—21no—
780#121—21no—
781#121—21no—
782#121—21no—
783#121—21no—
784#121—21no—
785#121—41no—
786#121—41no—
787#121—41no—
788#121—41no—
789#121C2×D411yescharacteristic
790#121C2×D411yescharacteristic
791#120—41no—
792#120—41no—
793C4×Q8—21no—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8—21no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8—21no—
801C4×Q8—21no—
802C4×Q8—21no—
803C4×Q8—21no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—21no—
807C4×Q8—21no—
808C4×Q8—21no—
809C4×Q8—21no—
810C4×Q8—21no—
811C4×Q8—41no—
812C4×Q8—41no—
813C4×Q8C2×D411yescharacteristic
814C4×Q8C2×D411yescharacteristic
815C4×Q8C2×D411yescharacteristic
816C4×Q8C2×D411yescharacteristic
817C4×Q8C2×D411yescharacteristic
818C4×Q8C2×D411yescharacteristic
819C4×Q8C2×D411yescharacteristic
820C4×Q8C2411yescharacteristic
821C4×Q8C2411yescharacteristic
822C4×Q8C2411yescharacteristic
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—21no—
833C4×D4—21no—
834C4×D4—21no—
835C4×D4—21no—
836C4×D4—21no—
837C4×D4—21no—
838C4×D4—41no—
839C4×D4—41no—
840C4×D4C2×D411yescharacteristic
841C4×D4C2×D411yescharacteristic
842C4×D4C2×D411yescharacteristic
843C4×D4C2×D411yescharacteristic
844C4×D4C2×D411yescharacteristic
845C4×D4C2×D411yescharacteristic
846C4×D4C2×D411yescharacteristic
847C4×D4C2411yescharacteristic
848#117—21no—
849#117—21no—
850#117—21no—
851#117—21no—
852#117—21no—
853#117—21no—
854#117—21no—
855#117—21no—
856#117—21no—
857#117—21no—
858#117—21no—
859#117—21no—
860#117—21no—
861#117—41no—
862#117—41no—
863#117C2×D411yescharacteristic
864#117#4111yescharacteristic
865#117#4111yescharacteristic
866#117#4111yescharacteristic
867C2×C4⋊C4—21no—
868C2×C4⋊C4—21no—
869C2×C4⋊C4—21no—
870C2×C4⋊C4—21no—
871C2×C4⋊C4C2×D411yescharacteristic
872C2×C4⋊C4C2×D411yescharacteristic
873C2×C22⋊C4—41no—
874C2×C22⋊C4—41no—
875C2×C42—21no—
876C2×C42—21no—
877C2×C42—21no—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881#107—21no—
882#107—21no—
883#107—21no—
884#107—21no—
885#107—21no—
886#107—21no—
887#107—21no—
888#107—21no—
889#107—21no—
890#107—21no—
891#106—21no—
892#106—21no—
893#106—21no—
894#106—21no—
895#106—21no—
896#106—21no—
897#106—21no—
898#106—21no—
899#106—21no—
900#106—21no—
901#106—21no—
902#106—21no—
903C4⋊C8—21no—
904C4⋊C8—21no—
905C4⋊C8—21no—
906C4⋊C8—21no—
907C4⋊C8—21no—
908C4⋊C8—21no—
909C4⋊C8—21no—
910C4⋊C8—21no—
911C4⋊C8—21no—
912C4⋊C8—21no—
913C4⋊C8—21no—
914C4⋊C8—21no—
915C4⋊C8—21no—
916C4⋊C8—21no—
917C4⋊C8—21no—
918C4⋊C8—21no—
919C4⋊C8—21no—
920C4⋊C8—21no—
921C4⋊C8—21no—
922C4⋊C8—21no—
923C4⋊C8—21no—
924C4⋊C8C2×D411yescharacteristic
925C4⋊C8C2×D411yescharacteristic
926C4⋊C8C2×D411yescharacteristic
927C4⋊C8C2×D411yescharacteristic
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2×D411yescharacteristic
930C4⋊C8C2411yescharacteristic
931C4⋊C8C2411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
934C4⋊C8C2411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941C4⋊C8C2411yescharacteristic
942#103—21no—
943#103—21no—
944#103—21no—
945#103—21no—
946#103—21no—
947#103—21no—
948#103—21no—
949#103—21no—
950#103—21no—
951#103—21no—
952#103—21no—
953#103—21no—
954#103—21no—
955#103—21no—
956#103—21no—
957#103—21no—
958#103—21no—
959#103—21no—
960#103—21no—
961#103—21no—
962#103—21no—
963#103—21no—
964#103—21no—
965#103—21no—
966#103—21no—
967#103—21no—
968#103—21no—
969#103—21no—
970#102—21no—
971#102—21no—
972#102—21no—
973#102—21no—
974#102—21no—
975#102—21no—
976#102—21no—
977#102—21no—
978#102—21no—
979#102—21no—
980#102—21no—
981#102—21no—
982#102—21no—
983#102—21no—
984#102—21no—
985#102—21no—
986#102—21no—
987#102—21no—
988#102—21no—
989#102—21no—
990#102—21no—
991#102—21no—
992#102—21no—
993#102—21no—
994C22⋊C8—21no—
995C22⋊C8—21no—
996C22⋊C8—21no—
997C22⋊C8—21no—
998C22⋊C8—21no—
999C22⋊C8—21no—
1000C22⋊C8—21no—
1001C22⋊C8—21no—
1002C22⋊C8—21no—
1003C22⋊C8—21no—
1004C22⋊C8—21no—
1005C22⋊C8—21no—
1006C22⋊C8—21no—
1007C22⋊C8C2×D411yescharacteristic
1008C22⋊C8C2×D411yescharacteristic
1009C22⋊C8C2×D411yescharacteristic
1010C22⋊C8C2×D411yescharacteristic
1011C22⋊C8C2×D411yescharacteristic
1012C22⋊C8C2×D411yescharacteristic
1013#97—21no—
1014#97—21no—
1015#97—21no—
1016#97—21no—
1017#97—21no—
1018#97—21no—
1019#97—21no—
1020#97—21no—
1021#97C2×D411yescharacteristic
1022#97C2×D411yescharacteristic
1023#97C2×D411yescharacteristic
1024#97C2×D411yescharacteristic
1025C4×C8—21no—
1026C4×C8—21no—
1027C4×C8—21no—
1028C4×C8—21no—
1029C4×C8—21no—
1030C4×C8—21no—
1031C4×C8—21no—
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8—21no—
1038C4×C8C2×D411yescharacteristic
1039C4×C8C2×D411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C4×C8C2411yescharacteristic
1042C4×C8C2411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C24—41no—
1045#41—22no—
1046#41—41no—
1047#41—81no—
1048#41—81no—
1049#41—81no—
1050#41—81no—
1051#41—81no—
1052#41—81no—
1053#41—81no—
1054#41—81no—
1055#41—81no—
1056#41—82no—
1057C2×Q8—21no—
1058C2×Q8—21no—
1059C2×Q8—21no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—41no—
1069C2×Q8—41no—
1070C2×Q8—41no—
1071C2×Q8—82no—
1072C2×Q8#12111yescharacteristic
1073C2×Q8C22×D411yescharacteristic
1074C2×Q8C22×D411yescharacteristic
1075C2×Q8C22×D411yescharacteristic
1076C2×D4—21no—
1077C2×D4—21no—
1078C2×D4—21no—
1079C2×D4—21no—
1080C2×D4—21no—
1081C2×D4—21no—
1082C2×D4—21no—
1083C2×D4—21no—
1084C2×D4—21no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—41no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4—81no—
1093C2×D4—81no—
1094C2×D4—81no—
1095C2×D4—81no—
1096C2×D4—82no—
1097C2×D4#12111yescharacteristic
1098C2×D4#12111yescharacteristic
1099C2×D4#12111yescharacteristic
1100C2×D4C22×D411yescharacteristic
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4C22×D411yescharacteristic
1114C22×C4C22×D411yescharacteristic
1115C22×C4C22×D411yescharacteristic
1116C22×C4C22×D411yescharacteristic
1117C22×C4C22×D411yescharacteristic
1118C22×C4C22×D411yescharacteristic
1119C22×C4C2×#4111yescharacteristic
1120C22×C4C2×#4111yescharacteristic
1121C22×C4C2×#4111yescharacteristic
1122Q16—42no—
1123Q16—42no—
1124Q16—81no—
1125Q16—81no—
1126Q16—81no—
1127Q16—81no—
1128Q16—81no—
1129Q16—81no—
1130SD16—42no—
1131SD16—42no—
1132SD16—81no—
1133SD16—81no—
1134SD16—81no—
1135SD16—81no—
1136SD16—81no—
1137SD16—81no—
1138SD16—81no—
1139SD16—81no—
1140SD16—81no—
1141SD16—81no—
1142D8—81no—
1143D8—81no—
1144M16—41no—
1145M16—41no—
1146M16—41no—
1147M16—41no—
1148M16—42no—
1149M16—81no—
1150M16—81no—
1151M16—81no—
1152M16—81no—
1153M16—81no—
1154M16—81no—
1155C2×C8—21no—
1156C2×C8—21no—
1157C2×C8—21no—
1158C2×C8—21no—
1159C2×C8—21no—
1160C2×C8—21no—
1161C2×C8—21no—
1162C2×C8—21no—
1163C2×C8—21no—
1164C2×C8—21no—
1165C2×C8—21no—
1166C2×C8—21no—
1167C2×C8—41no—
1168C2×C8—41no—
1169C2×C8—81no—
1170C2×C8—81no—
1171C2×C8—81no—
1172C2×C8—81no—
1173C2×C8—81no—
1174C2×C8—81no—
1175C2×C8C22×D411yescharacteristic
1176C2×C8C22×D411yescharacteristic
1177C2×C8C22×D411yescharacteristic
1178C2×C8C22×D411yescharacteristic
1179C2×C8C22×D411yescharacteristic
1180C2×C8C22×D411yescharacteristic
1181C2×C8C22×D411yescharacteristic
1182C2×C8C22×D411yescharacteristic
1183C4⋊C4—21no—
1184C4⋊C4—21no—
1185C4⋊C4—21no—
1186C4⋊C4—21no—
1187C4⋊C4—21no—
1188C4⋊C4—21no—
1189C4⋊C4—21no—
1190C4⋊C4—21no—
1191C4⋊C4—21no—
1192C4⋊C4—21no—
1193C4⋊C4—21no—
1194C4⋊C4—21no—
1195C4⋊C4—21no—
1196C4⋊C4—21no—
1197C4⋊C4—21no—
1198C4⋊C4—21no—
1199C4⋊C4—21no—
1200C4⋊C4—21no—
1201C4⋊C4—21no—
1202C4⋊C4—21no—
1203C4⋊C4—21no—
1204C4⋊C4—21no—
1205C4⋊C4—21no—
1206C4⋊C4—21no—
1207C4⋊C4—21no—
1208C4⋊C4—21no—
1209C4⋊C4—21no—
1210C4⋊C4—21no—
1211C4⋊C4—21no—
1212C4⋊C4—21no—
1213C4⋊C4—21no—
1214C4⋊C4—21no—
1215C4⋊C4—21no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4#12111yescharacteristic
1231C4⋊C4#12111yescharacteristic
1232C4⋊C4#12111yescharacteristic
1233C4⋊C4#12111yescharacteristic
1234C4⋊C4#12111yescharacteristic
1235C4⋊C4#12111yescharacteristic
1236C4⋊C4C22×D411yescharacteristic
1237C4⋊C4C22×D411yescharacteristic
1238C4⋊C4C22×D411yescharacteristic
1239C4⋊C4C22×D411yescharacteristic
1240C22⋊C4—21no—
1241C22⋊C4—21no—
1242C22⋊C4—21no—
1243C22⋊C4—21no—
1244C22⋊C4—21no—
1245C22⋊C4—21no—
1246C22⋊C4—21no—
1247C22⋊C4—21no—
1248C22⋊C4—21no—
1249C22⋊C4—21no—
1250C22⋊C4—21no—
1251C22⋊C4—21no—
1252C22⋊C4—21no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—41no—
1261C22⋊C4—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4#12111yescharacteristic
1268C22⋊C4#12111yescharacteristic
1269C22⋊C4#12111yescharacteristic
1270C22⋊C4#12111yescharacteristic
1271C22⋊C4#12111yescharacteristic
1272C22⋊C4#12111yescharacteristic
1273C42—21no—
1274C42—21no—
1275C42—21no—
1276C42—21no—
1277C42—21no—
1278C42—21no—
1279C42—21no—
1280C42—21no—
1281C42—21no—
1282C42—41no—
1283C42—41no—
1284C42—41no—
1285C42—41no—
1286C42—41no—
1287C42—41no—
1288C42C22×D411yescharacteristic
1289C42C22×D411yescharacteristic
1290C42C22×D411yescharacteristic
1291C42C22×D411yescharacteristic
1292C42C22×D411yescharacteristic
1293C42C22×D411yescharacteristic
1294C42C2×#4111yescharacteristic
1295C42C2×#4111yescharacteristic
1296C42C2×#4111yescharacteristic
1297C42C2511yescharacteristic
1298C23—21no—
1299C23—41no—
1300C23—41no—
1301C23—82no—
1302C23—161no—
1303C23—161no—
1304C23C2×#12111yescharacteristic
1305C23C2×#12111yescharacteristic
1306C23C2×#12111yescharacteristic
1307Q8—21no—
1308Q8—21no—
1309Q8—21no—
1310Q8—21no—
1311Q8—21no—
1312Q8—41no—
1313Q8—42no—
1314Q8—42no—
1315Q8—41no—
1316Q8—41no—
1317Q8—41no—
1318Q8—41no—
1319Q8—41no—
1320Q8—41no—
1321Q8—41no—
1322Q8—41no—
1323Q8—81no—
1324Q8—81no—
1325Q8—81no—
1326Q8—82no—
1327Q8#57712yes—
1328D4—21no—
1329D4—21no—
1330D4—41no—
1331D4—41no—
1332D4—41no—
1333D4—42no—
1334D4—42no—
1335D4—41no—
1336D4—41no—
1337D4—41no—
1338D4—41no—
1339D4—41no—
1340D4—41no—
1341D4—41no—
1342D4—41no—
1343D4—81no—
1344D4—81no—
1345D4—82no—
1346D4—81no—
1347D4—161no—
1348D4—161no—
1349D4—161no—
1350D4—161no—
1351D4—161no—
1352D4—161no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—42no—
1376C2×C4—42no—
1377C2×C4—42no—
1378C2×C4—42no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—81no—
1388C2×C4—81no—
1389C2×C4—82no—
1390C2×C4—161no—
1391C2×C4—161no—
1392C2×C4—161no—
1393C2×C4—161no—
1394C2×C4C2×#12111yescharacteristic
1395C2×C4C2×#12111yescharacteristic
1396C2×C4C2×#12111yescharacteristic
1397C2×C4C2×#12111yescharacteristic
1398C2×C4C2×#12111yescharacteristic
1399C2×C4C2×#12111yescharacteristic
1400C2×C4C2×#12111yescharacteristic
1401C2×C4C2×#12111yescharacteristic
1402C2×C4C2×#12111yescharacteristic
1403C2×C4C23×D411yescharacteristic
1404C2×C4C23×D411yescharacteristic
1405C2×C4C22×#4111yescharacteristic
1406C8—21no—
1407C8—21no—
1408C8—21no—
1409C8—21no—
1410C8—21no—
1411C8—21no—
1412C8—21no—
1413C8—21no—
1414C8—41no—
1415C8—41no—
1416C8—41no—
1417C8—41no—
1418C8—41no—
1419C8—41no—
1420C8—41no—
1421C8—41no—
1422C8—41no—
1423C8—41no—
1424C8—41no—
1425C8—41no—
1426C22—21no—
1427C22—21no—
1428C22—21no—
1429C22—21no—
1430C22—21no—
1431C22—21no—
1432C22—21no—
1433C22—21no—
1434C22—21no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—81no—
1442C22—81no—
1443C22—81no—
1444C22—322no—
1445C22C22×#12111yescharacteristic
1446C4—21no—
1447C4—21no—
1448C4—21no—
1449C4—21no—
1450C4—21no—
1451C4—21no—
1452C4—22no—
1453C4—21no—
1454C4—21no—
1455C4—21no—
1456C4—21no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—81no—
1464C4—81no—
1465C4—81no—
1466C4—81no—
1467C4—81no—
1468C4—81no—
1469C4C2×#57711yescharacteristic
1470C4#358411yescharacteristic
1471C4#358411yescharacteristic
1472C4#358611yescharacteristic
1473C2—41no—
1474C2—41no—
1475C2—41no—
1476C2—81no—
1477C2—161no—
1478C2—161no—
1479C2#6043311yescharacteristic
1480C2#6045711yescharacteristic
1481C2#6046911yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#61997C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62544C2semidirect
2. #62130C2semidirect
4. #60335C2semidirect
5. #19586C2semidirect
6. #19577C2semidirect
7. #19544C2semidirect
8. #19541C2semidirect
9. #19533C2semidirect
10. #19520C2semidirect
11. #19479C2semidirect
12. #19472C2semidirect
13. #19418C2semidirect
14. #19409C2semidirect
15. #19403C2semidirect
16. #19400C2semidirect
17. #19382C2semidirect
18. #19375C2semidirect
19. #19366C2semidirect
20. #19324C2semidirect
21. #19308C2semidirect
22. #19260C2semidirect
23. #19246C2semidirect
24. #19242C2semidirect
25. #19218C2semidirect
26. #19185C2semidirect
27. #19176C2semidirect
28. #19123C2semidirect
29. #17841C2semidirect
30. #17778C2semidirect
31. #17771C2semidirect
60. #3252C22semidirect
64. #3248C22semidirect
65. #3238C22semidirect
67. #3233C22semidirect
84. #3113C22semidirect
86. #3104C22semidirect
89. #3078C22semidirect
91. C2×#477C22semidirect
96. #2994C22semidirect
98. #2993C22semidirect
106. #2984C22semidirect
107. #2982C22semidirect
110. #2969C22semidirect
112. #2966C22semidirect
115. Q8×M16C22semidirect
118. C2×C8×Q8C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
122. #1703C22semidirect
127. #1700C22semidirect
128. #1699C22semidirect
135. #1694C22semidirect
136. #1694C22semidirect
137. #1692C22semidirect
138. #1691C22semidirect
139. #1690C22semidirect
140. #1689C22semidirect
143. #1684C22semidirect
144. #1684C22semidirect
145. #1684C22semidirect
146. #1683C22semidirect
151. #1680C22semidirect
152. #1680C22semidirect
153. #1680C22semidirect
154. #1680C22semidirect
155. #1680C22semidirect
156. #1679C22semidirect
167. #1674C22semidirect
168. #1673C22semidirect
169. #1672C22semidirect
170. #1672C22semidirect
171. #1672C22semidirect
172. #1672C22semidirect
173. #1672C22semidirect
174. #1671C22semidirect
175. #1670C22semidirect
176. #1670C22semidirect
183. #1574C22semidirect
184. #1574C22semidirect
186. #1572C22semidirect
188. #1570C22semidirect
190. #1569C22semidirect
191. #1566C22semidirect
193. #1565C22semidirect
194. #1564C22semidirect
195. #1561C22semidirect
197. #1559C22semidirect
202. #1554C22semidirect
208. #1550C22semidirect
209. #1548C22semidirect
210. #1548C22semidirect
213. #1544C22semidirect
215. #1542C22semidirect

Maximal subgroups

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

subgroupindex
#625442
#621302
#619972
#603352
#195862
#195772
#195442
#195412
#195332
#195202
#194792
#194722
#194182
#194092
#194032
#194002
#193822
#193752
#193662
#193242
#193082
#192602
#192462
#192422
#192182
#191852
#191762
#191232
#178412
#177782
#177712