Finite Group Databasebeta

← #6749793

Subgroups — #6749793

Order 512.

1370 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37888C211yesmaximal, characteristic
2#35665C211yesmaximal, characteristic
3#32967C211yesmaximal, characteristic, complemented
4#31795C211yesmaximal, characteristic
5#31777C211yesmaximal, characteristic
6#31677C211yesmaximal, characteristic
7#31673C211yesmaximal, characteristic
8#31453C211yesmaximal, characteristic, complemented
9#31451C211yesmaximal, characteristic, complemented
10#31316C211yesmaximal, characteristic, complemented
11#31316C211yesmaximal, characteristic, complemented
12#30005C211yesmaximal, characteristic, complemented
13#29695C211yesmaximal, characteristic, complemented
14#29138C211yesmaximal, characteristic, complemented
15#29030C211yesmaximal, characteristic, complemented
16#29017C211yesmaximal, characteristic, complemented
17#28961C211yesmaximal, characteristic, complemented
18#28956C211yesmaximal, characteristic, complemented
19#28294C211yesmaximal, characteristic, complemented
20#27682C211yesmaximal, characteristic, complemented
21#27638C211yesmaximal, characteristic, complemented
22#27420C211yesmaximal, characteristic, complemented
23#27401C211yesmaximal, characteristic, complemented
24#27185C211yesmaximal, characteristic, complemented
25#27172C211yesmaximal, characteristic, complemented
26#24715C211yesmaximal, characteristic, complemented
27#24707C211yesmaximal, characteristic, complemented
28#22801C211yesmaximal, characteristic
29#22128C211yesmaximal, characteristic, complemented
30#21870C211yesmaximal, characteristic, complemented
31#20745C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#433C2211yescharacteristic
38C2×#432C2211yescharacteristic
39#2851C2211yescharacteristic
40#2781—21no—
41#2781—21no—
42#2770—21no—
43#2770—21no—
44#2647C2211yescharacteristic
45#2629C2211yescharacteristic
46#2609—21no—
47#2599—21no—
48#2599—21no—
49#2581—21no—
50#2525—21no—
51#2525—21no—
52#2524—21no—
53#2524—21no—
54#2508C2211yescharacteristic
55#2508C2211yescharacteristic
56#2495C2211yescharacteristic
57#2495C2211yescharacteristic
58#2485C2211yescharacteristic
59#2485C2211yescharacteristic
60#2477—21no—
61#2475—21no—
62#2465—21no—
63#2462—21no—
64#2451C2211yescharacteristic
65#2446C2211yescharacteristic
66#2439C2211yescharacteristic
67#2434C2211yescharacteristic
68#2429C2211yescharacteristic
69#2421C2211yescharacteristic
70#2415C2211yescharacteristic
71#2409C2211yescharacteristic
72#2347C2211yescharacteristic
73#2347C2211yescharacteristic
74#2330C2211yescharacteristic
75#2327C2211yescharacteristic
76#2323C2211yescharacteristic
77#2320C2211yescharacteristic
78#2314C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80#2290C2211yescharacteristic
81#2285C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2097C2211yescharacteristic
87#2097C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2086C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2058C2211yescharacteristic
107#2057C2211yescharacteristic
108#2043C2211yescharacteristic
109#2043C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1989C2211yescharacteristic
125#1981C2211yescharacteristic
126#1981C2211yescharacteristic
127#1960C2211yescharacteristic
128#1960C2211yescharacteristic
129#1955C2211yescharacteristic
130#1954C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1947C2211yescharacteristic
136#1944C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1927C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1924C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1921C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1873C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1843C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1805C2211yescharacteristic
182#1805C2211yescharacteristic
183#1805C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1798C2211yescharacteristic
191#1797C2211yescharacteristic
192#1787C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1768C2211yescharacteristic
199#1763C2211yescharacteristic
200#1763C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204#533—24no—
205#533—42no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216#519—24no—
217#519—42no—
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117—21no—
229C2×#117—21no—
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#479—24no—
236#479—42no—
237#479—42no—
238#433—42no—
239#432—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
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#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#393—21no—
334#391—21no—
335#391—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
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#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388D411yescharacteristic
377#388D411yescharacteristic
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386D411yescharacteristic
405#386D411yescharacteristic
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385D411yescharacteristic
413#385D411yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#383—21no—
417#383—21no—
418#383—21no—
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452#376C2311yescharacteristic
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8—41no—
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4C2×D411yescharacteristic
499C23×C4—21no—
500C23×C4C2×D411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517C4⋊Q8—41no—
518#125—22no—
519#125—22no—
520#125—44no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526C22⋊Q8—41no—
527C22⋊Q8—41no—
528C22⋊Q8—41no—
529C22⋊Q8—44no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—44no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—44no—
541C4×Q8—44no—
542C4×Q8#4114yes—
543C4×D4—41no—
544C4×D4—41no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—44no—
549#117—44no—
550#117—44no—
551#117—41no—
552#117—41no—
553#117—41no—
554#117—41no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊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⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
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×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×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C42—21no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653#107—22no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107—41no—
659#106—22no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665C4⋊C8—22no—
666C4⋊C8—22no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697C22⋊C8—41no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700C22⋊C8—41no—
701C22⋊C8—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705#97—41no—
706#97—41no—
707#97—41no—
708#97—41no—
709C4×C8—41no—
710C4×C8—41no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#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#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—42no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—81no—
796C2×Q8C2×#4112yes—
797C2×Q82−1+412yes—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
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—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
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—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—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—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
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—
938C4⋊C4—81no—
939C4⋊C4C2×#4112yes—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—41no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C42—22no—
964C42—22no—
965C42—24no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42C2×#4112yes—
987C42H(5,𝔽2)12yes—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23C23×D411yescharacteristic
1003Q8—22no—
1004Q8—22no—
1005Q8—22no—
1006Q8—22no—
1007Q8—48no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—84no—
1017D4—82no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
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—82no—
1111C2×C4#54612yes—
1112C2×C4#54612yes—
1113C2×C4C22×#4111yescharacteristic
1114C2×C4C2×H(5,𝔽2)11yescharacteristic
1115C2×C4C2×2−1+411yescharacteristic
1116C2×C4#58511yescharacteristic
1117C2×C4#58511yescharacteristic
1118C2×C4#58511yescharacteristic
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22#344911yescharacteristic
1142C22C2×#54611yescharacteristic
1143C22#348911yescharacteristic
1144C22#358411yescharacteristic
1145C22#358611yescharacteristic
1146C22#358611yescharacteristic
1147C22#358611yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—41no—
1151C4—41no—
1152C4—42no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—42no—
1160C4—42no—
1161C4—41no—
1162C4—41no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4#349311yescharacteristic
1177C4#349511yescharacteristic
1178C4#353911yescharacteristic
1179C4#354111yescharacteristic
1180C2—81no—
1181C2—81no—
1182C2#3784711yescharacteristic
1183C2#6098411yescharacteristic
1184C2#6102011yescharacteristic
1185C2#6117611yescharacteristic
1186C2#6119711yescharacteristic
1187C2#6216111yescharacteristic
1188C2#6222511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32967C2semidirect
8. #31453C2semidirect
9. #31451C2semidirect
10. #31316C2semidirect
11. #31316C2semidirect
12. #30005C2semidirect
13. #29695C2semidirect
14. #29138C2semidirect
15. #29030C2semidirect
16. #29017C2semidirect
17. #28961C2semidirect
18. #28956C2semidirect
19. #28294C2semidirect
20. #27682C2semidirect
21. #27638C2semidirect
22. #27420C2semidirect
23. #27401C2semidirect
24. #27185C2semidirect
25. #27172C2semidirect
26. #24715C2semidirect
27. #24707C2semidirect
29. #22128C2semidirect
30. #21870C2semidirect
31. #20745C2semidirect

Maximal subgroups

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

subgroupindex
#378882
#356652
#329672
#317952
#317772
#316772
#316732
#314532
#314512
#313162
#300052
#296952
#291382
#290302
#290172
#289612
#289562
#282942
#276822
#276382
#274202
#274012
#271852
#271722
#247152
#247072
#228012
#221282
#218702
#207452