Finite Group Databasebeta

← #7306169

Subgroups — #7306169

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59147C211yesmaximal, characteristic, complemented
2#39794C211yesmaximal, characteristic, complemented
3#32624C211yesmaximal, characteristic, complemented
4#32599C211yesmaximal, characteristic, complemented
5#32177C211yesmaximal, characteristic, complemented
6#32097C211yesmaximal, characteristic, complemented
7#32097C211yesmaximal, characteristic, complemented
8#31967C211yesmaximal, characteristic, complemented
9#31917C211yesmaximal, characteristic, complemented
10#31296C211yesmaximal, characteristic, complemented
11#31004C211yesmaximal, characteristic, complemented
12#31000C211yesmaximal, characteristic
13#30740C211yesmaximal, characteristic, complemented
14#30457C211yesmaximal, characteristic, complemented
15#30014C211yesmaximal, characteristic, complemented
16#29623C211yesmaximal, characteristic, complemented
17#29414C211yesmaximal, characteristic, complemented
18#27523C211yesmaximal, characteristic, complemented
19#26762C211yesmaximal, characteristic, complemented
20#26615C211yesmaximal, characteristic, complemented
21#26611C211yesmaximal, characteristic, complemented
22#26165C211yesmaximal, characteristic, complemented
23#25373C211yesmaximal, characteristic, complemented
24#25152C211yesmaximal, characteristic, complemented
25#24922C211yesmaximal, characteristic, complemented
26#24914C211yesmaximal, characteristic, complemented
27#24747C211yesmaximal, characteristic, complemented
28#24217C211yesmaximal, characteristic, complemented
29#24198C211yesmaximal, characteristic, complemented
30#24194C211yesmaximal, characteristic, complemented
31#23341C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#495C2211yescharacteristic, complemented
35C2×#464C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#464C2211yescharacteristic, complemented
38C2×#460C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#451C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#441C2211yescharacteristic, complemented
46C2×#440C2211yescharacteristic, complemented
47C2×C4×SD16C2211yescharacteristic
48#2854C2211yescharacteristic
49#2796—21no—
50#2782—21no—
51#2775—21no—
52#2771—21no—
53#2712—21no—
54#2710—21no—
55#2663—21no—
56#2596—21no—
57#2592C2211yescharacteristic
58#2581C2211yescharacteristic, complemented
59#2580C2211yescharacteristic, complemented
60#2573—21no—
61#2557—21no—
62#2548C2211yescharacteristic
63#2544C2211yescharacteristic
64#2544C2211yescharacteristic
65#2513C2211yescharacteristic, complemented
66#2509C2211yescharacteristic, complemented
67#2509C2211yescharacteristic, complemented
68#2495C2211yescharacteristic
69#2472—21no—
70#2459—21no—
71#2448C2211yescharacteristic
72#2448C2211yescharacteristic, complemented
73#2447C2211yescharacteristic
74#2436C2211yescharacteristic
75#2433C2211yescharacteristic
76#2426C2211yescharacteristic
77#2421C2211yescharacteristic
78#2420C2211yescharacteristic
79#2418—21no—
80#2412—21no—
81#2367C2211yescharacteristic
82#2367C2211yescharacteristic, complemented
83#2358—21no—
84#2351C2211yescharacteristic, complemented
85Q8×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2335—21no—
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×#121C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2036C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic, complemented
129#2014C2211yescharacteristic
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic, complemented
136#2011C2211yescharacteristic
137#2000C2211yescharacteristic
138#1999C2211yescharacteristic
139#1985C2211yescharacteristic, complemented
140#1984C2211yescharacteristic, complemented
141#1983C2211yescharacteristic
142#1983C2211yescharacteristic
143#1983C2211yescharacteristic, complemented
144#1973C2211yescharacteristic
145#1972C2211yescharacteristic
146#1970C2211yescharacteristic
147#1961C2211yescharacteristic
148#1961C2211yescharacteristic
149#1958C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1926C2211yescharacteristic, complemented
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic, complemented
176#1880C2211yescharacteristic, complemented
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1878C2211yescharacteristic, complemented
182#1878C2211yescharacteristic, complemented
183#1877C2211yescharacteristic, complemented
184#1877C2211yescharacteristic, complemented
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1863C2211yescharacteristic, complemented
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1862C2211yescharacteristic, complemented
193#1817C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1805C2211yescharacteristic, complemented
196#1804C2211yescharacteristic
197#1797C2211yescharacteristic
198#1787C2211yescharacteristic
199#1787C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215#559—42no—
216#559—42no—
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—42no—
223C2×#124—42no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8D411yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#495—42no—
257#464—42no—
258#464—42no—
259#464—42no—
260#463—42no—
261#460—42no—
262#459—42no—
263#451—42no—
264#450—42no—
265#448—42no—
266#447—42no—
267#441—42no—
268#440—42no—
269C4×SD16—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
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×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#395—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#392—21no—
361#392—21no—
362#391—21no—
363#391—21no—
364#391D411yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389D411yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387D411yescharacteristic
422#387D411yescharacteristic
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385D411yescharacteristic
441#385D411yescharacteristic
442#383—21no—
443#382—21no—
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#381—21no—
448#381—21no—
449#380—21no—
450#380D411yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571#127—22no—
572#127—41no—
573#127—41no—
574#127—41no—
575#124—22no—
576#124—22no—
577#124—22no—
578#124—22no—
579#124—22no—
580#124—22no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—44no—
590#124—44no—
591#124—44no—
592#123—44no—
593#123—44no—
594#123—44no—
595C22⋊Q8—22no—
596C22⋊Q8—42no—
597C22⋊Q8—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#120—44no—
603#120—82no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—44no—
625C4×D4—82no—
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⋊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⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
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⋊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—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—41no—
717C2×C42—41no—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—41no—
727#107—41no—
728#107—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738#103—22no—
739#103—22no—
740#103—22no—
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#102—22no—
754#102—22no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778#97—41no—
779#97—41no—
780C4×C8—41no—
781C4×C8—41no—
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#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
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—21no—
852C2×Q8—21no—
853C2×Q8—41no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—81no—
859C2×Q8—82no—
860C2×Q8—82no—
861C2×Q8—82no—
862C2×Q8—82no—
863C2×Q8H(5,𝔽2)12yes—
864C2×Q8H(5,𝔽2)12yes—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4H(5,𝔽2)12yes—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C2511yescharacteristic
967Q16—44no—
968Q16—82no—
969SD16—44no—
970SD16—44no—
971SD16—82no—
972SD16—82no—
973SD16—82no—
974D8—82no—
975D8—82no—
976D8—82no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—41no—
1102C42—41no—
1103C42—42no—
1104C42—42no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—84no—
1146C23—84no—
1147C23—84no—
1148C23—84no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23#57512yes—
1153C23C23×D411yescharacteristic
1154Q8—22no—
1155Q8—22no—
1156Q8—22no—
1157Q8—22no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—82no—
1167Q8—84no—
1168D4—22no—
1169D4—22no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—82no—
1271C2×C4—82no—
1272C2×C4—84no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—168no—
1327C22#348411yescharacteristic
1328C22#348711yescharacteristic
1329C22#348811yescharacteristic
1330C22C2×#57511yescharacteristic
1331C22#358411yescharacteristic
1332C22#358411yescharacteristic
1333C22#358511yescharacteristic
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—42no—
1348C4—42no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4#353311yescharacteristic
1360C4#353411yescharacteristic
1361C4#353411yescharacteristic
1362C4#356011yescharacteristic
1363C2—42no—
1364C2—82no—
1365C2—161no—
1366C2—161no—
1367C2—161no—
1368C2#4784011yescharacteristic
1369C2#6159711yescharacteristic
1370C2#6162511yescharacteristic
1371C2#6189511yescharacteristic
1372C2#6193111yescharacteristic
1373C2#6199211yescharacteristic
1374C2#6204911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31000C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59147C2semidirect
2. #39794C2semidirect
3. #32624C2semidirect
4. #32599C2semidirect
5. #32177C2semidirect
6. #32097C2semidirect
7. #32097C2semidirect
8. #31967C2semidirect
9. #31917C2semidirect
10. #31296C2semidirect
11. #31004C2semidirect
13. #30740C2semidirect
14. #30457C2semidirect
15. #30014C2semidirect
16. #29623C2semidirect
17. #29414C2semidirect
18. #27523C2semidirect
19. #26762C2semidirect
20. #26615C2semidirect
21. #26611C2semidirect
22. #26165C2semidirect
23. #25373C2semidirect
24. #25152C2semidirect
25. #24922C2semidirect
26. #24914C2semidirect
27. #24747C2semidirect
28. #24217C2semidirect
29. #24198C2semidirect
30. #24194C2semidirect
31. #23341C2semidirect
34. C2×#495C22semidirect
37. C2×#464C22semidirect
45. C2×#441C22semidirect
46. C2×#440C22semidirect
58. #2581C22semidirect
59. #2580C22semidirect
65. #2513C22semidirect
66. #2509C22semidirect
67. #2509C22semidirect
72. #2448C22semidirect
82. #2367C22semidirect
84. #2351C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
93. #2097C22semidirect
94. #2088C22semidirect
101. #2067C22semidirect
102. #2066C22semidirect
106. #2065C22semidirect
107. #2056C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2054C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
128. #2015C22semidirect
135. #2012C22semidirect
139. #1985C22semidirect
140. #1984C22semidirect
143. #1983C22semidirect
149. #1958C22semidirect
150. #1940C22semidirect
151. #1939C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
159. #1926C22semidirect
161. #1925C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1918C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
172. #1916C22semidirect
175. #1880C22semidirect
176. #1880C22semidirect
179. #1879C22semidirect
180. #1878C22semidirect
181. #1878C22semidirect
182. #1878C22semidirect
183. #1877C22semidirect
184. #1877C22semidirect
185. #1865C22semidirect
187. #1864C22semidirect
188. #1863C22semidirect
189. #1863C22semidirect
192. #1862C22semidirect
194. #1805C22semidirect
195. #1805C22semidirect

Maximal subgroups

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

subgroupindex
#591472
#397942
#326242
#325992
#321772
#320972
#319672
#319172
#312962
#310042
#310002
#307402
#304572
#300142
#296232
#294142
#275232
#267622
#266152
#266112
#261652
#253732
#251522
#249222
#249142
#247472
#242172
#241982
#241942
#233412