Subgroups — #37564312

Order 24224.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₁₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₇₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic
4	Dic₁₅₁₄	—	2	1	no	—
5	Dic₁₅₁₄	C₄	1	2	yes	complemented
6	C₂×Dic₇₅₇	—	2	1	no	—
7	C₂×Dic₇₅₇	—	2	1	no	—
8	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
9	C₈×C₇₅₇	—	2	1	no	—
10	C₂²×C₇₅₇	D₄	1	1	yes	characteristic
11	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
12	C₄×C₇₅₇	D₄	1	1	yes	characteristic
13	Dic₇₅₇	—	2	2	no	—
14	Dic₇₅₇	—	4	1	no	—
15	C₂×C₇₅₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₇₅₇	SD₁₆	1	1	yes	characteristic
17	C₂×C₇₅₇	Q₁₆	1	1	yes	characteristic
18	C₇₅₇	#103	1	1	yes	characteristic, complemented, Sylow
19	#103	—	757	1	no	maximal, Sylow
20	C₂×Q₈	—	757	1	no	—
21	C₂×C₈	D₇₅₇	1	1	yes	characteristic
22	C₄⋊C₄	—	757	1	no	—
23	Q₈	—	1514	1	no	—
24	Q₈	—	757	2	no	—
25	C₂×C₄	—	1514	1	no	—
26	C₂×C₄	—	1514	1	no	—
27	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₂²	D₃₀₂₈	1	1	yes	characteristic
30	C₄	—	3028	1	no	—
31	C₄	—	1514	2	no	—
32	C₄	C₄×D₇₅₇	1	1	yes	characteristic
33	C₄	C₂²⋊D₇₅₇	1	1	yes	characteristic
34	C₂	#27131065	1	1	yes	characteristic
35	C₂	#27131077	1	1	yes	characteristic
36	C₂	Dic₃₀₂₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. Dic₁₅₁₄	C₄	semidirect
18. C₇₅₇	#103	semidirect

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