Finite Group Databasebeta

← #7549642

Subgroups — #7549642

Order 512.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45108C211yesmaximal, characteristic
2#35993C211yesmaximal, characteristic, complemented
3#32200C211yesmaximal, characteristic, complemented
4#32171C211yesmaximal, characteristic, complemented
5#31811C211yesmaximal, characteristic, complemented
6#31302C211yesmaximal, characteristic, complemented
7#29031C211yesmaximal, characteristic, complemented
8#28911C211yesmaximal, characteristic, complemented
9#27413C211yesmaximal, characteristic, complemented
10#27274C211yesmaximal, characteristic, complemented
11#27245C211yesmaximal, characteristic, complemented
12#27191C211yesmaximal, characteristic, complemented
13#26998C211yesmaximal, characteristic, complemented
14#26764C211yesmaximal, characteristic, complemented
15#26743C211yesmaximal, characteristic, complemented
16#26336C211yesmaximal, characteristic, complemented
17#26221C211yesmaximal, characteristic, complemented
18#25514C211yesmaximal, characteristic, complemented
19#25275C211yesmaximal, characteristic, complemented
20#25089C211yesmaximal, characteristic, complemented
21#25084C211yesmaximal, characteristic, complemented
22#24781C211yesmaximal, characteristic, complemented
23#24515C211yesmaximal, characteristic, complemented
24#24452C211yesmaximal, characteristic
25#23138C211yesmaximal, characteristic, complemented
26#23111C211yesmaximal, characteristic, complemented
27#22901C211yesmaximal, characteristic, complemented
28#22570C211yesmaximal, characteristic, complemented
29#22414C211yesmaximal, characteristic
30#21397C211yesmaximal, characteristic, complemented
31#21067C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#487C2211yescharacteristic, complemented
35C2×#474C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C2×#433C2211yescharacteristic, complemented
44C22×#107C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2708—21no—
49#2695—21no—
50#2687—21no—
51#2684—21no—
52#2655—21no—
53#2625C2211yescharacteristic, complemented
54#2577—21no—
55#2576—21no—
56#2547C2211yescharacteristic
57#2534—21no—
58#2520—21no—
59#2515—21no—
60#2514C2211yescharacteristic, complemented
61#2508C2211yescharacteristic, complemented
62#2497C2211yescharacteristic
63#2492C2211yescharacteristic
64#2492C2211yescharacteristic
65#2480—21no—
66#2477—21no—
67#2452C2211yescharacteristic
68#2447C2211yescharacteristic
69#2440C2211yescharacteristic, complemented
70#2437—21no—
71#2435C2211yescharacteristic
72#2432C2211yescharacteristic
73#2429C2211yescharacteristic
74#2427—21no—
75#2421—21no—
76#2417C2211yescharacteristic
77#2417C2211yescharacteristic
78#2396—21no—
79#2395C2211yescharacteristic
80#2367C2211yescharacteristic
81#2365C2211yescharacteristic, complemented
82#2362C2211yescharacteristic, complemented
83#2361C2211yescharacteristic
84#2360C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86#2352C2211yescharacteristic
87#2344C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2311C2211yescharacteristic
90#2274C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2093C2211yescharacteristic
93#2086C2211yescharacteristic, complemented
94#2076C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2072C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2057C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2043C2211yescharacteristic, complemented
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2024C2211yescharacteristic, complemented
118#2023C2211yescharacteristic
119#2016C2211yescharacteristic, complemented
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2001C2211yescharacteristic
123#1988C2211yescharacteristic, complemented
124#1987C2211yescharacteristic, complemented
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1981C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1969C2211yescharacteristic, complemented
131#1969C2211yescharacteristic, complemented
132#1959C2211yescharacteristic
133#1958C2211yescharacteristic
134#1947C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1921C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1823C2211yescharacteristic
186#1808C2211yescharacteristic
187#1804C2211yescharacteristic
188#1788C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1771C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#542—24no—
215#542—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×C4×Q8—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253#487—42no—
254#474—42no—
255#468—24no—
256#467—42no—
257#467—42no—
258#464—24no—
259#452—42no—
260#450—42no—
261C8×D4—42no—
262#433—42no—
263C2×#107—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277#417—42no—
278#416—24no—
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
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×#102—24no—
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×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400D411yescharacteristic
330#399D411yescharacteristic
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397D411yescharacteristic
345#397D411yescharacteristic
346#397D411yescharacteristic
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394D411yescharacteristic
358#394D411yescharacteristic
359#393—21no—
360#393—21no—
361#393—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
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#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—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#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#383—21no—
427#382—21no—
428#382—21no—
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#126—44no—
565#124—22no—
566#124—22no—
567#124—22no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—44no—
572#123—44no—
573#123—44no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—44no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—82no—
586C22⋊Q8—82no—
587#121—22no—
588#121—44no—
589#121#4114yes—
590#120—44no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—82no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—82no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—41no—
609#117—82no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—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—21no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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×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—44no—
687C2×C22⋊C4—82no—
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
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—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#107—22no—
714#107—22no—
715#107—22no—
716#107—41no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102#4114yes—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763#97—41no—
764#97—41no—
765C4×C8—41no—
766C4×C8—41no—
767C4×C8—41no—
768#95—21no—
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#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#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826#41—44no—
827#41—44no—
828#41—82no—
829#41—82no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
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—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—81no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4C2×#4112yes—
881C2×D4C2×#4112yes—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
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—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
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×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C2×#4112yes—
940C22×C4H(5,𝔽2)12yes—
941C22×C4C2511yescharacteristic
942Q16—82no—
943Q16—82no—
944SD16—82no—
945SD16—82no—
946M16—82no—
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—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—44no—
971C2×C8—82no—
972C2×C8C2×#4112yes—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
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—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
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—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4C2×#4112yes—
1024C4⋊C4C2×#4112yes—
1025C4⋊C4H(5,𝔽2)12yes—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—24no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
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—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—22no—
1097C23—22no—
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—84no—
1111C23—84no—
1112C23—84no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23#54612yes—
1118C23#57812yes—
1119C23C23×D411yescharacteristic
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—84no—
1133Q8—162no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—22no—
1138D4—44no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
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—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—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—84no—
1231C2×C4—84no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#54612yes—
1238C2×C4#57612yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—22no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—168no—
1282C22C2×#54611yescharacteristic
1283C22D4×#4111yescharacteristic
1284C22#348811yescharacteristic
1285C22C2×#57611yescharacteristic
1286C22C2×#57811yescharacteristic
1287C22#358411yescharacteristic
1288C22#358611yescharacteristic
1289C4—22no—
1290C4—22no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4#347511yescharacteristic
1316C4#351411yescharacteristic
1317C4#351911yescharacteristic
1318C4#356011yescharacteristic
1319C2—42no—
1320C2—42no—
1321C2—82no—
1322C2—82no—
1323C2#5909111yescharacteristic
1324C2#6117311yescharacteristic
1325C2#6119911yescharacteristic
1326C2#6148211yescharacteristic
1327C2#6153811yescharacteristic
1328C2#6202011yescharacteristic
1329C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35993C2semidirect
3. #32200C2semidirect
4. #32171C2semidirect
5. #31811C2semidirect
6. #31302C2semidirect
7. #29031C2semidirect
8. #28911C2semidirect
9. #27413C2semidirect
10. #27274C2semidirect
11. #27245C2semidirect
12. #27191C2semidirect
13. #26998C2semidirect
14. #26764C2semidirect
15. #26743C2semidirect
16. #26336C2semidirect
17. #26221C2semidirect
18. #25514C2semidirect
19. #25275C2semidirect
20. #25089C2semidirect
21. #25084C2semidirect
22. #24781C2semidirect
23. #24515C2semidirect
25. #23138C2semidirect
26. #23111C2semidirect
27. #22901C2semidirect
28. #22570C2semidirect
30. #21397C2semidirect
31. #21067C2semidirect
34. C2×#487C22semidirect
38. C2×#467C22semidirect
43. C2×#433C22semidirect
44. C22×#107C22semidirect
53. #2625C22semidirect
60. #2514C22semidirect
61. #2508C22semidirect
69. #2440C22semidirect
81. #2365C22semidirect
82. #2362C22semidirect
85. #2355C22semidirect
90. #2274C22semidirect
91. #2101C22semidirect
93. #2086C22semidirect
95. #2074C22semidirect
96. #2072C22semidirect
97. #2068C22semidirect
98. #2068C22semidirect
99. #2068C22semidirect
100. #2068C22semidirect
103. #2057C22semidirect
104. #2057C22semidirect
105. #2056C22semidirect
108. #2043C22semidirect
117. #2024C22semidirect
119. #2016C22semidirect
123. #1988C22semidirect
124. #1987C22semidirect
128. #1981C22semidirect
130. #1969C22semidirect
131. #1969C22semidirect
134. #1947C22semidirect
135. #1942C22semidirect
136. #1939C22semidirect
138. #1935C22semidirect
139. #1935C22semidirect
142. #1933C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
155. #1921C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1916C22semidirect
160. #1916C22semidirect
161. #1894C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
172. #1873C22semidirect
175. #1872C22semidirect
176. #1872C22semidirect
178. #1863C22semidirect
182. #1852C22semidirect
184. #1850C22semidirect
191. #1771C22semidirect
192. #1763C22semidirect
193. #1763C22semidirect
195. C4×#103C22semidirect
199. #1753C22semidirect
201. #1736C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#451082
#359932
#322002
#321712
#318112
#313022
#290312
#289112
#274132
#272742
#272452
#271912
#269982
#267642
#267432
#263362
#262212
#255142
#252752
#250892
#250842
#247812
#245152
#244522
#231382
#231112
#229012
#225702
#224142
#213972
#210672