Finite Group Databasebeta

← #7009957

Subgroups — #7009957

Order 512.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C211yesmaximal, characteristic, complemented
2#39384C211yesmaximal, characteristic, complemented
3#32655C211yesmaximal, characteristic, complemented
4#32605C211yesmaximal, characteristic, complemented
5#32533C211yesmaximal, characteristic, complemented
6#32394C211yesmaximal, characteristic, complemented
7#31929C211yesmaximal, characteristic, complemented
8#31910C211yesmaximal, characteristic, complemented
9#31592C211yesmaximal, characteristic, complemented
10#31218C211yesmaximal, characteristic, complemented
11#28882C211yesmaximal, characteristic, complemented
12#28343C211yesmaximal, characteristic, complemented
13#28301C211yesmaximal, characteristic
14#28276C211yesmaximal, characteristic, complemented
15#28029C211yesmaximal, characteristic, complemented
16#27939C211yesmaximal, characteristic, complemented
17#27218C211yesmaximal, characteristic, complemented
18#26608C211yesmaximal, characteristic, complemented
19#26542C211yesmaximal, characteristic, complemented
20#26102C211yesmaximal, characteristic, complemented
21#25305C211yesmaximal, characteristic, complemented
22#25212C211yesmaximal, characteristic, complemented
23#25088C211yesmaximal, characteristic, complemented
24#24753C211yesmaximal, characteristic, complemented
25#24576C211yesmaximal, characteristic, complemented
26#24526C211yesmaximal, characteristic, complemented
27C2×#2067C211yesmaximal, characteristic, complemented
28#22956C211yesmaximal, characteristic, complemented
29#22938C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic, complemented
31#22078C211yesmaximal, characteristic, complemented
32C2×#539—21no—
33C2×#483C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#460C2211yescharacteristic, complemented
39C2×#463C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#446C2211yescharacteristic, complemented
43C2×#442C2211yescharacteristic
44C22×#107C2211yescharacteristic
45C22×C4⋊C8C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2856C2211yescharacteristic
49#2796—21no—
50#2751—21no—
51#2732—21no—
52#2727—21no—
53#2694—21no—
54#2694—21no—
55#2618—21no—
56#2595—21no—
57#2592C2211yescharacteristic
58#2580C2211yescharacteristic
59#2561—21no—
60#2552C2211yescharacteristic, complemented
61#2552C2211yescharacteristic, complemented
62#2538C2211yescharacteristic, complemented
63#2538C2211yescharacteristic, complemented
64#2516—21no—
65#2513C2211yescharacteristic
66#2513C2211yescharacteristic
67#2512C2211yescharacteristic, complemented
68#2512C2211yescharacteristic, complemented
69#2503C2211yescharacteristic
70#2501C2211yescharacteristic
71#2501C2211yescharacteristic
72#2483—21no—
73#2482—21no—
74#2448C2211yescharacteristic
75#2447C2211yescharacteristic
76#2445C2211yescharacteristic, complemented
77#2445C2211yescharacteristic, complemented
78#2435C2211yescharacteristic
79#2425—21no—
80#2425—21no—
81#2367C2211yescharacteristic
82#2361C2211yescharacteristic
83#2361C2211yescharacteristic
84#2357C2211yescharacteristic
85#2344C2211yescharacteristic
86#2342—21no—
87D4×C22⋊C4C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C2×#390C2211yescharacteristic
91C2×#389C2211yescharacteristic
92#2095C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2093C2211yescharacteristic
98#2092C2211yescharacteristic, complemented
99#2092C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2083C2211yescharacteristic, complemented
102#2083C2211yescharacteristic, complemented
103#2073C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic, complemented
116#2067C2211yescharacteristic, complemented
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic, complemented
119#2065C2211yescharacteristic, complemented
120#2055C2211yescharacteristic, complemented
121#2055C2211yescharacteristic, complemented
122#2055C2211yescharacteristic, complemented
123#2054C2211yescharacteristic
124#2054C2211yescharacteristic
125#2054C2211yescharacteristic
126#2042C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#1984C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1982C2211yescharacteristic, complemented
135#1973C2211yescharacteristic, complemented
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic
140#1970C2211yescharacteristic
141#1970C2211yescharacteristic
142#1970C2211yescharacteristic
143#1970C2211yescharacteristic
144#1959C2211yescharacteristic
145#1959C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1948C2211yescharacteristic, complemented
148#1947C2211yescharacteristic, complemented
149#1947C2211yescharacteristic, complemented
150#1943C2211yescharacteristic, complemented
151#1941C2211yescharacteristic, complemented
152#1941C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1940C2211yescharacteristic, complemented
155#1939C2211yescharacteristic, complemented
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic, complemented
158#1933C2211yescharacteristic, complemented
159#1933C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1925C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1921C2211yescharacteristic, complemented
168#1919C2211yescharacteristic, complemented
169#1919C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1893C2211yescharacteristic
173#1893C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic, complemented
185#1853C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1847C2211yescharacteristic, complemented
190#1823C2211yescharacteristic
191#1804C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#539—48no—
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8D411yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#483—24no—
252#480—24no—
253#480—42no—
254#465—42no—
255#465—42no—
256#463—42no—
257#460—42no—
258#447—24no—
259#447—42no—
260#446—42no—
261#442—42no—
262C2×#107—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8—42no—
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
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×#102—42no—
293C2×#102—42no—
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—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#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#393—21no—
359#393—21no—
360#391D411yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389D411yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
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#387—21no—
415#387—21no—
416#387—21no—
417#387D411yescharacteristic
418#387D411yescharacteristic
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385D411yescharacteristic
433#385D411yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#381—21no—
444#381—21no—
445#381—21no—
446#380—21no—
447#380—21no—
448#380D411yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452#379—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C2×#95—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
494C25—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C22×C8—22no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554#127—41no—
555#127—41no—
556#126—44no—
557#126—44no—
558#125—44no—
559#125—44no—
560#124—22no—
561#124—41no—
562#124—41no—
563#124—41no—
564#123—44no—
565#123—44no—
566#123—44no—
567#123—44no—
568#123—82no—
569#123—82no—
570C22⋊Q8—24no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—44no—
580#121—82no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×D4—22no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—44no—
594C4×D4—44no—
595#117—82no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
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—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
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×C22⋊C4—21no—
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⋊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—44no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—41no—
705C2×C42—41no—
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#107—22no—
715#107—22no—
716#107—41no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#106—22no—
723#106—22no—
724#106—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#103—22no—
737#103—22no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
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—
764C22⋊C8—22no—
765C22⋊C8#4114yes—
766#97—22no—
767#97—41no—
768#97—41no—
769#97—41no—
770C4×C8—41no—
771C4×C8—41no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C2×Q8—22no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—41no—
827C2×Q8—41no—
828C2×D4—21no—
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—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D42−1+412yes—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
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—21no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4AGL(1,ℤ/8)14yes—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C2×#4112yes—
928C22×C4H(5,𝔽2)12yes—
929C22×C4C2511yescharacteristic
930SD16—82no—
931SD16—82no—
932D8—44no—
933D8—82no—
934D8—82no—
935D8—82no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—44no—
958C2×C8—82no—
959C2×C8C2×#4112yes—
960C2×C8C2×#4112yes—
961C2×C8H(5,𝔽2)12yes—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—41no—
1078C42—41no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23#55012yes—
1125C23C2×AGL(1,ℤ/8)12yes—
1126C23#57612yes—
1127C23C23×D411yescharacteristic
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—82no—
1133D4—22no—
1134D4—22no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—84no—
1150D4—84no—
1151D4—84no—
1152D4—162no—
1153D4—162no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—44no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—82no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4#55012yes—
1240C2×C4C2×AGL(1,ℤ/8)12yes—
1241C2×C4C2×AGL(1,ℤ/8)12yes—
1242C2×C4C22×#4111yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×2−1+411yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C8—22no—
1249C8—22no—
1250C8—22no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—168no—
1291C22#339914yes—
1292C22C2×#55011yescharacteristic
1293C22#348911yescharacteristic
1294C22#349611yescharacteristic
1295C22C22×AGL(1,ℤ/8)11yescharacteristic
1296C22C2×#57611yescharacteristic
1297C22#358411yescharacteristic
1298C22#358611yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#352011yescharacteristic
1325C4#352111yescharacteristic
1326C4#353411yescharacteristic
1327C4#353511yescharacteristic
1328C2—24no—
1329C2—82no—
1330C2—161no—
1331C2—161no—
1332C2—161no—
1333C2#4302911yescharacteristic
1334C2C2×#339911yescharacteristic
1335C2#6142311yescharacteristic
1336C2#6210711yescharacteristic
1337C2#6221111yescharacteristic
1338C2#6225311yescharacteristic
1339C2#6231111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28301C2
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. #59862C2semidirect
2. #39384C2semidirect
3. #32655C2semidirect
4. #32605C2semidirect
5. #32533C2semidirect
6. #32394C2semidirect
7. #31929C2semidirect
8. #31910C2semidirect
9. #31592C2semidirect
10. #31218C2semidirect
11. #28882C2semidirect
12. #28343C2semidirect
14. #28276C2semidirect
15. #28029C2semidirect
16. #27939C2semidirect
17. #27218C2semidirect
18. #26608C2semidirect
19. #26542C2semidirect
20. #26102C2semidirect
21. #25305C2semidirect
22. #25212C2semidirect
23. #25088C2semidirect
24. #24753C2semidirect
25. #24576C2semidirect
26. #24526C2semidirect
27. C2×#2067C2semidirect
28. #22956C2semidirect
29. #22938C2semidirect
30. #22858C2semidirect
31. #22078C2semidirect
38. C2×#460C22semidirect
42. C2×#446C22semidirect
60. #2552C22semidirect
61. #2552C22semidirect
62. #2538C22semidirect
63. #2538C22semidirect
67. #2512C22semidirect
68. #2512C22semidirect
76. #2445C22semidirect
77. #2445C22semidirect
92. #2095C22semidirect
93. #2095C22semidirect
98. #2092C22semidirect
99. #2092C22semidirect
100. #2085C22semidirect
101. #2083C22semidirect
102. #2083C22semidirect
103. #2073C22semidirect
106. #2068C22semidirect
115. #2067C22semidirect
116. #2067C22semidirect
118. #2065C22semidirect
119. #2065C22semidirect
120. #2055C22semidirect
121. #2055C22semidirect
122. #2055C22semidirect
132. #1984C22semidirect
134. #1982C22semidirect
135. #1973C22semidirect
136. #1973C22semidirect
146. #1949C22semidirect
147. #1948C22semidirect
148. #1947C22semidirect
149. #1947C22semidirect
150. #1943C22semidirect
151. #1941C22semidirect
152. #1941C22semidirect
153. #1940C22semidirect
154. #1940C22semidirect
155. #1939C22semidirect
157. #1936C22semidirect
158. #1933C22semidirect
159. #1933C22semidirect
160. #1928C22semidirect
163. #1926C22semidirect
164. #1925C22semidirect
165. #1925C22semidirect
166. #1921C22semidirect
167. #1921C22semidirect
168. #1919C22semidirect
169. #1919C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
179. #1877C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
184. #1864C22semidirect
188. #1847C22semidirect
189. #1847C22semidirect
191. #1804C22semidirect
192. #1803C22semidirect
195. #1776C22semidirect
196. #1770C22semidirect
198. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#393842
#326552
#326052
#325332
#323942
#319292
#319102
#315922
#312182
#288822
#283432
#283012
#282762
#280292
#279392
#272182
#266082
#265422
#261022
#253052
#252122
#250882
#247532
#245762
#245262
C2×#20672
#229562
#229382
#228582
#220782