Finite Group Databasebeta

← #7049244

Subgroups — #7049244

Order 512.

1250 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45288C211yesmaximal, characteristic, complemented
2#45205C211yesmaximal, characteristic
3#32471C211yesmaximal, characteristic, complemented
4#32213C211yesmaximal, characteristic, complemented
5#32040C211yesmaximal, characteristic
6#31976C211yesmaximal, characteristic, complemented
7#31752C211yesmaximal, characteristic, complemented
8#31587C211yesmaximal, characteristic, complemented
9#30785C211yesmaximal, characteristic, complemented
10#30783C211yesmaximal, characteristic, complemented
11#29246C211yesmaximal, characteristic, complemented
12#29020C211yesmaximal, characteristic, complemented
13#28090C211yesmaximal, characteristic, complemented
14#27642C211yesmaximal, characteristic, complemented
15#27340C211yesmaximal, characteristic, complemented
16#27338C211yesmaximal, characteristic, complemented
17#27331C211yesmaximal, characteristic, complemented
18#27103C211yesmaximal, characteristic, complemented
19#27040C211yesmaximal, characteristic, complemented
20#26886C211yesmaximal, characteristic, complemented
21#26871C211yesmaximal, characteristic, complemented
22#26696C211yesmaximal, characteristic, complemented
23#26514C211yesmaximal, characteristic, complemented
24#26435C211yesmaximal, characteristic, complemented
25#26242C211yesmaximal, characteristic
26#24953C211yesmaximal, characteristic, complemented
27#23767C211yesmaximal, characteristic, complemented
28#23165C211yesmaximal, characteristic, complemented
29#22943C211yesmaximal, characteristic, complemented
30#22364C211yesmaximal, characteristic, complemented
31#22089C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#483C2211yescharacteristic
35#2803—21no—
36#2796—21no—
37#2787—21no—
38#2776—21no—
39#2773—21no—
40#2752—21no—
41#2747—21no—
42#2738—21no—
43#2595—21no—
44#2590—21no—
45#2575—21no—
46#2570C2211yescharacteristic
47#2540C2211yescharacteristic
48#2513—21no—
49#2513—21no—
50#2507C2211yescharacteristic
51#2507C2211yescharacteristic
52#2496C2211yescharacteristic
53#2494C2211yescharacteristic
54#2490C2211yescharacteristic
55#2490C2211yescharacteristic
56#2489C2211yescharacteristic
57#2489C2211yescharacteristic
58#2485—21no—
59#2485C2211yescharacteristic
60#2485C2211yescharacteristic
61#2478—21no—
62#2468—21no—
63#2448C2211yescharacteristic
64#2447C2211yescharacteristic
65#2442C2211yescharacteristic
66#2442C2211yescharacteristic
67#2395C2211yescharacteristic
68#2370C2211yescharacteristic
69#2370C2211yescharacteristic
70#2370C2211yescharacteristic
71#2363C2211yescharacteristic
72#2362C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74#2347C2211yescharacteristic
75#2344C2211yescharacteristic
76#2324C2211yescharacteristic
77#2323C2211yescharacteristic
78#2316C2211yescharacteristic
79#2314C2211yescharacteristic
80#2101C2211yescharacteristic
81#2099C2211yescharacteristic
82#2097C2211yescharacteristic
83#2092C2211yescharacteristic
84#2088C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2083C2211yescharacteristic
89#2083C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2026C2211yescharacteristic
119#2025C2211yescharacteristic
120#1991C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1983C2211yescharacteristic
125#1959C2211yescharacteristic
126#1955C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1944C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1941C2211yescharacteristic
135#1939C2211yescharacteristic
136#1935C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1933C2211yescharacteristic
140#1933C2211yescharacteristic
141#1933C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1923C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1895C2211yescharacteristic
169#1894C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic
173#1872C2211yescharacteristic
174#1870C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1851C2211yescharacteristic
186#1825C2211yescharacteristic
187#1824C2211yescharacteristic
188#1809C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1798C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1770C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1750C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C2×#126—21no—
205C2×#125C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#124C2311yescharacteristic
209C2×C22⋊Q8C2311yescharacteristic
210C2×C22⋊Q8C2311yescharacteristic
211C2×#121C2311yescharacteristic
212C2×#121C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4—21no—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×#117—21no—
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223#499—24no—
224#483—24no—
225#481—24no—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275#401—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400D411yescharacteristic
283#399—21no—
284#399—21no—
285#399D411yescharacteristic
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398D411yescharacteristic
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397D411yescharacteristic
306#397D411yescharacteristic
307#397D411yescharacteristic
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394D411yescharacteristic
313#394D411yescharacteristic
314#392—21no—
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#390—21no—
319#390—21no—
320#390—21no—
321#390—21no—
322#390—21no—
323#390—21no—
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
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#386—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#383—21no—
400#382—21no—
401#382—21no—
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#380—21no—
407#380—21no—
408#380—21no—
409#380—21no—
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2411yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C2×D411yescharacteristic
485C22×D4C2411yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C2×M16—41no—
492C2×M16—41no—
493C2×M16—41no—
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502#126—82no—
503#125—22no—
504#125—22no—
505#125—22no—
506#125—41no—
507#125—41no—
508#125—41no—
509#124—41no—
510#124—41no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8—41no—
514C22⋊Q8—41no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519C4×Q8—41no—
520C4×Q8—41no—
521C4×D4—41no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—82no—
526#117—41no—
527#117—41no—
528#117—41no—
529#117—41no—
530#117—41no—
531#117—41no—
532#117—82no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638#107—22no—
639#107—22no—
640#107—22no—
641#107—22no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#106—22no—
647#106—22no—
648#106—22no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106#4114yes—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659#103—22no—
660#103—22no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#102—22no—
668#102—22no—
669#102—41no—
670#102—41no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675C22⋊C8—22no—
676C22⋊C8—22no—
677C22⋊C8—41no—
678C22⋊C8—41no—
679C22⋊C8—41no—
680C22⋊C8—41no—
681C22⋊C8—41no—
682#97—41no—
683#97—41no—
684C4×C8—22no—
685C4×C8—41no—
686C4×C8—41no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24—21no—
740C24C22×D411yescharacteristic
741C24C22×D411yescharacteristic
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4—81no—
762C2×D4—81no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C2511yescharacteristic
812M16—82no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8C2×#4112yes—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4C2×#4112yes—
899C4⋊C4C2×#4112yes—
900C4⋊C42−1+412yes—
901C22⋊C4—41no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—41no—
905C22⋊C4—41no—
906C22⋊C4—41no—
907C22⋊C4—41no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—42no—
945C42—81no—
946C42—81no—
947C42—81no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23C23×D411yescharacteristic
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983D4—44no—
984D4—41no—
985D4—41no—
986D4—41no—
987D4—41no—
988D4—162no—
989D4—162no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—84no—
1080C2×C4—162no—
1081C2×C4—162no—
1082C2×C4C22×#4111yescharacteristic
1083C2×C4C2×2−1+411yescharacteristic
1084C2×C4#58511yescharacteristic
1085C2×C4#58511yescharacteristic
1086C2×C4#58511yescharacteristic
1087C2×C4#58511yescharacteristic
1088C8—22no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22D4×#4111yescharacteristic
1118C22#348511yescharacteristic
1119C22#348911yescharacteristic
1120C22#358411yescharacteristic
1121C22#358411yescharacteristic
1122C22#358511yescharacteristic
1123C22#358611yescharacteristic
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—42no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4#350711yescharacteristic
1152C4#352411yescharacteristic
1153C4#355711yescharacteristic
1154C4#356611yescharacteristic
1155C2—81no—
1156C2—81no—
1157C2—161no—
1158C2#4354011yescharacteristic
1159C2#6152811yescharacteristic
1160C2#6153511yescharacteristic
1161C2#6177411yescharacteristic
1162C2#6179011yescharacteristic
1163C2#6217411yescharacteristic
1164C2#6219511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2540C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45288C2semidirect
3. #32471C2semidirect
4. #32213C2semidirect
6. #31976C2semidirect
7. #31752C2semidirect
8. #31587C2semidirect
9. #30785C2semidirect
10. #30783C2semidirect
11. #29246C2semidirect
12. #29020C2semidirect
13. #28090C2semidirect
14. #27642C2semidirect
15. #27340C2semidirect
16. #27338C2semidirect
17. #27331C2semidirect
18. #27103C2semidirect
19. #27040C2semidirect
20. #26886C2semidirect
21. #26871C2semidirect
22. #26696C2semidirect
23. #26514C2semidirect
24. #26435C2semidirect
26. #24953C2semidirect
27. #23767C2semidirect
28. #23165C2semidirect
29. #22943C2semidirect
30. #22364C2semidirect
31. #22089C2semidirect

Maximal subgroups

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

subgroupindex
#452882
#452052
#324712
#322132
#320402
#319762
#317522
#315872
#307852
#307832
#292462
#290202
#280902
#276422
#273402
#273382
#273312
#271032
#270402
#268862
#268712
#266962
#265142
#264352
#262422
#249532
#237672
#231652
#229432
#223642
#220892