Finite Group Databasebeta

← #7171364

Subgroups — #7171364

Order 512.

1611 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59039C211yesmaximal, characteristic
2#39931C211yesmaximal, characteristic, complemented
3#32019C211yesmaximal, characteristic, complemented
4#32012C211yesmaximal, characteristic, complemented
5#31621C211yesmaximal, characteristic, complemented
6#31617C211yesmaximal, characteristic, complemented
7#31372C211yesmaximal, characteristic, complemented
8#31355C211yesmaximal, characteristic, complemented
9#31279C211yesmaximal, characteristic, complemented
10#31275C211yesmaximal, characteristic, complemented
11#28715C211yesmaximal, characteristic, complemented
12#28113C211yesmaximal, characteristic, complemented
13#28106C211yesmaximal, characteristic, complemented
14#27832C211yesmaximal, characteristic, complemented
15#27549C211yesmaximal, characteristic, complemented
16#27528C211yesmaximal, characteristic, complemented
17#26472C211yesmaximal, characteristic, complemented
18#26315C211yesmaximal, characteristic, complemented
19#25980C211yesmaximal, characteristic, complemented
20#25962C211yesmaximal, characteristic, complemented
21#25893C211yesmaximal, characteristic, complemented
22#25676C211yesmaximal, characteristic, complemented
23#25467C211yesmaximal, characteristic, complemented
24#25355C211yesmaximal, characteristic, complemented
25#25346C211yesmaximal, characteristic, complemented
26#24842C211yesmaximal, characteristic, complemented
27#23765C211yesmaximal, characteristic, complemented
28#23229C211yesmaximal, characteristic, complemented
29#22988C211yesmaximal, characteristic, complemented
30#22422C211yesmaximal, characteristic, complemented
31#21891C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#423C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#416C2211yescharacteristic
45#2851C2211yescharacteristic
46#2766—21no—
47#2745—21no—
48#2737—21no—
49#2701—21no—
50#2686—21no—
51#2686—21no—
52#2653—21no—
53#2567C2211yescharacteristic
54#2563C2211yescharacteristic
55#2563C2211yescharacteristic
56#2562C2211yescharacteristic
57#2562C2211yescharacteristic
58#2550C2211yescharacteristic
59#2537C2211yescharacteristic
60#2537C2211yescharacteristic
61#2529—21no—
62#2527—21no—
63#2494C2211yescharacteristic
64#2494C2211yescharacteristic
65#2486C2211yescharacteristic
66#2485C2211yescharacteristic
67#2445—21no—
68#2442C2211yescharacteristic
69#2439C2211yescharacteristic
70#2430—21no—
71#2430—21no—
72#2428—21no—
73#2422C2211yescharacteristic
74#2422C2211yescharacteristic
75#2420—21no—
76#2407C2211yescharacteristic
77#2407C2211yescharacteristic
78#2370C2211yescharacteristic
79#2366C2211yescharacteristic
80#2352C2211yescharacteristic
81#2349—21no—
82#2339C2211yescharacteristic
83#2339C2211yescharacteristic
84#2335—21no—
85C4×C22⋊Q8C2211yescharacteristic
86C4×#121C2211yescharacteristic
87#2283C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2097C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2075C2211yescharacteristic
106#2075C2211yescharacteristic
107#2074C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic
113#2066C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2026C2211yescharacteristic
125#2025C2211yescharacteristic
126#2024C2211yescharacteristic
127#2023C2211yescharacteristic
128#1993C2211yescharacteristic
129#1992C2211yescharacteristic
130#1990C2211yescharacteristic
131#1989C2211yescharacteristic
132#1988C2211yescharacteristic
133#1988C2211yescharacteristic
134#1982C2211yescharacteristic
135#1982C2211yescharacteristic
136#1961C2211yescharacteristic
137#1955C2211yescharacteristic
138#1949C2211yescharacteristic
139#1948C2211yescharacteristic
140#1947C2211yescharacteristic
141#1940C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic
144#1934C2211yescharacteristic
145#1933C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1893C2211yescharacteristic
160#1875C2211yescharacteristic
161#1874C2211yescharacteristic
162#1870C2211yescharacteristic
163#1870C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1854C2211yescharacteristic
173#1852C2211yescharacteristic
174#1851C2211yescharacteristic
175#1850C2211yescharacteristic
176#1825C2211yescharacteristic
177#1824C2211yescharacteristic
178#1809C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1808C2211yescharacteristic
183#1807C2211yescharacteristic
184#1805C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197#1771C2211yescharacteristic
198#1763C2211yescharacteristic
199#1763C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C22×#41C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#550—24no—
211#550—42no—
212#532—24no—
213#532—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127—21no—
217C2×#127C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121D411yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C42C2311yescharacteristic
249#501—42no—
250#490—24no—
251#479—42no—
252#478—42no—
253#476—42no—
254#436—42no—
255#435—42no—
256#435—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269#423—42no—
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#417—42no—
277#416—42no—
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#401—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390D411yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389D411yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388D411yescharacteristic
382#388D411yescharacteristic
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386D411yescharacteristic
403#386D411yescharacteristic
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#382—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#381—21no—
423#381—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380D411yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
457C2×#95—21no—
458C2×#95—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#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—44no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—82no—
507C2×#41—82no—
508C22×Q8—21no—
509C22×Q8—21no—
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560#127—22no—
561#127—44no—
562#127#4114yes—
563#125—22no—
564#125—22no—
565#125—41no—
566#125—41no—
567#124—44no—
568#123—44no—
569#123—82no—
570#123—82no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—42no—
578#121—44no—
579#121—44no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—44no—
585#121—82no—
586#121—82no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—44no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—44no—
605C4×D4—44no—
606#117—41no—
607#117—41no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—22no—
688C2×C42—22no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#106—22no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752#97—22no—
753#97—22no—
754#97—41no—
755C4×C8—41no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
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#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—21no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806#41—44no—
807#41—44no—
808#41—82no—
809#41—82no—
810#41—82no—
811#41—82no—
812#41—82no—
813#41—82no—
814#41—816no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—42no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q82−1+412yes—
827C2×D4—24no—
828C2×D4—22no—
829C2×D4—24no—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4C2×#4112yes—
871C2×D4C2×#4112yes—
872C22×C4—21no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
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—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C2511yescharacteristic
943M16—82no—
944M16—82no—
945M16—82no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—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—82no—
970C2×C8H(5,𝔽2)12yes—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—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—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
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—81no—
1011C4⋊C4—81no—
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—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C42—22no—
1062C42—22no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42C2×#4112yes—
1077C42H(5,𝔽2)12yes—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23C23×D411yescharacteristic
1114Q8—22no—
1115Q8—22no—
1116Q8—41no—
1117Q8—41no—
1118Q8—84no—
1119Q8—162no—
1120D4—22no—
1121D4—22no—
1122D4—22no—
1123D4—22no—
1124D4—48no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—82no—
1130D4—82no—
1131D4—84no—
1132D4—82no—
1133D4—84no—
1134D4—84no—
1135D4—84no—
1136D4—84no—
1137D4—162no—
1138D4—162no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
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—21no—
1170C2×C4—44no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
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—82no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4#54612yes—
1233C2×C4#54612yes—
1234C2×C4#57512yes—
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4C2×2−1+411yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C8—22no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—42no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22C2×#54611yescharacteristic
1285C22#348911yescharacteristic
1286C22#349611yescharacteristic
1287C22C2×#57511yescharacteristic
1288C22#358511yescharacteristic
1289C22#358511yescharacteristic
1290C22#358611yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4#352011yescharacteristic
1317C4#352111yescharacteristic
1318C4#355811yescharacteristic
1319C4#356111yescharacteristic
1320C2—81no—
1321C2—81no—
1322C2—81no—
1323C2—82no—
1324C2—82no—
1325C2#4510811yescharacteristic
1326C2#6115911yescharacteristic
1327C2#6117511yescharacteristic
1328C2#6212311yescharacteristic
1329C2#6222611yescharacteristic
1330C2#6229811yescharacteristic
1331C2#6233811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59039C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39931C2semidirect
3. #32019C2semidirect
4. #32012C2semidirect
5. #31621C2semidirect
6. #31617C2semidirect
7. #31372C2semidirect
8. #31355C2semidirect
9. #31279C2semidirect
10. #31275C2semidirect
11. #28715C2semidirect
12. #28113C2semidirect
13. #28106C2semidirect
14. #27832C2semidirect
15. #27549C2semidirect
16. #27528C2semidirect
17. #26472C2semidirect
18. #26315C2semidirect
19. #25980C2semidirect
20. #25962C2semidirect
21. #25893C2semidirect
22. #25676C2semidirect
23. #25467C2semidirect
24. #25355C2semidirect
25. #25346C2semidirect
26. #24842C2semidirect
27. #23765C2semidirect
28. #23229C2semidirect
29. #22988C2semidirect
30. #22422C2semidirect
31. #21891C2semidirect

Maximal subgroups

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

subgroupindex
#590392
#399312
#320192
#320122
#316212
#316172
#313722
#313552
#312792
#312752
#287152
#281132
#281062
#278322
#275492
#275282
#264722
#263152
#259802
#259622
#258932
#256762
#254672
#253552
#253462
#248422
#237652
#232292
#229882
#224222
#218912