Finite Group Databasebeta

← #6966638

Subgroups — #6966638

Order 512.

1395 conjugacy classes of subgroups.

The subgroup lattice has 1221 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39689C211yesmaximal, characteristic
2#37387C211yesmaximal, characteristic
3#32780C211yesmaximal, characteristic
4#32771C211yesmaximal, characteristic
5#32350C211yesmaximal, characteristic, complemented
6#32345C211yesmaximal, characteristic, complemented
7#32100C211yesmaximal, characteristic, complemented
8#32082C211yesmaximal, characteristic, complemented
9#31548C211yesmaximal, characteristic, complemented
10#31521C211yesmaximal, characteristic, complemented
11#30880C211yesmaximal, characteristic, complemented
12#30880C211yesmaximal, characteristic, complemented
13#30124C211yesmaximal, characteristic
14#30116C211yesmaximal, characteristic
15#29848C211yesmaximal, characteristic
16#29844C211yesmaximal, characteristic
17#29701C211yesmaximal, characteristic
18#28535C211yesmaximal, characteristic, complemented
19#28423C211yesmaximal, characteristic, complemented
20#27827C211yesmaximal, characteristic, complemented
21#27769C211yesmaximal, characteristic, complemented
22#25683C211yesmaximal, characteristic
23#25460C211yesmaximal, characteristic, complemented
24#25290C211yesmaximal, characteristic, complemented
25#24826C211yesmaximal, characteristic, complemented
26#24732C211yesmaximal, characteristic, complemented
27#24664C211yesmaximal, characteristic
28#24652C211yesmaximal, characteristic
29#24165C211yesmaximal, characteristic
30#23586C211yesmaximal, characteristic
31#22604C211yesmaximal, characteristic
32C2×#541C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#491C2211yescharacteristic
36C2×#487C2211yescharacteristic
37C2×#487C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#462C2211yescharacteristic
42C2×#462C2211yescharacteristic
43C2×#462C2211yescharacteristic
44C2×#441C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×#433C2211yescharacteristic
47C2×#431C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2802—21no—
52#2792—21no—
53#2729—21no—
54#2726—21no—
55#2726—21no—
56#2726—21no—
57#2726—21no—
58#2722—21no—
59#2722—21no—
60#2722—21no—
61#2722—21no—
62#2720—21no—
63#2629C2211yescharacteristic
64#2628C2211yescharacteristic
65#2621C2211yescharacteristic
66#2621C2211yescharacteristic
67#2588—21no—
68#2574—21no—
69#2565C2211yescharacteristic
70#2565C2211yescharacteristic
71#2565C2211yescharacteristic
72#2565C2211yescharacteristic
73#2565C2211yescharacteristic
74#2551C2211yescharacteristic
75#2550—21no—
76#2546C2211yescharacteristic
77#2546C2211yescharacteristic
78#2546C2211yescharacteristic
79#2546C2211yescharacteristic
80#2522—21no—
81#2508C2211yescharacteristic
82#2506C2211yescharacteristic
83#2451C2211yescharacteristic
84#2451C2211yescharacteristic
85#2370C2211yescharacteristic
86Q8×C4⋊C4C2211yescharacteristic
87#2323C2211yescharacteristic
88#2323C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90#2296C2211yescharacteristic
91#2101C2211yescharacteristic
92#2099C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2096C2211yescharacteristic
98#2096C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2084C2211yescharacteristic
102#2084C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2066C2211yescharacteristic
110#2066C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2043C2211yescharacteristic
115#2043C2211yescharacteristic
116#2043C2211yescharacteristic
117#2043C2211yescharacteristic
118#2043C2211yescharacteristic
119#2043C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2043C2211yescharacteristic
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#2026C2211yescharacteristic
136#2024C2211yescharacteristic
137#2024C2211yescharacteristic
138#2024C2211yescharacteristic
139#2024C2211yescharacteristic
140#2016C2211yescharacteristic
141#2016C2211yescharacteristic
142#2016C2211yescharacteristic
143#2001C2211yescharacteristic
144#2001C2211yescharacteristic
145#2001C2211yescharacteristic
146#2001C2211yescharacteristic
147#1993C2211yescharacteristic
148#1992C2211yescharacteristic
149#1990C2211yescharacteristic
150#1989C2211yescharacteristic
151#1981C2211yescharacteristic
152#1981C2211yescharacteristic
153#1981C2211yescharacteristic
154#1971C2211yescharacteristic
155#1969C2211yescharacteristic
156#1969C2211yescharacteristic
157#1969C2211yescharacteristic
158#1960C2211yescharacteristic
159#1956C2211yescharacteristic
160#1956C2211yescharacteristic
161#1949C2211yescharacteristic
162#1947C2211yescharacteristic
163#1940C2211yescharacteristic
164#1939C2211yescharacteristic
165#1935C2211yescharacteristic
166#1933C2211yescharacteristic
167#1933C2211yescharacteristic
168#1933C2211yescharacteristic
169#1928C2211yescharacteristic
170#1927C2211yescharacteristic
171#1927C2211yescharacteristic
172#1927C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1865C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1846C2211yescharacteristic
190#1845C2211yescharacteristic
191#1818C2211yescharacteristic
192#1817C2211yescharacteristic
193#1805C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1803C2211yescharacteristic
197#1798C2211yescharacteristic
198#1771C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207#541—42no—
208#541—42no—
209#541—42no—
210#541—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#499—42no—
249#491—42no—
250#487—42no—
251#487—42no—
252#479—42no—
253#479—42no—
254#479—42no—
255#462—42no—
256#462—42no—
257#462—42no—
258#441—42no—
259C4×Q16—42no—
260#433—42no—
261#431—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
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
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—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#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#396—21no—
359#396—21no—
360#395—21no—
361#395—21no—
362#395—21no—
363#395—21no—
364#395—21no—
365#393—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389D411yescharacteristic
400#389D411yescharacteristic
401#389D411yescharacteristic
402#389D411yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#385—21no—
436#385D411yescharacteristic
437#385D411yescharacteristic
438#385D411yescharacteristic
439#385D411yescharacteristic
440#384—21no—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#382—21no—
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×Q16—41no—
517C2×Q16—41no—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—82no—
543#126—44no—
544#126—44no—
545#126—44no—
546#126—44no—
547#125—22no—
548#125—22no—
549#125—22no—
550#125—22no—
551#125—41no—
552#125—41no—
553#125—44no—
554#125—44no—
555#125—44no—
556#125—44no—
557#125—82no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—82no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583#117—22no—
584#117—22no—
585#117—41no—
586#117—41no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741C22⋊C8—22no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745#97—22no—
746#97—41no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—22no—
750C4×C8—41no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
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#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24C22×D411yescharacteristic
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—42no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q82−1+412yes—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C2511yescharacteristic
881Q16—44no—
882Q16—44no—
883Q16—82no—
884Q16—82no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8H(5,𝔽2)12yes—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C42−1+412yes—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—41no—
1015C42—41no—
1016C42—42no—
1017C42—42no—
1018C42—42no—
1019C42—42no—
1020C42—42no—
1021C42—42no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C42—81no—
1026C42H(5,𝔽2)12yes—
1027C42H(5,𝔽2)12yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23C23×D411yescharacteristic
1036Q8—22no—
1037Q8—22no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—41no—
1053Q8—41no—
1054Q8—41no—
1055Q8—41no—
1056Q8—162no—
1057Q8—162no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—44no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—82no—
1146C2×C4#53512yes—
1147C2×C4#53512yes—
1148C2×C4#57712yes—
1149C2×C4#57812yes—
1150C2×C4#57812yes—
1151C2×C4C2×H(5,𝔽2)11yescharacteristic
1152C2×C4C2×H(5,𝔽2)11yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4C2×2−1+411yescharacteristic
1155C2×C4C2×2−1+411yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—22no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22C2×#53511yescharacteristic
1173C22#348611yescharacteristic
1174C22#349611yescharacteristic
1175C22C2×#57711yescharacteristic
1176C22C2×#57811yescharacteristic
1177C22C2×#57811yescharacteristic
1178C22#358611yescharacteristic
1179C4—22no—
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—42no—
1192C4—41no—
1193C4—42no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4#353611yescharacteristic
1209C4#354111yescharacteristic
1210C4#354711yescharacteristic
1211C4#354811yescharacteristic
1212C2—81no—
1213C2#4243411yescharacteristic
1214C2#6082411yescharacteristic
1215C2#6083711yescharacteristic
1216C2#6185211yescharacteristic
1217C2#6186911yescharacteristic
1218C2#6227111yescharacteristic
1219C2#6230711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #32350C2semidirect
6. #32345C2semidirect
7. #32100C2semidirect
8. #32082C2semidirect
9. #31548C2semidirect
10. #31521C2semidirect
11. #30880C2semidirect
12. #30880C2semidirect
18. #28535C2semidirect
19. #28423C2semidirect
20. #27827C2semidirect
21. #27769C2semidirect
23. #25460C2semidirect
24. #25290C2semidirect
25. #24826C2semidirect
26. #24732C2semidirect

Maximal subgroups

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

subgroupindex
#396892
#373872
#327802
#327712
#323502
#323452
#321002
#320822
#315482
#315212
#308802
#301242
#301162
#298482
#298442
#297012
#285352
#284232
#278272
#277692
#256832
#254602
#252902
#248262
#247322
#246642
#246522
#241652
#235862
#226042