Subgroups — C₂×Dic₈₉₂ #20297322

Order 7136.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₄₆	C₂	1	2	yes	maximal
2	Dic₈₉₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	Dic₄₄₆	—	2	2	no	—
5	Dic₄₄₆	C₂²	1	4	yes	—
6	C₂×Dic₂₂₃	—	2	2	no	—
7	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
8	C₈×C₂₂₃	C₂²	1	2	yes	—
9	C₂²×C₂₂₃	D₄	1	1	yes	characteristic
10	C₄×C₂₂₃	D₄	1	1	yes	characteristic
11	C₄×C₂₂₃	C₂³	1	1	yes	characteristic
12	Dic₂₂₃	—	2	4	no	—
13	C₂×C₂₂₃	Q₁₆	1	2	yes	complemented
14	C₂×C₂₂₃	C₂×D₄	1	1	yes	characteristic
15	C₂₂₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂×Q₁₆	—	223	1	no	maximal, Sylow
17	C₂×Q₈	—	223	2	no	—
18	Q₁₆	—	223	4	no	—
19	C₂×C₈	D₂₂₃	1	1	yes	characteristic
20	Q₈	—	446	2	no	—
21	Q₈	—	223	4	no	—
22	C₂×C₄	—	446	2	no	—
23	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
24	C₈	C₂×D₂₂₃	1	2	yes	—
25	C₂²	D₈₉₂	1	1	yes	characteristic
26	C₄	—	446	4	no	—
27	C₄	D₈₉₂	1	1	yes	characteristic
28	C₄	C₂²×D₂₂₃	1	1	yes	characteristic
29	C₂	Dic₈₉₂	1	2	yes	direct product factor
30	C₂	C₂×D₈₉₂	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.