Subgroups — C₂×Q₈×D₇₅₇ #37564426

Order 24224.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₁₄	C₂	1	3	yes	maximal, complemented
2	Q₈×D₇₅₇	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₇₅₇	C₂	1	3	yes	maximal
4	C₂×Q₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₅₇	C₂²	1	1	yes	characteristic
6	Dic₁₅₁₄	C₂²	1	12	yes	complemented
7	C₂×Dic₇₅₇	C₂²	1	3	yes	—
8	C₄×D₇₅₇	C₂²	1	12	yes	—
9	Q₈×C₇₅₇	C₂²	1	4	yes	complemented
10	C₂×C₄×C₇₅₇	C₂²	1	3	yes	—
11	C₂²×C₇₅₇	C₂³	1	1	yes	characteristic
12	C₂×D₇₅₇	Q₈	1	4	yes	direct product factor
13	C₂×D₇₅₇	C₂³	1	2	yes	—
14	C₄×C₇₅₇	C₂³	1	6	yes	—
15	Dic₇₅₇	C₂³	1	6	yes	—
16	C₂×C₇₅₇	C₂×Q₈	1	2	yes	complemented
17	C₂×C₇₅₇	C₂⁴	1	1	yes	characteristic
18	D₇₅₇	C₂×Q₈	1	4	yes	direct product factor
19	C₇₅₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×Q₈	—	757	1	no	maximal, Sylow
21	C₂×Q₈	—	757	8	no	—
22	C₂×Q₈	—	757	3	no	—
23	C₂×Q₈	D₇₅₇	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	757	3	no	—
25	C₂³	—	757	1	no	—
26	Q₈	—	757	12	no	—
27	Q₈	C₂×D₇₅₇	1	4	yes	direct product factor
28	C₂×C₄	—	757	3	no	—
29	C₂×C₄	—	757	12	no	—
30	C₂×C₄	C₂×D₇₅₇	1	3	yes	—
31	C₂²	—	757	4	no	—
32	C₂²	—	757	2	no	—
33	C₂²	C₂²×D₇₅₇	1	1	yes	characteristic
34	C₄	—	757	6	no	—
35	C₄	C₂²×D₇₅₇	1	6	yes	—
36	C₂	—	757	4	no	—
37	C₂	Q₈×D₇₅₇	1	2	yes	direct product factor
38	C₂	C₂³×D₇₅₇	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.