Finite Group Databasebeta

← #6355039

Subgroups — #6355039

Order 512.

1514 conjugacy classes of subgroups.

The subgroup lattice has 1492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60972C211yesmaximal, characteristic, complemented
2#60961C211yesmaximal, characteristic, complemented
3#60948C211yesmaximal, 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#19455C211yesmaximal, characteristic, complemented
14#19454C211yesmaximal, characteristic, complemented
15#19449C211yesmaximal, characteristic, complemented
16#19448C211yesmaximal, characteristic, complemented
17#19419C211yesmaximal, characteristic, complemented
18#19418C211yesmaximal, characteristic, complemented
19#19413C211yesmaximal, characteristic, complemented
20#19412C211yesmaximal, characteristic, complemented
21#19253C211yesmaximal, characteristic, complemented
22#19252C211yesmaximal, characteristic, complemented
23#19251C211yesmaximal, characteristic, complemented
24#19250C211yesmaximal, characteristic, complemented
25#19249C211yesmaximal, characteristic, complemented
26#19248C211yesmaximal, characteristic, complemented
27#19247C211yesmaximal, characteristic, complemented
28#19246C211yesmaximal, characteristic, complemented
29#17810C211yesmaximal, characteristic, complemented
30#17713C211yesmaximal, characteristic, complemented
31#17700C211yesmaximal, characteristic, complemented
32#3444C2211yescharacteristic
33#3444C2211yescharacteristic
34#3444C2211yescharacteristic
35#3256—21no—
36#3256—21no—
37#3249C2211yescharacteristic
38#3248C2211yescharacteristic
39#3248C2211yescharacteristic
40#3247C2211yescharacteristic
41#3247C2211yescharacteristic
42#3246C2211yescharacteristic
43#3246C2211yescharacteristic
44#3245C2211yescharacteristic
45#3240—21no—
46#3237C2211yescharacteristic
47#3235C2211yescharacteristic
48#3233—21no—
49#3233C2211yescharacteristic
50#3233C2211yescharacteristic
51#3231C2211yescharacteristic
52#3231C2211yescharacteristic
53#3228C2211yescharacteristic
54#3228C2211yescharacteristic
55#3219—21no—
56#3216C2211yescharacteristic
57#3214C2211yescharacteristic
58#3212—21no—
59#3212C2211yescharacteristic
60#3212C2211yescharacteristic
61#3210C2211yescharacteristic
62#3210C2211yescharacteristic
63#3207C2211yescharacteristic
64#3207C2211yescharacteristic
65#3197—21no—
66#3197—21no—
67#3191—21no—
68#3191—21no—
69#3191—21no—
70#3191—21no—
71#3185C2211yescharacteristic
72#3184C2211yescharacteristic
73#3182C2211yescharacteristic
74#3182C2211yescharacteristic
75#3181—21no—
76#3180—21no—
77#3168—21no—
78#3168—21no—
79#3116C2211yescharacteristic
80#3116C2211yescharacteristic
81#3115C2211yescharacteristic
82#3115C2211yescharacteristic
83#3111—21no—
84#3111—21no—
85#3111—21no—
86#3111—21no—
87#3111—21no—
88#3111—21no—
89#3107—21no—
90#3107C2211yescharacteristic
91#3107C2211yescharacteristic
92#3106—21no—
93#3106C2211yescharacteristic
94#3106C2211yescharacteristic
95#2991—21no—
96#2990—21no—
97#2989C2211yescharacteristic
98#2989C2211yescharacteristic
99#2988C2211yescharacteristic
100#2988C2211yescharacteristic
101#2986C2211yescharacteristic
102#2986C2211yescharacteristic
103#2979C2211yescharacteristic
104#2979C2211yescharacteristic
105#2976—21no—
106#2976—21no—
107#2969C2211yescharacteristic
108#2969C2211yescharacteristic
109#2969C2211yescharacteristic
110#2969C2211yescharacteristic
111#2966—21no—
112#2966—21no—
113#2925—21no—
114#2925—21no—
115#2920C2211yescharacteristic
116C2×#432C2211yescharacteristic
117C2×#431C2211yescharacteristic
118C2×#431C2211yescharacteristic
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#1572C2211yescharacteristic
188#1572C2211yescharacteristic
189#1572C2211yescharacteristic
190#1572C2211yescharacteristic
191#1565C2211yescharacteristic
192#1565C2211yescharacteristic
193#1565C2211yescharacteristic
194#1565C2211yescharacteristic
195#1554C2211yescharacteristic
196#1554C2211yescharacteristic
197#1553C2211yescharacteristic
198#1553C2211yescharacteristic
199#1552C2211yescharacteristic
200#1552C2211yescharacteristic
201#1551C2211yescharacteristic
202#1551C2211yescharacteristic
203#1544C2211yescharacteristic
204#1544C2211yescharacteristic
205#1543C2211yescharacteristic
206#1543C2211yescharacteristic
207#1542C2211yescharacteristic
208#1542C2211yescharacteristic
209#1542C2211yescharacteristic
210#1542C2211yescharacteristic
211#1542C2211yescharacteristic
212#1542C2211yescharacteristic
213#1540C2211yescharacteristic
214#1540C2211yescharacteristic
215#1540C2211yescharacteristic
216#1540C2211yescharacteristic
217#1540C2211yescharacteristic
218#1540C2211yescharacteristic
219#533D411yescharacteristic
220#533D411yescharacteristic
221#533C2311yescharacteristic
222#533C2311yescharacteristic
223#533C2311yescharacteristic
224#533C2311yescharacteristic
225#533C2311yescharacteristic
226#533C2311yescharacteristic
227#533C2311yescharacteristic
228#532D411yescharacteristic
229#532D411yescharacteristic
230#532C2311yescharacteristic
231#532C2311yescharacteristic
232#532C2311yescharacteristic
233#532C2311yescharacteristic
234#532C2311yescharacteristic
235#532C2311yescharacteristic
236#532C2311yescharacteristic
237#529—21no—
238#529—21no—
239#529—21no—
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#529D411yescharacteristic
254#529D411yescharacteristic
255#529C2311yescharacteristic
256#529C2311yescharacteristic
257#525—21no—
258#525—21no—
259#525—21no—
260#525—21no—
261#525—21no—
262#525—21no—
263#525—21no—
264#525—21no—
265#525D411yescharacteristic
266#525D411yescharacteristic
267C4×#41—21no—
268C4×#41—21no—
269C4×#41—21no—
270C4×#41—21no—
271C4×#41—21no—
272C4×#41—21no—
273C4×#41—21no—
274C4×#41—21no—
275C4×#41C2311yescharacteristic
276C4×#41C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#501—21no—
279#501—21no—
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#499—21no—
283#499—21no—
284#498C2311yescharacteristic
285#498C2311yescharacteristic
286#497—21no—
287#496—21no—
288#495—21no—
289#495—21no—
290#494C2311yescharacteristic
291#493C2311yescharacteristic
292#492C2311yescharacteristic
293#492C2311yescharacteristic
294#491—21no—
295#490—21no—
296#489—21no—
297#489—21no—
298#488—21no—
299#488—21no—
300#488—21no—
301#488—21no—
302#487C2311yescharacteristic
303#487C2311yescharacteristic
304#487C2311yescharacteristic
305#487C2311yescharacteristic
306#486C2311yescharacteristic
307#486C2311yescharacteristic
308#486C2311yescharacteristic
309#486C2311yescharacteristic
310#485—21no—
311#485—21no—
312#485—21no—
313#485—21no—
314#485—21no—
315#485—21no—
316#485—21no—
317#485—21no—
318#485—21no—
319#485—21no—
320#485—21no—
321#485—21no—
322#482—21no—
323#482—21no—
324#482—21no—
325#482—21no—
326#482—21no—
327#482—21no—
328#482—21no—
329#482—21no—
330#482—21no—
331#482—21no—
332#482—21no—
333#482—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#478—21no—
346#477—21no—
347#477C2311yescharacteristic
348#477C2311yescharacteristic
349#477C2311yescharacteristic
350#477C2311yescharacteristic
351#476—21no—
352#476C2311yescharacteristic
353#476C2311yescharacteristic
354#476C2311yescharacteristic
355#476C2311yescharacteristic
356#475—21no—
357#475C2311yescharacteristic
358#475C2311yescharacteristic
359#475C2311yescharacteristic
360#475C2311yescharacteristic
361#474—21no—
362#474C2311yescharacteristic
363#474C2311yescharacteristic
364#474C2311yescharacteristic
365#474C2311yescharacteristic
366#470—21no—
367#470—21no—
368#469—21no—
369#469—21no—
370#468—21no—
371#468—21no—
372#468—21no—
373#468—21no—
374#467—21no—
375#467—21no—
376#467—21no—
377#467—21no—
378#466—21no—
379#466—21no—
380#466—21no—
381#466—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#464—21no—
391#464—21no—
392#464—21no—
393#464—21no—
394#464—21no—
395#464—21no—
396#463—21no—
397#463—21no—
398#463—21no—
399#463—21no—
400#463—21no—
401#463—21no—
402#462—21no—
403#462C2311yescharacteristic
404#462C2311yescharacteristic
405#462C2311yescharacteristic
406#462C2311yescharacteristic
407#461—21no—
408#461C2311yescharacteristic
409#461C2311yescharacteristic
410#461C2311yescharacteristic
411#461C2311yescharacteristic
412#460—21no—
413#460C2311yescharacteristic
414#460C2311yescharacteristic
415#460C2311yescharacteristic
416#460C2311yescharacteristic
417#459—21no—
418#459C2311yescharacteristic
419#459C2311yescharacteristic
420#459C2311yescharacteristic
421#459C2311yescharacteristic
422#452—21no—
423#452—21no—
424#452—21no—
425#452—21no—
426#452—21no—
427#452—21no—
428#452—21no—
429#452—21no—
430#452—21no—
431#452—21no—
432#452—21no—
433#452—21no—
434#449—21no—
435#449—21no—
436#449—21no—
437#449—21no—
438#449—21no—
439#449—21no—
440#449—21no—
441#449—21no—
442#449—21no—
443#449—21no—
444#449—21no—
445#449—21no—
446#446—21no—
447#446—21no—
448#446C2311yescharacteristic
449#446C2311yescharacteristic
450#446C2311yescharacteristic
451#446C2311yescharacteristic
452C8×Q8—21no—
453C8×Q8—21no—
454C8×Q8C2311yescharacteristic
455C8×Q8C2311yescharacteristic
456C8×Q8C2311yescharacteristic
457C8×Q8C2311yescharacteristic
458#442—21no—
459#442—21no—
460#442—21no—
461#442—21no—
462#441—21no—
463#441—21no—
464#441—21no—
465#441—21no—
466#440—21no—
467#440—21no—
468#440—21no—
469#440—21no—
470#440—21no—
471#440—21no—
472#440—21no—
473#440—21no—
474C4×Q16—21no—
475C4×Q16—21no—
476C4×SD16—21no—
477C4×SD16—21no—
478C4×SD16—21no—
479C4×SD16—21no—
480C4×D8—21no—
481C4×D8—21no—
482#436—21no—
483#436—21no—
484#436—21no—
485#436—21no—
486#436—21no—
487#436—21no—
488#436C2311yescharacteristic
489#436C2311yescharacteristic
490#436C2311yescharacteristic
491#436C2311yescharacteristic
492#435—21no—
493#435—21no—
494#435—21no—
495#435—21no—
496#435—21no—
497#435—21no—
498#435—21no—
499#435—21no—
500C8×D4—21no—
501C8×D4—21no—
502C8×D4—21no—
503C8×D4—21no—
504C8×D4—21no—
505C8×D4—21no—
506C8×D4C2311yescharacteristic
507C8×D4C2311yescharacteristic
508C8×D4C2311yescharacteristic
509C8×D4C2311yescharacteristic
510#433—21no—
511#433—21no—
512#433—21no—
513#433—21no—
514#433—21no—
515#433—21no—
516#433—21no—
517#433—21no—
518#432—21no—
519#432—21no—
520#432—21no—
521#432—21no—
522#432D411yescharacteristic
523#432D411yescharacteristic
524#432D411yescharacteristic
525#432D411yescharacteristic
526#432C2311yescharacteristic
527#432C2311yescharacteristic
528#432C2311yescharacteristic
529#432C2311yescharacteristic
530#431—21no—
531#431—21no—
532#431—21no—
533#431—21no—
534#431—21no—
535#431—21no—
536#431C2311yescharacteristic
537#431C2311yescharacteristic
538#431C2311yescharacteristic
539#431C2311yescharacteristic
540#431C2311yescharacteristic
541#431C2311yescharacteristic
542#431C2311yescharacteristic
543#431C2311yescharacteristic
544#431C2311yescharacteristic
545#431C2311yescharacteristic
546#431C2311yescharacteristic
547#431C2311yescharacteristic
548#423—21no—
549#423—21no—
550#423D411yescharacteristic
551#423D411yescharacteristic
552C2×C4⋊C8—21no—
553C2×C4⋊C8—21no—
554C2×C4⋊C8C2311yescharacteristic
555C2×C4⋊C8C2311yescharacteristic
556C2×C4⋊C8C2311yescharacteristic
557C2×C4⋊C8C2311yescharacteristic
558C2×C4⋊C8C2311yescharacteristic
559C2×C4⋊C8C2311yescharacteristic
560#408—21no—
561#408—21no—
562#408—21no—
563#408—21no—
564#407D411yescharacteristic
565#407D411yescharacteristic
566C2×C22⋊C8—21no—
567C2×C22⋊C8—21no—
568C2×C22⋊C8—21no—
569#405—21no—
570#405—21no—
571#405—21no—
572#405—21no—
573C4×M16C2311yescharacteristic
574C4×M16C2311yescharacteristic
575C2×#97—21no—
576C2×C4×C8—21no—
577C2×C4×C8—21no—
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
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×SD16—21no—
646C2×SD16—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×D8—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×D8—21no—
662C2×D8—21no—
663C2×M16—21no—
664C2×M16—21no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C2×D411yescharacteristic
668C2×M16C2×D411yescharacteristic
669C2×M16C2×D411yescharacteristic
670C2×M16C2×D411yescharacteristic
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—
681C4⋊Q8C2×D411yescharacteristic
682C4⋊Q8C2×D411yescharacteristic
683C4⋊Q8C2×D411yescharacteristic
684C4⋊Q8C2411yescharacteristic
685C4⋊Q8C2411yescharacteristic
686C4⋊Q8C2411yescharacteristic
687C4⋊Q8C2411yescharacteristic
688C4⋊Q8C2411yescharacteristic
689C4⋊Q8C2411yescharacteristic
690#127C2×D411yescharacteristic
691#127C2411yescharacteristic
692#127C2411yescharacteristic
693#126—21no—
694#126—21no—
695#126—21no—
696#126—21no—
697#126—41no—
698#126—41no—
699#126—41no—
700#126—41no—
701#125—21no—
702#125—21no—
703#125—21no—
704#125—21no—
705#125—21no—
706#125—21no—
707#125—21no—
708#125—21no—
709#125C2×D411yescharacteristic
710#125C2×D411yescharacteristic
711#124—21no—
712#124—21no—
713#124—21no—
714#124—21no—
715#124—21no—
716#124—21no—
717#124—21no—
718#124—21no—
719#124C2×D411yescharacteristic
720#124C2×D411yescharacteristic
721#123—21no—
722#123—21no—
723#123—21no—
724#123—21no—
725#123—21no—
726#123—21no—
727#123—41no—
728#123—41no—
729#123—41no—
730#123—41no—
731#123—41no—
732#123—41no—
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—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8C2×D411yescharacteristic
750C22⋊Q8C2×D411yescharacteristic
751C22⋊Q8C2×D411yescharacteristic
752C22⋊Q8C2×D411yescharacteristic
753#121—21no—
754#121—21no—
755#121—21no—
756#121—21no—
757#121—21no—
758#121—21no—
759#121—21no—
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#121C2×D411yescharacteristic
770#121C2×D411yescharacteristic
771#121C2×D411yescharacteristic
772#121C2×D411yescharacteristic
773#120—21no—
774#120—21no—
775#120—41no—
776#120—41no—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—21no—
780C4×Q8—21no—
781C4×Q8—21no—
782C4×Q8—21no—
783C4×Q8—21no—
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×Q8C2×D411yescharacteristic
794C4×Q8C2×D411yescharacteristic
795C4×Q8C2411yescharacteristic
796C4×Q8C2411yescharacteristic
797C4×D4—21no—
798C4×D4—21no—
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—21no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—41no—
826C4×D4—41no—
827C4×D4—41no—
828C4×D4—41no—
829C4×D4—41no—
830C4×D4—41no—
831C4×D4—41no—
832C4×D4—41no—
833C4×D4—41no—
834C4×D4—41no—
835C4×D4—41no—
836C4×D4—41no—
837C4×D4C2×D411yescharacteristic
838C4×D4C2×D411yescharacteristic
839C4×D4C2411yescharacteristic
840C4×D4C2411yescharacteristic
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—21no—
853#117—21no—
854#117—21no—
855#117—41no—
856#117—41no—
857#117—41no—
858#117—41no—
859#117—41no—
860#117—41no—
861#117C2×D411yescharacteristic
862#117C2×D411yescharacteristic
863C2×C42—21no—
864C2×C42—21no—
865C2×C42—41no—
866C2×C42—41no—
867C2×C42C2×D411yescharacteristic
868C2×C42C2×D411yescharacteristic
869C2×C42C2×D411yescharacteristic
870C2×C42C2×D411yescharacteristic
871C2×C42C2×D411yescharacteristic
872C2×C42C2×D411yescharacteristic
873C2×C42#4111yescharacteristic
874C2×C42#4111yescharacteristic
875C2×C42#4111yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879#107—21no—
880#107—21no—
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⋊C8C2×D411yescharacteristic
918C4⋊C8C2×D411yescharacteristic
919C4⋊C8C2×D411yescharacteristic
920C4⋊C8C2×D411yescharacteristic
921C4⋊C8C2×D411yescharacteristic
922C4⋊C8C2×D411yescharacteristic
923C4⋊C8C2×D411yescharacteristic
924C4⋊C8C2×D411yescharacteristic
925C4⋊C8C2411yescharacteristic
926C4⋊C8C2411yescharacteristic
927C4⋊C8C2411yescharacteristic
928C4⋊C8C2411yescharacteristic
929C4⋊C8C2411yescharacteristic
930C4⋊C8C2411yescharacteristic
931C4⋊C8C2411yescharacteristic
932C4⋊C8C2411yescharacteristic
933C4⋊C8C2411yescharacteristic
934C4⋊C8C2411yescharacteristic
935C4⋊C8C2411yescharacteristic
936C4⋊C8C2411yescharacteristic
937#103—21no—
938#103—21no—
939#103—21no—
940#103—21no—
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#102—21no—
962#102—21no—
963#102—21no—
964#102—21no—
965#102—21no—
966#102—21no—
967#102—21no—
968#102—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—
985C22⋊C8—21no—
986C22⋊C8—21no—
987C22⋊C8—21no—
988C22⋊C8—21no—
989C22⋊C8—21no—
990C22⋊C8—21no—
991C22⋊C8—21no—
992C22⋊C8—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⋊C8C2×D411yescharacteristic
1006C22⋊C8C2×D411yescharacteristic
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×C8C2411yescharacteristic
1038C4×C8C2411yescharacteristic
1039C4×C8C2411yescharacteristic
1040C4×C8C2411yescharacteristic
1041C24#12111yescharacteristic
1042#41—41no—
1043#41—41no—
1044#41—41no—
1045#41—41no—
1046#41—81no—
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—
1057#41—82no—
1058#41—82no—
1059C2×Q8—21no—
1060C2×Q8—21no—
1061C2×Q8—21no—
1062C2×Q8—21no—
1063C2×Q8—21no—
1064C2×Q8—21no—
1065C2×Q8—21no—
1066C2×Q8—21no—
1067C2×Q8C22×D411yescharacteristic
1068C2×Q8C22×D411yescharacteristic
1069C2×D4—21no—
1070C2×D4—21no—
1071C2×D4—21no—
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—41no—
1084C2×D4—41no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—41no—
1088C2×D4—41no—
1089C2×D4C22×D411yescharacteristic
1090C2×D4C22×D411yescharacteristic
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—41no—
1098C22×C4—41no—
1099C22×C4—41no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—81no—
1108C22×C4#12111yescharacteristic
1109C22×C4#12111yescharacteristic
1110C22×C4#12111yescharacteristic
1111C22×C4#12111yescharacteristic
1112C22×C4#12111yescharacteristic
1113C22×C4#12111yescharacteristic
1114C22×C4#12111yescharacteristic
1115C22×C4#12111yescharacteristic
1116C22×C4#12111yescharacteristic
1117C22×C4C22×D411yescharacteristic
1118C22×C4C22×D411yescharacteristic
1119C22×C4C22×D411yescharacteristic
1120C22×C4C22×D411yescharacteristic
1121C22×C4C22×D411yescharacteristic
1122C22×C4C22×D411yescharacteristic
1123C22×C4C2×#4111yescharacteristic
1124C22×C4C2×#4111yescharacteristic
1125C22×C4C2×#4111yescharacteristic
1126Q16—81no—
1127Q16—81no—
1128Q16—81no—
1129Q16—81no—
1130Q16—81no—
1131Q16—81no—
1132SD16—81no—
1133SD16—81no—
1134SD16—81no—
1135SD16—81no—
1136SD16—81no—
1137SD16—81no—
1138SD16—81no—
1139SD16—81no—
1140SD16—81no—
1141SD16—81no—
1142SD16—81no—
1143SD16—81no—
1144D8—81no—
1145D8—81no—
1146D8—81no—
1147D8—81no—
1148D8—81no—
1149D8—81no—
1150M16—41no—
1151M16—41no—
1152M16—41no—
1153M16—41no—
1154M16—81no—
1155M16—81no—
1156M16—81no—
1157M16—81no—
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—21no—
1168C2×C8—21no—
1169C2×C8—21no—
1170C2×C8—81no—
1171C2×C8—81no—
1172C2×C8—81no—
1173C2×C8—81no—
1174C2×C8—81no—
1175C2×C8—81no—
1176C2×C8—81no—
1177C2×C8—81no—
1178C2×C8—81no—
1179C2×C8—81no—
1180C2×C8C22×D411yescharacteristic
1181C2×C8C22×D411yescharacteristic
1182C2×C8C22×D411yescharacteristic
1183C2×C8C22×D411yescharacteristic
1184C2×C8C22×D411yescharacteristic
1185C2×C8C22×D411yescharacteristic
1186C2×C8C22×D411yescharacteristic
1187C2×C8C22×D411yescharacteristic
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⋊C4C22×D411yescharacteristic
1229C4⋊C4C22×D411yescharacteristic
1230C4⋊C4C22×D411yescharacteristic
1231C4⋊C4C22×D411yescharacteristic
1232C22⋊C4—21no—
1233C22⋊C4—21no—
1234C22⋊C4—21no—
1235C22⋊C4—21no—
1236C22⋊C4—21no—
1237C22⋊C4—21no—
1238C22⋊C4—21no—
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—41no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
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—41no—
1268C42—21no—
1269C42—21no—
1270C42—21no—
1271C42—21no—
1272C42—21no—
1273C42—21no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42#12111yescharacteristic
1281C42#12111yescharacteristic
1282C42#12111yescharacteristic
1283C42#12111yescharacteristic
1284C42#12111yescharacteristic
1285C42#12111yescharacteristic
1286C42C22×D411yescharacteristic
1287C42C22×D411yescharacteristic
1288C42C22×D411yescharacteristic
1289C42C22×D411yescharacteristic
1290C42C22×D411yescharacteristic
1291C42C22×D411yescharacteristic
1292C42C2×#4111yescharacteristic
1293C42C2×#4111yescharacteristic
1294C42C2×#4111yescharacteristic
1295C42C2511yescharacteristic
1296C23—21no—
1297C23—21no—
1298C23—41no—
1299C23—41no—
1300C23—41no—
1301C23—41no—
1302C23—41no—
1303C23C2×#12111yescharacteristic
1304C23C2×#12111yescharacteristic
1305C23C2×#12111yescharacteristic
1306Q8—21no—
1307Q8—21no—
1308Q8—21no—
1309Q8—21no—
1310Q8—42no—
1311Q8—41no—
1312Q8—41no—
1313Q8—41no—
1314Q8—41no—
1315Q8—41no—
1316Q8—41no—
1317Q8—41no—
1318Q8—41no—
1319Q8—81no—
1320Q8—81no—
1321Q8—81no—
1322D4—21no—
1323D4—21no—
1324D4—21no—
1325D4—21no—
1326D4—42no—
1327D4—42no—
1328D4—42no—
1329D4—41no—
1330D4—41no—
1331D4—41no—
1332D4—41no—
1333D4—41no—
1334D4—41no—
1335D4—41no—
1336D4—41no—
1337D4—81no—
1338D4—81no—
1339D4—81no—
1340D4—81no—
1341D4—81no—
1342D4—81no—
1343D4—81no—
1344D4—82no—
1345D4—82no—
1346D4—82no—
1347D4—82no—
1348D4—82no—
1349D4—82no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
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—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—42no—
1381C2×C4—42no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—81no—
1393C2×C4—81no—
1394C2×C4—82no—
1395C2×C4—82no—
1396C2×C4—82no—
1397C2×C4—82no—
1398C2×C4—82no—
1399C2×C4—82no—
1400C2×C4C2×#12111yescharacteristic
1401C2×C4C2×#12111yescharacteristic
1402C2×C4C2×#12111yescharacteristic
1403C2×C4C2×#12111yescharacteristic
1404C2×C4C2×#12111yescharacteristic
1405C2×C4C2×#12111yescharacteristic
1406C2×C4C2×#12111yescharacteristic
1407C2×C4C2×#12111yescharacteristic
1408C2×C4C2×#12111yescharacteristic
1409C2×C4C23×D411yescharacteristic
1410C2×C4C23×D411yescharacteristic
1411C2×C4C22×#4111yescharacteristic
1412C8—21no—
1413C8—21no—
1414C8—21no—
1415C8—21no—
1416C8—21no—
1417C8—21no—
1418C8—21no—
1419C8—21no—
1420C8—41no—
1421C8—41no—
1422C8—41no—
1423C8—41no—
1424C8—41no—
1425C8—41no—
1426C8—41no—
1427C8—41no—
1428C8—41no—
1429C8—41no—
1430C8—41no—
1431C8—41no—
1432C22—21no—
1433C22—21no—
1434C22—21no—
1435C22—21no—
1436C22—21no—
1437C22—21no—
1438C22—21no—
1439C22—21no—
1440C22—21no—
1441C22—41no—
1442C22—41no—
1443C22—41no—
1444C22—41no—
1445C22—41no—
1446C22—41no—
1447C22—82no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22C22×#12111yescharacteristic
1455C4—21no—
1456C4—21no—
1457C4—21no—
1458C4—21no—
1459C4—21no—
1460C4—21no—
1461C4—21no—
1462C4—21no—
1463C4—21no—
1464C4—21no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—81no—
1472C4—81no—
1473C4—81no—
1474C4—81no—
1475C4—81no—
1476C4—81no—
1477C4#358411yescharacteristic
1478C4#358411yescharacteristic
1479C4#358411yescharacteristic
1480C4#358411yescharacteristic
1481C2—41no—
1482C2—41no—
1483C2—41no—
1484C2—81no—
1485C2—81no—
1486C2—161no—
1487C2—161no—
1488C2#6042211yescharacteristic
1489C2#6045311yescharacteristic
1490C2#6046911yescharacteristic
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. #60972C2semidirect
2. #60961C2semidirect
3. #60948C2semidirect
4. #60292C2semidirect
5. #19575C2semidirect
6. #19574C2semidirect
7. #19569C2semidirect
8. #19568C2semidirect
9. #19563C2semidirect
10. #19562C2semidirect
11. #19557C2semidirect
12. #19556C2semidirect
13. #19455C2semidirect
14. #19454C2semidirect
15. #19449C2semidirect
16. #19448C2semidirect
17. #19419C2semidirect
18. #19418C2semidirect
19. #19413C2semidirect
20. #19412C2semidirect
21. #19253C2semidirect
22. #19252C2semidirect
23. #19251C2semidirect
24. #19250C2semidirect
25. #19249C2semidirect
26. #19248C2semidirect
27. #19247C2semidirect
28. #19246C2semidirect
29. #17810C2semidirect
30. #17713C2semidirect
31. #17700C2semidirect
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
#609722
#609612
#609482
#602922
#195752
#195742
#195692
#195682
#195632
#195622
#195572
#195562
#194552
#194542
#194492
#194482
#194192
#194182
#194132
#194122
#192532
#192522
#192512
#192502
#192492
#192482
#192472
#192462
#178102
#177132
#177002