Finite Group Databasebeta

← #6883837

Subgroups — #6883837

Order 512.

1613 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39119C211yesmaximal, characteristic, complemented
2#38024C211yesmaximal, characteristic
3#33047C211yesmaximal, characteristic, complemented
4#31412C211yesmaximal, characteristic, complemented
5#31410C211yesmaximal, characteristic, complemented
6#31328C211yesmaximal, characteristic, complemented
7#31324C211yesmaximal, characteristic, complemented
8#31274C211yesmaximal, characteristic, complemented
9#31270C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#30406C211yesmaximal, characteristic, complemented
12#30368C211yesmaximal, characteristic, complemented
13#30363C211yesmaximal, characteristic, complemented
14#29490C211yesmaximal, characteristic, complemented
15#29462C211yesmaximal, characteristic, complemented
16#29120C211yesmaximal, characteristic, complemented
17#29104C211yesmaximal, characteristic, complemented
18#26329C211yesmaximal, characteristic, complemented
19#26308C211yesmaximal, characteristic, complemented
20#25937C211yesmaximal, characteristic, complemented
21#25890C211yesmaximal, characteristic, complemented
22#24993C211yesmaximal, characteristic, complemented
23#24971C211yesmaximal, characteristic, complemented
24#24713C211yesmaximal, characteristic, complemented
25#24665C211yesmaximal, characteristic, complemented
26#24346C211yesmaximal, characteristic, complemented
27#24259C211yesmaximal, characteristic, complemented
28#22057C211yesmaximal, characteristic, complemented
29#22049C211yesmaximal, characteristic, complemented
30#21531C211yesmaximal, characteristic, complemented
31#21381C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#546C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#433C2211yescharacteristic, complemented
43C2×#405C2211yescharacteristic, complemented
44#2855C2211yescharacteristic
45#2851C2211yescharacteristic
46#2731—21no—
47#2729—21no—
48#2719—21no—
49#2711—21no—
50#2707—21no—
51#2705—21no—
52#2691—21no—
53#2676—21no—
54#2629C2211yescharacteristic, complemented
55#2628C2211yescharacteristic, complemented
56#2624C2211yescharacteristic
57#2620C2211yescharacteristic
58#2592C2211yescharacteristic
59#2563C2211yescharacteristic
60#2562C2211yescharacteristic
61#2562C2211yescharacteristic, complemented
62#2558—21no—
63#2538C2211yescharacteristic
64#2538C2211yescharacteristic
65#2536C2211yescharacteristic
66#2536C2211yescharacteristic, complemented
67#2534—21no—
68#2519—21no—
69#2469—21no—
70#2458—21no—
71#2437—21no—
72#2424—21no—
73#2417C2211yescharacteristic
74#2416C2211yescharacteristic
75#2412—21no—
76#2408C2211yescharacteristic
77#2407C2211yescharacteristic
78#2355C2211yescharacteristic, complemented
79D4×C4⋊C4C2211yescharacteristic
80#2324C2211yescharacteristic
81#2323C2211yescharacteristic, complemented
82#2323C2211yescharacteristic, complemented
83#2311C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C2×#390C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2097C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2076C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2059C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2036C2211yescharacteristic
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic, complemented
108#2036C2211yescharacteristic, complemented
109#2035C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2026C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2001C2211yescharacteristic
123#2001C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1984C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1969C2211yescharacteristic, complemented
134#1959C2211yescharacteristic
135#1955C2211yescharacteristic
136#1954C2211yescharacteristic
137#1947C2211yescharacteristic, complemented
138#1947C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic, complemented
163#1894C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic, complemented
174#1870C2211yescharacteristic
175#1870C2211yescharacteristic, complemented
176#1869C2211yescharacteristic
177#1869C2211yescharacteristic, complemented
178#1865C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic, complemented
182#1834C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic
185#1824C2211yescharacteristic, complemented
186#1823C2211yescharacteristic, complemented
187#1808C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1750C2211yescharacteristic, complemented
200#1750C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#557—42no—
211#557—42no—
212#546—42no—
213#546—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216#529—42no—
217#529—42no—
218C2×#126D411yescharacteristic
219C2×#126D411yescharacteristic
220C2×#125—21no—
221C2×#125—21no—
222C2×#125D411yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#124D411yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123D411yescharacteristic
229C2×#123D411yescharacteristic
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8D411yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#121D411yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263#488—42no—
264#478—42no—
265#465—24no—
266#464—42no—
267#452—24no—
268#450—24no—
269#440—42no—
270#433—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#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×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318#405—42no—
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#395—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#393—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#392—21no—
364#392—21no—
365#391—21no—
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
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#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—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#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16#4114yes—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—44no—
555#126—42no—
556#126—42no—
557#125—22no—
558#125—22no—
559#125—41no—
560#125—41no—
561#125—42no—
562#125—44no—
563#125—44no—
564#124—22no—
565#124—22no—
566#124—42no—
567#123—42no—
568#123—42no—
569#123—44no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—42no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—82no—
582#121—22no—
583#121—42no—
584#121—44no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—82no—
591#120—44no—
592#120—82no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—44no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—82no—
611#117—22no—
612#117—22no—
613#117—41no—
614#117—41no—
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—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—82no—
703C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—41no—
722C2×C42—41no—
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#106—22no—
737#106—41no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740#103—22no—
741#103—22no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776#97—22no—
777#97—41no—
778#97—41no—
779C4×C8—22no—
780C4×C8—41no—
781C4×C8—41no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828#41—82no—
829#41—82no—
830#41—82no—
831#41—82no—
832C2×Q8—22no—
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—41no—
845C2×Q8—41no—
846C2×Q8—42no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8C2×#4112yes—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—81no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—82no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4C2×#4112yes—
890C22×C4—21no—
891C22×C4—22no—
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—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—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
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×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
952Q16—82no—
953SD16—44no—
954SD16—82no—
955M16—44no—
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—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—44no—
980C2×C8C2×#4112yes—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
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—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—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—42no—
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—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—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—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—41no—
1092C42—41no—
1093C42—42no—
1094C42—42no—
1095C42—42no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42H(5,𝔽2)12yes—
1101C42H(5,𝔽2)12yes—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
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—84no—
1137C23—84no—
1138C23—84no—
1139C23—84no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23#57812yes—
1144C23C23×D411yescharacteristic
1145Q8—22no—
1146Q8—22no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—82no—
1154Q8—84no—
1155D4—22no—
1156D4—22no—
1157D4—44no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—82no—
1165D4—82no—
1166D4—84no—
1167D4—84no—
1168D4—162no—
1169D4—162no—
1170D4—162no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
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—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—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—82no—
1257C2×C4—82no—
1258C2×C4—84no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4#53412yes—
1263C2×C4#53412yes—
1264C2×C4C22×#4111yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4#58511yescharacteristic
1268C2×C4#58511yescharacteristic
1269C2×C4#58511yescharacteristic
1270C8—22no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—168no—
1314C22C2×#53411yescharacteristic
1315C22D4×#4111yescharacteristic
1316C22#350011yescharacteristic
1317C22C2×#57811yescharacteristic
1318C22#358411yescharacteristic
1319C22#358511yescharacteristic
1320C22#358511yescharacteristic
1321C4—22no—
1322C4—22no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—42no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4#350511yescharacteristic
1347C4#351411yescharacteristic
1348C4#354011yescharacteristic
1349C4#356211yescharacteristic
1350C2—42no—
1351C2—81no—
1352C2—81no—
1353C2—82no—
1354C2—161no—
1355C2#3996011yescharacteristic
1356C2#6076411yescharacteristic
1357C2#6076711yescharacteristic
1358C2#6152411yescharacteristic
1359C2#6153511yescharacteristic
1360C2#6255911yescharacteristic
1361C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38024C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39119C2semidirect
3. #33047C2semidirect
4. #31412C2semidirect
5. #31410C2semidirect
6. #31328C2semidirect
7. #31324C2semidirect
8. #31274C2semidirect
9. #31270C2semidirect
10. #30408C2semidirect
11. #30406C2semidirect
12. #30368C2semidirect
13. #30363C2semidirect
14. #29490C2semidirect
15. #29462C2semidirect
16. #29120C2semidirect
17. #29104C2semidirect
18. #26329C2semidirect
19. #26308C2semidirect
20. #25937C2semidirect
21. #25890C2semidirect
22. #24993C2semidirect
23. #24971C2semidirect
24. #24713C2semidirect
25. #24665C2semidirect
26. #24346C2semidirect
27. #24259C2semidirect
28. #22057C2semidirect
29. #22049C2semidirect
30. #21531C2semidirect
31. #21381C2semidirect
32. C2×#557C22semidirect
42. C2×#433C22semidirect
43. C2×#405C22semidirect
54. #2629C22semidirect
55. #2628C22semidirect
61. #2562C22semidirect
66. #2536C22semidirect
78. #2355C22semidirect
81. #2323C22semidirect
82. #2323C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2097C22semidirect
91. #2077C22semidirect
92. #2077C22semidirect
95. #2076C22semidirect
96. #2076C22semidirect
97. #2075C22semidirect
98. #2074C22semidirect
102. #2059C22semidirect
103. #2057C22semidirect
107. #2036C22semidirect
108. #2036C22semidirect
116. #2026C22semidirect
119. #2024C22semidirect
123. #2001C22semidirect
126. #1992C22semidirect
127. #1989C22semidirect
128. #1985C22semidirect
129. #1984C22semidirect
133. #1969C22semidirect
137. #1947C22semidirect
138. #1947C22semidirect
139. #1944C22semidirect
140. #1943C22semidirect
141. #1942C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
158. #1921C22semidirect
159. #1921C22semidirect
162. #1894C22semidirect
163. #1894C22semidirect
165. #1892C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
173. #1872C22semidirect
175. #1870C22semidirect
177. #1869C22semidirect
178. #1865C22semidirect
179. #1863C22semidirect
181. #1852C22semidirect
182. #1834C22semidirect
185. #1824C22semidirect
186. #1823C22semidirect
187. #1808C22semidirect
188. #1803C22semidirect
196. #1776C22semidirect
197. C4×#103C22semidirect
199. #1750C22semidirect
200. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#391192
#380242
#330472
#314122
#314102
#313282
#313242
#312742
#312702
#304082
#304062
#303682
#303632
#294902
#294622
#291202
#291042
#263292
#263082
#259372
#258902
#249932
#249712
#247132
#246652
#243462
#242592
#220572
#220492
#215312
#213812