Finite Group Databasebeta

← #7224853

Subgroups — #7224853

Order 512.

1437 conjugacy classes of subgroups.

The subgroup lattice has 1219 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46019C211yesmaximal, characteristic, complemented
2#45993C211yesmaximal, characteristic, complemented
3#33310C211yesmaximal, characteristic, complemented
4#33266C211yesmaximal, characteristic, complemented
5#32835C211yesmaximal, characteristic, complemented
6#32834C211yesmaximal, characteristic, complemented
7#32378C211yesmaximal, characteristic, complemented
8#32375C211yesmaximal, characteristic, complemented
9#32349C211yesmaximal, characteristic, complemented
10#32344C211yesmaximal, characteristic, complemented
11#32282C211yesmaximal, characteristic, complemented
12#32279C211yesmaximal, characteristic, complemented
13#31092C211yesmaximal, characteristic, complemented
14#31086C211yesmaximal, characteristic, complemented
15#30954C211yesmaximal, characteristic, complemented
16#30947C211yesmaximal, characteristic, complemented
17#30780C211yesmaximal, characteristic, complemented
18#30775C211yesmaximal, characteristic, complemented
19#28837C211yesmaximal, characteristic, complemented
20#28819C211yesmaximal, characteristic, complemented
21#28548C211yesmaximal, characteristic, complemented
22#28021C211yesmaximal, characteristic, complemented
23#28000C211yesmaximal, characteristic, complemented
24#27941C211yesmaximal, characteristic
25#27853C211yesmaximal, characteristic, complemented
26#27804C211yesmaximal, characteristic
27#26490C211yesmaximal, characteristic, complemented
28#26078C211yesmaximal, characteristic, complemented
29#26072C211yesmaximal, characteristic, complemented
30#25046C211yesmaximal, characteristic
31#21666C211yesmaximal, characteristic, complemented
32C2×#563—21no—
33C2×#501C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#498C2211yescharacteristic
37C2×#498C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#476C2211yescharacteristic
42C2×#469C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×#428C2211yescharacteristic
45#2868C2211yescharacteristic
46#2868C2211yescharacteristic
47#2860C2211yescharacteristic
48#2860C2211yescharacteristic
49#2823—21no—
50#2821—21no—
51#2793—21no—
52#2731—21no—
53#2729—21no—
54#2721—21no—
55#2720—21no—
56#2718—21no—
57#2718—21no—
58#2716—21no—
59#2680—21no—
60#2677—21no—
61#2674—21no—
62#2674—21no—
63#2570C2211yescharacteristic
64#2566C2211yescharacteristic
65#2552C2211yescharacteristic
66#2551C2211yescharacteristic
67#2550C2211yescharacteristic
68#2542C2211yescharacteristic
69#2512C2211yescharacteristic
70#2512C2211yescharacteristic
71#2507C2211yescharacteristic
72#2506C2211yescharacteristic
73#2501C2211yescharacteristic
74#2500C2211yescharacteristic
75#2497C2211yescharacteristic
76#2496C2211yescharacteristic
77#2491C2211yescharacteristic
78#2491C2211yescharacteristic
79#2452C2211yescharacteristic
80#2452C2211yescharacteristic
81#2441C2211yescharacteristic
82#2440C2211yescharacteristic
83#2440C2211yescharacteristic
84#2439C2211yescharacteristic
85#2422C2211yescharacteristic
86#2422C2211yescharacteristic
87#2383—21no—
88C4×#126C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic
97#2093C2211yescharacteristic
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2088C2211yescharacteristic
102#2088C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2084C2211yescharacteristic
108#2084C2211yescharacteristic
109#2083C2211yescharacteristic
110#2083C2211yescharacteristic
111#2077C2211yescharacteristic
112#2077C2211yescharacteristic
113#2071C2211yescharacteristic
114#2071C2211yescharacteristic
115#2071C2211yescharacteristic
116#2071C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2059C2211yescharacteristic
122#2059C2211yescharacteristic
123#2058C2211yescharacteristic
124#2058C2211yescharacteristic
125#2058C2211yescharacteristic
126#2058C2211yescharacteristic
127#2057C2211yescharacteristic
128#2057C2211yescharacteristic
129#2034C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#2034C2211yescharacteristic
133#2023C2211yescharacteristic
134#2023C2211yescharacteristic
135#2023C2211yescharacteristic
136#2023C2211yescharacteristic
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1970C2211yescharacteristic
140#1970C2211yescharacteristic
141#1970C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1948C2211yescharacteristic
145#1948C2211yescharacteristic
146#1944C2211yescharacteristic
147#1944C2211yescharacteristic
148#1943C2211yescharacteristic
149#1943C2211yescharacteristic
150#1942C2211yescharacteristic
151#1942C2211yescharacteristic
152#1942C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1920C2211yescharacteristic
167#1920C2211yescharacteristic
168#1919C2211yescharacteristic
169#1919C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1916C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1847C2211yescharacteristic
182#1847C2211yescharacteristic
183#1844C2211yescharacteristic
184#1844C2211yescharacteristic
185#1844C2211yescharacteristic
186#1844C2211yescharacteristic
187#1844C2211yescharacteristic
188#1844C2211yescharacteristic
189#1844C2211yescharacteristic
190#1844C2211yescharacteristic
191#1839C2211yescharacteristic
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1771C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202C42×C8C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205#563—48no—
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126D411yescharacteristic
222C2×#125—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#124—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243#501—42no—
244#498—42no—
245#498—42no—
246#498—42no—
247#498—42no—
248#482—42no—
249#481—42no—
250#478—42no—
251#476—42no—
252#469—42no—
253#442—42no—
254#428—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#395—21no—
347#395—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#391—21no—
360#391—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388D411yescharacteristic
404#388D411yescharacteristic
405#388D411yescharacteristic
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387D411yescharacteristic
415#387D411yescharacteristic
416#387D411yescharacteristic
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384—21no—
426#384—21no—
427#384—21no—
428#384—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#383D411yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C43C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2411yescharacteristic
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—22no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—44no—
529C4⋊Q8—44no—
530C4⋊Q8—82no—
531C4⋊Q8—82no—
532C4⋊Q8—82no—
533#126—24no—
534#126—44no—
535#126—44no—
536#126—44no—
537#126—44no—
538#126—82no—
539#125—41no—
540#125—41no—
541#125—44no—
542#125—44no—
543#124—44no—
544#124—82no—
545#123—44no—
546#123—44no—
547#123—82no—
548#123—82no—
549C22⋊Q8—44no—
550C22⋊Q8—44no—
551C22⋊Q8—44no—
552C22⋊Q8—44no—
553C22⋊Q8—82no—
554C22⋊Q8—82no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563#117—41no—
564#117—41no—
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⋊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—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679#107—22no—
680#107—22no—
681#107—22no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#106—22no—
687#106—22no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726#97—22no—
727#97—22no—
728#97—22no—
729C4×C8—22no—
730C4×C8—22no—
731C4×C8—22no—
732C4×C8—22no—
733C4×C8—22no—
734C4×C8—22no—
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#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24—21no—
775C24C22×D411yescharacteristic
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
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—42no—
830C22×C4—42no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
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×C4C22×D411yescharacteristic
851C22×C4C2511yescharacteristic
852D8—44no—
853M16—44no—
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×C8H(5,𝔽2)12yes—
873C2×C8H(5,𝔽2)12yes—
874C2×C82−1+412yes—
875C2×C82−1+412yes—
876C2×C82−1+412yes—
877C2×C82−1+412yes—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
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—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—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—42no—
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—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
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—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
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—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
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—22no—
991C42—22no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—42no—
1005C42—42no—
1006C42—81no—
1007C42—81no—
1008C42—81no—
1009C42AGL(1,ℤ/8)14yes—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23C23×D411yescharacteristic
1032Q8—162no—
1033Q8—162no—
1034Q8—162no—
1035Q8—162no—
1036Q8—162no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—162no—
1046D4—162no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—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—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—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—162no—
1127C2×C4—162no—
1128C2×C4—162no—
1129C2×C4C2×AGL(1,ℤ/8)12yes—
1130C2×C4C2×AGL(1,ℤ/8)12yes—
1131C2×C4C2×AGL(1,ℤ/8)12yes—
1132C2×C4#57712yes—
1133C2×C4#57712yes—
1134C2×C4#57712yes—
1135C2×C4C2×H(5,𝔽2)11yescharacteristic
1136C2×C4C2×H(5,𝔽2)11yescharacteristic
1137C2×C4C2×2−1+411yescharacteristic
1138C2×C4C2×2−1+411yescharacteristic
1139C2×C4C2×2−1+411yescharacteristic
1140C2×C4C2×2−1+411yescharacteristic
1141C8—22no—
1142C8—22no—
1143C8—22no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8#56314yescomplemented
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22#349811yescharacteristic
1171C22#349911yescharacteristic
1172C22#349911yescharacteristic
1173C22C22×AGL(1,ℤ/8)11yescharacteristic
1174C22C2×#57711yescharacteristic
1175C22C2×#57711yescharacteristic
1176C22C2×#57711yescharacteristic
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4C2×#56311yescharacteristic
1205C4#354411yescharacteristic
1206C4#355211yescharacteristic
1207C4#355211yescharacteristic
1208C2—81no—
1209C2—161no—
1210C2—161no—
1211C2#4599311yescharacteristic
1212C2#6242111yescharacteristic
1213C2#6243011yescharacteristic
1214C2#6247711yescharacteristic
1215C2#6247711yescharacteristic
1216C2#6248611yescharacteristic
1217C2#6248611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#469C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46019C2semidirect
2. #45993C2semidirect
3. #33310C2semidirect
4. #33266C2semidirect
5. #32835C2semidirect
6. #32834C2semidirect
7. #32378C2semidirect
8. #32375C2semidirect
9. #32349C2semidirect
10. #32344C2semidirect
11. #32282C2semidirect
12. #32279C2semidirect
13. #31092C2semidirect
14. #31086C2semidirect
15. #30954C2semidirect
16. #30947C2semidirect
17. #30780C2semidirect
18. #30775C2semidirect
19. #28837C2semidirect
20. #28819C2semidirect
21. #28548C2semidirect
22. #28021C2semidirect
23. #28000C2semidirect
25. #27853C2semidirect
27. #26490C2semidirect
28. #26078C2semidirect
29. #26072C2semidirect
31. #21666C2semidirect
1148. C8#563semidirect

Maximal subgroups

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

subgroupindex
#460192
#459932
#333102
#332662
#328352
#328342
#323782
#323752
#323492
#323442
#322822
#322792
#310922
#310862
#309542
#309472
#307802
#307752
#288372
#288192
#285482
#280212
#280002
#279412
#278532
#278042
#264902
#260782
#260722
#250462
#216662