Subgroups — C₂×Dic₃₄₄ #14583327

Order 2752.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₂	C₂	1	2	yes	maximal
2	Dic₃₄₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₆	—	2	2	no	—
5	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
6	Dic₁₇₂	—	2	2	no	—
7	Dic₁₇₂	C₂²	1	4	yes	—
8	C₁₆×C₄₃	C₂²	1	2	yes	—
9	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
10	C₂×Dic₄₃	—	4	2	no	—
11	Dic₈₆	—	2	4	no	—
12	Dic₈₆	—	4	2	no	—
13	C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₈×C₄₃	C₂³	1	1	yes	characteristic
15	C₂²×C₄₃	D₈	1	1	yes	characteristic
16	C₄×C₄₃	D₈	1	1	yes	characteristic
17	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
18	Dic₄₃	—	4	4	no	—
19	C₂×C₄₃	Q₃₂	1	2	yes	complemented
20	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
21	C₂×Q₃₂	—	43	1	no	maximal, Sylow
22	C₄₃	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
23	C₂×Q₁₆	—	43	2	no	—
24	Q₃₂	—	43	4	no	—
25	C₂×C₁₆	D₄₃	1	1	yes	characteristic
26	C₂×Q₈	—	86	2	no	—
27	Q₁₆	—	43	4	no	—
28	Q₁₆	—	86	2	no	—
29	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
30	C₁₆	C₂×D₄₃	1	2	yes	—
31	Q₈	—	86	4	no	—
32	Q₈	—	172	2	no	—
33	C₂×C₄	—	172	2	no	—
34	C₂×C₄	D₁₇₂	1	1	yes	characteristic
35	C₈	D₁₇₂	1	1	yes	characteristic
36	C₈	C₂²×D₄₃	1	1	yes	characteristic
37	C₂²	D₃₄₄	1	1	yes	characteristic
38	C₄	—	172	4	no	—
39	C₄	D₃₄₄	1	1	yes	characteristic
40	C₄	C₂×D₁₇₂	1	1	yes	characteristic
41	C₂	Dic₃₄₄	1	2	yes	direct product factor
42	C₂	C₂×D₃₄₄	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.