Subgroups — #37564307

Order 24224.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#20258493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₇₅₇	—	2	1	no	—
5	D₃₀₂₈	—	2	1	no	—
6	D₃₀₂₈	C₄	1	2	yes	complemented
7	#20258493	—	2	1	no	—
8	C₂×C₄×C₇₅₇	—	2	1	no	—
9	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
10	C₂²×C₇₅₇	D₄	1	1	yes	characteristic
11	C₂×D₇₅₇	—	2	2	no	—
12	C₂×D₇₅₇	—	4	1	no	—
13	C₂×D₇₅₇	—	4	1	no	—
14	C₄×C₇₅₇	—	4	1	no	—
15	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇₅₇	D₄	1	1	yes	characteristic
17	C₂×C₇₅₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₇₅₇	D₈	1	1	yes	characteristic
19	C₂×C₇₅₇	SD₁₆	1	1	yes	characteristic
20	D₇₅₇	—	4	2	no	—
21	C₇₅₇	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	757	1	no	maximal, Sylow
23	C₂×D₄	—	757	1	no	—
24	C₂×C₈	—	757	1	no	—
25	C₄⋊C₄	D₇₅₇	1	1	yes	characteristic, complemented
26	C₂³	—	1514	1	no	—
27	D₄	—	1514	1	no	—
28	D₄	—	757	2	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
31	C₈	—	1514	1	no	—
32	C₂²	—	3028	1	no	—
33	C₂²	—	3028	1	no	—
34	C₂²	—	1514	2	no	—
35	C₂²	C₂²⋊D₇₅₇	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₇₅₇	1	1	yes	characteristic
38	C₄	D₃₀₂₈	1	1	yes	characteristic
39	C₂	—	3028	2	no	—
40	C₂	#27131065	1	1	yes	characteristic
41	C₂	#27131073	1	1	yes	characteristic
42	C₂	#27131075	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.