Finite Group Databasebeta

← #6484113

Subgroups — #6484113

Order 512.

1456 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35207C211yesmaximal, characteristic, complemented
2#35107C211yesmaximal, characteristic, complemented
3#33217C211yesmaximal, characteristic, complemented
4#33211C211yesmaximal, characteristic, complemented
5#33143C211yesmaximal, characteristic, complemented
6#33135C211yesmaximal, characteristic, complemented
7#30365C211yesmaximal, characteristic, complemented
8#30362C211yesmaximal, characteristic, complemented
9#30362C211yesmaximal, characteristic, complemented
10#30362C211yesmaximal, characteristic, complemented
11#28822C211yesmaximal, characteristic, complemented
12#28715C211yesmaximal, characteristic, complemented
13#28544C211yesmaximal, characteristic, complemented
14#28237C211yesmaximal, characteristic
15#28074C211yesmaximal, characteristic, complemented
16#28072C211yesmaximal, characteristic, complemented
17#28068C211yesmaximal, characteristic, complemented
18#28067C211yesmaximal, characteristic, complemented
19#27844C211yesmaximal, characteristic, complemented
20#27836C211yesmaximal, characteristic, complemented
21#27829C211yesmaximal, characteristic, complemented
22#27826C211yesmaximal, characteristic, complemented
23#27794C211yesmaximal, characteristic, complemented
24#27790C211yesmaximal, characteristic, complemented
25#25355C211yesmaximal, characteristic, complemented
26#25350C211yesmaximal, characteristic, complemented
27#22120C211yesmaximal, characteristic, complemented
28#22116C211yesmaximal, characteristic, complemented
29C4×#501C211yesmaximal, characteristic, complemented
30#21286C211yesmaximal, characteristic, complemented
31#20491C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×C4×M16C2211yescharacteristic
43C22×#97C2211yescharacteristic
44#2857C2211yescharacteristic
45#2854C2211yescharacteristic
46#2854C2211yescharacteristic
47#2854C2211yescharacteristic
48#2854C2211yescharacteristic
49#2851C2211yescharacteristic
50#2851C2211yescharacteristic
51#2851C2211yescharacteristic
52#2653—21no—
53#2653—21no—
54#2650—21no—
55#2630—21no—
56#2566C2211yescharacteristic
57#2563C2211yescharacteristic
58#2563C2211yescharacteristic
59#2562C2211yescharacteristic
60#2552C2211yescharacteristic
61#2550C2211yescharacteristic
62#2537C2211yescharacteristic
63#2535C2211yescharacteristic
64#2525—21no—
65#2497C2211yescharacteristic
66#2495C2211yescharacteristic
67#2494—21no—
68#2494C2211yescharacteristic
69#2494C2211yescharacteristic
70#2491C2211yescharacteristic
71#2490C2211yescharacteristic
72#2490C2211yescharacteristic
73#2490C2211yescharacteristic
74#2477—21no—
75#2470—21no—
76#2461—21no—
77#2458—21no—
78#2458—21no—
79#2422—21no—
80#2337—21no—
81#2335—21no—
82#2324—21no—
83#2314—21no—
84C4×C4⋊Q8C2211yescharacteristic
85C4×#125C2211yescharacteristic
86#2293C2211yescharacteristic
87#2293C2211yescharacteristic
88C42×D4C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2101C2211yescharacteristic
92#2099C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2058C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2023C2211yescharacteristic
121#1993C2211yescharacteristic
122#1993C2211yescharacteristic
123#1992C2211yescharacteristic
124#1992C2211yescharacteristic
125#1991C2211yescharacteristic
126#1991C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1972C2211yescharacteristic
130#1972C2211yescharacteristic
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1944C2211yescharacteristic
136#1944C2211yescharacteristic
137#1944C2211yescharacteristic
138#1944C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1943C2211yescharacteristic
142#1943C2211yescharacteristic
143#1943C2211yescharacteristic
144#1943C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1921C2211yescharacteristic
164#1921C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1895C2211yescharacteristic
168#1895C2211yescharacteristic
169#1893C2211yescharacteristic
170#1893C2211yescharacteristic
171#1847C2211yescharacteristic
172#1847C2211yescharacteristic
173#1846C2211yescharacteristic
174#1809C2211yescharacteristic
175#1809C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1808C2211yescharacteristic
180#1808C2211yescharacteristic
181#1807C2211yescharacteristic
182#1807C2211yescharacteristic
183#1807C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#107C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1767C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1749C2211yescharacteristic
201#1749C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×#121—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8—21no—
226C2×C4×D4D411yescharacteristic
227C2×C4×D4D411yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#501—24no—
236#501—42no—
237#499—42no—
238#478—24no—
239#474—24no—
240#469—42no—
241#466—42no—
242#442—24no—
243#435—24no—
244#435—24no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
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
284C4×M16—42no—
285C2×#97—42no—
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#401—21no—
299#401—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#393—21no—
325#393—21no—
326#393—21no—
327#393—21no—
328#393—21no—
329#392—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
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#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#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#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4D411yescharacteristic
437C4×C4⋊C4D411yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C43C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C2×D411yescharacteristic
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—41no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534#125—22no—
535#125—22no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—41no—
540#125—41no—
541#125—41no—
542#124—44no—
543#123—44no—
544#123—82no—
545#123—82no—
546#123—82no—
547C22⋊Q8—82no—
548#121—44no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557C4×Q8—82no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—42no—
565C4×D4—42no—
566#117—44no—
567#117—82no—
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—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
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×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42—41no—
660C2×C42—41no—
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674#107—22no—
675#107—22no—
676#107—22no—
677#107—22no—
678#107—22no—
679#107—22no—
680#107—22no—
681#107—41no—
682#107—41no—
683#106—22no—
684#106—22no—
685#106—22no—
686#106—22no—
687#106—22no—
688#106—22no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693C4⋊C8—22no—
694C4⋊C8#4114yes—
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—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709C22⋊C8—22no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—22no—
713#97—22no—
714#97—22no—
715#97—22no—
716#97—41no—
717#97—41no—
718#97—41no—
719#97—41no—
720#97#4114yes—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8—41no—
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#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24C22×D411yescharacteristic
772C24C22×D411yescharacteristic
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—81no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×Q8—81no—
779C2×D4—22no—
780C2×D4—22no—
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—41no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C22×C4—22no—
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—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—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—81no—
849C22×C4—81no—
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×C4C2511yescharacteristic
863D8—44no—
864M16—44no—
865M16—44no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—44no—
884C2×C8—44no—
885C2×C8C2×#4112yes—
886C2×C8C2×#4112yes—
887C2×C8C2×#4112yes—
888C2×C8C2×#4112yes—
889C2×C8H(5,𝔽2)12yes—
890C2×C82−1+412yes—
891C2×C82−1+412yes—
892C4⋊C4—22no—
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—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—41no—
922C4⋊C4—41no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
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⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—41no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
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—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
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—
989C42—22no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—42no—
1006C42—42no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42C2×#4112yes—
1012C42C2×#4112yes—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23#57512yes—
1041C23C23×D411yescharacteristic
1042Q8—84no—
1043Q8—162no—
1044D4—44no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—162no—
1054D4—162no—
1055D4—162no—
1056D4—162no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
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—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—84no—
1141C2×C4—84no—
1142C2×C4—82no—
1143C2×C4—82no—
1144C2×C4—82no—
1145C2×C4—82no—
1146C2×C4#53212yes—
1147C2×C4#53212yes—
1148C2×C4#57512yes—
1149C2×C4C22×#4111yescharacteristic
1150C2×C4C22×#4111yescharacteristic
1151C2×C4C2×H(5,𝔽2)11yescharacteristic
1152C2×C4C2×2−1+411yescharacteristic
1153C2×C4C2×2−1+411yescharacteristic
1154C2×C4#58511yescharacteristic
1155C8—22no—
1156C8—22no—
1157C8—22no—
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8#54214yes—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22C2×#53211yescharacteristic
1192C22#349611yescharacteristic
1193C22#349911yescharacteristic
1194C22C2×#57511yescharacteristic
1195C22C2×#57511yescharacteristic
1196C22#358511yescharacteristic
1197C22#358511yescharacteristic
1198C4—22no—
1199C4—22no—
1200C4—22no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4C2×#54211yescharacteristic
1225C4#346111yescharacteristic
1226C4#351811yescharacteristic
1227C4#352011yescharacteristic
1228C2—42no—
1229C2—81no—
1230C2—161no—
1231C2—161no—
1232C2#3517011yescharacteristic
1233C2#6069811yescharacteristic
1234C2#6070211yescharacteristic
1235C2#6230111yescharacteristic
1236C2#6230511yescharacteristic
1237C2#6250611yescharacteristic
1238C2#6250611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28237C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35207C2semidirect
2. #35107C2semidirect
3. #33217C2semidirect
4. #33211C2semidirect
5. #33143C2semidirect
6. #33135C2semidirect
7. #30365C2semidirect
8. #30362C2semidirect
9. #30362C2semidirect
10. #30362C2semidirect
11. #28822C2semidirect
12. #28715C2semidirect
13. #28544C2semidirect
15. #28074C2semidirect
16. #28072C2semidirect
17. #28068C2semidirect
18. #28067C2semidirect
19. #27844C2semidirect
20. #27836C2semidirect
21. #27829C2semidirect
22. #27826C2semidirect
23. #27794C2semidirect
24. #27790C2semidirect
25. #25355C2semidirect
26. #25350C2semidirect
27. #22120C2semidirect
28. #22116C2semidirect
29. C4×#501C2semidirect
30. #21286C2semidirect
31. #20491C2semidirect

Maximal subgroups

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

subgroupindex
#352072
#351072
#332172
#332112
#331432
#331352
#303652
#303622
#288222
#287152
#285442
#282372
#280742
#280722
#280682
#280672
#278442
#278362
#278292
#278262
#277942
#277902
#253552
#253502
#221202
#221162
C4×#5012
#212862
#204912