Finite Group Databasebeta

← #7331449

Subgroups — #7331449

Order 512.

1480 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52974C211yesmaximal, characteristic, complemented
2#44883C211yesmaximal, characteristic, complemented
3#32637C211yesmaximal, characteristic, complemented
4#32607C211yesmaximal, characteristic, complemented
5#32204C211yesmaximal, characteristic, complemented
6#32179C211yesmaximal, characteristic, complemented
7#32102C211yesmaximal, characteristic, complemented
8#31831C211yesmaximal, characteristic, complemented
9#31498C211yesmaximal, characteristic, complemented
10#31461C211yesmaximal, characteristic, complemented
11#31252C211yesmaximal, characteristic, complemented
12#30946C211yesmaximal, characteristic, complemented
13#30906C211yesmaximal, characteristic
14#30661C211yesmaximal, characteristic, complemented
15#30022C211yesmaximal, characteristic, complemented
16#29696C211yesmaximal, characteristic, complemented
17#29175C211yesmaximal, characteristic, complemented
18#29060C211yesmaximal, characteristic, complemented
19#28091C211yesmaximal, characteristic, complemented
20#27802C211yesmaximal, characteristic, complemented
21#27148C211yesmaximal, characteristic, complemented
22#27072C211yesmaximal, characteristic, complemented
23#26969C211yesmaximal, characteristic, complemented
24#26889C211yesmaximal, characteristic, complemented
25#26879C211yesmaximal, characteristic, complemented
26#26538C211yesmaximal, characteristic, complemented
27#26478C211yesmaximal, characteristic, complemented
28#25838C211yesmaximal, characteristic, complemented
29#25510C211yesmaximal, characteristic, complemented
30#24326C211yesmaximal, characteristic, complemented
31#22290C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#477C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×C4×D8C2211yescharacteristic
42#2838—21no—
43#2837—21no—
44#2831—21no—
45#2814—21no—
46#2787—21no—
47#2731—21no—
48#2730—21no—
49#2728—21no—
50#2702—21no—
51#2681—21no—
52#2677—21no—
53#2674—21no—
54#2628C2211yescharacteristic
55#2624C2211yescharacteristic
56#2592C2211yescharacteristic
57#2570C2211yescharacteristic
58#2560—21no—
59#2551C2211yescharacteristic
60#2546C2211yescharacteristic
61#2544C2211yescharacteristic
62#2538C2211yescharacteristic
63#2513C2211yescharacteristic
64#2513C2211yescharacteristic
65#2507C2211yescharacteristic
66#2497C2211yescharacteristic
67#2494C2211yescharacteristic
68#2492C2211yescharacteristic
69#2491C2211yescharacteristic
70#2491C2211yescharacteristic
71#2461—21no—
72#2452C2211yescharacteristic
73#2452C2211yescharacteristic
74#2451C2211yescharacteristic
75#2436—21no—
76#2428C2211yescharacteristic
77#2427C2211yescharacteristic
78#2422C2211yescharacteristic
79#2409—21no—
80#2396C2211yescharacteristic
81#2369C2211yescharacteristic
82#2367C2211yescharacteristic
83#2366C2211yescharacteristic
84#2324C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2094C2211yescharacteristic
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2074C2211yescharacteristic
95#2072C2211yescharacteristic
96#2068C2211yescharacteristic
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2057C2211yescharacteristic
104#2057C2211yescharacteristic
105#2057C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2041C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2024C2211yescharacteristic
125#2023C2211yescharacteristic
126#2023C2211yescharacteristic
127#2023C2211yescharacteristic
128#2023C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2011C2211yescharacteristic
132#1999C2211yescharacteristic
133#1990C2211yescharacteristic
134#1988C2211yescharacteristic
135#1984C2211yescharacteristic
136#1984C2211yescharacteristic
137#1983C2211yescharacteristic
138#1982C2211yescharacteristic
139#1973C2211yescharacteristic
140#1968C2211yescharacteristic
141#1961C2211yescharacteristic
142#1959C2211yescharacteristic
143#1949C2211yescharacteristic
144#1947C2211yescharacteristic
145#1943C2211yescharacteristic
146#1940C2211yescharacteristic
147#1940C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1921C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1895C2211yescharacteristic
172#1895C2211yescharacteristic
173#1893C2211yescharacteristic
174#1892C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1877C2211yescharacteristic
181#1863C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1809C2211yescharacteristic
192#1808C2211yescharacteristic
193#1805C2211yescharacteristic
194#1804C2211yescharacteristic
195#1802C2211yescharacteristic
196#1798C2211yescharacteristic
197#1776C2211yescharacteristic
198#1776C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8—21no—
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209D4×Q8—42no—
210D4×Q8—42no—
211#542—42no—
212#542—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250#500—42no—
251#477—42no—
252#474—42no—
253#474—42no—
254#474—42no—
255#468—42no—
256#466—42no—
257C4×D8—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#401—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400D411yescharacteristic
315#399—21no—
316#399—21no—
317#399D411yescharacteristic
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398D411yescharacteristic
325#398D411yescharacteristic
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396D411yescharacteristic
341#396D411yescharacteristic
342#395—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#395D411yescharacteristic
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#393D411yescharacteristic
364#392—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—44no—
496C22×Q8—82no—
497C22×Q8—82no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2411yescharacteristic
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8—41no—
523C2×M16—22no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—82no—
548C4⋊Q8—82no—
549#127—22no—
550#127—41no—
551#126—44no—
552#124—22no—
553#124—41no—
554#124—41no—
555#124—41no—
556#124—44no—
557#124—82no—
558#124—82no—
559#123—44no—
560#123—82no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—82no—
568C22⋊Q8—82no—
569C22⋊Q8—82no—
570#121—22no—
571#121—22no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—82no—
577C4×Q8—22no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—82no—
592#117—41no—
593#117—41no—
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⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#107—22no—
695#107—22no—
696#107—22no—
697#107—22no—
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—22no—
705#106—41no—
706#106—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741#97—41no—
742#97—41no—
743C4×C8—41no—
744C4×C8—41no—
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#95—21no—
776#95—21no—
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787C24—21no—
788C24—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—41no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—816no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D42−1+412yes—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C2511yescharacteristic
897SD16—82no—
898D8—44no—
899D8—82no—
900M16—82no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—82no—
925C2×C82−1+412yes—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4H(5,𝔽2)12yes—
983C4⋊C4H(5,𝔽2)12yes—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—42no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23C23×D411yescharacteristic
1073Q8—44no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—84no—
1079Q8—84no—
1080Q8—84no—
1081Q8—162no—
1082Q8—162no—
1083D4—22no—
1084D4—22no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—84no—
1096D4—162no—
1097D4—162no—
1098D4—162no—
1099D4—162no—
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—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—162no—
1184C2×C4—162no—
1185C2×C4#57612yes—
1186C2×C4#57612yes—
1187C2×C4C2×H(5,𝔽2)11yescharacteristic
1188C2×C4C2×H(5,𝔽2)11yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4C2×2−1+411yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—22no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—41no—
1202C22—42no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—42no—
1208C22—41no—
1209C22—42no—
1210C22—41no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22#348411yescharacteristic
1230C22#348911yescharacteristic
1231C22#349711yescharacteristic
1232C22C2×#57611yescharacteristic
1233C22C2×#57611yescharacteristic
1234C22#358611yescharacteristic
1235C22#358611yescharacteristic
1236C4—22no—
1237C4—22no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—42no—
1242C4—42no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4#354111yescharacteristic
1263C4#355111yescharacteristic
1264C4#355211yescharacteristic
1265C4#356111yescharacteristic
1266C2—81no—
1267C2—82no—
1268C2—161no—
1269C2—161no—
1270C2#4794111yescharacteristic
1271C2#6163011yescharacteristic
1272C2#6167211yescharacteristic
1273C2#6218011yescharacteristic
1274C2#6219011yescharacteristic
1275C2#6240311yescharacteristic
1276C2#6240311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30906C2
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
1. #52974C2semidirect
2. #44883C2semidirect
3. #32637C2semidirect
4. #32607C2semidirect
5. #32204C2semidirect
6. #32179C2semidirect
7. #32102C2semidirect
8. #31831C2semidirect
9. #31498C2semidirect
10. #31461C2semidirect
11. #31252C2semidirect
12. #30946C2semidirect
14. #30661C2semidirect
15. #30022C2semidirect
16. #29696C2semidirect
17. #29175C2semidirect
18. #29060C2semidirect
19. #28091C2semidirect
20. #27802C2semidirect
21. #27148C2semidirect
22. #27072C2semidirect
23. #26969C2semidirect
24. #26889C2semidirect
25. #26879C2semidirect
26. #26538C2semidirect
27. #26478C2semidirect
28. #25838C2semidirect
29. #25510C2semidirect
30. #24326C2semidirect
31. #22290C2semidirect

Maximal subgroups

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

subgroupindex
#529742
#448832
#326372
#326072
#322042
#321792
#321022
#318312
#314982
#314612
#312522
#309462
#309062
#306612
#300222
#296962
#291752
#290602
#280912
#278022
#271482
#270722
#269692
#268892
#268792
#265382
#264782
#258382
#255102
#243262
#222902