Subgroups — #37564314

Order 24224.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131072	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×Dic₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₇₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₅₇	—	2	1	no	—
5	#20258493	—	2	1	no	—
6	Q₈×C₇₅₇	C₄	1	1	yes	characteristic, complemented
7	D₄×C₇₅₇	—	2	1	no	—
8	D₄×C₇₅₇	C₄	1	1	yes	characteristic, complemented
9	C₂×C₄×C₇₅₇	—	2	1	no	—
10	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
11	C₂²×C₇₅₇	—	2	1	no	—
12	C₂²×C₇₅₇	D₄	1	1	yes	characteristic
13	C₄×C₇₅₇	—	2	1	no	—
14	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
15	C₄×C₇₅₇	D₄	1	1	yes	characteristic
16	Dic₇₅₇	—	2	2	no	—
17	C₂×C₇₅₇	—	2	1	no	—
18	C₂×C₇₅₇	—	4	1	no	—
19	C₂×C₇₅₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₇₅₇	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	757	1	no	maximal, Sylow
22	#41	D₇₅₇	1	1	yes	characteristic
23	M₁₆	—	757	1	no	—
24	C₄²	—	757	1	no	—
25	Q₈	Dic₇₅₇	1	1	yes	characteristic, complemented
26	D₄	—	2	1	no	—
27	D₄	Dic₇₅₇	1	1	yes	characteristic, complemented
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	1514	1	no	—
30	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
31	C₈	—	1514	1	no	—
32	C₂²	—	2	1	no	—
33	C₂²	C₂²⋊D₇₅₇	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	1514	2	no	—
36	C₄	C₂×Dic₇₅₇	1	1	yes	characteristic
37	C₄	C₂²⋊D₇₅₇	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	4	1	no	—
40	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.