Subgroups — #37564302

Order 24224.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊Dic₇₅₇	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₇₅₇	—	2	2	no	—
4	C₂³×C₇₅₇	C₄	1	1	yes	characteristic, complemented
5	C₂³×C₇₅₇	C₂²	1	1	yes	characteristic
6	D₄×C₇₅₇	—	2	2	no	—
7	C₂×C₄×C₇₅₇	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₇₅₇	—	2	1	no	—
9	C₂²×C₇₅₇	—	4	1	no	—
10	C₂²×C₇₅₇	—	4	1	no	—
11	C₂²×C₇₅₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₇₅₇	D₄	1	2	yes	—
13	C₄×C₇₅₇	—	2	1	no	—
14	Dic₇₅₇	—	4	2	no	—
15	C₂×C₇₅₇	—	2	2	no	—
16	C₂×C₇₅₇	—	2	1	no	—
17	C₂×C₇₅₇	—	4	1	no	—
18	C₂×C₇₅₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₇₅₇	#99	1	1	yes	characteristic, complemented, Sylow
20	#99	—	757	1	no	maximal, Sylow
21	C₂×D₄	D₇₅₇	1	1	yes	characteristic
22	C₂²⋊C₄	—	757	2	no	—
23	C₂³	Dic₇₅₇	1	1	yes	characteristic, complemented
24	C₂³	C₂×D₇₅₇	1	1	yes	characteristic
25	D₄	—	2	2	no	—
26	C₂×C₄	—	1514	2	no	—
27	C₂×C₄	Dic₇₅₇	1	1	yes	characteristic, complemented
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂×Dic₇₅₇	1	1	yes	characteristic
32	C₂²	C₂²⋊D₇₅₇	1	2	yes	—
33	C₄	—	2	1	no	—
34	C₄	—	3028	2	no	—
35	C₂	—	2	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
38	C₂	C₂²⋊Dic₇₅₇	1	1	yes	characteristic

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

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