Subgroups — C₂²×C₂₂₃⋊C₈ #20297306

Order 7136.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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