Finite Group Databasebeta

← #6434076

Subgroups — #6434076

Order 512.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35325C211yesmaximal, characteristic
2#35310C211yesmaximal, characteristic
3#30374C211yesmaximal, characteristic, complemented
4#30370C211yesmaximal, characteristic, complemented
5#30363C211yesmaximal, characteristic, complemented
6#30361C211yesmaximal, characteristic, complemented
7#30331C211yesmaximal, characteristic, complemented
8#30331C211yesmaximal, characteristic, complemented
9#30326C211yesmaximal, characteristic, complemented
10#30318C211yesmaximal, characteristic, complemented
11#30299C211yesmaximal, characteristic, complemented
12#30257C211yesmaximal, characteristic, complemented
13#30196C211yesmaximal, characteristic, complemented
14#30193C211yesmaximal, characteristic, complemented
15#29743C211yesmaximal, characteristic
16#29743C211yesmaximal, characteristic
17#29733C211yesmaximal, characteristic
18#29731C211yesmaximal, characteristic
19#23773C211yesmaximal, characteristic, complemented
20#23769C211yesmaximal, characteristic, complemented
21#23765C211yesmaximal, characteristic, complemented
22#23759C211yesmaximal, characteristic, complemented
23#23586C211yesmaximal, characteristic, complemented
24#23586C211yesmaximal, characteristic, complemented
25#23577C211yesmaximal, characteristic, complemented
26#23571C211yesmaximal, characteristic, complemented
27#21542C211yesmaximal, characteristic, complemented
28#21537C211yesmaximal, characteristic, complemented
29#21530C211yesmaximal, characteristic, complemented
30#21525C211yesmaximal, characteristic, complemented
31#20379C211yesmaximal, characteristic
32C2×#541C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#441C2211yescharacteristic, complemented
40C2×#441C2211yescharacteristic, complemented
41C2×C4×Q16C2211yescharacteristic, complemented
42C2×C4×Q16C2211yescharacteristic, complemented
43C2×#407C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C2×#405C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2857C2211yescharacteristic
48#2855C2211yescharacteristic
49#2855C2211yescharacteristic
50#2851C2211yescharacteristic
51#2848C2211yescharacteristic
52#2848C2211yescharacteristic
53#2848C2211yescharacteristic
54#2848C2211yescharacteristic
55#2629C2211yescharacteristic
56#2628C2211yescharacteristic
57#2628C2211yescharacteristic
58#2625C2211yescharacteristic
59#2625C2211yescharacteristic
60#2621C2211yescharacteristic
61#2621C2211yescharacteristic
62#2621C2211yescharacteristic
63#2611—21no—
64#2611—21no—
65#2599—21no—
66#2599—21no—
67#2583—21no—
68#2561—21no—
69#2484—21no—
70#2482—21no—
71#2480—21no—
72#2480—21no—
73#2478—21no—
74#2478—21no—
75#2475—21no—
76#2475—21no—
77#2473—21no—
78#2473—21no—
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2323C2211yescharacteristic
82#2323C2211yescharacteristic
83#2323C2211yescharacteristic
84#2323C2211yescharacteristic
85#2314C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88#2283C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2077C2211yescharacteristic
105#2076C2211yescharacteristic
106#2076C2211yescharacteristic
107#2075C2211yescharacteristic
108#2075C2211yescharacteristic
109#2074C2211yescharacteristic, complemented
110#2074C2211yescharacteristic, complemented
111#2072C2211yescharacteristic, complemented
112#2072C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2058C2211yescharacteristic, complemented
116#2057C2211yescharacteristic, complemented
117#2043C2211yescharacteristic, complemented
118#2043C2211yescharacteristic, complemented
119#2043C2211yescharacteristic, complemented
120#2043C2211yescharacteristic, complemented
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic
128#2036C2211yescharacteristic
129#2035C2211yescharacteristic
130#2035C2211yescharacteristic
131#2035C2211yescharacteristic
132#2035C2211yescharacteristic
133#2035C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2035C2211yescharacteristic
137#2026C2211yescharacteristic, complemented
138#2026C2211yescharacteristic, complemented
139#2024C2211yescharacteristic, complemented
140#2024C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2016C2211yescharacteristic, complemented
144#2016C2211yescharacteristic, complemented
145#2001C2211yescharacteristic
146#2001C2211yescharacteristic
147#2001C2211yescharacteristic
148#2001C2211yescharacteristic
149#2001C2211yescharacteristic
150#2001C2211yescharacteristic
151#2001C2211yescharacteristic
152#2001C2211yescharacteristic
153#1971C2211yescharacteristic, complemented
154#1971C2211yescharacteristic, complemented
155#1969C2211yescharacteristic, complemented
156#1969C2211yescharacteristic, complemented
157#1944C2211yescharacteristic, complemented
158#1943C2211yescharacteristic, complemented
159#1942C2211yescharacteristic, complemented
160#1941C2211yescharacteristic, complemented
161#1935C2211yescharacteristic, complemented
162#1935C2211yescharacteristic, complemented
163#1935C2211yescharacteristic, complemented
164#1935C2211yescharacteristic, complemented
165#1933C2211yescharacteristic, complemented
166#1933C2211yescharacteristic, complemented
167#1933C2211yescharacteristic, complemented
168#1933C2211yescharacteristic, complemented
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1894C2211yescharacteristic
173#1892C2211yescharacteristic
174#1892C2211yescharacteristic
175#1892C2211yescharacteristic
176#1892C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1808C2211yescharacteristic
180#1807C2211yescharacteristic
181#1776C2211yescharacteristic, complemented
182#1776C2211yescharacteristic, complemented
183C4×#107C2211yescharacteristic, complemented
184C4×#106C2211yescharacteristic, complemented
185#1763C2211yescharacteristic, complemented
186#1763C2211yescharacteristic, complemented
187#1763C2211yescharacteristic, complemented
188#1763C2211yescharacteristic, complemented
189C4×#103C2211yescharacteristic, complemented
190C4×#103C2211yescharacteristic, complemented
191C4×#103C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193#1750C2211yescharacteristic
194#1750C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1749C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#541—42no—
213#541—42no—
214#533—42no—
215#533—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C4×Q8—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×#117—21no—
244C2×#117—42no—
245C2×#117—42no—
246C2×#117D411yescharacteristic
247C2×#117D411yescharacteristic
248C2×#117D411yescharacteristic
249C2×#117D411yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4D411yescharacteristic
255C22×C4⋊C4D411yescharacteristic
256C22×C22⋊C4D411yescharacteristic
257C22×C22⋊C4D411yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260#470—24no—
261#470—24no—
262#467—24no—
263#467—24no—
264#441—42no—
265#441—42no—
266C4×Q16—42no—
267C4×Q16—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304#407—24no—
305C2×C22⋊C8—24no—
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314#405—42no—
315#405—42no—
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#395—21no—
354#393—21no—
355#393—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#383—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463#376—21no—
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—41no—
505C23×C4—41no—
506C23×C4—41no—
507C23×C4—41no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16#4114yes—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8#4114yes—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556#126—44no—
557#126—44no—
558#125—41no—
559#125—41no—
560#125—44no—
561#125—44no—
562#125—44no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—44no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—44no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—42no—
606#117—42no—
607#117—42no—
608#117—42no—
609#117—44no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4—42no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—42no—
690C2×C22⋊C4—42no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C42—22no—
700C2×C42—22no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719#107—22no—
720#107—22no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#106—22no—
726#106—22no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763#97—22no—
764#97—22no—
765#97—41no—
766#97—41no—
767C4×C8—22no—
768C4×C8—22no—
769C4×C8—41no—
770C4×C8—41no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817C24—22no—
818C24—22no—
819C24—41no—
820C24—41no—
821C24—41no—
822C24—41no—
823C24—41no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—42no—
852C2×Q8—81no—
853C2×Q8—81no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C2×#4112yes—
923C22×C4C2×#4112yes—
924C22×C4C2511yescharacteristic
925Q16—44no—
926Q16—44no—
927Q16—44no—
928Q16—44no—
929M16—44no—
930M16—44no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—44no—
952C2×C8—44no—
953C2×C8C2×#4112yes—
954C2×C8C2×#4112yes—
955C2×C8C2×#4112yes—
956C2×C8C2×#4112yes—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C42—22no—
1055C42—22no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—41no—
1063C42—41no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42H(5,𝔽2)12yes—
1073C42H(5,𝔽2)12yes—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—44no—
1094C23—44no—
1095C23—82no—
1096C23—82no—
1097C23—82no—
1098C23—82no—
1099C23—82no—
1100C23#53212yes—
1101C23#57812yes—
1102C23C23×D411yescharacteristic
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—84no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—82no—
1215C2×C4—82no—
1216C2×C4—82no—
1217C2×C4#53212yes—
1218C2×C4#53412yes—
1219C2×C4#53412yes—
1220C2×C4C22×#4111yescharacteristic
1221C2×C4C22×#4111yescharacteristic
1222C2×C4C2×H(5,𝔽2)11yescharacteristic
1223C2×C4C2×H(5,𝔽2)11yescharacteristic
1224C2×C4#58511yescharacteristic
1225C2×C4#58511yescharacteristic
1226C8—22no—
1227C8—22no—
1228C8—22no—
1229C8—22no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—88no—
1256C22C2×#53211yescharacteristic
1257C22C2×#53411yescharacteristic
1258C22#344911yescharacteristic
1259C22C2×#57811yescharacteristic
1260C22#358411yescharacteristic
1261C22#358611yescharacteristic
1262C22#358611yescharacteristic
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#345911yescharacteristic
1291C4#345911yescharacteristic
1292C4#346011yescharacteristic
1293C4#346011yescharacteristic
1294C2—42no—
1295C2—42no—
1296C2—81no—
1297C2#3457511yescharacteristic
1298C2#6070811yescharacteristic
1299C2#6071111yescharacteristic
1300C2#6075911yescharacteristic
1301C2#6076611yescharacteristic
1302C2#6098311yescharacteristic
1303C2#6098411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #30374C2semidirect
4. #30370C2semidirect
5. #30363C2semidirect
6. #30361C2semidirect
7. #30331C2semidirect
8. #30331C2semidirect
9. #30326C2semidirect
10. #30318C2semidirect
11. #30299C2semidirect
12. #30257C2semidirect
13. #30196C2semidirect
14. #30193C2semidirect
19. #23773C2semidirect
20. #23769C2semidirect
21. #23765C2semidirect
22. #23759C2semidirect
23. #23586C2semidirect
24. #23586C2semidirect
25. #23577C2semidirect
26. #23571C2semidirect
27. #21542C2semidirect
28. #21537C2semidirect
29. #21530C2semidirect
30. #21525C2semidirect
39. C2×#441C22semidirect
40. C2×#441C22semidirect
41. C2×C4×Q16C22semidirect
42. C2×C4×Q16C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2097C22semidirect
96. #2097C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
109. #2074C22semidirect
110. #2074C22semidirect
111. #2072C22semidirect
112. #2072C22semidirect
113. #2059C22semidirect
114. #2059C22semidirect
115. #2058C22semidirect
116. #2057C22semidirect
117. #2043C22semidirect
118. #2043C22semidirect
119. #2043C22semidirect
120. #2043C22semidirect
137. #2026C22semidirect
138. #2026C22semidirect
139. #2024C22semidirect
140. #2024C22semidirect
141. #2016C22semidirect
142. #2016C22semidirect
143. #2016C22semidirect
144. #2016C22semidirect
153. #1971C22semidirect
154. #1971C22semidirect
155. #1969C22semidirect
156. #1969C22semidirect
157. #1944C22semidirect
158. #1943C22semidirect
159. #1942C22semidirect
160. #1941C22semidirect
161. #1935C22semidirect
162. #1935C22semidirect
163. #1935C22semidirect
164. #1935C22semidirect
165. #1933C22semidirect
166. #1933C22semidirect
167. #1933C22semidirect
168. #1933C22semidirect
181. #1776C22semidirect
182. #1776C22semidirect
183. C4×#107C22semidirect
184. C4×#106C22semidirect
185. #1763C22semidirect
186. #1763C22semidirect
187. #1763C22semidirect
188. #1763C22semidirect
189. C4×#103C22semidirect
190. C4×#103C22semidirect
191. C4×#103C22semidirect
192. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#353252
#353102
#303742
#303702
#303632
#303612
#303312
#303262
#303182
#302992
#302572
#301962
#301932
#297432
#297332
#297312
#237732
#237692
#237652
#237592
#235862
#235772
#235712
#215422
#215372
#215302
#215252
#203792