Finite Group Databasebeta

← #6354976

Subgroups — #6354976

Order 512.

1538 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#60961C211yesmaximal, characteristic, complemented
2#60944C211yesmaximal, characteristic, complemented
3#60900C211yesmaximal, characteristic, complemented
4#60292C211yesmaximal, characteristic, complemented
5#19575C211yesmaximal, characteristic, complemented
6#19574C211yesmaximal, characteristic, complemented
7#19569C211yesmaximal, characteristic, complemented
8#19568C211yesmaximal, characteristic, complemented
9#19563C211yesmaximal, characteristic, complemented
10#19562C211yesmaximal, characteristic, complemented
11#19557C211yesmaximal, characteristic, complemented
12#19556C211yesmaximal, characteristic, complemented
13#19499C211yesmaximal, characteristic, complemented
14#19498C211yesmaximal, characteristic, complemented
15#19493C211yesmaximal, characteristic, complemented
16#19492C211yesmaximal, characteristic, complemented
17#19487C211yesmaximal, characteristic, complemented
18#19486C211yesmaximal, characteristic, complemented
19#19481C211yesmaximal, characteristic, complemented
20#19480C211yesmaximal, characteristic, complemented
21#19229C211yesmaximal, characteristic, complemented
22#19229C211yesmaximal, characteristic, complemented
23#19228C211yesmaximal, characteristic, complemented
24#19227C211yesmaximal, characteristic, complemented
25#19223C211yesmaximal, characteristic, complemented
26#19222C211yesmaximal, characteristic, complemented
27#19221C211yesmaximal, characteristic, complemented
28#19221C211yesmaximal, characteristic, complemented
29C2×#1573C211yesmaximal, characteristic, complemented
30#17756C211yesmaximal, characteristic, complemented
31#17719C211yesmaximal, characteristic, complemented
32#3444C2211yescharacteristic
33#3444C2211yescharacteristic
34#3444C2211yescharacteristic
35#3250—21no—
36#3250—21no—
37#3250—21no—
38#3250—21no—
39#3249C2211yescharacteristic
40#3248—21no—
41#3248C2211yescharacteristic
42#3248C2211yescharacteristic
43#3248C2211yescharacteristic
44#3248C2211yescharacteristic
45#3247—21no—
46#3247C2211yescharacteristic
47#3247C2211yescharacteristic
48#3247C2211yescharacteristic
49#3247C2211yescharacteristic
50#3246C2211yescharacteristic
51#3246C2211yescharacteristic
52#3245C2211yescharacteristic
53#3240—21no—
54#3237C2211yescharacteristic
55#3235C2211yescharacteristic
56#3231C2211yescharacteristic
57#3231C2211yescharacteristic
58#3228C2211yescharacteristic
59#3228C2211yescharacteristic
60#3219—21no—
61#3216C2211yescharacteristic
62#3214C2211yescharacteristic
63#3210C2211yescharacteristic
64#3210C2211yescharacteristic
65#3207C2211yescharacteristic
66#3207C2211yescharacteristic
67#3191—21no—
68#3191—21no—
69#3191—21no—
70#3191—21no—
71#3181—21no—
72#3180—21no—
73#3170C2211yescharacteristic
74#3169C2211yescharacteristic
75#3167C2211yescharacteristic
76#3167C2211yescharacteristic
77#3116C2211yescharacteristic
78#3116C2211yescharacteristic
79#3115C2211yescharacteristic
80#3115C2211yescharacteristic
81#3111—21no—
82#3111—21no—
83#3102—21no—
84#3102—21no—
85#3102—21no—
86#3102—21no—
87#3076—21no—
88#3076C2211yescharacteristic
89#3076C2211yescharacteristic
90#3050—21no—
91#3050—21no—
92#3035—21no—
93#3035C2211yescharacteristic
94#3035C2211yescharacteristic
95#2991C2211yescharacteristic
96#2991C2211yescharacteristic
97#2990C2211yescharacteristic
98#2990C2211yescharacteristic
99#2989—21no—
100#2988—21no—
101#2986C2211yescharacteristic
102#2986C2211yescharacteristic
103#2979C2211yescharacteristic
104#2979C2211yescharacteristic
105#2976—21no—
106#2976—21no—
107#2969—21no—
108#2969—21no—
109#2966C2211yescharacteristic
110#2966C2211yescharacteristic
111#2966C2211yescharacteristic
112#2966C2211yescharacteristic
113#2925—21no—
114#2925—21no—
115#2920C2211yescharacteristic
116C2×#432C2211yescharacteristic
117C2×#431C2211yescharacteristic
118C22×C4⋊C8C2211yescharacteristic
119#1704C2211yescharacteristic, complemented
120#1704C2211yescharacteristic, complemented
121#1703C2211yescharacteristic, complemented
122#1703C2211yescharacteristic, complemented
123#1702C2211yescharacteristic, complemented
124#1702C2211yescharacteristic, complemented
125#1701C2211yescharacteristic, complemented
126#1701C2211yescharacteristic, complemented
127#1700C2211yescharacteristic, complemented
128#1700C2211yescharacteristic, complemented
129#1699C2211yescharacteristic, complemented
130#1699C2211yescharacteristic, complemented
131#1698C2211yescharacteristic, complemented
132#1698C2211yescharacteristic, complemented
133#1697C2211yescharacteristic, complemented
134#1697C2211yescharacteristic, complemented
135#1696C2211yescharacteristic, complemented
136#1695C2211yescharacteristic, complemented
137#1694C2211yescharacteristic, complemented
138#1693C2211yescharacteristic, complemented
139#1692C2211yescharacteristic, complemented
140#1692C2211yescharacteristic, complemented
141#1691C2211yescharacteristic, complemented
142#1691C2211yescharacteristic, complemented
143#1690C2211yescharacteristic, complemented
144#1689C2211yescharacteristic, complemented
145#1688C2211yescharacteristic, complemented
146#1687C2211yescharacteristic, complemented
147#1686C2211yescharacteristic, complemented
148#1686C2211yescharacteristic, complemented
149#1685C2211yescharacteristic, complemented
150#1685C2211yescharacteristic, complemented
151#1684C2211yescharacteristic, complemented
152#1684C2211yescharacteristic, complemented
153#1683C2211yescharacteristic, complemented
154#1683C2211yescharacteristic, complemented
155#1682C2211yescharacteristic, complemented
156#1682C2211yescharacteristic, complemented
157#1681C2211yescharacteristic, complemented
158#1681C2211yescharacteristic, complemented
159#1680C2211yescharacteristic, complemented
160#1680C2211yescharacteristic, complemented
161#1679C2211yescharacteristic, complemented
162#1679C2211yescharacteristic, complemented
163#1678C2211yescharacteristic, complemented
164#1678C2211yescharacteristic, complemented
165#1677C2211yescharacteristic, complemented
166#1677C2211yescharacteristic, complemented
167#1676C2211yescharacteristic, complemented
168#1675C2211yescharacteristic, complemented
169#1674C2211yescharacteristic, complemented
170#1673C2211yescharacteristic, complemented
171#1672C2211yescharacteristic, complemented
172#1672C2211yescharacteristic, complemented
173#1671C2211yescharacteristic, complemented
174#1671C2211yescharacteristic, complemented
175#1670C2211yescharacteristic, complemented
176#1669C2211yescharacteristic, complemented
177#1668C2211yescharacteristic, complemented
178#1667C2211yescharacteristic, complemented
179#1666C2211yescharacteristic, complemented
180#1666C2211yescharacteristic, complemented
181#1665C2211yescharacteristic, complemented
182#1665C2211yescharacteristic, complemented
183#1573C2211yescharacteristic
184#1573C2211yescharacteristic
185#1573C2211yescharacteristic
186#1573C2211yescharacteristic
187#1573C2211yescharacteristic
188#1573C2211yescharacteristic
189#1573C2211yescharacteristic
190#1573C2211yescharacteristic
191C2×#335C2211yescharacteristic
192C2×#335C2211yescharacteristic
193C2×#334C2211yescharacteristic
194C2×#334C2211yescharacteristic
195#1559C2211yescharacteristic
196#1559C2211yescharacteristic
197#1557C2211yescharacteristic
198#1557C2211yescharacteristic
199#1554C2211yescharacteristic
200#1554C2211yescharacteristic
201#1553C2211yescharacteristic
202#1553C2211yescharacteristic
203#1552C2211yescharacteristic
204#1552C2211yescharacteristic
205#1552C2211yescharacteristic
206#1552C2211yescharacteristic
207#1551C2211yescharacteristic
208#1551C2211yescharacteristic
209#1551C2211yescharacteristic
210#1551C2211yescharacteristic
211#1550C2211yescharacteristic
212#1550C2211yescharacteristic
213#1547C2211yescharacteristic
214#1547C2211yescharacteristic
215#1542C2211yescharacteristic
216#1542C2211yescharacteristic
217#1540C2211yescharacteristic
218#1540C2211yescharacteristic
219C2×#135—21no—
220C2×#135—21no—
221C23×C8—21no—
222#533D411yescharacteristic
223#533D411yescharacteristic
224#533C2311yescharacteristic
225#533C2311yescharacteristic
226#533C2311yescharacteristic
227#533C2311yescharacteristic
228#533C2311yescharacteristic
229#533C2311yescharacteristic
230#533C2311yescharacteristic
231#532D411yescharacteristic
232#532D411yescharacteristic
233#532C2311yescharacteristic
234#532C2311yescharacteristic
235#532C2311yescharacteristic
236#532C2311yescharacteristic
237#532C2311yescharacteristic
238#532C2311yescharacteristic
239#532C2311yescharacteristic
240#529—21no—
241#529—21no—
242#529—21no—
243#529—21no—
244#529—21no—
245#529—21no—
246#529—21no—
247#529—21no—
248#529—21no—
249#529—21no—
250#529—21no—
251#529—21no—
252#529—21no—
253#529—21no—
254#529—21no—
255#529—21no—
256#529D411yescharacteristic
257#529D411yescharacteristic
258#529C2311yescharacteristic
259#529C2311yescharacteristic
260#525—21no—
261#525—21no—
262#525—21no—
263#525—21no—
264#525—21no—
265#525—21no—
266#525—21no—
267#525—21no—
268#525D411yescharacteristic
269#525D411yescharacteristic
270C4×#41—21no—
271C4×#41—21no—
272C4×#41—21no—
273C4×#41—21no—
274C4×#41—21no—
275C4×#41—21no—
276C4×#41—21no—
277C4×#41—21no—
278C4×#41C2311yescharacteristic
279C4×#41C2311yescharacteristic
280C22×C42C2311yescharacteristic
281#501—21no—
282#501—21no—
283#500C2311yescharacteristic
284#500C2311yescharacteristic
285#498C2311yescharacteristic
286#498C2311yescharacteristic
287#497—21no—
288#496—21no—
289#494C2311yescharacteristic
290#493C2311yescharacteristic
291#492C2311yescharacteristic
292#492C2311yescharacteristic
293#491—21no—
294#490—21no—
295#489—21no—
296#489—21no—
297#487C2311yescharacteristic
298#487C2311yescharacteristic
299#487C2311yescharacteristic
300#487C2311yescharacteristic
301#486C2311yescharacteristic
302#486C2311yescharacteristic
303#486C2311yescharacteristic
304#486C2311yescharacteristic
305#485—21no—
306#485—21no—
307#485—21no—
308#485—21no—
309#485—21no—
310#485—21no—
311#485—21no—
312#485—21no—
313#482—21no—
314#482—21no—
315#482—21no—
316#482—21no—
317#482—21no—
318#482—21no—
319#482—21no—
320#482—21no—
321#479—21no—
322#479—21no—
323#479—21no—
324#479—21no—
325#479—21no—
326#479—21no—
327#479—21no—
328#479—21no—
329#479—21no—
330#479—21no—
331#478—21no—
332#478—21no—
333#478—21no—
334#478—21no—
335#478—21no—
336#478—21no—
337#478—21no—
338#478—21no—
339#478—21no—
340#478—21no—
341#477—21no—
342#477C2311yescharacteristic
343#477C2311yescharacteristic
344#477C2311yescharacteristic
345#477C2311yescharacteristic
346#476—21no—
347#476C2311yescharacteristic
348#476C2311yescharacteristic
349#476C2311yescharacteristic
350#476C2311yescharacteristic
351#475—21no—
352#475C2311yescharacteristic
353#475C2311yescharacteristic
354#475C2311yescharacteristic
355#475C2311yescharacteristic
356#474—21no—
357#474C2311yescharacteristic
358#474C2311yescharacteristic
359#474C2311yescharacteristic
360#474C2311yescharacteristic
361#467—21no—
362#467—21no—
363#467—21no—
364#467—21no—
365#467—21no—
366#467—21no—
367#467—21no—
368#467—21no—
369#466—21no—
370#466—21no—
371#466—21no—
372#466—21no—
373#466—21no—
374#466—21no—
375#466—21no—
376#466—21no—
377#465—21no—
378#465—21no—
379#465—21no—
380#465—21no—
381#465—21no—
382#465—21no—
383#465—21no—
384#465—21no—
385#465—21no—
386#465—21no—
387#465—21no—
388#465—21no—
389#465—21no—
390#465—21no—
391#465—21no—
392#465—21no—
393#464—21no—
394#464—21no—
395#464—21no—
396#464—21no—
397#464—21no—
398#464—21no—
399#464—21no—
400#464—21no—
401#464—21no—
402#464—21no—
403#463—21no—
404#463—21no—
405#463—21no—
406#463—21no—
407#463—21no—
408#463—21no—
409#463—21no—
410#463—21no—
411#463—21no—
412#463—21no—
413#462—21no—
414#462C2311yescharacteristic
415#462C2311yescharacteristic
416#462C2311yescharacteristic
417#462C2311yescharacteristic
418#461—21no—
419#461C2311yescharacteristic
420#461C2311yescharacteristic
421#461C2311yescharacteristic
422#461C2311yescharacteristic
423#460—21no—
424#460C2311yescharacteristic
425#460C2311yescharacteristic
426#460C2311yescharacteristic
427#460C2311yescharacteristic
428#459—21no—
429#459C2311yescharacteristic
430#459C2311yescharacteristic
431#459C2311yescharacteristic
432#459C2311yescharacteristic
433#452—21no—
434#452—21no—
435#452—21no—
436#452—21no—
437#452—21no—
438#452—21no—
439#452—21no—
440#452—21no—
441#449—21no—
442#449—21no—
443#449—21no—
444#449—21no—
445#449—21no—
446#449—21no—
447#449—21no—
448#449—21no—
449#446—21no—
450#446—21no—
451#446C2311yescharacteristic
452#446C2311yescharacteristic
453#446C2311yescharacteristic
454#446C2311yescharacteristic
455C8×Q8—21no—
456C8×Q8—21no—
457C8×Q8C2311yescharacteristic
458C8×Q8C2311yescharacteristic
459C8×Q8C2311yescharacteristic
460C8×Q8C2311yescharacteristic
461#442—21no—
462#442—21no—
463#441—21no—
464#441—21no—
465#440—21no—
466#440—21no—
467#440—21no—
468#440—21no—
469C4×Q16—21no—
470C4×Q16—21no—
471C4×SD16—21no—
472C4×SD16—21no—
473C4×SD16—21no—
474C4×SD16—21no—
475C4×D8—21no—
476C4×D8—21no—
477#436—21no—
478#436—21no—
479#436—21no—
480#436—21no—
481#436—21no—
482#436—21no—
483#436C2311yescharacteristic
484#436C2311yescharacteristic
485#436C2311yescharacteristic
486#436C2311yescharacteristic
487#435—21no—
488#435—21no—
489#435—21no—
490#435—21no—
491#435—21no—
492#435—21no—
493#435—21no—
494#435—21no—
495C8×D4—21no—
496C8×D4—21no—
497C8×D4—21no—
498C8×D4—21no—
499C8×D4—21no—
500C8×D4—21no—
501C8×D4C2311yescharacteristic
502C8×D4C2311yescharacteristic
503C8×D4C2311yescharacteristic
504C8×D4C2311yescharacteristic
505#433—21no—
506#433—21no—
507#433—21no—
508#433—21no—
509#433—21no—
510#433—21no—
511#433—21no—
512#433—21no—
513#432—21no—
514#432—21no—
515#432—21no—
516#432—21no—
517#432—21no—
518#432C2311yescharacteristic
519#432C2311yescharacteristic
520#432C2311yescharacteristic
521#432C2311yescharacteristic
522#432C2311yescharacteristic
523#432C2311yescharacteristic
524#431—21no—
525#431—21no—
526#431—21no—
527#431D411yescharacteristic
528#431D411yescharacteristic
529#431D411yescharacteristic
530#431D411yescharacteristic
531#431C2311yescharacteristic
532#431C2311yescharacteristic
533#431C2311yescharacteristic
534#431C2311yescharacteristic
535#431C2311yescharacteristic
536#431C2311yescharacteristic
537#427—21no—
538#427—21no—
539#423—21no—
540#423—21no—
541#423C2311yescharacteristic
542#423C2311yescharacteristic
543C2×C4⋊C8—21no—
544C2×C4⋊C8—21no—
545C2×C4⋊C8—21no—
546C2×C4⋊C8—21no—
547C2×C4⋊C8—21no—
548C2×C4⋊C8D411yescharacteristic
549C2×C4⋊C8D411yescharacteristic
550C2×C4⋊C8C2311yescharacteristic
551C2×C4⋊C8C2311yescharacteristic
552C2×C4⋊C8C2311yescharacteristic
553C2×C4⋊C8C2311yescharacteristic
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557C2×C4⋊C8C2311yescharacteristic
558#416—21no—
559#416—21no—
560#416—21no—
561#416—21no—
562#408—21no—
563#408—21no—
564#408—21no—
565#408—21no—
566#407—21no—
567C2×C22⋊C8—21no—
568C2×C22⋊C8D411yescharacteristic
569C2×C22⋊C8D411yescharacteristic
570#405—21no—
571#405—21no—
572#405—21no—
573#405—21no—
574C4×M16—21no—
575C2×#97—21no—
576C2×C4×C8C2311yescharacteristic
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
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—21no—
632C2×#41—21no—
633C2×#41—21no—
634C2×#41C2×D411yescharacteristic
635C2×#41C2×D411yescharacteristic
636C23×C4C2×D411yescharacteristic
637C23×C4C2×D411yescharacteristic
638C23×C4#4111yescharacteristic
639#135—82no—
640#135—82no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×Q16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—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×D8—21no—
660C2×D8—21no—
661C2×D8—21no—
662C2×D8—21no—
663C2×D8—21no—
664C2×D8—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16—21no—
668C2×M16—21no—
669C2×M16—21no—
670C2×M16—21no—
671C22×C8—21no—
672C22×C8—21no—
673C22×C8—21no—
674C22×C8—21no—
675C22×C8—21no—
676C22×C8—21no—
677C22×C8—21no—
678C22×C8—21no—
679C22×C8—21no—
680C22×C8—21no—
681C22×C8—21no—
682C22×C8—21no—
683C22×C8—82no—
684C22×C8C2×D411yescharacteristic
685C22×C8C2×D411yescharacteristic
686C22×C8C2×D411yescharacteristic
687C22×C8C2×D411yescharacteristic
688C4⋊Q8C2×D411yescharacteristic
689C4⋊Q8C2×D411yescharacteristic
690C4⋊Q8C2×D411yescharacteristic
691C4⋊Q8C2411yescharacteristic
692C4⋊Q8C2411yescharacteristic
693C4⋊Q8C2411yescharacteristic
694C4⋊Q8C2411yescharacteristic
695C4⋊Q8C2411yescharacteristic
696C4⋊Q8C2411yescharacteristic
697#127C2×D411yescharacteristic
698#127C2411yescharacteristic
699#127C2411yescharacteristic
700#126—21no—
701#126—21no—
702#126—21no—
703#126—21no—
704#126—41no—
705#126—41no—
706#126—41no—
707#126—41no—
708#125—21no—
709#125—21no—
710#125—21no—
711#125—21no—
712#125—21no—
713#125—21no—
714#125—21no—
715#125—21no—
716#125C2×D411yescharacteristic
717#125C2×D411yescharacteristic
718#124—21no—
719#124—21no—
720#124—21no—
721#124—21no—
722#124—21no—
723#124—21no—
724#124—21no—
725#124—21no—
726#124C2×D411yescharacteristic
727#124C2×D411yescharacteristic
728#123—21no—
729#123—21no—
730#123—21no—
731#123—21no—
732#123—21no—
733#123—21no—
734#123—41no—
735#123—41no—
736#123—41no—
737#123—41no—
738#123—41no—
739#123—41no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8—21no—
755C22⋊Q8—21no—
756C22⋊Q8C2×D411yescharacteristic
757C22⋊Q8C2×D411yescharacteristic
758C22⋊Q8C2×D411yescharacteristic
759C22⋊Q8C2×D411yescharacteristic
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—21no—
774#121—21no—
775#121—21no—
776#121C2×D411yescharacteristic
777#121C2×D411yescharacteristic
778#121C2×D411yescharacteristic
779#121C2×D411yescharacteristic
780#120—21no—
781#120—21no—
782#120—41no—
783#120—41no—
784C4×Q8—21no—
785C4×Q8—21no—
786C4×Q8—21no—
787C4×Q8—21no—
788C4×Q8—21no—
789C4×Q8—21no—
790C4×Q8—21no—
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8—21no—
798C4×Q8—21no—
799C4×Q8—21no—
800C4×Q8C2×D411yescharacteristic
801C4×Q8C2×D411yescharacteristic
802C4×Q8C2411yescharacteristic
803C4×Q8C2411yescharacteristic
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—21no—
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—41no—
833C4×D4—41no—
834C4×D4—41no—
835C4×D4—41no—
836C4×D4—41no—
837C4×D4—41no—
838C4×D4—41no—
839C4×D4—41no—
840C4×D4—41no—
841C4×D4—41no—
842C4×D4—41no—
843C4×D4—41no—
844C4×D4C2×D411yescharacteristic
845C4×D4C2×D411yescharacteristic
846C4×D4C2411yescharacteristic
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—21no—
862#117—41no—
863#117—41no—
864#117—41no—
865#117—41no—
866#117—41no—
867#117—41no—
868#117C2×D411yescharacteristic
869#117C2×D411yescharacteristic
870C2×C42—21no—
871C2×C42—21no—
872C2×C42—41no—
873C2×C42—41no—
874C2×C42C2×D411yescharacteristic
875C2×C42C2×D411yescharacteristic
876C2×C42C2×D411yescharacteristic
877C2×C42C2×D411yescharacteristic
878C2×C42C2×D411yescharacteristic
879C2×C42C2×D411yescharacteristic
880C2×C42#4111yescharacteristic
881C2×C42#4111yescharacteristic
882C2×C42#4111yescharacteristic
883C2×C42C2411yescharacteristic
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886#107—21no—
887#107—21no—
888#107—21no—
889#107—21no—
890#107—21no—
891#107—21no—
892#107—21no—
893#107—21no—
894#107—21no—
895#107—21no—
896#107—21no—
897#107—21no—
898#106—21no—
899#106—21no—
900#106—21no—
901#106—21no—
902#106—21no—
903#106—21no—
904#106—21no—
905#106—21no—
906#106—21no—
907#106—21no—
908#106—21no—
909#106—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⋊C8—21no—
925C4⋊C8—21no—
926C4⋊C8—21no—
927C4⋊C8—21no—
928C4⋊C8C2×D411yescharacteristic
929C4⋊C8C2×D411yescharacteristic
930C4⋊C8C2×D411yescharacteristic
931C4⋊C8C2×D411yescharacteristic
932C4⋊C8C2×D411yescharacteristic
933C4⋊C8C2×D411yescharacteristic
934C4⋊C8C2×D411yescharacteristic
935C4⋊C8C2×D411yescharacteristic
936C4⋊C8C2411yescharacteristic
937C4⋊C8C2411yescharacteristic
938C4⋊C8C2411yescharacteristic
939C4⋊C8C2411yescharacteristic
940C4⋊C8C2411yescharacteristic
941C4⋊C8C2411yescharacteristic
942C4⋊C8C2411yescharacteristic
943C4⋊C8C2411yescharacteristic
944C4⋊C8C2411yescharacteristic
945C4⋊C8C2411yescharacteristic
946C4⋊C8C2411yescharacteristic
947C4⋊C8C2411yescharacteristic
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#103—21no—
971#103—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—
994#102—21no—
995#102—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⋊C8—21no—
1009C22⋊C8—21no—
1010C22⋊C8—21no—
1011C22⋊C8—21no—
1012C22⋊C8C2×D411yescharacteristic
1013C22⋊C8C2×D411yescharacteristic
1014C22⋊C8C2×D411yescharacteristic
1015C22⋊C8C2×D411yescharacteristic
1016C22⋊C8C2×D411yescharacteristic
1017C22⋊C8C2×D411yescharacteristic
1018C22⋊C8C2×D411yescharacteristic
1019C22⋊C8C2×D411yescharacteristic
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#97—21no—
1029#97—21no—
1030C4×C8—21no—
1031C4×C8—21no—
1032C4×C8—21no—
1033C4×C8—21no—
1034C4×C8—21no—
1035C4×C8—21no—
1036C4×C8C2×D411yescharacteristic
1037C4×C8C2×D411yescharacteristic
1038C4×C8C2×D411yescharacteristic
1039C4×C8C2×D411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C4×C8C2411yescharacteristic
1042C4×C8C2411yescharacteristic
1043C4×C8C2411yescharacteristic
1044C24#12111yescharacteristic
1045#41—44no—
1046#41—41no—
1047#41—41no—
1048#41—41no—
1049#41—41no—
1050#41—42no—
1051#41—42no—
1052#41—81no—
1053#41—81no—
1054#41—81no—
1055#41—81no—
1056#41—81no—
1057#41—81no—
1058#41—81no—
1059#41—81no—
1060#41—82no—
1061#41—82no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8—21no—
1068C2×Q8—21no—
1069C2×Q8—21no—
1070C2×Q8C22×D411yescharacteristic
1071C2×Q8C22×D411yescharacteristic
1072C2×D4—21no—
1073C2×D4—21no—
1074C2×D4—21no—
1075C2×D4—21no—
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—21no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4—41no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4C22×D411yescharacteristic
1093C2×D4C22×D411yescharacteristic
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—42no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4#12111yescharacteristic
1112C22×C4#12111yescharacteristic
1113C22×C4#12111yescharacteristic
1114C22×C4#12111yescharacteristic
1115C22×C4#12111yescharacteristic
1116C22×C4#12111yescharacteristic
1117C22×C4#12111yescharacteristic
1118C22×C4#12111yescharacteristic
1119C22×C4#12111yescharacteristic
1120C22×C4C22×D411yescharacteristic
1121C22×C4C22×D411yescharacteristic
1122C22×C4C22×D411yescharacteristic
1123C22×C4C22×D411yescharacteristic
1124C22×C4C22×D411yescharacteristic
1125C22×C4C22×D411yescharacteristic
1126C22×C4C2×#4111yescharacteristic
1127C22×C4C2×#4111yescharacteristic
1128C22×C4C2×#4111yescharacteristic
1129Q16—81no—
1130Q16—81no—
1131Q16—81no—
1132Q16—81no—
1133Q16—81no—
1134Q16—81no—
1135SD16—81no—
1136SD16—81no—
1137SD16—81no—
1138SD16—81no—
1139SD16—81no—
1140SD16—81no—
1141SD16—81no—
1142SD16—81no—
1143SD16—81no—
1144SD16—81no—
1145SD16—81no—
1146SD16—81no—
1147D8—81no—
1148D8—81no—
1149D8—81no—
1150D8—81no—
1151D8—81no—
1152D8—81no—
1153M16—81no—
1154M16—81no—
1155M16—81no—
1156M16—81no—
1157M16—81no—
1158M16—81no—
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—21no—
1168C2×C8—21no—
1169C2×C8—21no—
1170C2×C8—21no—
1171C2×C8—41no—
1172C2×C8—41no—
1173C2×C8—41no—
1174C2×C8—41no—
1175C2×C8—42no—
1176C2×C8—42no—
1177C2×C8—81no—
1178C2×C8—81no—
1179C2×C8—81no—
1180C2×C8—81no—
1181C2×C8—81no—
1182C2×C8—81no—
1183C2×C8—81no—
1184C2×C8—81no—
1185C2×C8—81no—
1186C2×C8—81no—
1187C2×C8C22×D411yescharacteristic
1188C2×C8C22×D411yescharacteristic
1189C2×C8C22×D411yescharacteristic
1190C2×C8C22×D411yescharacteristic
1191C2×C8C22×D411yescharacteristic
1192C2×C8C22×D411yescharacteristic
1193C2×C8C22×D411yescharacteristic
1194C2×C8C22×D411yescharacteristic
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—21no—
1217C4⋊C4—21no—
1218C4⋊C4—21no—
1219C4⋊C4—21no—
1220C4⋊C4—21no—
1221C4⋊C4—21no—
1222C4⋊C4—21no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
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⋊C4C22×D411yescharacteristic
1236C4⋊C4C22×D411yescharacteristic
1237C4⋊C4C22×D411yescharacteristic
1238C4⋊C4C22×D411yescharacteristic
1239C22⋊C4—21no—
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—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—41no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—41no—
1275C42—21no—
1276C42—21no—
1277C42—21no—
1278C42—21no—
1279C42—21no—
1280C42—21no—
1281C42—41no—
1282C42—41no—
1283C42—41no—
1284C42—41no—
1285C42—41no—
1286C42—41no—
1287C42#12111yescharacteristic
1288C42#12111yescharacteristic
1289C42#12111yescharacteristic
1290C42#12111yescharacteristic
1291C42#12111yescharacteristic
1292C42#12111yescharacteristic
1293C42C22×D411yescharacteristic
1294C42C22×D411yescharacteristic
1295C42C22×D411yescharacteristic
1296C42C22×D411yescharacteristic
1297C42C22×D411yescharacteristic
1298C42C22×D411yescharacteristic
1299C42C2×#4111yescharacteristic
1300C42C2×#4111yescharacteristic
1301C42C2×#4111yescharacteristic
1302C42C2511yescharacteristic
1303C23—22no—
1304C23—21no—
1305C23—21no—
1306C23—41no—
1307C23—41no—
1308C23—41no—
1309C23—41no—
1310C23C2×#12111yescharacteristic
1311C23C2×#12111yescharacteristic
1312C23C2×#12111yescharacteristic
1313Q8—21no—
1314Q8—21no—
1315Q8—21no—
1316Q8—21no—
1317Q8—42no—
1318Q8—41no—
1319Q8—41no—
1320Q8—41no—
1321Q8—41no—
1322Q8—41no—
1323Q8—41no—
1324Q8—41no—
1325Q8—41no—
1326Q8—81no—
1327Q8—81no—
1328Q8—81no—
1329D4—21no—
1330D4—21no—
1331D4—21no—
1332D4—21no—
1333D4—42no—
1334D4—42no—
1335D4—42no—
1336D4—41no—
1337D4—41no—
1338D4—41no—
1339D4—41no—
1340D4—41no—
1341D4—41no—
1342D4—41no—
1343D4—41no—
1344D4—81no—
1345D4—81no—
1346D4—81no—
1347D4—81no—
1348D4—81no—
1349D4—81no—
1350D4—81no—
1351D4—82no—
1352D4—82no—
1353D4—82no—
1354D4—82no—
1355D4—82no—
1356D4—82no—
1357C2×C4—22no—
1358C2×C4—22no—
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—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—41no—
1378C2×C4—41no—
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—42no—
1388C2×C4—42no—
1389C2×C4—41no—
1390C2×C4—41no—
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—82no—
1402C2×C4—82no—
1403C2×C4—82no—
1404C2×C4—82no—
1405C2×C4—82no—
1406C2×C4—82no—
1407C2×C4C2×#12111yescharacteristic
1408C2×C4C2×#12111yescharacteristic
1409C2×C4C2×#12111yescharacteristic
1410C2×C4C2×#12111yescharacteristic
1411C2×C4C2×#12111yescharacteristic
1412C2×C4C2×#12111yescharacteristic
1413C2×C4C2×#12111yescharacteristic
1414C2×C4C2×#12111yescharacteristic
1415C2×C4C2×#12111yescharacteristic
1416C2×C4C23×D411yescharacteristic
1417C2×C4C23×D411yescharacteristic
1418C2×C4C22×#4111yescharacteristic
1419C8—21no—
1420C8—21no—
1421C8—21no—
1422C8—21no—
1423C8—21no—
1424C8—21no—
1425C8—21no—
1426C8—21no—
1427C8—41no—
1428C8—41no—
1429C8—41no—
1430C8—41no—
1431C8—41no—
1432C8—41no—
1433C8—41no—
1434C8—41no—
1435C8—41no—
1436C8—41no—
1437C8—41no—
1438C8—41no—
1439C22—21no—
1440C22—21no—
1441C22—21no—
1442C22—21no—
1443C22—21no—
1444C22—21no—
1445C22—21no—
1446C22—21no—
1447C22—44no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—81no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—81no—
1459C22—81no—
1460C22#306712yes—
1461C22C22×#12111yescharacteristic
1462C4—21no—
1463C4—21no—
1464C4—21no—
1465C4—21no—
1466C4—21no—
1467C4—21no—
1468C4—21no—
1469C4—21no—
1470C4—21no—
1471C4—21no—
1472C4—41no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—41no—
1478C4—81no—
1479C4—81no—
1480C4—81no—
1481C4—81no—
1482C4—81no—
1483C4—81no—
1484C4#358411yescharacteristic
1485C4#358411yescharacteristic
1486C4#358511yescharacteristic
1487C4#358611yescharacteristic
1488C2—22no—
1489C2—41no—
1490C2—41no—
1491C2—81no—
1492C2—81no—
1493C2—161no—
1494C2—161no—
1495C2#6042211yescharacteristic
1496C2#6045611yescharacteristic
1497C2C2×#306711yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60961C2semidirect
2. #60944C2semidirect
3. #60900C2semidirect
4. #60292C2semidirect
5. #19575C2semidirect
6. #19574C2semidirect
7. #19569C2semidirect
8. #19568C2semidirect
9. #19563C2semidirect
10. #19562C2semidirect
11. #19557C2semidirect
12. #19556C2semidirect
13. #19499C2semidirect
14. #19498C2semidirect
15. #19493C2semidirect
16. #19492C2semidirect
17. #19487C2semidirect
18. #19486C2semidirect
19. #19481C2semidirect
20. #19480C2semidirect
21. #19229C2semidirect
22. #19229C2semidirect
23. #19228C2semidirect
24. #19227C2semidirect
25. #19223C2semidirect
26. #19222C2semidirect
27. #19221C2semidirect
28. #19221C2semidirect
29. C2×#1573C2semidirect
30. #17756C2semidirect
31. #17719C2semidirect
119. #1704C22semidirect
120. #1704C22semidirect
121. #1703C22semidirect
122. #1703C22semidirect
123. #1702C22semidirect
124. #1702C22semidirect
125. #1701C22semidirect
126. #1701C22semidirect
127. #1700C22semidirect
128. #1700C22semidirect
129. #1699C22semidirect
130. #1699C22semidirect
131. #1698C22semidirect
132. #1698C22semidirect
133. #1697C22semidirect
134. #1697C22semidirect
135. #1696C22semidirect
136. #1695C22semidirect
137. #1694C22semidirect
138. #1693C22semidirect
139. #1692C22semidirect
140. #1692C22semidirect
141. #1691C22semidirect
142. #1691C22semidirect
143. #1690C22semidirect
144. #1689C22semidirect
145. #1688C22semidirect
146. #1687C22semidirect
147. #1686C22semidirect
148. #1686C22semidirect
149. #1685C22semidirect
150. #1685C22semidirect
151. #1684C22semidirect
152. #1684C22semidirect
153. #1683C22semidirect
154. #1683C22semidirect
155. #1682C22semidirect
156. #1682C22semidirect
157. #1681C22semidirect
158. #1681C22semidirect
159. #1680C22semidirect
160. #1680C22semidirect
161. #1679C22semidirect
162. #1679C22semidirect
163. #1678C22semidirect
164. #1678C22semidirect
165. #1677C22semidirect
166. #1677C22semidirect
167. #1676C22semidirect
168. #1675C22semidirect
169. #1674C22semidirect
170. #1673C22semidirect
171. #1672C22semidirect
172. #1672C22semidirect
173. #1671C22semidirect
174. #1671C22semidirect
175. #1670C22semidirect
176. #1669C22semidirect
177. #1668C22semidirect
178. #1667C22semidirect
179. #1666C22semidirect
180. #1666C22semidirect
181. #1665C22semidirect
182. #1665C22semidirect

Maximal subgroups

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

subgroupindex
#609612
#609442
#609002
#602922
#195752
#195742
#195692
#195682
#195632
#195622
#195572
#195562
#194992
#194982
#194932
#194922
#194872
#194862
#194812
#194802
#192292
#192282
#192272
#192232
#192222
#192212
C2×#15732
#177562
#177192