Subgroups — C₂×D₃₄₄ #13063336

Order 1376.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₄₄	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₄₃	—	2	2	no	—
5	C₂×C₄×C₄₃	C₂²	1	1	yes	characteristic
6	D₁₇₂	—	2	2	no	—
7	D₁₇₂	C₂²	1	4	yes	complemented
8	C₈×C₄₃	C₂²	1	2	yes	complemented
9	C₂²×C₄₃	D₄	1	1	yes	characteristic
10	C₂×D₄₃	—	2	4	no	—
11	C₂×D₄₃	—	4	4	no	—
12	C₄×C₄₃	D₄	1	1	yes	characteristic
13	C₄×C₄₃	C₂³	1	1	yes	characteristic
14	C₂×C₄₃	D₈	1	2	yes	complemented
15	C₂×C₄₃	C₂×D₄	1	1	yes	characteristic
16	D₄₃	—	4	4	no	—
17	C₄₃	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×D₈	—	43	1	no	maximal, Sylow
19	C₂×D₄	—	43	2	no	—
20	D₈	—	43	4	no	—
21	C₂×C₈	D₄₃	1	1	yes	characteristic, complemented
22	C₂³	—	86	2	no	—
23	D₄	—	43	4	no	—
24	D₄	—	86	2	no	—
25	C₂×C₄	C₂×D₄₃	1	1	yes	characteristic
26	C₈	C₂×D₄₃	1	2	yes	complemented
27	C₂²	—	86	4	no	—
28	C₂²	—	172	4	no	—
29	C₂²	D₁₇₂	1	1	yes	characteristic
30	C₄	D₁₇₂	1	1	yes	characteristic
31	C₄	C₂²×D₄₃	1	1	yes	characteristic
32	C₂	—	172	4	no	—
33	C₂	D₃₄₄	1	2	yes	direct product factor
34	C₂	C₂×D₁₇₂	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.