Finite Group Databasebeta

← #7026062

Subgroups — #7026062

Order 512.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45235C211yesmaximal, characteristic, complemented
2#45108C211yesmaximal, characteristic
3#32089C211yesmaximal, characteristic, complemented
4#31875C211yesmaximal, characteristic, complemented
5#31722C211yesmaximal, characteristic, complemented
6#31301C211yesmaximal, characteristic, complemented
7#30996C211yesmaximal, characteristic, complemented
8#30668C211yesmaximal, characteristic, complemented
9#30569C211yesmaximal, characteristic, complemented
10#30450C211yesmaximal, characteristic, complemented
11#28874C211yesmaximal, characteristic, complemented
12#28133C211yesmaximal, characteristic, complemented
13#27409C211yesmaximal, characteristic, complemented
14#27091C211yesmaximal, characteristic, complemented
15#27033C211yesmaximal, characteristic, complemented
16#26928C211yesmaximal, characteristic, complemented
17#26902C211yesmaximal, characteristic, complemented
18#26726C211yesmaximal, characteristic, complemented
19#26181C211yesmaximal, characteristic, complemented
20#25415C211yesmaximal, characteristic, complemented
21#25365C211yesmaximal, characteristic, complemented
22#25176C211yesmaximal, characteristic, complemented
23#25084C211yesmaximal, characteristic, complemented
24#24426C211yesmaximal, characteristic
25#24247C211yesmaximal, characteristic
26#24169C211yesmaximal, characteristic, complemented
27#23585C211yesmaximal, characteristic, complemented
28#23000C211yesmaximal, characteristic, complemented
29#22574C211yesmaximal, characteristic, complemented
30#22358C211yesmaximal, characteristic, complemented
31#22057C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#494C2211yescharacteristic, complemented
35C2×#483C2211yescharacteristic, complemented
36C2×#475C2211yescharacteristic, complemented
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#461C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×C4×Q16C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2802—21no—
52#2779—21no—
53#2772—21no—
54#2766—21no—
55#2708—21no—
56#2695—21no—
57#2687—21no—
58#2684—21no—
59#2594—21no—
60#2547C2211yescharacteristic
61#2536C2211yescharacteristic
62#2534—21no—
63#2522—21no—
64#2518—21no—
65#2514C2211yescharacteristic, complemented
66#2508C2211yescharacteristic, complemented
67#2494—21no—
68#2494C2211yescharacteristic, complemented
69#2492C2211yescharacteristic
70#2480—21no—
71#2452C2211yescharacteristic
72#2447C2211yescharacteristic
73#2437—21no—
74#2435C2211yescharacteristic
75#2432C2211yescharacteristic
76#2429C2211yescharacteristic
77#2429C2211yescharacteristic
78#2429C2211yescharacteristic, complemented
79#2427—21no—
80#2421C2211yescharacteristic
81#2417C2211yescharacteristic
82#2417C2211yescharacteristic
83#2395C2211yescharacteristic
84#2367C2211yescharacteristic
85#2365C2211yescharacteristic, complemented
86#2361C2211yescharacteristic
87#2360C2211yescharacteristic
88#2351C2211yescharacteristic, complemented
89#2345C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2323C2211yescharacteristic, complemented
92#2323C2211yescharacteristic, complemented
93#2311C2211yescharacteristic
94#2097C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2057C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2043C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2013C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic, complemented
131#2001C2211yescharacteristic, complemented
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1987C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1981C2211yescharacteristic, complemented
137#1973C2211yescharacteristic
138#1969C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1958C2211yescharacteristic
141#1958C2211yescharacteristic
142#1954C2211yescharacteristic
143#1949C2211yescharacteristic, complemented
144#1942C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic, complemented
161#1923C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1872C2211yescharacteristic
177#1872C2211yescharacteristic
178#1872C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1852C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1824C2211yescharacteristic
189#1824C2211yescharacteristic, complemented
190#1807C2211yescharacteristic
191#1804C2211yescharacteristic
192#1798C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#546—42no—
215#546—42no—
216#542—42no—
217#542—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255#494—42no—
256#483—42no—
257#475—42no—
258#467—42no—
259#467—42no—
260#464—24no—
261#464—42no—
262#464—42no—
263#461—42no—
264#452—24no—
265#452—42no—
266#450—42no—
267#450—42no—
268#440—42no—
269C4×Q16—42no—
270C4×SD16—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#102—24no—
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#401—21no—
330#401—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400D411yescharacteristic
336#399D411yescharacteristic
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398D411yescharacteristic
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397D411yescharacteristic
352#397D411yescharacteristic
353#397D411yescharacteristic
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394D411yescharacteristic
366#394D411yescharacteristic
367#393—21no—
368#393—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
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#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#383—21no—
440#382—21no—
441#382—21no—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457#379—21no—
458#379—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#126—44no—
573#124—22no—
574#124—22no—
575#124—22no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—44no—
580#123—44no—
581#123—44no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—44no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—82no—
598#121—22no—
599#121—22no—
600#121—44no—
601#120—44no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—82no—
621#117—41no—
622#117—41no—
623C2×C4⋊C4—22no—
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—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—82no—
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—41no—
732#106—41no—
733#106—41no—
734C4⋊C8—22no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102#4114yes—
771C22⋊C8—22no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778#97—41no—
779C4×C8—41no—
780C4×C8—41no—
781C4×C8—41no—
782C4×C8—41no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840#41—82no—
841#41—82no—
842#41—82no—
843#41—82no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—42no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8H(5,𝔽2)12yes—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—44no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4C2×#4112yes—
898C2×D4H(5,𝔽2)12yes—
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—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
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×C4—81no—
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
956Q16—44no—
957Q16—82no—
958Q16—82no—
959Q16—82no—
960SD16—44no—
961SD16—44no—
962SD16—82no—
963SD16—82no—
964C2×C8—21no—
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—82no—
988C2×C8C2×#4112yes—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
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—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4C2×#4112yes—
1042C4⋊C4H(5,𝔽2)12yes—
1043C22⋊C4—24no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—42no—
1093C42—42no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
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—84no—
1129C23—84no—
1130C23—84no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23#57812yes—
1136C23C23×D411yescharacteristic
1137Q8—22no—
1138Q8—22no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—162no—
1154D4—22no—
1155D4—22no—
1156D4—22no—
1157D4—22no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—82no—
1163D4—84no—
1164D4—84no—
1165D4—84no—
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—22no—
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—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
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—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—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—84no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4#57712yes—
1258C2×C4C22×#4111yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4#58511yescharacteristic
1263C2×C4#58511yescharacteristic
1264C8—22no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—42no—
1283C22—41no—
1284C22—42no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—168no—
1301C22D4×#4111yescharacteristic
1302C22#348411yescharacteristic
1303C22#348811yescharacteristic
1304C22C2×#57711yescharacteristic
1305C22C2×#57811yescharacteristic
1306C22#358411yescharacteristic
1307C22#358411yescharacteristic
1308C4—22no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4#349411yescharacteristic
1335C4#351911yescharacteristic
1336C4#353411yescharacteristic
1337C4#356211yescharacteristic
1338C2—42no—
1339C2—81no—
1340C2—82no—
1341C2—82no—
1342C2#4310711yescharacteristic
1343C2#6148711yescharacteristic
1344C2#6149711yescharacteristic
1345C2#6164211yescharacteristic
1346C2#6165811yescharacteristic
1347C2#6206511yescharacteristic
1348C2#6206611yescharacteristic
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
1. #45235C2semidirect
3. #32089C2semidirect
4. #31875C2semidirect
5. #31722C2semidirect
6. #31301C2semidirect
7. #30996C2semidirect
8. #30668C2semidirect
9. #30569C2semidirect
10. #30450C2semidirect
11. #28874C2semidirect
12. #28133C2semidirect
13. #27409C2semidirect
14. #27091C2semidirect
15. #27033C2semidirect
16. #26928C2semidirect
17. #26902C2semidirect
18. #26726C2semidirect
19. #26181C2semidirect
20. #25415C2semidirect
21. #25365C2semidirect
22. #25176C2semidirect
23. #25084C2semidirect
26. #24169C2semidirect
27. #23585C2semidirect
28. #23000C2semidirect
29. #22574C2semidirect
30. #22358C2semidirect
31. #22057C2semidirect
34. C2×#494C22semidirect
35. C2×#483C22semidirect
36. C2×#475C22semidirect
48. C2×C4×Q16C22semidirect
65. #2514C22semidirect
66. #2508C22semidirect
68. #2494C22semidirect
78. #2429C22semidirect
85. #2365C22semidirect
88. #2351C22semidirect
91. #2323C22semidirect
92. #2323C22semidirect
94. #2097C22semidirect
95. #2097C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2085C22semidirect
102. #2066C22semidirect
104. #2057C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
109. #2043C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
117. #2036C22semidirect
120. #2035C22semidirect
123. #2024C22semidirect
130. #2001C22semidirect
131. #2001C22semidirect
134. #1987C22semidirect
136. #1981C22semidirect
138. #1969C22semidirect
143. #1949C22semidirect
144. #1942C22semidirect
145. #1939C22semidirect
146. #1935C22semidirect
149. #1933C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
154. #1927C22semidirect
160. #1923C22semidirect
161. #1923C22semidirect
162. #1921C22semidirect
163. #1919C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
178. #1872C22semidirect
180. #1865C22semidirect
181. #1865C22semidirect
186. #1852C22semidirect
189. #1824C22semidirect
192. #1798C22semidirect
196. C8×C4⋊C4C22semidirect
197. #1763C22semidirect
198. C4×#103C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#452352
#451082
#320892
#318752
#317222
#313012
#309962
#306682
#305692
#304502
#288742
#281332
#274092
#270912
#270332
#269282
#269022
#267262
#261812
#254152
#253652
#251762
#250842
#244262
#242472
#241692
#235852
#230002
#225742
#223582
#220572