Finite Group Databasebeta

← #7037763

Subgroups — #7037763

Order 512.

1485 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59290C211yesmaximal, characteristic, complemented
2#40169C211yesmaximal, characteristic
3#32368C211yesmaximal, characteristic, complemented
4#31998C211yesmaximal, characteristic, complemented
5#31754C211yesmaximal, characteristic, complemented
6#31702C211yesmaximal, characteristic, complemented
7#31666C211yesmaximal, characteristic
8#31592C211yesmaximal, characteristic, complemented
9#31306C211yesmaximal, characteristic, complemented
10#30653C211yesmaximal, characteristic, complemented
11#29336C211yesmaximal, characteristic, complemented
12#29025C211yesmaximal, characteristic, complemented
13#28081C211yesmaximal, characteristic, complemented
14#28052C211yesmaximal, characteristic, complemented
15#27894C211yesmaximal, characteristic, complemented
16#27846C211yesmaximal, characteristic, complemented
17#27739C211yesmaximal, characteristic, complemented
18#27539C211yesmaximal, characteristic, complemented
19#27406C211yesmaximal, characteristic, complemented
20#27344C211yesmaximal, characteristic, complemented
21#27342C211yesmaximal, characteristic, complemented
22#27262C211yesmaximal, characteristic, complemented
23#27143C211yesmaximal, characteristic, complemented
24#26776C211yesmaximal, characteristic, complemented
25#24969C211yesmaximal, characteristic, complemented
26#24861C211yesmaximal, characteristic
27#23760C211yesmaximal, characteristic, complemented
28#23302C211yesmaximal, characteristic, complemented
29#23228C211yesmaximal, characteristic, complemented
30#22562C211yesmaximal, characteristic, complemented
31#22081C211yesmaximal, characteristic, complemented
32C2×#552—21no—
33C2×#489C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C22×#102C2211yescharacteristic
36#2850C2211yescharacteristic
37#2779—21no—
38#2749—21no—
39#2735—21no—
40#2719—21no—
41#2698—21no—
42#2697—21no—
43#2636—21no—
44#2566C2211yescharacteristic
45#2552C2211yescharacteristic, complemented
46#2538C2211yescharacteristic
47#2518—21no—
48#2512C2211yescharacteristic
49#2506C2211yescharacteristic, complemented
50#2506C2211yescharacteristic, complemented
51#2496C2211yescharacteristic
52#2496C2211yescharacteristic
53#2495C2211yescharacteristic
54#2490C2211yescharacteristic
55#2489C2211yescharacteristic
56#2486C2211yescharacteristic
57#2484—21no—
58#2480—21no—
59#2478—21no—
60#2462—21no—
61#2448C2211yescharacteristic
62#2440C2211yescharacteristic
63#2440C2211yescharacteristic, complemented
64#2438—21no—
65#2435C2211yescharacteristic
66#2427C2211yescharacteristic
67#2419—21no—
68#2408C2211yescharacteristic
69#2367C2211yescharacteristic
70#2365C2211yescharacteristic, complemented
71D4×C4⋊C4C2211yescharacteristic
72#2344C2211yescharacteristic
73#2344C2211yescharacteristic, complemented
74D4×C22⋊C4C2211yescharacteristic
75#2321—21no—
76C4×#123C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#389C2211yescharacteristic, complemented
79#2285C2211yescharacteristic, complemented
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2100C2211yescharacteristic, complemented
83#2100C2211yescharacteristic, complemented
84#2095C2211yescharacteristic, complemented
85#2094C2211yescharacteristic
86#2093C2211yescharacteristic
87#2087C2211yescharacteristic, complemented
88#2084C2211yescharacteristic, complemented
89#2083C2211yescharacteristic, complemented
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2071C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#1992C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1987C2211yescharacteristic, complemented
123#1983C2211yescharacteristic
124#1959C2211yescharacteristic
125#1959C2211yescharacteristic
126#1954C2211yescharacteristic
127#1948C2211yescharacteristic, complemented
128#1944C2211yescharacteristic, complemented
129#1943C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1928C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1892C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1872C2211yescharacteristic
167#1872C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1869C2211yescharacteristic
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1853C2211yescharacteristic, complemented
177#1852C2211yescharacteristic
178#1847C2211yescharacteristic, complemented
179#1836C2211yescharacteristic, complemented
180#1834C2211yescharacteristic, complemented
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic, complemented
183#1808C2211yescharacteristic
184#1807C2211yescharacteristic
185#1803C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1749C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205#552—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123D411yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117—21no—
234C2×#117—21no—
235C22×C4⋊C4—21no—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C42C2311yescharacteristic
241#489—24no—
242#480—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×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#102—24no—
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×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#395—21no—
326#395—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#392—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#388—21no—
370#388—21no—
371#388—21no—
372#388D411yescharacteristic
373#388D411yescharacteristic
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#387D411yescharacteristic
385#387D411yescharacteristic
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386D411yescharacteristic
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385D411yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#382—21no—
408#382—21no—
409#382C2311yescharacteristic
410#381—21no—
411#381—21no—
412#381—21no—
413#381D411yescharacteristic
414#380—21no—
415#380—21no—
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#379—21no—
425#379—21no—
426#379—21no—
427#379—21no—
428C4×C4⋊C4—21no—
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×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C2×#95—21no—
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#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C25—21no—
483C22×Q8—21no—
484C22×Q8C2411yescharacteristic
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4C2×D411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C22×C8—22no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519#126—44no—
520#126—44no—
521#126—82no—
522#125—41no—
523#125—41no—
524#125—44no—
525#125—44no—
526#125—44no—
527#124—22no—
528#124—41no—
529#124—41no—
530#124—41no—
531#123—24no—
532#123—44no—
533C22⋊Q8—44no—
534C22⋊Q8—44no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—41no—
538C22⋊Q8—41no—
539#121—22no—
540#121—41no—
541#121—41no—
542#121—41no—
543#120—44no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—44no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—44no—
554C4×D4—82no—
555#117—44no—
556#117—44no—
557#117—44no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
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⋊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—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
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—82no—
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—41no—
662C2×C42—41no—
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#107—22no—
671#107—22no—
672#107—41no—
673#107—41no—
674#107—41no—
675#107—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685#103—22no—
686#103—22no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102#4114yes—
709C22⋊C8—22no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712C22⋊C8—41no—
713C22⋊C8—41no—
714C22⋊C8—41no—
715C22⋊C8—41no—
716#97—22no—
717#97—41no—
718#97—41no—
719#97—41no—
720#97—41no—
721#97—41no—
722C4×C8—41no—
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#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#95—21no—
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
765#95C2×D411yescharacteristic
766C24—21no—
767C24—21no—
768C24—42no—
769C24—42no—
770C24—81no—
771C24—81no—
772C24—81no—
773C24—81no—
774C24—81no—
775C24C22×D411yescharacteristic
776C24C22×D411yescharacteristic
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—81no—
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—21no—
796C2×D4—21no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—82no—
807C2×D4—82no—
808C2×D4—82no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4AGL(1,ℤ/8)14yes—
813C2×D4C2×#4112yes—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
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—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—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
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×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C2511yescharacteristic
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—21no—
896C2×C8—21no—
897C2×C8—82no—
898C2×C8C2×#4112yes—
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—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4C2×#4112yes—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
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—
998C22⋊C4—81no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—41no—
1010C42—41no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—42no—
1016C42—42no—
1017C42—81no—
1018C42—81no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—84no—
1046C23—84no—
1047C23—162no—
1048C23—162no—
1049C23—162no—
1050C23—162no—
1051C23—162no—
1052C23C2×AGL(1,ℤ/8)12yes—
1053C23C2×AGL(1,ℤ/8)12yes—
1054C23C23×D411yescharacteristic
1055Q8—41no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—84no—
1060D4—22no—
1061D4—22no—
1062D4—44no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—84no—
1070D4—84no—
1071D4—162no—
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—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—44no—
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—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—82no—
1159C2×C4—84no—
1160C2×C4—84no—
1161C2×C4—84no—
1162C2×C4—162no—
1163C2×C4—162no—
1164C2×C4C2×AGL(1,ℤ/8)12yes—
1165C2×C4C22×#4111yescharacteristic
1166C2×C4#58511yescharacteristic
1167C2×C4#58511yescharacteristic
1168C2×C4#58511yescharacteristic
1169C2×C4#58511yescharacteristic
1170C2×C4#58511yescharacteristic
1171C8—22no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C8—41no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—168no—
1208C22D4×#4111yescharacteristic
1209C22#348511yescharacteristic
1210C22#350011yescharacteristic
1211C22C22×AGL(1,ℤ/8)11yescharacteristic
1212C22#358511yescharacteristic
1213C22#358611yescharacteristic
1214C22#358611yescharacteristic
1215C4—22no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—42no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4#349311yescharacteristic
1242C4#352111yescharacteristic
1243C4#356611yescharacteristic
1244C4#356611yescharacteristic
1245C2—42no—
1246C2—42no—
1247C2—82no—
1248C2—161no—
1249C2#4350111yescharacteristic
1250C2#6145111yescharacteristic
1251C2#6151411yescharacteristic
1252C2#6170611yescharacteristic
1253C2#6178011yescharacteristic
1254C2#6257511yescharacteristic
1255C2#6258311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59290C2semidirect
3. #32368C2semidirect
4. #31998C2semidirect
5. #31754C2semidirect
6. #31702C2semidirect
8. #31592C2semidirect
9. #31306C2semidirect
10. #30653C2semidirect
11. #29336C2semidirect
12. #29025C2semidirect
13. #28081C2semidirect
14. #28052C2semidirect
15. #27894C2semidirect
16. #27846C2semidirect
17. #27739C2semidirect
18. #27539C2semidirect
19. #27406C2semidirect
20. #27344C2semidirect
21. #27342C2semidirect
22. #27262C2semidirect
23. #27143C2semidirect
24. #26776C2semidirect
25. #24969C2semidirect
27. #23760C2semidirect
28. #23302C2semidirect
29. #23228C2semidirect
30. #22562C2semidirect
31. #22081C2semidirect
45. #2552C22semidirect
49. #2506C22semidirect
50. #2506C22semidirect
63. #2440C22semidirect
70. #2365C22semidirect
73. #2344C22semidirect
78. C2×#389C22semidirect
79. #2285C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2100C22semidirect
83. #2100C22semidirect
84. #2095C22semidirect
87. #2087C22semidirect
88. #2084C22semidirect
89. #2083C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
99. #2068C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2057C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
120. #1992C22semidirect
121. #1989C22semidirect
122. #1987C22semidirect
127. #1948C22semidirect
128. #1944C22semidirect
129. #1943C22semidirect
130. #1943C22semidirect
137. #1935C22semidirect
138. #1935C22semidirect
139. #1935C22semidirect
142. #1928C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
153. #1924C22semidirect
154. #1924C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
167. #1872C22semidirect
168. #1872C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
176. #1853C22semidirect
178. #1847C22semidirect
179. #1836C22semidirect
180. #1834C22semidirect
182. #1823C22semidirect
185. #1803C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
198. C4×#103C22semidirect
201. #1749C22semidirect
202. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#592902
#401692
#323682
#319982
#317542
#317022
#316662
#315922
#313062
#306532
#293362
#290252
#280812
#280522
#278942
#278462
#277392
#275392
#274062
#273442
#273422
#272622
#271432
#267762
#249692
#248612
#237602
#233022
#232282
#225622
#220812