Subgroups — #107×C₇₅₇ #37564255

Order 24224.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×C₇₅₇	C₂	1	2	yes	maximal
3	C₂×C₄×C₇₅₇	—	2	2	no	—
4	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
5	C₈×C₇₅₇	C₄	1	2	yes	complemented
6	C₂²×C₇₅₇	D₄	1	1	yes	characteristic
7	C₄×C₇₅₇	—	4	2	no	—
8	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₇₅₇	Q₈	1	1	yes	characteristic
10	C₂×C₇₅₇	C₄⋊C₄	1	1	yes	characteristic
11	C₂×C₇₅₇	D₈	1	1	yes	characteristic
12	C₂×C₇₅₇	Q₁₆	1	1	yes	characteristic
13	C₇₅₇	#107	1	1	yes	characteristic, direct product factor, Sylow
14	#107	C₇₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₈	C₂×C₇₅₇	1	1	yes	characteristic
16	C₄⋊C₄	C₂×C₇₅₇	1	2	yes	—
17	C₂×C₄	—	2	2	no	—
18	C₂×C₄	C₂²×C₇₅₇	1	1	yes	characteristic
19	C₈	C₄×C₇₅₇	1	2	yes	complemented
20	C₂²	D₄×C₇₅₇	1	1	yes	characteristic
21	C₄	—	4	2	no	—
22	C₄	C₂×C₄×C₇₅₇	1	1	yes	characteristic
23	C₄	Q₈×C₇₅₇	1	1	yes	characteristic
24	C₂	C₄⋊C₄×C₇₅₇	1	1	yes	characteristic
25	C₂	D₈×C₇₅₇	1	1	yes	characteristic
26	C₂	Q₁₆×C₇₅₇	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.