Finite Group Databasebeta

← #6528432

Subgroups — #6528432

Order 512.

1300 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35239C211yesmaximal, characteristic
2#34948C211yesmaximal, characteristic
3#29305C211yesmaximal, characteristic
4#29304C211yesmaximal, characteristic
5#29300C211yesmaximal, characteristic
6#29299C211yesmaximal, characteristic
7#28840C211yesmaximal, characteristic, complemented
8#28840C211yesmaximal, characteristic, complemented
9#28839C211yesmaximal, characteristic, complemented
10#28839C211yesmaximal, characteristic, complemented
11#28838C211yesmaximal, characteristic, complemented
12#28838C211yesmaximal, characteristic, complemented
13#28837C211yesmaximal, characteristic, complemented
14#28837C211yesmaximal, characteristic, complemented
15#28808C211yesmaximal, characteristic, complemented
16#28807C211yesmaximal, characteristic, complemented
17#28806C211yesmaximal, characteristic, complemented
18#28805C211yesmaximal, characteristic, complemented
19#28804C211yesmaximal, characteristic, complemented
20#28803C211yesmaximal, characteristic, complemented
21#28802C211yesmaximal, characteristic, complemented
22#28801C211yesmaximal, characteristic, complemented
23#27955C211yesmaximal, characteristic
24#27954C211yesmaximal, characteristic
25#27951C211yesmaximal, characteristic
26#27949C211yesmaximal, characteristic
27#21989C211yesmaximal, characteristic
28#21988C211yesmaximal, characteristic
29#21366C211yesmaximal, characteristic
30#21364C211yesmaximal, characteristic
31#20534C211yesmaximal, characteristic
32C2×#432C2211yescharacteristic
33C2×#432C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2666—21no—
39#2666—21no—
40#2571C2211yescharacteristic
41#2571C2211yescharacteristic
42#2571C2211yescharacteristic
43#2570C2211yescharacteristic
44#2570C2211yescharacteristic
45#2570C2211yescharacteristic
46#2570C2211yescharacteristic
47#2570C2211yescharacteristic
48#2570C2211yescharacteristic
49#2569—21no—
50#2569—21no—
51#2552C2211yescharacteristic
52#2552C2211yescharacteristic
53#2552C2211yescharacteristic
54#2552C2211yescharacteristic
55#2551C2211yescharacteristic
56#2550C2211yescharacteristic
57#2550C2211yescharacteristic
58#2442—21no—
59#2442—21no—
60#2442—21no—
61#2440—21no—
62#2438—21no—
63#2438—21no—
64#2402—21no—
65#2402—21no—
66#2331—21no—
67#2330—21no—
68C4×#125—21no—
69C4×#125—21no—
70#2296C2211yescharacteristic
71#2296C2211yescharacteristic
72#2285C2211yescharacteristic
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2285C2211yescharacteristic
76#2283C2211yescharacteristic
77C4×#117C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79#2085C2211yescharacteristic
80#2085C2211yescharacteristic
81#2085C2211yescharacteristic
82#2085C2211yescharacteristic
83#2085C2211yescharacteristic
84#2085C2211yescharacteristic
85#2085C2211yescharacteristic
86#2085C2211yescharacteristic
87#2085C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2084C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2083C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#1993C2211yescharacteristic
112#1993C2211yescharacteristic
113#1992C2211yescharacteristic
114#1992C2211yescharacteristic
115#1991C2211yescharacteristic
116#1991C2211yescharacteristic
117#1990C2211yescharacteristic
118#1990C2211yescharacteristic
119#1949C2211yescharacteristic
120#1949C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1947C2211yescharacteristic
134#1947C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1942C2211yescharacteristic
147#1941C2211yescharacteristic
148#1941C2211yescharacteristic
149#1941C2211yescharacteristic
150#1941C2211yescharacteristic
151#1854C2211yescharacteristic
152#1854C2211yescharacteristic
153#1854C2211yescharacteristic
154#1854C2211yescharacteristic
155#1854C2211yescharacteristic
156#1854C2211yescharacteristic
157#1854C2211yescharacteristic
158#1854C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1847C2211yescharacteristic
170#1847C2211yescharacteristic
171#1847C2211yescharacteristic
172#1847C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1846C2211yescharacteristic
176#1846C2211yescharacteristic
177#1845C2211yescharacteristic
178#1844C2211yescharacteristic
179#1836C2211yescharacteristic
180#1836C2211yescharacteristic
181#1836C2211yescharacteristic
182#1836C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1771C2211yescharacteristic
199#1749C2211yescharacteristic
200#1749C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8—21no—
213C2×#117—21no—
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C22×C4⋊C4D411yescharacteristic
219C22×C4⋊C4D411yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#432Q818yescomplemented
224#432Q818yescomplemented
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#395—21no—
306#395—21no—
307#395—21no—
308#395—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#385—21no—
358#385—21no—
359#385—21no—
360#385—21no—
361#385—21no—
362#385—21no—
363#385—21no—
364#385—21no—
365#384—21no—
366#384C2311yescharacteristic
367#384C2311yescharacteristic
368#384C2311yescharacteristic
369#384C2311yescharacteristic
370#384C2311yescharacteristic
371#384C2311yescharacteristic
372#384C2311yescharacteristic
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#383—21no—
377#382—21no—
378#382—21no—
379#382—21no—
380#382—21no—
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2311yescharacteristic
384#382C2311yescharacteristic
385#382C2311yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#381—21no—
392#380—21no—
393#380—21no—
394#380—21no—
395#380—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4D411yescharacteristic
417C4×C4⋊C4D411yescharacteristic
418C4×C4⋊C4D411yescharacteristic
419C4×C4⋊C4D411yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435#376—21no—
436#376—21no—
437C2×#95D411yescharacteristic
438C2×#95D411yescharacteristic
439C43—21no—
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C22×Q8—21no—
481C22×Q8—21no—
482C23×C4C2×D411yescharacteristic
483C23×C4C2×D411yescharacteristic
484C23×C4C2×D411yescharacteristic
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2×D411yescharacteristic
488C23×C4C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C4⋊Q8—41no—
498C4⋊Q8—41no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—44no—
502#125—41no—
503#125—41no—
504#125—41no—
505#125—41no—
506#125—44no—
507#125—44no—
508#125—44no—
509C22⋊Q8—82no—
510C22⋊Q8—82no—
511#117—41no—
512#117—41no—
513#117—41no—
514#117—41no—
515#117—41no—
516#117—41no—
517#117—41no—
518#117—41no—
519#117—82no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—42no—
563C2×C4⋊C4—42no—
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—41no—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—41no—
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2×D411yescharacteristic
616C2×C42C2×D411yescharacteristic
617C2×C42C2×D411yescharacteristic
618C2×C42C2×Q814yes—
619C2×C42C2×Q814yes—
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626#107—41no—
627#107—41no—
628#107—41no—
629#107—41no—
630#107—41no—
631#107—41no—
632#107—41no—
633#107—41no—
634#107—41no—
635#107—41no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658C4⋊C8C2×Q814yes—
659C4⋊C8C2×Q814yes—
660C4⋊C8C2×Q814yes—
661C4⋊C8C2×Q814yes—
662C22⋊C8C2×Q814yes—
663C22⋊C8C2×Q814yes—
664C22⋊C8C2×Q814yes—
665C22⋊C8C2×Q814yes—
666#97—41no—
667#97—41no—
668#97—41no—
669#97—41no—
670#97C2×Q814yes—
671#97C2×Q814yes—
672#97C2×Q814yes—
673#97C2×Q814yes—
674C4×C8—41no—
675C4×C8—41no—
676C4×C8—41no—
677C4×C8—41no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734C24C22×D411yescharacteristic
735C2×Q8—42no—
736C2×Q8—42no—
737C2×Q8—81no—
738C2×Q8—81no—
739C2×Q8—81no—
740C2×Q8—81no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4C4⋊Q814yes—
778C22×C4C4⋊Q814yes—
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×Q812yes—
793C22×C4C22×Q812yes—
794C22×C4C2511yescharacteristic
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8C22×Q812yes—
812C2×C8C22×Q812yes—
813C2×C8C22×Q812yes—
814C2×C8C22×Q812yes—
815C2×C8C22×Q812yes—
816C2×C8C22×Q812yes—
817C2×C8C22×Q812yes—
818C2×C8C22×Q812yes—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—41no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4—41no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C42—21no—
910C42—21no—
911C42—21no—
912C42—21no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—41no—
918C42—41no—
919C42—41no—
920C42—41no—
921C42—42no—
922C42—42no—
923C42—42no—
924C42—42no—
925C42—42no—
926C42—42no—
927C42—42no—
928C42—42no—
929C42—81no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42C4⋊Q814yes—
934C42C4⋊Q814yes—
935C42C22×Q812yes—
936C42C22×Q812yes—
937C42C22×Q812yes—
938C42C22×Q812yes—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23C2×C4⋊Q812yes—
946C23C23×D411yescharacteristic
947Q8—162no—
948Q8—162no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—82no—
1036C2×C4—82no—
1037C2×C4—82no—
1038C2×C4—82no—
1039C2×C4C2×C4⋊Q812yes—
1040C2×C4C2×C4⋊Q812yes—
1041C2×C4C2×C4⋊Q812yes—
1042C2×C4C2×C4⋊Q812yes—
1043C2×C4C2×C4⋊Q812yes—
1044C2×C4#57512yes—
1045C2×C4#57512yes—
1046C2×C4C23×Q811yescharacteristic
1047C2×C4C23×Q811yescharacteristic
1048C2×C4#58511yescharacteristic
1049C2×C4#58511yescharacteristic
1050C2×C4#58511yescharacteristic
1051C2×C4#58511yescharacteristic
1052C8—22no—
1053C8—22no—
1054C8—22no—
1055C8—22no—
1056C8—22no—
1057C8—22no—
1058C8—22no—
1059C8—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22C22×C4⋊Q811yescharacteristic
1068C22#348511yescharacteristic
1069C22#348711yescharacteristic
1070C22C2×#57511yescharacteristic
1071C22C2×#57511yescharacteristic
1072C22#358511yescharacteristic
1073C22#358611yescharacteristic
1074C4—22no—
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—81no—
1088C4—81no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4#350411yescharacteristic
1104C4#350411yescharacteristic
1105C4#350411yescharacteristic
1106C4#350411yescharacteristic
1107C2—42no—
1108C2#3564011yescharacteristic
1109C2#6066311yescharacteristic
1110C2#6066411yescharacteristic
1111C2#6171411yescharacteristic
1112C2#6171511yescharacteristic
1113C2#6189611yescharacteristic
1114C2#6189711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #28840C2semidirect
8. #28840C2semidirect
9. #28839C2semidirect
10. #28839C2semidirect
11. #28838C2semidirect
12. #28838C2semidirect
13. #28837C2semidirect
14. #28837C2semidirect
15. #28808C2semidirect
16. #28807C2semidirect
17. #28806C2semidirect
18. #28805C2semidirect
19. #28804C2semidirect
20. #28803C2semidirect
21. #28802C2semidirect
22. #28801C2semidirect
223. #432Q8semidirect
224. #432Q8semidirect

Maximal subgroups

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

subgroupindex
#352392
#349482
#293052
#293042
#293002
#292992
#288402
#288392
#288382
#288372
#288082
#288072
#288062
#288052
#288042
#288032
#288022
#288012
#279552
#279542
#279512
#279492
#219892
#219882
#213662
#213642
#205342