Finite Group Databasebeta

← #7207590

Subgroups — #7207590

Order 512.

1663 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45709C211yesmaximal, characteristic, complemented
2#36236C211yesmaximal, characteristic
3#32959C211yesmaximal, characteristic, complemented
4#32959C211yesmaximal, characteristic, complemented
5#32746C211yesmaximal, characteristic, complemented
6#32746C211yesmaximal, characteristic, complemented
7#32465C211yesmaximal, characteristic, complemented
8#32298C211yesmaximal, characteristic, complemented
9#32294C211yesmaximal, characteristic, complemented
10#32274C211yesmaximal, characteristic, complemented
11#31993C211yesmaximal, characteristic, complemented
12#31989C211yesmaximal, characteristic, complemented
13#31633C211yesmaximal, characteristic, complemented
14#31629C211yesmaximal, characteristic, complemented
15#31106C211yesmaximal, characteristic, complemented
16#31098C211yesmaximal, characteristic, complemented
17#30835C211yesmaximal, characteristic, complemented
18#30827C211yesmaximal, characteristic, complemented
19#27541C211yesmaximal, characteristic, complemented
20#27539C211yesmaximal, characteristic, complemented
21#27536C211yesmaximal, characteristic, complemented
22#27534C211yesmaximal, characteristic, complemented
23#27325C211yesmaximal, characteristic, complemented
24#27323C211yesmaximal, characteristic, complemented
25#26059C211yesmaximal, characteristic, complemented
26#26059C211yesmaximal, characteristic, complemented
27#25976C211yesmaximal, characteristic, complemented
28#25968C211yesmaximal, characteristic, complemented
29#25891C211yesmaximal, characteristic
30#24044C211yesmaximal, characteristic
31#23324C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic, complemented
40C2×#478C2211yescharacteristic, complemented
41C2×#418C2211yescharacteristic
42#2854C2211yescharacteristic
43#2851C2211yescharacteristic, complemented
44#2851C2211yescharacteristic, complemented
45#2849—21no—
46#2827—21no—
47#2794—21no—
48#2793—21no—
49#2776—21no—
50#2773—21no—
51#2765—21no—
52#2718—21no—
53#2562C2211yescharacteristic
54#2552C2211yescharacteristic, complemented
55#2552C2211yescharacteristic, complemented
56#2509C2211yescharacteristic, complemented
57#2508C2211yescharacteristic, complemented
58#2504C2211yescharacteristic
59#2497C2211yescharacteristic, complemented
60#2496C2211yescharacteristic, complemented
61#2495C2211yescharacteristic, complemented
62#2494C2211yescharacteristic, complemented
63#2487C2211yescharacteristic
64#2485C2211yescharacteristic
65#2445C2211yescharacteristic
66#2445C2211yescharacteristic
67#2444—21no—
68#2444—21no—
69#2441C2211yescharacteristic, complemented
70#2441C2211yescharacteristic, complemented
71#2420C2211yescharacteristic
72#2420C2211yescharacteristic
73#2418—21no—
74#2418—21no—
75#2412—21no—
76#2405—21no—
77#2383—21no—
78#2349C2211yescharacteristic
79#2349C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83C4×#123C2211yescharacteristic
84C2×#386—21no—
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2094C2211yescharacteristic, complemented
88#2093C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2076C2211yescharacteristic, complemented
104#2076C2211yescharacteristic, complemented
105#2075C2211yescharacteristic, complemented
106#2075C2211yescharacteristic, complemented
107#2073C2211yescharacteristic, complemented
108#2073C2211yescharacteristic, complemented
109#2071C2211yescharacteristic, complemented
110#2071C2211yescharacteristic, complemented
111#2067C2211yescharacteristic, complemented
112#2067C2211yescharacteristic, complemented
113#2067C2211yescharacteristic, complemented
114#2067C2211yescharacteristic, complemented
115#2065C2211yescharacteristic, complemented
116#2065C2211yescharacteristic, complemented
117#2065C2211yescharacteristic, complemented
118#2065C2211yescharacteristic, complemented
119#2059C2211yescharacteristic, complemented
120#2059C2211yescharacteristic, complemented
121#2059C2211yescharacteristic, complemented
122#2059C2211yescharacteristic, complemented
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2025C2211yescharacteristic, complemented
132#2025C2211yescharacteristic, complemented
133#1982C2211yescharacteristic
134#1955C2211yescharacteristic
135#1949C2211yescharacteristic, complemented
136#1949C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1936C2211yescharacteristic, complemented
142#1936C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1936C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1925C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1924C2211yescharacteristic, complemented
150#1924C2211yescharacteristic, complemented
151#1924C2211yescharacteristic, complemented
152#1924C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1917C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1870C2211yescharacteristic
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic, complemented
165#1864C2211yescharacteristic, complemented
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic, complemented
172#1862C2211yescharacteristic, complemented
173#1854C2211yescharacteristic, complemented
174#1854C2211yescharacteristic, complemented
175#1853C2211yescharacteristic, complemented
176#1853C2211yescharacteristic, complemented
177#1852C2211yescharacteristic, complemented
178#1852C2211yescharacteristic, complemented
179#1851C2211yescharacteristic, complemented
180#1851C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1809C2211yescharacteristic, complemented
184#1809C2211yescharacteristic, complemented
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1797C2211yescharacteristic, complemented
192#1797C2211yescharacteristic, complemented
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4—21no—
207C22×M16C2311yescharacteristic
208D42—42no—
209D42—42no—
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123D411yescharacteristic
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—42no—
227C2×C4×D4—42no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C42C2311yescharacteristic
243#490—42no—
244#482—42no—
245#478—42no—
246#478—42no—
247#478—42no—
248#478—42no—
249#478—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—42no—
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308#401—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388D411yescharacteristic
378#388D411yescharacteristic
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
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#387D411yescharacteristic
392#387D411yescharacteristic
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#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386D411yescharacteristic
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385D411yescharacteristic
418#384—21no—
419#384—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#383—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#381—21no—
430#381D411yescharacteristic
431#380—21no—
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C2×#95—21no—
455C2×#95—21no—
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—44no—
511C22×D4—44no—
512C22×D4—82no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—44no—
526C23×C4—82no—
527C23×C4—82no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543#127—22no—
544#127—41no—
545#126—44no—
546#125—41no—
547#125—41no—
548#125—41no—
549#125—41no—
550#125—41no—
551#125—41no—
552#123—42no—
553#123—82no—
554#123—82no—
555#123—82no—
556#121—22no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—44no—
561#120—44no—
562#120—44no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—44no—
580C4×D4—44no—
581#117—41no—
582#117—41no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
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—44no—
661C2×C22⋊C4—82no—
662C2×C22⋊C4—82no—
663C2×C22⋊C4—82no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—41no—
740#97—41no—
741#97—41no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
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#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787C24—21no—
788C24—24no—
789C24—21no—
790C24—21no—
791C24—42no—
792C24—42no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—81no—
849C2×D4—816no—
850C2×D4H(5,𝔽2)12yes—
851C2×D4H(5,𝔽2)12yes—
852C2×D42−1+412yes—
853C2×D42−1+412yes—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—816no—
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C2511yescharacteristic
923M16—82no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—41no—
1055C42—41no—
1056C42—42no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—21no—
1065C23—22no—
1066C23—22no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—48no—
1078C23—48no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—84no—
1097C23—84no—
1098C23—84no—
1099C23—84no—
1100C23—84no—
1101C23—84no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23—162no—
1106C23—162no—
1107C23—162no—
1108C23#57512yes—
1109C23C23×D411yescharacteristic
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—22no—
1114D4—22no—
1115D4—48no—
1116D4—44no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—84no—
1124D4—84no—
1125D4—84no—
1126D4—84no—
1127D4—162no—
1128D4#56314yes—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
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—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—44no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
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—82no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4C2×H(5,𝔽2)11yescharacteristic
1223C2×C4C2×H(5,𝔽2)11yescharacteristic
1224C2×C4C2×2−1+411yescharacteristic
1225C2×C4C2×2−1+411yescharacteristic
1226C2×C4#58511yescharacteristic
1227C2×C4#58511yescharacteristic
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C22—22no—
1237C22—24no—
1238C22—22no—
1239C22—22no—
1240C22—42no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—42no—
1245C22—41no—
1246C22—42no—
1247C22—42no—
1248C22—41no—
1249C22—42no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—41no—
1260C22—816no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—168no—
1273C22#348411yescharacteristic
1274C22#348911yescharacteristic
1275C22#348911yescharacteristic
1276C22C2×#57511yescharacteristic
1277C22#358511yescharacteristic
1278C22#358511yescharacteristic
1279C22#358511yescharacteristic
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4C2×#56311yescharacteristic
1306C4#353311yescharacteristic
1307C4#353511yescharacteristic
1308C4#353511yescharacteristic
1309C2—42no—
1310C2—44no—
1311C2—81no—
1312C2—82no—
1313C2—161no—
1314C2#4545611yescharacteristic
1315C2#6157611yescharacteristic
1316C2#6164311yescharacteristic
1317C2#6211911yescharacteristic
1318C2#6211911yescharacteristic
1319C2#6222311yescharacteristic
1320C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45709C2semidirect
3. #32959C2semidirect
4. #32959C2semidirect
5. #32746C2semidirect
6. #32746C2semidirect
7. #32465C2semidirect
8. #32298C2semidirect
9. #32294C2semidirect
10. #32274C2semidirect
11. #31993C2semidirect
12. #31989C2semidirect
13. #31633C2semidirect
14. #31629C2semidirect
15. #31106C2semidirect
16. #31098C2semidirect
17. #30835C2semidirect
18. #30827C2semidirect
19. #27541C2semidirect
20. #27539C2semidirect
21. #27536C2semidirect
22. #27534C2semidirect
23. #27325C2semidirect
24. #27323C2semidirect
25. #26059C2semidirect
26. #26059C2semidirect
27. #25976C2semidirect
28. #25968C2semidirect
31. #23324C2semidirect
39. C2×#478C22semidirect
40. C2×#478C22semidirect
43. #2851C22semidirect
44. #2851C22semidirect
54. #2552C22semidirect
55. #2552C22semidirect
56. #2509C22semidirect
57. #2508C22semidirect
59. #2497C22semidirect
60. #2496C22semidirect
61. #2495C22semidirect
62. #2494C22semidirect
69. #2441C22semidirect
70. #2441C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2094C22semidirect
88. #2093C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2088C22semidirect
92. #2086C22semidirect
93. #2086C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
103. #2076C22semidirect
104. #2076C22semidirect
105. #2075C22semidirect
106. #2075C22semidirect
107. #2073C22semidirect
108. #2073C22semidirect
109. #2071C22semidirect
110. #2071C22semidirect
111. #2067C22semidirect
112. #2067C22semidirect
113. #2067C22semidirect
114. #2067C22semidirect
115. #2065C22semidirect
116. #2065C22semidirect
117. #2065C22semidirect
118. #2065C22semidirect
119. #2059C22semidirect
120. #2059C22semidirect
121. #2059C22semidirect
122. #2059C22semidirect
131. #2025C22semidirect
132. #2025C22semidirect
135. #1949C22semidirect
136. #1949C22semidirect
137. #1944C22semidirect
138. #1943C22semidirect
139. #1940C22semidirect
140. #1940C22semidirect
141. #1936C22semidirect
142. #1936C22semidirect
143. #1936C22semidirect
144. #1936C22semidirect
145. #1926C22semidirect
146. #1926C22semidirect
147. #1925C22semidirect
148. #1925C22semidirect
149. #1924C22semidirect
150. #1924C22semidirect
151. #1924C22semidirect
152. #1924C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1917C22semidirect
156. #1917C22semidirect
164. #1864C22semidirect
165. #1864C22semidirect
171. #1862C22semidirect
172. #1862C22semidirect
173. #1854C22semidirect
174. #1854C22semidirect
175. #1853C22semidirect
176. #1853C22semidirect
177. #1852C22semidirect
178. #1852C22semidirect
179. #1851C22semidirect
180. #1851C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1809C22semidirect
184. #1809C22semidirect
187. #1804C22semidirect
188. #1804C22semidirect
191. #1797C22semidirect
192. #1797C22semidirect

Maximal subgroups

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

subgroupindex
#457092
#362362
#329592
#327462
#324652
#322982
#322942
#322742
#319932
#319892
#316332
#316292
#311062
#310982
#308352
#308272
#275412
#275392
#275362
#275342
#273252
#273232
#260592
#259762
#259682
#258912
#240442
#233242