Finite Group Databasebeta

← #7605550

Subgroups — #7605550

Order 512.

1296 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59682C211yesmaximal, characteristic
2#59467C211yesmaximal, characteristic, complemented
3#32257C211yesmaximal, characteristic
4#32251C211yesmaximal, characteristic, complemented
5#32101C211yesmaximal, characteristic
6#32098C211yesmaximal, characteristic, complemented
7#29261C211yesmaximal, characteristic
8#29023C211yesmaximal, characteristic
9#29009C211yesmaximal, characteristic, complemented
10#28206C211yesmaximal, characteristic, complemented
11#28058C211yesmaximal, characteristic
12#28040C211yesmaximal, characteristic, complemented
13#27781C211yesmaximal, characteristic
14#27781C211yesmaximal, characteristic
15#27777C211yesmaximal, characteristic, complemented
16#27765C211yesmaximal, characteristic
17#26763C211yesmaximal, characteristic
18#26758C211yesmaximal, characteristic, complemented
19#26703C211yesmaximal, characteristic, complemented
20#26700C211yesmaximal, characteristic
21#26122C211yesmaximal, characteristic, complemented
22#26039C211yesmaximal, characteristic, complemented
23#25286C211yesmaximal, characteristic
24#25286C211yesmaximal, characteristic
25#23227C211yesmaximal, characteristic, complemented
26#23218C211yesmaximal, characteristic
27#23073C211yesmaximal, characteristic, complemented
28#22977C211yesmaximal, characteristic, complemented
29#21674C211yesmaximal, characteristic, complemented
30#21657C211yesmaximal, characteristic, complemented
31C4×#489C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#491C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#477C2211yescharacteristic
38#2791—21no—
39#2791—21no—
40#2772—21no—
41#2725—21no—
42#2608—21no—
43#2590—21no—
44#2590—21no—
45#2587—21no—
46#2565—21no—
47#2552C2211yescharacteristic
48#2552C2211yescharacteristic
49#2552C2211yescharacteristic
50#2552C2211yescharacteristic
51#2546C2211yescharacteristic
52#2545C2211yescharacteristic
53#2545C2211yescharacteristic
54#2545C2211yescharacteristic
55#2529—21no—
56#2525—21no—
57#2515—21no—
58#2512C2211yescharacteristic
59#2511C2211yescharacteristic
60#2509C2211yescharacteristic
61#2509C2211yescharacteristic
62#2507C2211yescharacteristic
63#2507C2211yescharacteristic
64#2453—21no—
65#2453—21no—
66#2447C2211yescharacteristic
67#2446C2211yescharacteristic
68#2373—21no—
69#2370C2211yescharacteristic
70#2370C2211yescharacteristic
71#2367C2211yescharacteristic
72#2365C2211yescharacteristic
73#2365C2211yescharacteristic
74#2365C2211yescharacteristic
75#2356C2211yescharacteristic
76#2351C2211yescharacteristic
77Q8×C4⋊C4—21no—
78C4×C4⋊Q8C2211yescharacteristic
79C4×C4⋊Q8C2211yescharacteristic
80C4×#125C2211yescharacteristic
81C4×#125C2211yescharacteristic
82C4×#124C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2097C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2086C2211yescharacteristic
89#2083C2211yescharacteristic
90#2083C2211yescharacteristic
91#2072C2211yescharacteristic
92#2071C2211yescharacteristic
93#2068C2211yescharacteristic
94#2068C2211yescharacteristic
95#2068C2211yescharacteristic
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic
98#2066C2211yescharacteristic
99#2043C2211yescharacteristic
100#2043C2211yescharacteristic
101#2043C2211yescharacteristic
102#2043C2211yescharacteristic
103#2043C2211yescharacteristic
104#2043C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2026C2211yescharacteristic
112#2026C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#1993C2211yescharacteristic
116#1992C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1981C2211yescharacteristic
124#1981C2211yescharacteristic
125#1960C2211yescharacteristic
126#1959C2211yescharacteristic
127#1959C2211yescharacteristic
128#1956C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1943C2211yescharacteristic
132#1942C2211yescharacteristic
133#1940C2211yescharacteristic
134#1940C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1933C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1928C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1927C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1919C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1862C2211yescharacteristic
177#1836C2211yescharacteristic
178#1836C2211yescharacteristic
179#1831C2211yescharacteristic
180#1803C2211yescharacteristic
181#1803C2211yescharacteristic
182#1803C2211yescharacteristic
183#1803C2211yescharacteristic
184#1776C2211yescharacteristic
185C4×#107C2211yescharacteristic
186#1771C2211yescharacteristic
187#1771C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1770C2211yescharacteristic
191C8×C4⋊C4C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#125—21no—
209C2×#125D411yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225#491—24no—
226#491—24no—
227#489—24no—
228#488—24no—
229#477—24no—
230#477—24no—
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389D411yescharacteristic
351#389D411yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
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#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#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387D411yescharacteristic
400#387D411yescharacteristic
401#387D411yescharacteristic
402#387D411yescharacteristic
403#385—21no—
404#385—21no—
405#384—21no—
406#384—21no—
407#384—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383—21no—
413#382—21no—
414#382D411yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#381—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446#376—21no—
447C43C2311yescharacteristic
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#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8—22no—
500C4⋊Q8—22no—
501C4⋊Q8—41no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8#4114yes—
506#126—44no—
507#125—22no—
508#125—22no—
509#125—22no—
510#125—41no—
511#125—41no—
512#125—41no—
513#125—42no—
514#125—82no—
515#124—22no—
516#124—22no—
517#124—22no—
518#124—41no—
519#124—41no—
520#124—41no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—41no—
526C4×Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×Q8—44no—
532C4×Q8—82no—
533C4×Q8—82no—
534C4×D4—41no—
535C4×D4—41no—
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—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
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×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639#107—22no—
640#107—22no—
641#107—22no—
642#107—22no—
643#107—41no—
644#107—41no—
645#106—41no—
646#106—41no—
647C4⋊C8—22no—
648C4⋊C8—22no—
649C4⋊C8—41no—
650C4⋊C8—41no—
651C4⋊C8—41no—
652C4⋊C8—41no—
653#103—22no—
654#103—22no—
655#103—22no—
656#103—22no—
657#103—22no—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#103#4114yes—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#97—22no—
686#97—22no—
687#97—22no—
688#97—22no—
689#97—41no—
690#97—41no—
691C4×C8—22no—
692C4×C8—41no—
693C4×C8—41no—
694C4×C8—41no—
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#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C2×Q8—24no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8C2×#4112yes—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—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—21no—
791C22×C4—21no—
792C22×C4—42no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
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×C8C2×#4112yes—
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
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—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—42no—
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—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
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⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4C2×#4112yes—
908C4⋊C4C2×#4112yes—
909C4⋊C4C2×#4112yes—
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—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C42—22no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—41no—
937C42—41no—
938C42—41no—
939C42—42no—
940C42—42no—
941C42—42no—
942C42—42no—
943C42—42no—
944C42—42no—
945C42—42no—
946C42—81no—
947C42—81no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C42—81no—
954C42C2×#4112yes—
955C422−1+412yes—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23C23×D411yescharacteristic
964Q8—22no—
965Q8—22no—
966Q8—48no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—41no—
971Q8—41no—
972Q8—41no—
973Q8—41no—
974Q8—41no—
975Q8—41no—
976Q8—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—41no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
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—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
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—162no—
1065C2×C4#54812yes—
1066C2×C4#54812yes—
1067C2×C4#57512yes—
1068C2×C4#57812yes—
1069C2×C4C22×#4111yescharacteristic
1070C2×C4C22×#4111yescharacteristic
1071C2×C4C2×2−1+411yescharacteristic
1072C2×C4#58511yescharacteristic
1073C2×C4#58511yescharacteristic
1074C2×C4#58511yescharacteristic
1075C8—22no—
1076C8—41no—
1077C8—41no—
1078C8—41no—
1079C8—41no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C2×#54811yescharacteristic
1091C22D4×#4111yescharacteristic
1092C22#350011yescharacteristic
1093C22C2×#57511yescharacteristic
1094C22C2×#57811yescharacteristic
1095C22#358511yescharacteristic
1096C22#358611yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—22no—
1100C4—22no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—42no—
1105C4—42no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—42no—
1112C4—42no—
1113C4—41no—
1114C4—41no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4#348011yescharacteristic
1127C4#351511yescharacteristic
1128C4#352411yescharacteristic
1129C4#356511yescharacteristic
1130C2—161no—
1131C2#5965811yescharacteristic
1132C2#6131811yescharacteristic
1133C2#6134211yescharacteristic
1134C2#6144711yescharacteristic
1135C2#6151511yescharacteristic
1136C2#6257911yescharacteristic
1137C2#6260411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59467C2semidirect
4. #32251C2semidirect
6. #32098C2semidirect
9. #29009C2semidirect
10. #28206C2semidirect
12. #28040C2semidirect
15. #27777C2semidirect
18. #26758C2semidirect
19. #26703C2semidirect
21. #26122C2semidirect
22. #26039C2semidirect
25. #23227C2semidirect
27. #23073C2semidirect
28. #22977C2semidirect
29. #21674C2semidirect
30. #21657C2semidirect

Maximal subgroups

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

subgroupindex
#596822
#594672
#322572
#322512
#321012
#320982
#292612
#290232
#290092
#282062
#280582
#280402
#277812
#277772
#277652
#267632
#267582
#267032
#267002
#261222
#260392
#252862
#232272
#232182
#230732
#229772
#216742
#216572
C4×#4892