Finite Group Databasebeta

← #6798138

Subgroups — #6798138

Order 512.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39494C211yesmaximal, characteristic, complemented
2#39387C211yesmaximal, characteristic
3#33237C211yesmaximal, characteristic, complemented
4#30644C211yesmaximal, characteristic, complemented
5#30643C211yesmaximal, characteristic, complemented
6#30642C211yesmaximal, characteristic, complemented
7#30641C211yesmaximal, characteristic, complemented
8#30640C211yesmaximal, characteristic, complemented
9#30639C211yesmaximal, characteristic, complemented
10#30638C211yesmaximal, characteristic, complemented
11#30637C211yesmaximal, characteristic, complemented
12#29850C211yesmaximal, characteristic, complemented
13#29849C211yesmaximal, characteristic, complemented
14#29207C211yesmaximal, characteristic, complemented
15#28752C211yesmaximal, characteristic, complemented
16#27921C211yesmaximal, characteristic, complemented
17#27920C211yesmaximal, characteristic, complemented
18#26541C211yesmaximal, characteristic, complemented
19#26540C211yesmaximal, characteristic, complemented
20#26539C211yesmaximal, characteristic, complemented
21#26538C211yesmaximal, characteristic, complemented
22#26249C211yesmaximal, characteristic, complemented
23#26248C211yesmaximal, characteristic
24#26247C211yesmaximal, characteristic, complemented
25#26246C211yesmaximal, characteristic
26#25684C211yesmaximal, characteristic, complemented
27#25684C211yesmaximal, characteristic, complemented
28#21871C211yesmaximal, characteristic, complemented
29#21871C211yesmaximal, characteristic, complemented
30#21731C211yesmaximal, characteristic, complemented
31#21269C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#488C2211yescharacteristic
38C2×#488C2211yescharacteristic
39C2×#488C2211yescharacteristic
40C2×#488C2211yescharacteristic
41C2×#484C2211yescharacteristic
42C2×#481C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#485C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#483C2211yescharacteristic
48C2×#480C2211yescharacteristic
49C2×#433C2211yescharacteristic
50C2×#433C2211yescharacteristic
51#2859C2211yescharacteristic
52#2858C2211yescharacteristic
53#2802—21no—
54#2802—21no—
55#2780—21no—
56#2780—21no—
57#2730—21no—
58#2730—21no—
59#2705—21no—
60#2705—21no—
61#2629C2211yescharacteristic
62#2629C2211yescharacteristic
63#2620C2211yescharacteristic
64#2620C2211yescharacteristic
65#2587—21no—
66#2587—21no—
67#2570C2211yescharacteristic
68#2570C2211yescharacteristic
69#2548—21no—
70#2542C2211yescharacteristic
71#2541C2211yescharacteristic
72#2538—21no—
73#2522—21no—
74#2522—21no—
75#2512—21no—
76#2445—21no—
77#2442C2211yescharacteristic
78#2442C2211yescharacteristic
79#2441C2211yescharacteristic
80#2441C2211yescharacteristic
81#2427C2211yescharacteristic
82#2427C2211yescharacteristic
83#2426C2211yescharacteristic
84#2426C2211yescharacteristic
85#2366C2211yescharacteristic
86#2365C2211yescharacteristic
87#2352C2211yescharacteristic
88#2352C2211yescharacteristic
89#2317C2211yescharacteristic
90#2317C2211yescharacteristic
91C4×C4⋊Q8C2211yescharacteristic
92C4×#125C2211yescharacteristic
93#2293C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2094C2211yescharacteristic
99#2093C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2034C2211yescharacteristic
130#2033C2211yescharacteristic
131#2033C2211yescharacteristic
132#2033C2211yescharacteristic
133#2033C2211yescharacteristic
134#1993C2211yescharacteristic
135#1992C2211yescharacteristic
136#1990C2211yescharacteristic
137#1990C2211yescharacteristic
138#1982C2211yescharacteristic
139#1982C2211yescharacteristic
140#1981C2211yescharacteristic
141#1981C2211yescharacteristic
142#1961C2211yescharacteristic
143#1961C2211yescharacteristic
144#1960C2211yescharacteristic
145#1960C2211yescharacteristic
146#1959C2211yescharacteristic
147#1959C2211yescharacteristic
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic
150#1958C2211yescharacteristic
151#1958C2211yescharacteristic
152#1955C2211yescharacteristic
153#1955C2211yescharacteristic
154#1949C2211yescharacteristic
155#1949C2211yescharacteristic
156#1949C2211yescharacteristic
157#1949C2211yescharacteristic
158#1942C2211yescharacteristic
159#1942C2211yescharacteristic
160#1941C2211yescharacteristic
161#1941C2211yescharacteristic
162#1940C2211yescharacteristic
163#1940C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1847C2211yescharacteristic
185#1845C2211yescharacteristic
186#1844C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202C4×#97C2211yescharacteristic
203#542—24no—
204#542—24no—
205#542—42no—
206#542—42no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127—21no—
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247#501—24no—
248#488—42no—
249#488—42no—
250#488—42no—
251#488—42no—
252#488—42no—
253#488—42no—
254#485—42no—
255#485—42no—
256#484—42no—
257#483—42no—
258#482—42no—
259#482—42no—
260#481—42no—
261#480—42no—
262#433—42no—
263#433—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#399—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#397—21no—
351#397—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#392—21no—
373#392—21no—
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390D411yescharacteristic
387#390D411yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
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#389—21no—
400#389—21no—
401#389—21no—
402#389D411yescharacteristic
403#389D411yescharacteristic
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#388D411yescharacteristic
417#388D411yescharacteristic
418#388D411yescharacteristic
419#388D411yescharacteristic
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#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#384—21no—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#380—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476C43C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C22×Q8—21no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8#4114yes—
529#127—22no—
530#127—22no—
531#127—82no—
532#126—44no—
533#126—44no—
534#125—22no—
535#125—22no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—41no—
540#124—22no—
541#124—22no—
542#124—22no—
543#124—22no—
544#124—41no—
545#124—41no—
546#124—41no—
547#124—41no—
548#124—44no—
549#124—44no—
550#123—44no—
551#123—44no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562#121—22no—
563#121—22no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569#121—41no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—82no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—82no—
582#117—22no—
583#117—22no—
584#117—22no—
585#117—22no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—41no—
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—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
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⋊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⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—22no—
704#107—22no—
705#107—22no—
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—22no—
713#106—22no—
714#106—22no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
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—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765#97—22no—
766#97—22no—
767#97—22no—
768#97—22no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—22no—
772C4×C8—22no—
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#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809C24—21no—
810C24—21no—
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813C2×Q8—24no—
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—81no—
827C2×Q8—81no—
828C2×D4—22no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
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—21no—
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—42no—
888C22×C4—42no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C2511yescharacteristic
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8H(5,𝔽2)12yes—
935C2×C8H(5,𝔽2)12yes—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
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⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4C2×#4112yes—
1001C4⋊C4C2×#4112yes—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—41no—
1047C42—41no—
1048C42—41no—
1049C42—41no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42C2×#4112yes—
1059C42H(5,𝔽2)12yes—
1060C422−1+412yes—
1061C422−1+412yes—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23C23×D411yescharacteristic
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—84no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—82no—
1109D4—84no—
1110D4—162no—
1111D4—162no—
1112D4—162no—
1113D4—162no—
1114D4—162no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
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—22no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
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—162no—
1198C2×C4—162no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4#53612yes—
1202C2×C4#53612yes—
1203C2×C4#54612yes—
1204C2×C4#54612yes—
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4C2×H(5,𝔽2)11yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4C2×2−1+411yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C8—22no—
1212C8—22no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22C2×#53611yescharacteristic
1248C22C2×#54611yescharacteristic
1249C22#349811yescharacteristic
1250C22#358411yescharacteristic
1251C22#358411yescharacteristic
1252C22#358511yescharacteristic
1253C22#358611yescharacteristic
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—42no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4#352211yescharacteristic
1281C4#352211yescharacteristic
1282C4#354811yescharacteristic
1283C4#354811yescharacteristic
1284C2—81no—
1285C2—81no—
1286C2—161no—
1287C2—161no—
1288C2#3895211yescharacteristic
1289C2#6087011yescharacteristic
1290C2#6087911yescharacteristic
1291C2#6120111yescharacteristic
1292C2#6120411yescharacteristic
1293C2#6246111yescharacteristic
1294C2#6246211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2541C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39494C2semidirect
3. #33237C2semidirect
4. #30644C2semidirect
5. #30643C2semidirect
6. #30642C2semidirect
7. #30641C2semidirect
8. #30640C2semidirect
9. #30639C2semidirect
10. #30638C2semidirect
11. #30637C2semidirect
12. #29850C2semidirect
13. #29849C2semidirect
14. #29207C2semidirect
15. #28752C2semidirect
16. #27921C2semidirect
17. #27920C2semidirect
18. #26541C2semidirect
19. #26540C2semidirect
20. #26539C2semidirect
21. #26538C2semidirect
22. #26249C2semidirect
24. #26247C2semidirect
26. #25684C2semidirect
27. #25684C2semidirect
28. #21871C2semidirect
29. #21871C2semidirect
30. #21731C2semidirect
31. #21269C2semidirect

Maximal subgroups

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

subgroupindex
#394942
#393872
#332372
#306442
#306432
#306422
#306412
#306402
#306392
#306382
#306372
#298502
#298492
#292072
#287522
#279212
#279202
#265412
#265402
#265392
#265382
#262492
#262482
#262472
#262462
#256842
#218712
#217312
#212692