Finite Group Databasebeta

← #7582694

Subgroups — #7582694

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45048C211yesmaximal, characteristic, complemented
2#36000C211yesmaximal, characteristic, complemented
3#31784C211yesmaximal, characteristic, complemented
4#31740C211yesmaximal, characteristic, complemented
5#30797C211yesmaximal, characteristic, complemented
6#30701C211yesmaximal, characteristic
7#29485C211yesmaximal, characteristic, complemented
8#29484C211yesmaximal, characteristic, complemented
9#29011C211yesmaximal, characteristic, complemented
10#28902C211yesmaximal, characteristic, complemented
11#28062C211yesmaximal, characteristic, complemented
12#27798C211yesmaximal, characteristic, complemented
13#27340C211yesmaximal, characteristic, complemented
14#27211C211yesmaximal, characteristic, complemented
15#27139C211yesmaximal, characteristic, complemented
16#27056C211yesmaximal, characteristic, complemented
17#26875C211yesmaximal, characteristic, complemented
18#26812C211yesmaximal, characteristic, complemented
19#26812C211yesmaximal, characteristic, complemented
20#26730C211yesmaximal, characteristic, complemented
21#26729C211yesmaximal, characteristic, complemented
22#26688C211yesmaximal, characteristic, complemented
23#26237C211yesmaximal, characteristic, complemented
24#24946C211yesmaximal, characteristic, complemented
25#23299C211yesmaximal, characteristic, complemented
26#23166C211yesmaximal, characteristic, complemented
27#23130C211yesmaximal, characteristic, complemented
28#23060C211yesmaximal, characteristic, complemented
29#22933C211yesmaximal, characteristic, complemented
30#21588C211yesmaximal, characteristic, complemented
31#21586C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#466C2211yescharacteristic
38#2803—21no—
39#2797—21no—
40#2710—21no—
41#2709—21no—
42#2651—21no—
43#2624C2211yescharacteristic
44#2597—21no—
45#2578—21no—
46#2560—21no—
47#2557—21no—
48#2548—21no—
49#2541C2211yescharacteristic
50#2525—21no—
51#2521—21no—
52#2512C2211yescharacteristic
53#2507C2211yescharacteristic
54#2497C2211yescharacteristic
55#2491C2211yescharacteristic
56#2491C2211yescharacteristic
57#2491C2211yescharacteristic
58#2490C2211yescharacteristic
59#2490C2211yescharacteristic
60#2485C2211yescharacteristic
61#2476—21no—
62#2458—21no—
63#2445C2211yescharacteristic
64#2445C2211yescharacteristic
65#2440C2211yescharacteristic
66#2426—21no—
67#2416C2211yescharacteristic
68#2396—21no—
69#2395C2211yescharacteristic
70#2370C2211yescharacteristic
71#2365C2211yescharacteristic
72#2365C2211yescharacteristic
73#2363C2211yescharacteristic
74#2363C2211yescharacteristic
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic
77#2354C2211yescharacteristic
78#2354C2211yescharacteristic
79#2347C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic
82#2274C2211yescharacteristic
83#2100C2211yescharacteristic
84#2094C2211yescharacteristic
85#2086C2211yescharacteristic
86#2084C2211yescharacteristic
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2077C2211yescharacteristic
90#2071C2211yescharacteristic
91#2065C2211yescharacteristic
92#2065C2211yescharacteristic
93#2065C2211yescharacteristic
94#2065C2211yescharacteristic
95#2059C2211yescharacteristic
96#2058C2211yescharacteristic
97#2058C2211yescharacteristic
98#2054C2211yescharacteristic
99#2041C2211yescharacteristic
100#2034C2211yescharacteristic
101#2034C2211yescharacteristic
102#2034C2211yescharacteristic
103#2034C2211yescharacteristic
104#2033C2211yescharacteristic
105#2033C2211yescharacteristic
106#2033C2211yescharacteristic
107#2033C2211yescharacteristic
108#2025C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2011C2211yescharacteristic
112#1999C2211yescharacteristic
113#1999C2211yescharacteristic
114#1999C2211yescharacteristic
115#1990C2211yescharacteristic
116#1989C2211yescharacteristic
117#1987C2211yescharacteristic
118#1982C2211yescharacteristic
119#1972C2211yescharacteristic
120#1972C2211yescharacteristic
121#1972C2211yescharacteristic
122#1957C2211yescharacteristic
123#1954C2211yescharacteristic
124#1948C2211yescharacteristic
125#1947C2211yescharacteristic
126#1944C2211yescharacteristic
127#1943C2211yescharacteristic
128#1941C2211yescharacteristic
129#1936C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1921C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1893C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1869C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1853C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1824C2211yescharacteristic
184#1807C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127—21no—
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#124—21no—
213C2×#124—21no—
214C2×#124—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237#501—24no—
238#482—24no—
239#482—24no—
240#480—24no—
241#474—24no—
242#466—24no—
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400D411yescharacteristic
296#399—21no—
297#399D411yescharacteristic
298#398—21no—
299#398—21no—
300#398—21no—
301#398D411yescharacteristic
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397D411yescharacteristic
308#397D411yescharacteristic
309#397D411yescharacteristic
310#396—21no—
311#396—21no—
312#396—21no—
313#395—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394D411yescharacteristic
328#394D411yescharacteristic
329#393—21no—
330#393—21no—
331#393—21no—
332#392—21no—
333#392—21no—
334#391—21no—
335#391—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
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#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—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#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#385—21no—
407#385—21no—
408#385—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C2×D411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×D8—22no—
505C2×D8—41no—
506C2×D8—41no—
507C2×D8—41no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525#127—41no—
526#127—41no—
527#127—82no—
528#126—82no—
529#125—22no—
530#125—41no—
531#124—82no—
532#124—82no—
533#124—82no—
534#123—82no—
535#123—82no—
536C22⋊Q8—82no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547#121—41no—
548#121—41no—
549#121—82no—
550C4×Q8—82no—
551C4×Q8—82no—
552C4×D4—22no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560#117—22no—
561#117—22no—
562#117—41no—
563#117—41no—
564#117—41no—
565#117—41no—
566#117—41no—
567#117—41no—
568#117—82no—
569C2×C4⋊C4—22no—
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⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
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—41no—
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677#107—22no—
678#107—22no—
679#107—22no—
680#107—41no—
681#107#4114yes—
682#107#4114yes—
683#106—22no—
684#106—22no—
685#106—22no—
686#106—22no—
687#106—41no—
688#106—41no—
689#106—41no—
690#106—41no—
691C4⋊C8—22no—
692C4⋊C8—41no—
693C4⋊C8—41no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714C22⋊C8—22no—
715C22⋊C8—22no—
716C22⋊C8—22no—
717C22⋊C8—41no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721#97—22no—
722#97—41no—
723#97—41no—
724C4×C8—41no—
725C4×C8—41no—
726C4×C8—41no—
727C4×C8—41no—
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#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
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#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765C24—21no—
766C24—21no—
767C24—21no—
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—81no—
775C2×Q8—81no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
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—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
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—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C2511yescharacteristic
871D8—82no—
872D8—82no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—82no—
896C2×C8C2×#4112yes—
897C2×C8C2×#4112yes—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4C2×#4112yes—
947C4⋊C4C2×#4112yes—
948C4⋊C4C2×#4112yes—
949C4⋊C4C2×#4112yes—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C42—81no—
1020C42—81no—
1021C42—81no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23C23×D411yescharacteristic
1058Q8—84no—
1059Q8—84no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—82no—
1073D4—162no—
1074D4—162no—
1075D4—162no—
1076D4—162no—
1077D4—162no—
1078D4—162no—
1079D4—162no—
1080D4—162no—
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—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—84no—
1163C2×C4—162no—
1164C2×C4—162no—
1165C2×C4—162no—
1166C2×C4#57612yes—
1167C2×C4#57712yes—
1168C2×C4C22×#4111yescharacteristic
1169C2×C4C22×#4111yescharacteristic
1170C2×C4#58511yescharacteristic
1171C2×C4#58511yescharacteristic
1172C2×C4#58511yescharacteristic
1173C2×C4#58511yescharacteristic
1174C8—22no—
1175C8—22no—
1176C8—41no—
1177C8—41no—
1178C8—41no—
1179C8—41no—
1180C8—41no—
1181C8—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22D4×#4111yescharacteristic
1218C22D4×#4111yescharacteristic
1219C22#348511yescharacteristic
1220C22C2×#57611yescharacteristic
1221C22C2×#57711yescharacteristic
1222C22#358411yescharacteristic
1223C22#358511yescharacteristic
1224C4—22no—
1225C4—22no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—42no—
1230C4—42no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—42no—
1236C4—42no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4#348011yescharacteristic
1250C4#351011yescharacteristic
1251C4#352411yescharacteristic
1252C4#356611yescharacteristic
1253C2—81no—
1254C2—81no—
1255C2—161no—
1256C2—161no—
1257C2—161no—
1258C2#5917511yescharacteristic
1259C2#6149511yescharacteristic
1260C2#6149611yescharacteristic
1261C2#6153411yescharacteristic
1262C2#6153911yescharacteristic
1263C2#6177211yescharacteristic
1264C2#6181511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30701C2
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. #45048C2semidirect
2. #36000C2semidirect
3. #31784C2semidirect
4. #31740C2semidirect
5. #30797C2semidirect
7. #29485C2semidirect
8. #29484C2semidirect
9. #29011C2semidirect
10. #28902C2semidirect
11. #28062C2semidirect
12. #27798C2semidirect
13. #27340C2semidirect
14. #27211C2semidirect
15. #27139C2semidirect
16. #27056C2semidirect
17. #26875C2semidirect
18. #26812C2semidirect
19. #26812C2semidirect
20. #26730C2semidirect
21. #26729C2semidirect
22. #26688C2semidirect
23. #26237C2semidirect
24. #24946C2semidirect
25. #23299C2semidirect
26. #23166C2semidirect
27. #23130C2semidirect
28. #23060C2semidirect
29. #22933C2semidirect
30. #21588C2semidirect
31. #21586C2semidirect

Maximal subgroups

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

subgroupindex
#450482
#360002
#317842
#317402
#307972
#307012
#294852
#294842
#290112
#289022
#280622
#277982
#273402
#272112
#271392
#270562
#268752
#268122
#267302
#267292
#266882
#262372
#249462
#232992
#231662
#231302
#230602
#229332
#215882
#215862