Subgroups — C₂×D₃₁₇₆ #27163107

Order 12704.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₈₈	C₂	1	2	yes	maximal, complemented
2	D₃₁₇₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃₉₇	—	2	2	no	—
5	D₁₅₈₈	—	2	2	no	—
6	D₁₅₈₈	C₂²	1	4	yes	complemented
7	C₂×C₄×C₃₉₇	C₂²	1	1	yes	characteristic
8	C₈×C₃₉₇	C₂²	1	2	yes	complemented
9	C₂²×C₃₉₇	D₄	1	1	yes	characteristic
10	C₂×D₃₉₇	—	2	4	no	—
11	C₂×D₃₉₇	—	4	4	no	—
12	C₄×C₃₉₇	D₄	1	1	yes	characteristic
13	C₄×C₃₉₇	C₂³	1	1	yes	characteristic
14	C₂×C₃₉₇	D₈	1	2	yes	complemented
15	C₂×C₃₉₇	C₂×D₄	1	1	yes	characteristic
16	D₃₉₇	—	4	4	no	—
17	C₃₉₇	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×D₈	—	397	1	no	maximal, Sylow
19	C₂×D₄	—	397	2	no	—
20	D₈	—	397	4	no	—
21	C₂×C₈	D₃₉₇	1	1	yes	characteristic, complemented
22	C₂³	—	794	2	no	—
23	D₄	—	794	2	no	—
24	D₄	—	397	4	no	—
25	C₂×C₄	C₂×D₃₉₇	1	1	yes	characteristic
26	C₈	C₂×D₃₉₇	1	2	yes	complemented
27	C₂²	—	794	4	no	—
28	C₂²	—	1588	4	no	—
29	C₂²	D₁₅₈₈	1	1	yes	characteristic
30	C₄	D₁₅₈₈	1	1	yes	characteristic
31	C₄	C₂²×D₃₉₇	1	1	yes	characteristic
32	C₂	—	1588	4	no	—
33	C₂	D₃₁₇₆	1	2	yes	direct product factor
34	C₂	C₂×D₁₅₈₈	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.