Finite Group Databasebeta

← #6356179

Subgroups — #6356179

Order 512.

1582 conjugacy classes of subgroups.

The subgroup lattice has 1499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62544C211yesmaximal, characteristic, complemented
2#60594C211yesmaximal, characteristic, complemented
3#60593C211yesmaximal, characteristic
4#60343C211yesmaximal, characteristic, complemented
5#19489C211yesmaximal, characteristic, complemented
6#19487C211yesmaximal, characteristic, complemented
7#19483C211yesmaximal, characteristic, complemented
8#19481C211yesmaximal, characteristic, complemented
9#19478C211yesmaximal, characteristic, complemented
10#19474C211yesmaximal, characteristic, complemented
11#19472C211yesmaximal, characteristic, complemented
12#19468C211yesmaximal, characteristic, complemented
13#19442C211yesmaximal, characteristic, complemented
14#19436C211yesmaximal, characteristic, complemented
15#19419C211yesmaximal, characteristic, complemented
16#19413C211yesmaximal, characteristic, complemented
17#19319C211yesmaximal, characteristic, complemented
18#19316C211yesmaximal, characteristic, complemented
19#19311C211yesmaximal, characteristic, complemented
20#19309C211yesmaximal, characteristic, complemented
21#19288C211yesmaximal, characteristic, complemented
22#19278C211yesmaximal, characteristic, complemented
23#19181C211yesmaximal, characteristic, complemented
24#19179C211yesmaximal, characteristic, complemented
25#19177C211yesmaximal, characteristic, complemented
26#19174C211yesmaximal, characteristic, complemented
27#19155C211yesmaximal, characteristic, complemented
28#19127C211yesmaximal, characteristic, complemented
29#17833C211yesmaximal, characteristic, complemented
30#17767C211yesmaximal, characteristic, complemented
31#17766C211yesmaximal, characteristic, complemented
32#3509C2211yescharacteristic
33#3508C2211yescharacteristic
34C4×2−1+4C2211yescharacteristic
35#3371—21no—
36#3371—21no—
37#3323—21no—
38#3323—21no—
39#3317—21no—
40#3317—21no—
41#3311—21no—
42#3311—21no—
43#3231C2211yescharacteristic
44#3228C2211yescharacteristic
45#3227C2211yescharacteristic
46#3210C2211yescharacteristic
47#3210C2211yescharacteristic
48#3208C2211yescharacteristic
49#3185C2211yescharacteristic
50#3182C2211yescharacteristic
51#3167C2211yescharacteristic
52#3141C2211yescharacteristic
53#3138C2211yescharacteristic
54#3131C2211yescharacteristic
55#3127—21no—
56#3127—21no—
57#3126—21no—
58#3126—21no—
59#3120—21no—
60#3120—21no—
61#3119—21no—
62#3119—21no—
63#3116C2211yescharacteristic
64#3116C2211yescharacteristic, complemented
65#3115C2211yescharacteristic
66#3115C2211yescharacteristic
67#3113C2211yescharacteristic
68#3113C2211yescharacteristic, complemented
69#3112C2211yescharacteristic
70#3112C2211yescharacteristic
71#3107C2211yescharacteristic
72#3107C2211yescharacteristic, complemented
73#3106C2211yescharacteristic
74#3106C2211yescharacteristic
75#3104C2211yescharacteristic
76#3104C2211yescharacteristic, complemented
77#3103C2211yescharacteristic
78#3103C2211yescharacteristic
79#3097—21no—
80#3096—21no—
81#3078C2211yescharacteristic
82#3078C2211yescharacteristic, complemented
83#3076C2211yescharacteristic
84#3076C2211yescharacteristic, complemented
85#3039C2211yescharacteristic, complemented
86#3038C2211yescharacteristic
87C2×#462C2211yescharacteristic, complemented
88C2×#460C2211yescharacteristic
89#3011—21no—
90#3010—21no—
91#2990—21no—
92#2990—21no—
93#2990C2211yescharacteristic
94#2990C2211yescharacteristic, complemented
95#2989—21no—
96#2989C2211yescharacteristic
97#2988C2211yescharacteristic, complemented
98#2984C2211yescharacteristic
99#2984C2211yescharacteristic, complemented
100#2983—21no—
101#2983C2211yescharacteristic, complemented
102#2970—21no—
103#2970—21no—
104#2970C2211yescharacteristic
105#2970C2211yescharacteristic, complemented
106#2965—21no—
107#2965C2211yescharacteristic
108C8×#41C2211yescharacteristic, complemented
109Q8×M16C2211yescharacteristic
110Q8×M16C2211yescharacteristic, complemented
111C2×#446—21no—
112C2×#446C2211yescharacteristic, complemented
113#2950—21no—
114#2949—21no—
115#2947—21no—
116#2946—21no—
117#2925C2211yescharacteristic
118#2925C2211yescharacteristic
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1704C2211yescharacteristic, complemented
122#1704C2211yescharacteristic, complemented
123#1702C2211yescharacteristic
124#1702C2211yescharacteristic
125#1702C2211yescharacteristic
126#1702C2211yescharacteristic
127#1702C2211yescharacteristic
128#1702C2211yescharacteristic
129#1702C2211yescharacteristic
130#1702C2211yescharacteristic
131#1700C2211yescharacteristic, complemented
132#1700C2211yescharacteristic, complemented
133#1700C2211yescharacteristic, complemented
134#1700C2211yescharacteristic, complemented
135#1698C2211yescharacteristic
136#1698C2211yescharacteristic
137#1698C2211yescharacteristic
138#1698C2211yescharacteristic
139#1696C2211yescharacteristic, complemented
140#1696C2211yescharacteristic, complemented
141#1692C2211yescharacteristic, complemented
142#1692C2211yescharacteristic, complemented
143#1692C2211yescharacteristic, complemented
144#1692C2211yescharacteristic, complemented
145#1690C2211yescharacteristic, complemented
146#1690C2211yescharacteristic, complemented
147#1686C2211yescharacteristic
148#1686C2211yescharacteristic
149#1686C2211yescharacteristic
150#1686C2211yescharacteristic
151#1684C2211yescharacteristic, complemented
152#1684C2211yescharacteristic, complemented
153#1683C2211yescharacteristic, complemented
154#1683C2211yescharacteristic, complemented
155#1682C2211yescharacteristic
156#1682C2211yescharacteristic
157#1682C2211yescharacteristic
158#1682C2211yescharacteristic
159#1681C2211yescharacteristic
160#1681C2211yescharacteristic
161#1681C2211yescharacteristic
162#1681C2211yescharacteristic
163#1680C2211yescharacteristic, complemented
164#1680C2211yescharacteristic, complemented
165#1679C2211yescharacteristic, complemented
166#1679C2211yescharacteristic, complemented
167#1678C2211yescharacteristic
168#1678C2211yescharacteristic
169#1677C2211yescharacteristic
170#1677C2211yescharacteristic
171#1676C2211yescharacteristic, complemented
172#1675C2211yescharacteristic, complemented
173#1672C2211yescharacteristic, complemented
174#1672C2211yescharacteristic, complemented
175#1671C2211yescharacteristic, complemented
176#1671C2211yescharacteristic, complemented
177#1670C2211yescharacteristic, complemented
178#1669C2211yescharacteristic, complemented
179#1666C2211yescharacteristic
180#1666C2211yescharacteristic
181#1665C2211yescharacteristic
182#1665C2211yescharacteristic
183#1574C2211yescharacteristic
184#1574C2211yescharacteristic, complemented
185#1573C2211yescharacteristic
186#1573C2211yescharacteristic, complemented
187#1572C2211yescharacteristic, complemented
188#1572C2211yescharacteristic, complemented
189#1569C2211yescharacteristic
190#1569C2211yescharacteristic, complemented
191#1568C2211yescharacteristic, complemented
192#1565C2211yescharacteristic
193#1565C2211yescharacteristic, complemented
194#1564C2211yescharacteristic, complemented
195#1561C2211yescharacteristic
196#1560C2211yescharacteristic
197#1559C2211yescharacteristic
198#1559C2211yescharacteristic
199#1559C2211yescharacteristic, complemented
200#1557C2211yescharacteristic
201#1556C2211yescharacteristic, complemented
202#1555C2211yescharacteristic
203#1554C2211yescharacteristic
204#1554C2211yescharacteristic, complemented
205#1554C2211yescharacteristic, complemented
206#1553C2211yescharacteristic
207#1552C2211yescharacteristic
208#1552C2211yescharacteristic, complemented
209#1551C2211yescharacteristic
210#1551C2211yescharacteristic
211#1550C2211yescharacteristic
212#1549C2211yescharacteristic, complemented
213#1547C2211yescharacteristic
214#1545C2211yescharacteristic
215#1544C2211yescharacteristic, complemented
216#1543C2211yescharacteristic
217#1542C2211yescharacteristic, complemented
218#1540C2211yescharacteristic
219C2×2−1+4D411yescharacteristic
220C2×#137—21no—
221C2×AGL(1,ℤ/8)—21no—
222C22×Q16—21no—
223C22×SD16—21no—
224#559—21no—
225#559—21no—
226#557—21no—
227#557—21no—
228#556—21no—
229#556—21no—
230#552—21no—
231#552—21no—
232#552—21no—
233#552—21no—
234#550—21no—
235#550—21no—
236#546—21no—
237#546—21no—
238#546—21no—
239#546—21no—
240#541—21no—
241#541—21no—
242#540—21no—
243#540—21no—
244#536—21no—
245#535—21no—
246#533C2311yescharacteristic
247#533C2311yescharacteristic
248#533C2311yescharacteristic
249#533C2311yescharacteristic
250#533C2311yescharacteristic
251#533C2311yescharacteristic
252#532C2311yescharacteristic
253#532C2311yescharacteristic
254#532C2311yescharacteristic
255#532C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×#127C2311yescharacteristic
258#520—21no—
259#520—21no—
260#520—21no—
261#520D411yescharacteristic
262#520D411yescharacteristic
263#520D411yescharacteristic
264#520D411yescharacteristic
265#519—21no—
266#519—21no—
267#519D411yescharacteristic
268#519D411yescharacteristic
269#519D411yescharacteristic
270#518—21no—
271C4×#41—21no—
272C4×#41—21no—
273C4×#41—21no—
274C4×#41C2311yescharacteristic
275C4×#41C2311yescharacteristic
276C4×#41C2311yescharacteristic
277C4×#41C2311yescharacteristic
278C2×C4×Q8—21no—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282#500C2311yescharacteristic
283#498C2311yescharacteristic
284#498C2311yescharacteristic
285#494C2311yescharacteristic
286#492C2311yescharacteristic
287#492C2311yescharacteristic
288#490—21no—
289#490—21no—
290#489—21no—
291#489—21no—
292#488—21no—
293#488—21no—
294#487C2311yescharacteristic
295#487C2311yescharacteristic
296#487C2311yescharacteristic
297#487C2311yescharacteristic
298#486C2311yescharacteristic
299#486C2311yescharacteristic
300#486C2311yescharacteristic
301#486C2311yescharacteristic
302#486C2311yescharacteristic
303#486C2311yescharacteristic
304#485—21no—
305#485—21no—
306#485—21no—
307#485—21no—
308#485—21no—
309#485—21no—
310#484—21no—
311#484—21no—
312#483—21no—
313#483—21no—
314#482—21no—
315#482—21no—
316#482—21no—
317#482—21no—
318#482—21no—
319#482—21no—
320#481—21no—
321#481—21no—
322#481—21no—
323#481—21no—
324#480—21no—
325#480—21no—
326#479—21no—
327#479—21no—
328#479—21no—
329#479—21no—
330#479—21no—
331#479—21no—
332#479—21no—
333#479—21no—
334#478—21no—
335#478—21no—
336#478—21no—
337#478—21no—
338#477C2311yescharacteristic
339#477C2311yescharacteristic
340#477C2311yescharacteristic
341#477C2311yescharacteristic
342#477C2311yescharacteristic
343#477C2311yescharacteristic
344#476—21no—
345#476—21no—
346#476C2311yescharacteristic
347#476C2311yescharacteristic
348#475C2311yescharacteristic
349#475C2311yescharacteristic
350#475C2311yescharacteristic
351#475C2311yescharacteristic
352#475C2311yescharacteristic
353#475C2311yescharacteristic
354#474C2311yescharacteristic
355#474C2311yescharacteristic
356#470—21no—
357#470—21no—
358#468—21no—
359#468—21no—
360#465—21no—
361#465—21no—
362#464—21no—
363#464—21no—
364#464—21no—
365#464—21no—
366#462—21no—
367#462—21no—
368#462—21no—
369#462C2311yescharacteristic
370#462C2311yescharacteristic
371#462C2311yescharacteristic
372#462C2311yescharacteristic
373#462C2311yescharacteristic
374#462C2311yescharacteristic
375#461—21no—
376#461C2311yescharacteristic
377#461C2311yescharacteristic
378#460—21no—
379#460—21no—
380#460—21no—
381#460—21no—
382#460—21no—
383#460C2311yescharacteristic
384#460C2311yescharacteristic
385#460C2311yescharacteristic
386#460C2311yescharacteristic
387#460C2311yescharacteristic
388#460C2311yescharacteristic
389#459—21no—
390#459C2311yescharacteristic
391#459C2311yescharacteristic
392#452—21no—
393#452—21no—
394#452—21no—
395#452—21no—
396#452—21no—
397#452—21no—
398#452—21no—
399#452—21no—
400#451—21no—
401#451—21no—
402#451—21no—
403#451—21no—
404#450—21no—
405#450—21no—
406#449—21no—
407#449—21no—
408#449—21no—
409#449—21no—
410#448—21no—
411#448—21no—
412#448—21no—
413#448—21no—
414#446—21no—
415#446—21no—
416#446—21no—
417#446—21no—
418#446—21no—
419#446—21no—
420#446—21no—
421#446—21no—
422#446—21no—
423#446—21no—
424#446—21no—
425#446—21no—
426#446—21no—
427#446D411yescharacteristic
428#446D411yescharacteristic
429#446C2311yescharacteristic
430#446C2311yescharacteristic
431#446C2311yescharacteristic
432#446C2311yescharacteristic
433#446C2311yescharacteristic
434#446C2311yescharacteristic
435#446C2311yescharacteristic
436#446C2311yescharacteristic
437C8×Q8C2311yescharacteristic
438C8×Q8C2311yescharacteristic
439C8×Q8C2311yescharacteristic
440C8×Q8C2311yescharacteristic
441#442—21no—
442#442—21no—
443#441—21no—
444#441—21no—
445#441—21no—
446#441—21no—
447#441—21no—
448#441—21no—
449#441—21no—
450#441—21no—
451#440—21no—
452#440—21no—
453#440—21no—
454#440—21no—
455#440—21no—
456#440—21no—
457#440—21no—
458#440—21no—
459#440—21no—
460#440—21no—
461C4×Q16—21no—
462C4×Q16—21no—
463C4×Q16—21no—
464C4×Q16—21no—
465C4×Q16—21no—
466C4×Q16—21no—
467C4×SD16—21no—
468C4×SD16—21no—
469C4×SD16—21no—
470C4×SD16—21no—
471C4×SD16—21no—
472C4×SD16—21no—
473C4×SD16—21no—
474C4×SD16—21no—
475C4×SD16—21no—
476C4×SD16—21no—
477C4×D8—21no—
478C4×D8—21no—
479#436—21no—
480#436D411yescharacteristic
481#436D411yescharacteristic
482#435—21no—
483#435—21no—
484#435—21no—
485#435—21no—
486#435—21no—
487#435—21no—
488#435—21no—
489#435—21no—
490#435—21no—
491#435—21no—
492#435D411yescharacteristic
493#435D411yescharacteristic
494#435D411yescharacteristic
495#435D411yescharacteristic
496C8×D4—21no—
497C8×D4—21no—
498C8×D4—21no—
499C8×D4—21no—
500C8×D4C2311yescharacteristic
501C8×D4C2311yescharacteristic
502C8×D4C2311yescharacteristic
503C8×D4C2311yescharacteristic
504#433—21no—
505#433—21no—
506#433—21no—
507#433—21no—
508#432—21no—
509#432—21no—
510#432—21no—
511#432—21no—
512#432—21no—
513#432—21no—
514#432—21no—
515#432—21no—
516#432C2311yescharacteristic
517#432C2311yescharacteristic
518#432C2311yescharacteristic
519#432C2311yescharacteristic
520#432C2311yescharacteristic
521#432C2311yescharacteristic
522#431—21no—
523#431—21no—
524#431—21no—
525#431—21no—
526#431C2311yescharacteristic
527#431C2311yescharacteristic
528#431C2311yescharacteristic
529#431C2311yescharacteristic
530#431C2311yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#428—21no—
535#428—21no—
536#427—21no—
537#427—21no—
538#423—21no—
539#423—21no—
540#423C2311yescharacteristic
541#423C2311yescharacteristic
542#423C2311yescharacteristic
543#423C2311yescharacteristic
544C2×C4⋊C8—21no—
545C2×C4⋊C8—21no—
546C2×C4⋊C8—21no—
547C2×C4⋊C8—21no—
548C2×C4⋊C8C2311yescharacteristic
549C2×C4⋊C8C2311yescharacteristic
550C2×C4⋊C8C2311yescharacteristic
551#419—21no—
552#419—21no—
553#419—21no—
554#418—21no—
555#418—21no—
556#418—21no—
557#417—21no—
558#417—21no—
559#416—21no—
560#416—21no—
561#416—21no—
562#416—21no—
563C2×#103—21no—
564C2×#102—21no—
565#408—21no—
566#408—21no—
567#405—21no—
568#405—21no—
569C4×M16—21no—
570C4×M16—21no—
571C4×M16C2311yescharacteristic
572C4×M16C2311yescharacteristic
573C2×#97—21no—
574C2×#97—21no—
575C2×#97—21no—
576C2×C4×C8—21no—
577C2×C4×C8C2311yescharacteristic
578#335C2311yescharacteristic
579#335C2311yescharacteristic
580#335C2311yescharacteristic
581#335C2311yescharacteristic
582#335C2311yescharacteristic
583#335C2311yescharacteristic
584#335C2311yescharacteristic
585#335C2311yescharacteristic
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
6262−1+4—42no—
6272−1+4—42no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—21no—
632C2×#41—21no—
633C2×#41—21no—
634C2×#41—21no—
635C2×#41C2×D411yescharacteristic
636C2×#41C2×D411yescharacteristic
637C2×#41C2×D411yescharacteristic
638C2×#41C2×D411yescharacteristic
639C22×Q8—21no—
640C22×Q8—21no—
641C22×Q8C2×D411yescharacteristic
642C22×Q8C2×D411yescharacteristic
643C22×Q8C2×D411yescharacteristic
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647#137—44no—
648AGL(1,ℤ/8)—44no—
649C2×Q16—21no—
650C2×Q16—21no—
651C2×Q16—21no—
652C2×Q16—21no—
653C2×Q16—21no—
654C2×Q16—21no—
655C2×Q16—21no—
656C2×Q16—21no—
657C2×Q16—44no—
658C2×SD16—21no—
659C2×SD16—21no—
660C2×SD16—21no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×SD16—21no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—21no—
668C2×SD16—21no—
669C2×SD16—21no—
670C2×SD16—44no—
671C2×D8—21no—
672C2×D8—21no—
673C2×M16—21no—
674C2×M16—21no—
675C2×M16—21no—
676C2×M16—21no—
677C2×M16C2×D411yescharacteristic
678C2×M16C2×D411yescharacteristic
679C2×M16C2×D411yescharacteristic
680C2×M16C2×D411yescharacteristic
681C22×C8—21no—
682C22×C8—21no—
683C22×C8—21no—
684C22×C8—21no—
685C22×C8—21no—
686C22×C8—21no—
687C22×C8—21no—
688C22×C8C2×D411yescharacteristic
689C22×C8C2×D411yescharacteristic
690C4⋊Q8—21no—
691C4⋊Q8—21no—
692C4⋊Q8—21no—
693C4⋊Q8—41no—
694C4⋊Q8C2411yescharacteristic
695C4⋊Q8C2411yescharacteristic
696C4⋊Q8C2411yescharacteristic
697C4⋊Q8C2411yescharacteristic
698C4⋊Q8C2411yescharacteristic
699C4⋊Q8C2411yescharacteristic
700#127—21no—
701#127—21no—
702#127—21no—
703#127—41no—
704#127C2411yescharacteristic
705#127C2411yescharacteristic
706#126—41no—
707#126—41no—
708#126—41no—
709#126—41no—
710#125—21no—
711#125—21no—
712#125—21no—
713#125—21no—
714#125—21no—
715#125—21no—
716#125—41no—
717#125—41no—
718#125—41no—
719#125—41no—
720#124—21no—
721#124—21no—
722#124—21no—
723#124—21no—
724#124—41no—
725#124—41no—
726#123—41no—
727#123—41no—
728#123—41no—
729#123—41no—
730#123—41no—
731#123—41no—
732C22⋊Q8—21no—
733C22⋊Q8—21no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744#121—21no—
745#121—21no—
746#121—21no—
747#121—21no—
748#121—21no—
749#121—21no—
750#121—21no—
751#121—21no—
752#121—41no—
753#121—41no—
754#121—41no—
755#121—41no—
756#120—41no—
757#120—41no—
758C4×Q8—21no—
759C4×Q8—21no—
760C4×Q8—21no—
761C4×Q8—21no—
762C4×Q8—21no—
763C4×Q8—21no—
764C4×Q8—21no—
765C4×Q8—21no—
766C4×Q8—21no—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—21no—
770C4×Q8—21no—
771C4×Q8—21no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8—21no—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—21no—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8—21no—
783C4×Q8—41no—
784C4×Q8—41no—
785C4×Q8C2×D411yescharacteristic
786C4×Q8C2×D411yescharacteristic
787C4×Q8C2×D411yescharacteristic
788C4×Q8C2×D411yescharacteristic
789C4×Q8C2×D411yescharacteristic
790C4×Q8C2×D411yescharacteristic
791C4×Q8C2×D411yescharacteristic
792C4×Q8C2×D411yescharacteristic
793C4×Q8C2×D411yescharacteristic
794C4×Q8C2×D411yescharacteristic
795C4×Q8#4111yescharacteristic
796C4×Q8C2411yescharacteristic
797C4×Q8C2411yescharacteristic
798C4×Q8C2411yescharacteristic
799C4×D4—21no—
800C4×D4—21no—
801C4×D4—21no—
802C4×D4—21no—
803C4×D4—21no—
804C4×D4—21no—
805C4×D4—21no—
806C4×D4—21no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—21no—
810C4×D4—21no—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—21no—
820C4×D4—21no—
821C4×D4—21no—
822C4×D4—41no—
823C4×D4—41no—
824C4×D4C2×D411yescharacteristic
825C4×D4C2×D411yescharacteristic
826C4×D4C2×D411yescharacteristic
827C4×D4C2×D411yescharacteristic
828C4×D4C2×D411yescharacteristic
829C4×D4C2×D411yescharacteristic
830C4×D4#4111yescharacteristic
831C4×D4#4111yescharacteristic
832C4×D4#4111yescharacteristic
833C4×D4C2411yescharacteristic
834#117—21no—
835#117—21no—
836#117—21no—
837#117—21no—
838#117—21no—
839#117—21no—
840#117—21no—
841#117—21no—
842#117—21no—
843#117—21no—
844#117—21no—
845#117—21no—
846#117—21no—
847#117—21no—
848#117—21no—
849#117—21no—
850#117—21no—
851#117—21no—
852#117—41no—
853#117—41no—
854#117C2×D411yescharacteristic
855#117C2×D411yescharacteristic
856#117C2×D411yescharacteristic
857#117C2×D411yescharacteristic
858#117C2×D411yescharacteristic
859#117C2×D411yescharacteristic
860C2×C4⋊C4—21no—
861C2×C4⋊C4—21no—
862C2×C4⋊C4—21no—
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—21no—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—21no—
868C2×C4⋊C4C2×D411yescharacteristic
869C2×C4⋊C4C2×D411yescharacteristic
870C2×C4⋊C4C2×D411yescharacteristic
871C2×C22⋊C4—41no—
872C2×C22⋊C4—41no—
873C2×C42—21no—
874C2×C42—21no—
875C2×C42—21no—
876C2×C42—21no—
877C2×C42—21no—
878C2×C42—21no—
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
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#107—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—
903#106—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⋊C8C2×D411yescharacteristic
924C4⋊C8C2×D411yescharacteristic
925C4⋊C8C2×D411yescharacteristic
926C4⋊C8C2×D411yescharacteristic
927C4⋊C8C2×D411yescharacteristic
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2411yescharacteristic
930C4⋊C8C2411yescharacteristic
931C4⋊C8C2411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
934C4⋊C8C2411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941#103—21no—
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#102—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—
993C22⋊C8—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⋊C8—21no—
1008C22⋊C8C2×D411yescharacteristic
1009C22⋊C8C2×D411yescharacteristic
1010C22⋊C8C2×D411yescharacteristic
1011C22⋊C8C2×D411yescharacteristic
1012C22⋊C8C2×D411yescharacteristic
1013C22⋊C8C2×D411yescharacteristic
1014#97—21no—
1015#97—21no—
1016#97—21no—
1017#97—21no—
1018#97—21no—
1019#97—21no—
1020#97—21no—
1021#97—21no—
1022#97—21no—
1023#97—21no—
1024#97—21no—
1025#97—21no—
1026#97—21no—
1027#97—21no—
1028#97C2×D411yescharacteristic
1029#97C2×D411yescharacteristic
1030#97C2×D411yescharacteristic
1031#97C2×D411yescharacteristic
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8—21no—
1037C4×C8—21no—
1038C4×C8—21no—
1039C4×C8—21no—
1040C4×C8—21no—
1041C4×C8C2×D411yescharacteristic
1042C4×C8C2×D411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C4×C8C2411yescharacteristic
1045C4×C8C2411yescharacteristic
1046C4×C8C2411yescharacteristic
1047C24—41no—
1048#41—22no—
1049#41—22no—
1050#41—22no—
1051#41—22no—
1052#41—41no—
1053#41—41no—
1054#41—41no—
1055#41—41no—
1056#41—44no—
1057#41—44no—
1058#41—44no—
1059#41—81no—
1060#41—81no—
1061#41—81no—
1062#41—81no—
1063#41—161no—
1064#41—161no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—21no—
1071C2×Q8—21no—
1072C2×Q8—21no—
1073C2×Q8—21no—
1074C2×Q8—21no—
1075C2×Q8—21no—
1076C2×Q8—41no—
1077C2×Q8—41no—
1078C2×Q8—41no—
1079C2×Q8—41no—
1080C2×Q8—44no—
1081C2×Q8—42no—
1082C2×Q8—42no—
1083C2×Q8—41no—
1084C2×Q8#12111yescharacteristic
1085C2×Q8C22×D411yescharacteristic
1086C2×Q8C22×D411yescharacteristic
1087C2×Q8C22×D411yescharacteristic
1088C2×D4—21no—
1089C2×D4—21no—
1090C2×D4—21no—
1091C2×D4—21no—
1092C2×D4—21no—
1093C2×D4—21no—
1094C2×D4—21no—
1095C2×D4—21no—
1096C2×D4—21no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—41no—
1100C2×D4—41no—
1101C2×D4—41no—
1102C2×D4—41no—
1103C2×D4—41no—
1104C2×D4—41no—
1105C2×D4—41no—
1106C2×D4—81no—
1107C2×D4—81no—
1108C2×D4—161no—
1109C2×D4#12111yescharacteristic
1110C2×D4#12111yescharacteristic
1111C2×D4#12111yescharacteristic
1112C2×D4C22×D411yescharacteristic
1113C22×C4—21no—
1114C22×C4—21no—
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—21no—
1124C22×C4—21no—
1125C22×C4—21no—
1126C22×C4—41no—
1127C22×C4—41no—
1128C22×C4—41no—
1129C22×C4—41no—
1130C22×C4—41no—
1131C22×C4C22×D411yescharacteristic
1132C22×C4C22×D411yescharacteristic
1133C22×C4C22×D411yescharacteristic
1134C22×C4C22×D411yescharacteristic
1135C22×C4C22×D411yescharacteristic
1136C22×C4C22×D411yescharacteristic
1137C22×C4C2×#4111yescharacteristic
1138C22×C4C2×#4111yescharacteristic
1139C22×C4C2×#4111yescharacteristic
1140Q16—42no—
1141Q16—42no—
1142Q16—42no—
1143Q16—42no—
1144Q16—42no—
1145Q16—42no—
1146Q16—81no—
1147Q16—81no—
1148SD16—42no—
1149SD16—42no—
1150SD16—42no—
1151SD16—42no—
1152SD16—42no—
1153SD16—42no—
1154SD16—42no—
1155SD16—42no—
1156SD16—81no—
1157SD16—81no—
1158SD16—81no—
1159SD16—81no—
1160D8—42no—
1161D8—42no—
1162M16—41no—
1163M16—41no—
1164M16—41no—
1165M16—41no—
1166M16—42no—
1167M16—42no—
1168M16—81no—
1169M16—81no—
1170C2×C8—21no—
1171C2×C8—21no—
1172C2×C8—21no—
1173C2×C8—21no—
1174C2×C8—21no—
1175C2×C8—21no—
1176C2×C8—21no—
1177C2×C8—21no—
1178C2×C8—21no—
1179C2×C8—21no—
1180C2×C8—21no—
1181C2×C8—21no—
1182C2×C8—41no—
1183C2×C8—41no—
1184C2×C8—42no—
1185C2×C8—42no—
1186C2×C8—42no—
1187C2×C8—81no—
1188C2×C8—81no—
1189C2×C8—81no—
1190C2×C8—81no—
1191C2×C8C22×D411yescharacteristic
1192C2×C8C22×D411yescharacteristic
1193C2×C8C22×D411yescharacteristic
1194C2×C8C22×D411yescharacteristic
1195C2×C8C22×D411yescharacteristic
1196C2×C8C22×D411yescharacteristic
1197C2×C8C22×D411yescharacteristic
1198C2×C8C22×D411yescharacteristic
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—21no—
1217C4⋊C4—21no—
1218C4⋊C4—21no—
1219C4⋊C4—21no—
1220C4⋊C4—21no—
1221C4⋊C4—21no—
1222C4⋊C4—21no—
1223C4⋊C4—21no—
1224C4⋊C4—21no—
1225C4⋊C4—21no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4#12111yescharacteristic
1241C4⋊C4#12111yescharacteristic
1242C4⋊C4#12111yescharacteristic
1243C4⋊C4#12111yescharacteristic
1244C4⋊C4#12111yescharacteristic
1245C4⋊C4#12111yescharacteristic
1246C4⋊C4C22×D411yescharacteristic
1247C4⋊C4C22×D411yescharacteristic
1248C4⋊C4C22×D411yescharacteristic
1249C4⋊C4C22×D411yescharacteristic
1250C22⋊C4—21no—
1251C22⋊C4—21no—
1252C22⋊C4—21no—
1253C22⋊C4—21no—
1254C22⋊C4—21no—
1255C22⋊C4—21no—
1256C22⋊C4—21no—
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—41no—
1268C22⋊C4—41no—
1269C22⋊C4—41no—
1270C22⋊C4—41no—
1271C22⋊C4#12111yescharacteristic
1272C22⋊C4#12111yescharacteristic
1273C22⋊C4#12111yescharacteristic
1274C22⋊C4#12111yescharacteristic
1275C22⋊C4#12111yescharacteristic
1276C22⋊C4#12111yescharacteristic
1277C42—21no—
1278C42—21no—
1279C42—21no—
1280C42—21no—
1281C42—21no—
1282C42—21no—
1283C42—21no—
1284C42—21no—
1285C42—21no—
1286C42—21no—
1287C42—21no—
1288C42—21no—
1289C42—21no—
1290C42—21no—
1291C42—21no—
1292C42—41no—
1293C42—41no—
1294C42—41no—
1295C42—41no—
1296C42—41no—
1297C42—41no—
1298C42C22×D411yescharacteristic
1299C42C22×D411yescharacteristic
1300C42C22×D411yescharacteristic
1301C42C22×D411yescharacteristic
1302C42C22×D411yescharacteristic
1303C42C22×D411yescharacteristic
1304C42C2×#4111yescharacteristic
1305C42C2×#4111yescharacteristic
1306C42C2×#4111yescharacteristic
1307C42C2511yescharacteristic
1308C23—21no—
1309C23—41no—
1310C23—41no—
1311C23—82no—
1312C23—161no—
1313C23—161no—
1314C23C2×#12111yescharacteristic
1315C23C2×#12111yescharacteristic
1316C23C2×#12111yescharacteristic
1317Q8—21no—
1318Q8—21no—
1319Q8—21no—
1320Q8—21no—
1321Q8—21no—
1322Q8—41no—
1323Q8—42no—
1324Q8—42no—
1325Q8—42no—
1326Q8—41no—
1327Q8—41no—
1328Q8—41no—
1329Q8—41no—
1330Q8—41no—
1331Q8—41no—
1332Q8—41no—
1333Q8—41no—
1334Q8—81no—
1335Q8—81no—
1336Q8—82no—
1337Q8#57512yes—
1338D4—24no—
1339D4—21no—
1340D4—41no—
1341D4—41no—
1342D4—41no—
1343D4—42no—
1344D4—42no—
1345D4—41no—
1346D4—41no—
1347D4—41no—
1348D4—41no—
1349D4—41no—
1350D4—41no—
1351D4—41no—
1352D4—41no—
1353D4—81no—
1354D4—81no—
1355D4—82no—
1356D4—161no—
1357D4—161no—
1358D4—161no—
1359D4—161no—
1360D4—161no—
1361D4—161no—
1362D4#57512yes—
1363C2×C4—24no—
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—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—42no—
1387C2×C4—42no—
1388C2×C4—42no—
1389C2×C4—42no—
1390C2×C4—42no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—81no—
1400C2×C4—81no—
1401C2×C4—81no—
1402C2×C4—81no—
1403C2×C4—81no—
1404C2×C4—81no—
1405C2×C4—82no—
1406C2×C4—161no—
1407C2×C4—161no—
1408C2×C4—161no—
1409C2×C4—161no—
1410C2×C4C2×#12111yescharacteristic
1411C2×C4C2×#12111yescharacteristic
1412C2×C4C2×#12111yescharacteristic
1413C2×C4C2×#12111yescharacteristic
1414C2×C4C2×#12111yescharacteristic
1415C2×C4C2×#12111yescharacteristic
1416C2×C4C2×#12111yescharacteristic
1417C2×C4C2×#12111yescharacteristic
1418C2×C4C2×#12111yescharacteristic
1419C2×C4C23×D411yescharacteristic
1420C2×C4C23×D411yescharacteristic
1421C2×C4C22×#4111yescharacteristic
1422C8—21no—
1423C8—21no—
1424C8—21no—
1425C8—21no—
1426C8—21no—
1427C8—21no—
1428C8—21no—
1429C8—21no—
1430C8—41no—
1431C8—41no—
1432C8—41no—
1433C8—41no—
1434C8—41no—
1435C8—41no—
1436C8—41no—
1437C8—41no—
1438C8—41no—
1439C8—41no—
1440C8—41no—
1441C8—41no—
1442C22—21no—
1443C22—21no—
1444C22—21no—
1445C22—21no—
1446C22—21no—
1447C22—22no—
1448C22—21no—
1449C22—21no—
1450C22—21no—
1451C22—21no—
1452C22—41no—
1453C22—41no—
1454C22—81no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—81no—
1459C22—81no—
1460C22—322no—
1461C22C22×#12111yescharacteristic
1462C4—21no—
1463C4—21no—
1464C4—21no—
1465C4—21no—
1466C4—22no—
1467C4—21no—
1468C4—21no—
1469C4—21no—
1470C4—21no—
1471C4—21no—
1472C4—21no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—41no—
1478C4—41no—
1479C4—81no—
1480C4—81no—
1481C4—81no—
1482C4—81no—
1483C4—81no—
1484C4—81no—
1485C4C2×#57511yescharacteristic
1486C4C2×#57511yescharacteristic
1487C4#358411yescharacteristic
1488C4#358611yescharacteristic
1489C2—41no—
1490C2—41no—
1491C2—41no—
1492C2—42no—
1493C2—161no—
1494C2—161no—
1495C2#6043311yescharacteristic
1496C2#6044411yescharacteristic
1497C2#6047011yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
prime radical#60593C2
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. #60594C2semidirect
4. #60343C2semidirect
5. #19489C2semidirect
6. #19487C2semidirect
7. #19483C2semidirect
8. #19481C2semidirect
9. #19478C2semidirect
10. #19474C2semidirect
11. #19472C2semidirect
12. #19468C2semidirect
13. #19442C2semidirect
14. #19436C2semidirect
15. #19419C2semidirect
16. #19413C2semidirect
17. #19319C2semidirect
18. #19316C2semidirect
19. #19311C2semidirect
20. #19309C2semidirect
21. #19288C2semidirect
22. #19278C2semidirect
23. #19181C2semidirect
24. #19179C2semidirect
25. #19177C2semidirect
26. #19174C2semidirect
27. #19155C2semidirect
28. #19127C2semidirect
29. #17833C2semidirect
30. #17767C2semidirect
31. #17766C2semidirect
64. #3116C22semidirect
68. #3113C22semidirect
72. #3107C22semidirect
76. #3104C22semidirect
82. #3078C22semidirect
84. #3076C22semidirect
85. #3039C22semidirect
87. C2×#462C22semidirect
94. #2990C22semidirect
97. #2988C22semidirect
99. #2984C22semidirect
101. #2983C22semidirect
105. #2970C22semidirect
108. C8×#41C22semidirect
110. Q8×M16C22semidirect
112. C2×#446C22semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1704C22semidirect
122. #1704C22semidirect
131. #1700C22semidirect
132. #1700C22semidirect
133. #1700C22semidirect
134. #1700C22semidirect
139. #1696C22semidirect
140. #1696C22semidirect
141. #1692C22semidirect
142. #1692C22semidirect
143. #1692C22semidirect
144. #1692C22semidirect
145. #1690C22semidirect
146. #1690C22semidirect
151. #1684C22semidirect
152. #1684C22semidirect
153. #1683C22semidirect
154. #1683C22semidirect
163. #1680C22semidirect
164. #1680C22semidirect
165. #1679C22semidirect
166. #1679C22semidirect
171. #1676C22semidirect
172. #1675C22semidirect
173. #1672C22semidirect
174. #1672C22semidirect
175. #1671C22semidirect
176. #1671C22semidirect
177. #1670C22semidirect
178. #1669C22semidirect
184. #1574C22semidirect
186. #1573C22semidirect
187. #1572C22semidirect
188. #1572C22semidirect
190. #1569C22semidirect
191. #1568C22semidirect
193. #1565C22semidirect
194. #1564C22semidirect
199. #1559C22semidirect
201. #1556C22semidirect
204. #1554C22semidirect
205. #1554C22semidirect
208. #1552C22semidirect
212. #1549C22semidirect
215. #1544C22semidirect
217. #1542C22semidirect

Maximal subgroups

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

subgroupindex
#625442
#605942
#605932
#603432
#194892
#194872
#194832
#194812
#194782
#194742
#194722
#194682
#194422
#194362
#194192
#194132
#193192
#193162
#193112
#193092
#192882
#192782
#191812
#191792
#191772
#191742
#191552
#191272
#178332
#177672
#177662