Finite Group Databasebeta

← #6940731

Subgroups — #6940731

Order 512.

1515 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36390C211yesmaximal, characteristic, complemented
2#36265C211yesmaximal, characteristic, complemented
3#32861C211yesmaximal, characteristic, complemented
4#32820C211yesmaximal, characteristic, complemented
5#32543C211yesmaximal, characteristic, complemented
6#32497C211yesmaximal, characteristic, complemented
7#31990C211yesmaximal, characteristic, complemented
8#31984C211yesmaximal, characteristic, complemented
9#31926C211yesmaximal, characteristic, complemented
10#31886C211yesmaximal, characteristic, complemented
11#31247C211yesmaximal, characteristic, complemented
12#31165C211yesmaximal, characteristic, complemented
13#30152C211yesmaximal, characteristic, complemented
14#30133C211yesmaximal, characteristic, complemented
15#29994C211yesmaximal, characteristic, complemented
16#29828C211yesmaximal, characteristic, complemented
17#29784C211yesmaximal, characteristic, complemented
18#29532C211yesmaximal, characteristic, complemented
19#28282C211yesmaximal, characteristic, complemented
20#26355C211yesmaximal, characteristic, complemented
21#26354C211yesmaximal, characteristic, complemented
22#26006C211yesmaximal, characteristic, complemented
23#25978C211yesmaximal, characteristic, complemented
24#25217C211yesmaximal, characteristic, complemented
25#25094C211yesmaximal, characteristic
26#24606C211yesmaximal, characteristic, complemented
27#24544C211yesmaximal, characteristic
28#24510C211yesmaximal, characteristic
29#24489C211yesmaximal, characteristic, complemented
30#23617C211yesmaximal, characteristic, complemented
31#21978C211yesmaximal, characteristic, complemented
32C2×#552—21no—
33C2×#484C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#432C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#423C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45#2863C2211yescharacteristic
46#2862C2211yescharacteristic
47#2860C2211yescharacteristic
48#2859C2211yescharacteristic
49#2855C2211yescharacteristic
50#2854C2211yescharacteristic
51#2611—21no—
52#2609—21no—
53#2604—21no—
54#2576—21no—
55#2572—21no—
56#2556—21no—
57#2527—21no—
58#2519—21no—
59#2515—21no—
60#2514C2211yescharacteristic
61#2512C2211yescharacteristic
62#2506C2211yescharacteristic
63#2506C2211yescharacteristic
64#2501C2211yescharacteristic
65#2488—21no—
66#2477—21no—
67#2452C2211yescharacteristic
68#2452C2211yescharacteristic
69#2447C2211yescharacteristic
70#2446C2211yescharacteristic
71#2440C2211yescharacteristic
72#2439C2211yescharacteristic
73#2432C2211yescharacteristic
74#2413—21no—
75#2368—21no—
76#2362C2211yescharacteristic
77#2361C2211yescharacteristic
78#2359—21no—
79#2344C2211yescharacteristic
80#2343—21no—
81#2339C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic
83C4×#124C2211yescharacteristic
84#2297C2211yescharacteristic
85#2293C2211yescharacteristic
86#2293C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C4×#117C2211yescharacteristic
89#2101C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2086C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2083C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2066C2211yescharacteristic
125#2065C2211yescharacteristic
126#2065C2211yescharacteristic
127#2065C2211yescharacteristic
128#2065C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2058C2211yescharacteristic
132#2055C2211yescharacteristic
133#2055C2211yescharacteristic
134#2055C2211yescharacteristic
135#2055C2211yescharacteristic
136#2055C2211yescharacteristic
137#2055C2211yescharacteristic
138#2055C2211yescharacteristic
139#2054C2211yescharacteristic
140#2043C2211yescharacteristic
141#2043C2211yescharacteristic
142#2042C2211yescharacteristic
143#2024C2211yescharacteristic
144#2012C2211yescharacteristic
145#1987C2211yescharacteristic
146#1983C2211yescharacteristic
147#1983C2211yescharacteristic
148#1981C2211yescharacteristic
149#1973C2211yescharacteristic
150#1972C2211yescharacteristic
151#1949C2211yescharacteristic
152#1949C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1944C2211yescharacteristic
156#1944C2211yescharacteristic
157#1940C2211yescharacteristic
158#1940C2211yescharacteristic
159#1940C2211yescharacteristic
160#1940C2211yescharacteristic
161#1936C2211yescharacteristic
162#1935C2211yescharacteristic
163#1935C2211yescharacteristic
164#1935C2211yescharacteristic
165#1928C2211yescharacteristic
166#1928C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1919C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1895C2211yescharacteristic
174#1894C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1875C2211yescharacteristic
180#1872C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1853C2211yescharacteristic
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic
191#1842C2211yescharacteristic
192#1842C2211yescharacteristic
193#1831C2211yescharacteristic
194#1831C2211yescharacteristic
195#1824C2211yescharacteristic
196#1809C2211yescharacteristic
197#1803C2211yescharacteristic
198#1802C2211yescharacteristic
199#1802C2211yescharacteristic
200#1802C2211yescharacteristic
201#1788C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#552—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117—21no—
235C2×#117—21no—
236C2×#117D411yescharacteristic
237C2×#117D411yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C4⋊C4—21no—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C42C2311yescharacteristic
243#484—42no—
244#477—42no—
245#476—42no—
246#476—42no—
247#468—42no—
248#461—42no—
249#449—42no—
250#432—42no—
251#428—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265#423—42no—
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#417—42no—
281#417—42no—
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×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312#401—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#395—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#393—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—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#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#383—21no—
424#383—21no—
425#382—21no—
426#382—21no—
427#382—21no—
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4D411yescharacteristic
438C4×C4⋊C4D411yescharacteristic
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⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4D411yescharacteristic
452C4×C22⋊C4D411yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#376D411yescharacteristic
456#376D411yescharacteristic
457C2×#95—21no—
458C2×#95—21no—
459C43C2311yescharacteristic
460C43C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×D8—22no—
521C2×D8—41no—
522C2×D8—41no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#126—44no—
544#126—44no—
545#125—44no—
546#125—44no—
547#125—44no—
548#124—22no—
549#124—41no—
550#123—44no—
551#123—44no—
552#123—44no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558#121—22no—
559#121—22no—
560C4×Q8—44no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—44no—
570#117—24no—
571#117—42no—
572#117—44no—
573#117—44no—
574#117—44no—
575#117—41no—
576#117—41no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
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⋊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—41no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C42—22no—
659C2×C42—22no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682#107—22no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#106—22no—
690#106—22no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
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#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
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—
735C22⋊C8—22no—
736C22⋊C8—22no—
737#97—41no—
738#97—41no—
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#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
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—
789C24C22×D411yescharacteristic
790#41—44no—
791#41—44no—
792#41—82no—
793#41—82no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—42no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—81no—
829C2×D42−1+412yes—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4H(5,𝔽2)12yes—
886C22×C42−1+412yes—
887C22×C4C2511yescharacteristic
888SD16—82no—
889SD16—82no—
890D8—82no—
891M16—44no—
892M16—82no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
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—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
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—41no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4H(5,𝔽2)12yes—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—41no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
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—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C42—22no—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—41no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42AGL(1,ℤ/8)14yes—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—22no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23#53712yes—
1054C23C23×D411yescharacteristic
1055Q8—41no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—84no—
1064Q8—162no—
1065D4—22no—
1066D4—22no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—84no—
1074D4—84no—
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—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—22no—
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—44no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—84no—
1157C2×C4—84no—
1158C2×C4—84no—
1159C2×C4—82no—
1160C2×C4—84no—
1161C2×C4—84no—
1162C2×C4—162no—
1163C2×C4#53712yes—
1164C2×C4C2×AGL(1,ℤ/8)12yes—
1165C2×C4C2×AGL(1,ℤ/8)12yes—
1166C2×C4C2×AGL(1,ℤ/8)12yes—
1167C2×C4#57512yes—
1168C2×C4C2×H(5,𝔽2)11yescharacteristic
1169C2×C4C2×H(5,𝔽2)11yescharacteristic
1170C2×C4C2×2−1+411yescharacteristic
1171C2×C4C2×2−1+411yescharacteristic
1172C2×C4#58511yescharacteristic
1173C2×C4#58511yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C8—41no—
1179C8—41no—
1180C8—41no—
1181C8—41no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22C2×#53711yescharacteristic
1204C22#348811yescharacteristic
1205C22#348911yescharacteristic
1206C22C22×AGL(1,ℤ/8)11yescharacteristic
1207C22C2×#57511yescharacteristic
1208C22#358611yescharacteristic
1209C22#358611yescharacteristic
1210C4—22no—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—41no—
1216C4—42no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4#353511yescharacteristic
1238C4#353811yescharacteristic
1239C4#354211yescharacteristic
1240C4#356411yescharacteristic
1241C2—42no—
1242C2—82no—
1243C2—161no—
1244C2#4198411yescharacteristic
1245C2#6091611yescharacteristic
1246C2#6093911yescharacteristic
1247C2#6196211yescharacteristic
1248C2#6197211yescharacteristic
1249C2#6210711yescharacteristic
1250C2#6212111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36390C2semidirect
2. #36265C2semidirect
3. #32861C2semidirect
4. #32820C2semidirect
5. #32543C2semidirect
6. #32497C2semidirect
7. #31990C2semidirect
8. #31984C2semidirect
9. #31926C2semidirect
10. #31886C2semidirect
11. #31247C2semidirect
12. #31165C2semidirect
13. #30152C2semidirect
14. #30133C2semidirect
15. #29994C2semidirect
16. #29828C2semidirect
17. #29784C2semidirect
18. #29532C2semidirect
19. #28282C2semidirect
20. #26355C2semidirect
21. #26354C2semidirect
22. #26006C2semidirect
23. #25978C2semidirect
24. #25217C2semidirect
26. #24606C2semidirect
29. #24489C2semidirect
30. #23617C2semidirect
31. #21978C2semidirect

Maximal subgroups

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

subgroupindex
#363902
#362652
#328612
#328202
#325432
#324972
#319902
#319842
#319262
#318862
#312472
#311652
#301522
#301332
#299942
#298282
#297842
#295322
#282822
#263552
#263542
#260062
#259782
#252172
#250942
#246062
#245442
#245102
#244892
#236172
#219782