Finite Group Databasebeta

← #7572262

Subgroups — #7572262

Order 512.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1197 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45405C211yesmaximal, characteristic
2#35711C211yesmaximal, characteristic
3#32664C211yesmaximal, characteristic, complemented
4#32590C211yesmaximal, characteristic, complemented
5#32369C211yesmaximal, characteristic, complemented
6#31533C211yesmaximal, characteristic, complemented
7#29308C211yesmaximal, characteristic
8#29170C211yesmaximal, characteristic
9#28961C211yesmaximal, characteristic, complemented
10#28785C211yesmaximal, characteristic
11#27319C211yesmaximal, characteristic, complemented
12#27305C211yesmaximal, characteristic, complemented
13#27013C211yesmaximal, characteristic, complemented
14#26497C211yesmaximal, characteristic, complemented
15#26428C211yesmaximal, characteristic
16#26391C211yesmaximal, characteristic, complemented
17#26389C211yesmaximal, characteristic, complemented
18#26383C211yesmaximal, characteristic, complemented
19#26337C211yesmaximal, characteristic
20#26070C211yesmaximal, characteristic
21#25973C211yesmaximal, characteristic
22#25957C211yesmaximal, characteristic
23#25847C211yesmaximal, characteristic, complemented
24#24345C211yesmaximal, characteristic, complemented
25#23245C211yesmaximal, characteristic
26#22973C211yesmaximal, characteristic, complemented
27#22869C211yesmaximal, characteristic
28#22859C211yesmaximal, characteristic
29#22679C211yesmaximal, characteristic, complemented
30#21463C211yesmaximal, characteristic
31#20880C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#475C2211yescharacteristic
38C2×#451C2211yescharacteristic
39C2×#441C2211yescharacteristic
40C2×#441C2211yescharacteristic
41C2×#441C2211yescharacteristic
42C2×C4×Q16C2211yescharacteristic
43C2×#427C2211yescharacteristic
44C2×#419C2211yescharacteristic
45C22×#103C2211yescharacteristic
46#2802—21no—
47#2792—21no—
48#2768—21no—
49#2742—21no—
50#2628—21no—
51#2628C2211yescharacteristic
52#2590—21no—
53#2584C2211yescharacteristic
54#2581—21no—
55#2581C2211yescharacteristic
56#2581C2211yescharacteristic
57#2568—21no—
58#2568C2211yescharacteristic
59#2522—21no—
60#2509—21no—
61#2508C2211yescharacteristic
62#2507C2211yescharacteristic
63#2497—21no—
64#2453C2211yescharacteristic
65#2453C2211yescharacteristic
66#2451—21no—
67#2451—21no—
68#2451C2211yescharacteristic
69#2451C2211yescharacteristic
70#2442C2211yescharacteristic
71#2441C2211yescharacteristic
72#2439—21no—
73#2439—21no—
74#2439C2211yescharacteristic
75#2439C2211yescharacteristic
76#2396—21no—
77#2396C2211yescharacteristic
78#2370C2211yescharacteristic
79#2362C2211yescharacteristic
80#2360C2211yescharacteristic
81#2351C2211yescharacteristic
82#2351C2211yescharacteristic
83#2351C2211yescharacteristic
84Q8×C4⋊C4C2211yescharacteristic
85Q8×C22⋊C4C2211yescharacteristic
86Q8×C22⋊C4C2211yescharacteristic
87#2323C2211yescharacteristic
88#2316C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2096C2211yescharacteristic
95#2088C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2066C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2026C2211yescharacteristic
118#2026C2211yescharacteristic
119#2024C2211yescharacteristic
120#2024C2211yescharacteristic
121#1993C2211yescharacteristic
122#1991C2211yescharacteristic
123#1988C2211yescharacteristic
124#1985C2211yescharacteristic
125#1985C2211yescharacteristic
126#1971C2211yescharacteristic
127#1969C2211yescharacteristic
128#1949C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1943C2211yescharacteristic
133#1943C2211yescharacteristic
134#1942C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1927C2211yescharacteristic
140#1927C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1920C2211yescharacteristic
144#1919C2211yescharacteristic
145#1917C2211yescharacteristic
146#1917C2211yescharacteristic
147#1916C2211yescharacteristic
148#1916C2211yescharacteristic
149#1894C2211yescharacteristic
150#1892C2211yescharacteristic
151#1878C2211yescharacteristic
152#1878C2211yescharacteristic
153#1878C2211yescharacteristic
154#1878C2211yescharacteristic
155#1878C2211yescharacteristic
156#1878C2211yescharacteristic
157#1873C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic
185#1847C2211yescharacteristic
186#1809C2211yescharacteristic
187#1807C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1787C2211yescharacteristic
192#1771C2211yescharacteristic
193#1770C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1750C2211yescharacteristic
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208Q82—42no—
209Q82—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219#519—42no—
220#519—42no—
221C2×C4×Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242#501—42no—
243#479—24no—
244#479—42no—
245#475—42no—
246#451Q818yescomplemented
247#441—24no—
248#441—42no—
249#441—42no—
250C4×Q16—42no—
251#427—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274#419—42no—
275C2×#103—24no—
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400D411yescharacteristic
314#399—21no—
315#399—21no—
316#399D411yescharacteristic
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398D411yescharacteristic
327#398D411yescharacteristic
328#396—21no—
329#396—21no—
330#396—21no—
331#396D411yescharacteristic
332#396D411yescharacteristic
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395D411yescharacteristic
340#393—21no—
341#393—21no—
342#393—21no—
343#393D411yescharacteristic
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#385—21no—
420#385—21no—
421#384—21no—
422#384C2311yescharacteristic
423#382—21no—
424#382—21no—
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2×Q814yes—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16C2×Q814yes—
516C2×Q16C2×Q814yes—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8—22no—
521C22×C8—22no—
522C22×C8—41no—
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540#125—22no—
541#125—41no—
542#125—41no—
543#125—41no—
544C22⋊Q8—22no—
545C22⋊Q8C2×Q814yes—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—44no—
573#117—22no—
574#117—41no—
575#117—41no—
576#117—44no—
577#117—41no—
578#117—44no—
579#117—41no—
580#117—41no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
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—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
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×C42—21no—
673C2×C42—21no—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#107—22no—
681#107—22no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—22no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103C2×Q814yes—
720#103C2×Q814yes—
721#103#4114yes—
722C22⋊C8—22no—
723C22⋊C8C2×Q814yes—
724#97—22no—
725#97—41no—
726#97—41no—
727#97—41no—
728C4×C8—41no—
729C4×C8—41no—
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#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24C22×D411yescharacteristic
786C2×Q8—24no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—28no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—41no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—44no—
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8—42no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×Q8C22×Q812yes—
819C2×Q8C22×Q812yes—
820C2×Q8C22×Q812yes—
821C2×Q8C2×#4112yes—
822C2×Q8H(5,𝔽2)12yes—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—24no—
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—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×Q812yes—
863C22×C42−1+412yes—
864C22×C4C2511yescharacteristic
865Q16—28no—
866Q16—44no—
867M16—82no—
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—
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—44no—
890C2×C8C22×Q812yes—
891C2×C8C22×Q812yes—
892C2×C8C2×#4112yes—
893C4⋊C4—24no—
894C4⋊C4—24no—
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—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—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
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—81no—
947C4⋊C4—81no—
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⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4C22×Q812yes—
967C4⋊C4C2×#4112yes—
968C4⋊C4H(5,𝔽2)12yes—
969C22⋊C4—24no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—42no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C42—24no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—42no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C42—81no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23D4×Q812yes—
1016C23C23×D411yescharacteristic
1017Q8—22no—
1018Q8—22no—
1019Q8—22no—
1020Q8—22no—
1021Q8—22no—
1022Q8—22no—
1023Q8—22no—
1024Q8—48no—
1025Q8—44no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—162no—
1031Q8—162no—
1032Q8—162no—
1033Q8#55414yes—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
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—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—48no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
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×C4D4×Q812yes—
1127C2×C4C23×Q811yescharacteristic
1128C2×C4C22×#4111yescharacteristic
1129C2×C4C2×H(5,𝔽2)11yescharacteristic
1130C2×C4C2×H(5,𝔽2)11yescharacteristic
1131C2×C4C2×2−1+411yescharacteristic
1132C2×C4#58511yescharacteristic
1133C8—22no—
1134C8—22no—
1135C8—22no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22C2×D4×Q811yescharacteristic
1149C22D4×#4111yescharacteristic
1150C22#348411yescharacteristic
1151C22#358411yescharacteristic
1152C22#358611yescharacteristic
1153C22#358611yescharacteristic
1154C22#358611yescharacteristic
1155C4—22no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—42no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4C2×#55411yescharacteristic
1185C4#350111yescharacteristic
1186C4#352011yescharacteristic
1187C4#353511yescharacteristic
1188C2—42no—
1189C2#5915011yescharacteristic
1190C2#6137911yescharacteristic
1191C2#6138611yescharacteristic
1192C2#6151111yescharacteristic
1193C2#6152811yescharacteristic
1194C2#6164511yescharacteristic
1195C2#6169111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32664C2semidirect
4. #32590C2semidirect
5. #32369C2semidirect
6. #31533C2semidirect
9. #28961C2semidirect
11. #27319C2semidirect
12. #27305C2semidirect
13. #27013C2semidirect
14. #26497C2semidirect
16. #26391C2semidirect
17. #26389C2semidirect
18. #26383C2semidirect
23. #25847C2semidirect
24. #24345C2semidirect
26. #22973C2semidirect
29. #22679C2semidirect
246. #451Q8semidirect

Maximal subgroups

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

subgroupindex
#454052
#357112
#326642
#325902
#323692
#315332
#293082
#291702
#289612
#287852
#273192
#273052
#270132
#264972
#264282
#263912
#263892
#263832
#263372
#260702
#259732
#259572
#258472
#243452
#232452
#229732
#228692
#228592
#226792
#214632
#208802