Subgroups — C₂×Dic₁₈₄ #13092845

Order 1472.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₂	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	Dic₁₈₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₄₆	—	2	2	no	—
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	Dic₉₂	—	2	2	no	—
7	Dic₉₂	C₂²	1	4	yes	—
8	C₁₆×C₂₃	C₂²	1	2	yes	—
9	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
10	C₂×Dic₂₃	—	4	2	no	—
11	Dic₄₆	—	2	4	no	—
12	Dic₄₆	—	4	2	no	—
13	C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₈×C₂₃	C₂³	1	1	yes	characteristic
15	C₂²×C₂₃	D₈	1	1	yes	characteristic
16	C₄×C₂₃	D₈	1	1	yes	characteristic
17	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
18	Dic₂₃	—	4	4	no	—
19	C₂×Q₃₂	—	23	1	no	maximal, Sylow
20	C₂×C₂₃	Q₃₂	1	2	yes	complemented
21	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
22	C₂×Q₁₆	—	23	2	no	—
23	Q₃₂	—	23	4	no	—
24	C₂×C₁₆	D₂₃	1	1	yes	characteristic
25	C₂₃	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
26	C₂×Q₈	—	46	2	no	—
27	Q₁₆	—	23	4	no	—
28	Q₁₆	—	46	2	no	—
29	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
30	C₁₆	C₂×D₂₃	1	2	yes	—
31	Q₈	—	46	4	no	—
32	Q₈	—	92	2	no	—
33	C₂×C₄	—	92	2	no	—
34	C₂×C₄	D₉₂	1	1	yes	characteristic
35	C₈	D₉₂	1	1	yes	characteristic
36	C₈	C₂²×D₂₃	1	1	yes	characteristic
37	C₂²	D₁₈₄	1	1	yes	characteristic
38	C₄	—	92	4	no	—
39	C₄	D₁₈₄	1	1	yes	characteristic
40	C₄	C₂×D₉₂	1	1	yes	characteristic
41	C₂	Dic₁₈₄	1	2	yes	direct product factor
42	C₂	C₂×D₁₈₄	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.