Finite Group Databasebeta

← #7086370

Subgroups — #7086370

Order 512.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45081C211yesmaximal, characteristic, complemented
2#45038C211yesmaximal, characteristic, complemented
3#32066C211yesmaximal, characteristic, complemented
4#31965C211yesmaximal, characteristic, complemented
5#31634C211yesmaximal, characteristic, complemented
6#31490C211yesmaximal, characteristic, complemented
7#31222C211yesmaximal, characteristic, complemented
8#30914C211yesmaximal, characteristic, complemented
9#30749C211yesmaximal, characteristic, complemented
10#30468C211yesmaximal, characteristic, complemented
11#29545C211yesmaximal, characteristic, complemented
12#29087C211yesmaximal, characteristic, complemented
13#28171C211yesmaximal, characteristic, complemented
14#27374C211yesmaximal, characteristic, complemented
15#27113C211yesmaximal, characteristic, complemented
16#27093C211yesmaximal, characteristic, complemented
17#26962C211yesmaximal, characteristic, complemented
18#26904C211yesmaximal, characteristic, complemented
19#26675C211yesmaximal, characteristic, complemented
20#26160C211yesmaximal, characteristic, complemented
21#25168C211yesmaximal, characteristic, complemented
22#25168C211yesmaximal, characteristic, complemented
23#25088C211yesmaximal, characteristic, complemented
24#24829C211yesmaximal, characteristic, complemented
25#24626C211yesmaximal, characteristic, complemented
26#24531C211yesmaximal, characteristic, complemented
27#23693C211yesmaximal, characteristic, complemented
28#23193C211yesmaximal, characteristic, complemented
29#22870C211yesmaximal, characteristic, complemented
30#22346C211yesmaximal, characteristic, complemented
31#22158C211yesmaximal, characteristic, complemented
32C2×#496C2211yescharacteristic
33C2×#476C2211yescharacteristic, complemented
34C2×#465C2211yescharacteristic
35C2×#463C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic, complemented
45C2×C4×D8C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2778—21no—
48#2753—21no—
49#2746—21no—
50#2743—21no—
51#2735—21no—
52#2728—21no—
53#2708—21no—
54#2688—21no—
55#2561—21no—
56#2543—21no—
57#2542C2211yescharacteristic
58#2541C2211yescharacteristic, complemented
59#2535—21no—
60#2513C2211yescharacteristic, complemented
61#2508C2211yescharacteristic, complemented
62#2504C2211yescharacteristic
63#2497C2211yescharacteristic
64#2492C2211yescharacteristic
65#2482—21no—
66#2477—21no—
67#2456—21no—
68#2452C2211yescharacteristic
69#2447C2211yescharacteristic
70#2447C2211yescharacteristic
71#2445C2211yescharacteristic, complemented
72#2444—21no—
73#2437—21no—
74#2435C2211yescharacteristic
75#2428C2211yescharacteristic
76#2428C2211yescharacteristic
77#2428C2211yescharacteristic
78#2423C2211yescharacteristic
79#2401C2211yescharacteristic
80#2367C2211yescharacteristic
81#2366C2211yescharacteristic, complemented
82#2361C2211yescharacteristic
83#2361C2211yescharacteristic
84#2354C2211yescharacteristic
85#2349C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88#2328C2211yescharacteristic, complemented
89#2326C2211yescharacteristic
90#2319C2211yescharacteristic
91#2319C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2041C2211yescharacteristic, complemented
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2023C2211yescharacteristic, complemented
123#2014C2211yescharacteristic, complemented
124#2014C2211yescharacteristic, complemented
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#2011C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1993C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1982C2211yescharacteristic, complemented
135#1982C2211yescharacteristic, complemented
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1970C2211yescharacteristic
140#1957C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1919C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1880C2211yescharacteristic, complemented
167#1880C2211yescharacteristic, complemented
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic, complemented
184#1864C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1852C2211yescharacteristic
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic
190#1832C2211yescharacteristic, complemented
191#1824C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1802C2211yescharacteristic, complemented
197#1776C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1768C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250#496—24no—
251#476—42no—
252#465—42no—
253#463—42no—
254#463—42no—
255#459—24no—
256#459—42no—
257#447—24no—
258#447—42no—
259#447—42no—
260#442—42no—
261#442—42no—
262C4×SD16—42no—
263C4×D8—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102—42no—
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#401D411yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#400D411yescharacteristic
322#400D411yescharacteristic
323#400D411yescharacteristic
324#399—21no—
325#399—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397D411yescharacteristic
338#397D411yescharacteristic
339#397D411yescharacteristic
340#396—21no—
341#396—21no—
342#396D411yescharacteristic
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#391—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382—21no—
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#381—21no—
438#381—21no—
439#381—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376C2311yescharacteristic
462C2×#95—21no—
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
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#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8#4114yes—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568#127—22no—
569#127—22no—
570#127—41no—
571#127—41no—
572#127—41no—
573#127—41no—
574#124—22no—
575#124—22no—
576#124—41no—
577#124—41no—
578#123—82no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—82no—
582C22⋊Q8—82no—
583C22⋊Q8—82no—
584#121—22no—
585#121—22no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—82no—
591#121—82no—
592#121—82no—
593#121—82no—
594#121—82no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—82no—
616C4×D4—82no—
617C4×D4—82no—
618#117—82no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
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—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—82no—
699C2×C22⋊C4—82no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—41no—
718#107—41no—
719#106—22no—
720#106—22no—
721#106—22no—
722#106—41no—
723#106—41no—
724C4⋊C8—22no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
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—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—22no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764#97—22no—
765#97—41no—
766#97—41no—
767C4×C8—41no—
768C4×C8—41no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
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
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—42no—
829C2×Q8—81no—
830C2×Q8—81no—
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—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—44no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4C2×#4112yes—
893C2×D4C2×#4112yes—
894C2×D4H(5,𝔽2)12yes—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2511yescharacteristic
956SD16—44no—
957SD16—82no—
958SD16—82no—
959D8—44no—
960D8—44no—
961D8—44no—
962D8—82no—
963D8—82no—
964D8—82no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
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—82no—
989C2×C8C2×#4112yes—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—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—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4H(5,𝔽2)12yes—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
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—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
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—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—42no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
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—84no—
1142C23—84no—
1143C23—84no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23#57712yes—
1149C23C23×D411yescharacteristic
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—162no—
1155D4—22no—
1156D4—22no—
1157D4—22no—
1158D4—22no—
1159D4—22no—
1160D4—22no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—84no—
1176D4—84no—
1177D4—84no—
1178D4—84no—
1179D4—162no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
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—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—22no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
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—84no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4#57612yes—
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C2×C4#58511yescharacteristic
1277C8—22no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
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—81no—
1327C22—168no—
1328C22D4×#4111yescharacteristic
1329C22#348811yescharacteristic
1330C22#348811yescharacteristic
1331C22C2×#57611yescharacteristic
1332C22C2×#57711yescharacteristic
1333C22#358511yescharacteristic
1334C22#358511yescharacteristic
1335C4—22no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4#350511yescharacteristic
1360C4#351311yescharacteristic
1361C4#354211yescharacteristic
1362C4#356611yescharacteristic
1363C2—42no—
1364C2—82no—
1365C2—82no—
1366C2—82no—
1367C2—161no—
1368C2—161no—
1369C2#4416511yescharacteristic
1370C2#6149611yescharacteristic
1371C2#6150511yescharacteristic
1372C2#6200711yescharacteristic
1373C2#6201611yescharacteristic
1374C2#6201811yescharacteristic
1375C2#6203711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45081C2semidirect
2. #45038C2semidirect
3. #32066C2semidirect
4. #31965C2semidirect
5. #31634C2semidirect
6. #31490C2semidirect
7. #31222C2semidirect
8. #30914C2semidirect
9. #30749C2semidirect
10. #30468C2semidirect
11. #29545C2semidirect
12. #29087C2semidirect
13. #28171C2semidirect
14. #27374C2semidirect
15. #27113C2semidirect
16. #27093C2semidirect
17. #26962C2semidirect
18. #26904C2semidirect
19. #26675C2semidirect
20. #26160C2semidirect
21. #25168C2semidirect
22. #25168C2semidirect
23. #25088C2semidirect
24. #24829C2semidirect
25. #24626C2semidirect
26. #24531C2semidirect
27. #23693C2semidirect
28. #23193C2semidirect
29. #22870C2semidirect
30. #22346C2semidirect
31. #22158C2semidirect
33. C2×#476C22semidirect
44. C2×C4×SD16C22semidirect
58. #2541C22semidirect
60. #2513C22semidirect
61. #2508C22semidirect
71. #2445C22semidirect
81. #2366C22semidirect
85. #2349C22semidirect
88. #2328C22semidirect
91. #2319C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
94. #2088C22semidirect
95. #2086C22semidirect
96. #2084C22semidirect
97. #2084C22semidirect
98. #2074C22semidirect
101. #2071C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
107. #2065C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
116. #2041C22semidirect
121. #2023C22semidirect
122. #2023C22semidirect
123. #2014C22semidirect
124. #2014C22semidirect
132. #1993C22semidirect
134. #1982C22semidirect
135. #1982C22semidirect
136. #1973C22semidirect
140. #1957C22semidirect
141. #1949C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
148. #1934C22semidirect
149. #1933C22semidirect
152. #1925C22semidirect
153. #1925C22semidirect
157. #1919C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
161. #1917C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
166. #1880C22semidirect
167. #1880C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
183. #1864C22semidirect
184. #1864C22semidirect
186. #1862C22semidirect
190. #1832C22semidirect
194. #1802C22semidirect
195. #1802C22semidirect
196. #1802C22semidirect
197. #1776C22semidirect
198. #1771C22semidirect
199. #1768C22semidirect
200. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#450812
#450382
#320662
#319652
#316342
#314902
#312222
#309142
#307492
#304682
#295452
#290872
#281712
#273742
#271132
#270932
#269622
#269042
#266752
#261602
#251682
#250882
#248292
#246262
#245312
#236932
#231932
#228702
#223462
#221582