Finite Group Databasebeta

← #7487724

Subgroups — #7487724

Order 512.

1262 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53157C211yesmaximal, characteristic, complemented
2#42529C211yesmaximal, characteristic
3#32097C211yesmaximal, characteristic, complemented
4#32096C211yesmaximal, characteristic, complemented
5#32096C211yesmaximal, characteristic, complemented
6#32094C211yesmaximal, characteristic, complemented
7#32094C211yesmaximal, characteristic, complemented
8#32093C211yesmaximal, characteristic, complemented
9#32088C211yesmaximal, characteristic, complemented
10#32086C211yesmaximal, characteristic, complemented
11#31589C211yesmaximal, characteristic, complemented
12#31587C211yesmaximal, characteristic, complemented
13#31577C211yesmaximal, characteristic, complemented
14#31573C211yesmaximal, characteristic, complemented
15#30222C211yesmaximal, characteristic, complemented
16#30222C211yesmaximal, characteristic, complemented
17#29590C211yesmaximal, characteristic, complemented
18#29586C211yesmaximal, characteristic, complemented
19#29037C211yesmaximal, characteristic, complemented
20#29031C211yesmaximal, characteristic, complemented
21#29024C211yesmaximal, characteristic, complemented
22#29019C211yesmaximal, characteristic, complemented
23#27766C211yesmaximal, characteristic, complemented
24#27760C211yesmaximal, characteristic, complemented
25#27760C211yesmaximal, characteristic, complemented
26#27753C211yesmaximal, characteristic, complemented
27#26783C211yesmaximal, characteristic, complemented
28#26779C211yesmaximal, characteristic, complemented
29#26770C211yesmaximal, characteristic, complemented
30#26755C211yesmaximal, characteristic, complemented
31#23268C211yesmaximal, characteristic, complemented
32#2839—21no—
33#2839—21no—
34#2839—21no—
35#2839—21no—
36#2828—21no—
37#2767—21no—
38#2767—21no—
39#2767—21no—
40#2767—21no—
41#2703—21no—
42#2699—21no—
43#2688—21no—
44#2671—21no—
45#2661—21no—
46#2657C2211yescharacteristic
47#2647C2211yescharacteristic
48#2647C2211yescharacteristic
49#2635—21no—
50#2570C2211yescharacteristic
51#2570C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2548C2211yescharacteristic
55#2544C2211yescharacteristic
56#2544C2211yescharacteristic
57#2541C2211yescharacteristic
58#2541C2211yescharacteristic
59#2541C2211yescharacteristic
60#2509C2211yescharacteristic
61#2509C2211yescharacteristic
62#2509C2211yescharacteristic
63#2509C2211yescharacteristic
64#2508C2211yescharacteristic
65#2508C2211yescharacteristic
66#2508C2211yescharacteristic
67#2508C2211yescharacteristic
68#2464—21no—
69#2448C2211yescharacteristic
70#2447C2211yescharacteristic
71#2445C2211yescharacteristic
72#2445C2211yescharacteristic
73#2402C2211yescharacteristic
74#2367C2211yescharacteristic
75#2366C2211yescharacteristic
76#2319C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2097C2211yescharacteristic
80#2092C2211yescharacteristic
81#2092C2211yescharacteristic
82#2092C2211yescharacteristic
83#2092C2211yescharacteristic
84#2092C2211yescharacteristic
85#2084C2211yescharacteristic
86#2083C2211yescharacteristic
87#2074C2211yescharacteristic
88#2073C2211yescharacteristic
89#2073C2211yescharacteristic
90#2073C2211yescharacteristic
91#2071C2211yescharacteristic
92#2071C2211yescharacteristic
93#2068C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2066C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2065C2211yescharacteristic
101#2042C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#1983C2211yescharacteristic
126#1982C2211yescharacteristic
127#1982C2211yescharacteristic
128#1982C2211yescharacteristic
129#1961C2211yescharacteristic
130#1961C2211yescharacteristic
131#1961C2211yescharacteristic
132#1961C2211yescharacteristic
133#1961C2211yescharacteristic
134#1959C2211yescharacteristic
135#1959C2211yescharacteristic
136#1958C2211yescharacteristic
137#1958C2211yescharacteristic
138#1958C2211yescharacteristic
139#1957C2211yescharacteristic
140#1957C2211yescharacteristic
141#1944C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1935C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1928C2211yescharacteristic
158#1927C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1921C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1918C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1865C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1805C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1771C2211yescharacteristic
196#1770C2211yescharacteristic
197#1763C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C2×#127C2311yescharacteristic
204C2×#127C2311yescharacteristic
205C2×#127C2311yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#121—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
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#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400D411yescharacteristic
308#400D411yescharacteristic
309#400D411yescharacteristic
310#400D411yescharacteristic
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398D411yescharacteristic
325#398D411yescharacteristic
326#398D411yescharacteristic
327#398D411yescharacteristic
328#397—21no—
329#397—21no—
330#397—21no—
331#394—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#392—21no—
342#392—21no—
343#392—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#382—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#381—21no—
432#380—21no—
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×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445#376C2311yescharacteristic
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#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8C2411yescharacteristic
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2411yescharacteristic
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507#127—41no—
508#127—41no—
509#127—41no—
510#127—41no—
511#127—41no—
512#127—41no—
513#127—41no—
514#127—41no—
515#127—41no—
516#127—41no—
517#127—41no—
518#127—41no—
519#124—41no—
520#124—41no—
521#124—41no—
522#124—41no—
523#124—41no—
524#124—41no—
525#124—41no—
526#124—41no—
527#123—82no—
528#123—82no—
529#121—82no—
530#121—82no—
531#121—82no—
532#121—82no—
533#121—82no—
534#121—82no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—82no—
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⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—41no—
634#107—41no—
635#107—41no—
636#107—41no—
637#106—41no—
638#106—41no—
639#106—41no—
640#106—41no—
641C4⋊C8—41no—
642C4⋊C8—41no—
643C4⋊C8—41no—
644C4⋊C8—41no—
645#103—41no—
646#103—41no—
647#103—41no—
648#103—41no—
649#103—41no—
650#103—41no—
651#103—41no—
652#103—41no—
653#102—41no—
654#102—41no—
655#102—41no—
656#102—41no—
657#102—41no—
658#102—41no—
659#102—41no—
660#102—41no—
661#102—41no—
662#102—41no—
663#102—41no—
664#102—41no—
665#102—41no—
666#102—41no—
667#102—41no—
668#102—41no—
669#102—41no—
670#102—41no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#97—41no—
686#97—41no—
687#97—41no—
688#97—41no—
689#97—41no—
690C4×C8—41no—
691C4×C8—41no—
692C4×C8—41no—
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#95—21no—
730#95—21no—
731#95—21no—
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
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
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C2511yescharacteristic
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23C23×D411yescharacteristic
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—84no—
1036D4—162no—
1037D4—162no—
1038D4—162no—
1039D4—162no—
1040D4—162no—
1041D4—162no—
1042D4—162no—
1043D4—162no—
1044D4—162no—
1045D4—162no—
1046D4—162no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—162no—
1126C2×C4—162no—
1127C2×C4—162no—
1128C2×C4—162no—
1129C2×C4#58511yescharacteristic
1130C2×C4#58511yescharacteristic
1131C2×C4#58511yescharacteristic
1132C2×C4#58511yescharacteristic
1133C2×C4#58511yescharacteristic
1134C2×C4#58511yescharacteristic
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22#348711yescharacteristic
1172C22#350011yescharacteristic
1173C22#350011yescharacteristic
1174C22#358411yescharacteristic
1175C22#358511yescharacteristic
1176C22#358511yescharacteristic
1177C22#358511yescharacteristic
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4#356711yescharacteristic
1205C4#356711yescharacteristic
1206C4#356711yescharacteristic
1207C4#356711yescharacteristic
1208C2—161no—
1209C2—161no—
1210C2—161no—
1211C2—161no—
1212C2#5197911yescharacteristic
1213C2#6191911yescharacteristic
1214C2#6194511yescharacteristic
1215C2#6256411yescharacteristic
1216C2#6256411yescharacteristic
1217C2#6260711yescharacteristic
1218C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42529C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53157C2semidirect
3. #32097C2semidirect
4. #32096C2semidirect
5. #32096C2semidirect
6. #32094C2semidirect
7. #32094C2semidirect
8. #32093C2semidirect
9. #32088C2semidirect
10. #32086C2semidirect
11. #31589C2semidirect
12. #31587C2semidirect
13. #31577C2semidirect
14. #31573C2semidirect
15. #30222C2semidirect
16. #30222C2semidirect
17. #29590C2semidirect
18. #29586C2semidirect
19. #29037C2semidirect
20. #29031C2semidirect
21. #29024C2semidirect
22. #29019C2semidirect
23. #27766C2semidirect
24. #27760C2semidirect
25. #27760C2semidirect
26. #27753C2semidirect
27. #26783C2semidirect
28. #26779C2semidirect
29. #26770C2semidirect
30. #26755C2semidirect
31. #23268C2semidirect

Maximal subgroups

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

subgroupindex
#531572
#425292
#320972
#320962
#320942
#320932
#320882
#320862
#315892
#315872
#315772
#315732
#302222
#295902
#295862
#290372
#290312
#290242
#290192
#277662
#277602
#277532
#267832
#267792
#267702
#267552
#232682