Subgroups — Q₈×Dic₂₂₃ #20297271

Order 7136.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₂₂₃	C₂	1	3	yes	maximal
2	C₄×Dic₂₂₃	C₂	1	3	yes	maximal
3	C₂×Q₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₂₃	C₂²	1	3	yes	—
5	C₂×Dic₂₂₃	C₂²	1	1	yes	characteristic
6	Q₈×C₂₂₃	C₄	1	4	yes	complemented
7	C₂×C₄×C₂₂₃	C₂²	1	3	yes	—
8	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
9	C₄×C₂₂₃	C₂×C₄	1	6	yes	—
10	Dic₂₂₃	—	2	3	no	—
11	Dic₂₂₃	Q₈	1	2	yes	direct product factor
12	C₂×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₂₂₃	C₂×Q₈	1	1	yes	characteristic
14	C₂×C₂₂₃	#41	1	1	yes	characteristic
15	C₂₂₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
16	C₄×Q₈	—	223	1	no	maximal, Sylow
17	C₂×Q₈	D₂₂₃	1	1	yes	characteristic
18	C₄⋊C₄	—	223	3	no	—
19	C₄²	—	223	3	no	—
20	Q₈	Dic₂₂₃	1	4	yes	direct product factor
21	C₂×C₄	—	223	3	no	—
22	C₂×C₄	—	223	1	no	—
23	C₂×C₄	C₂×D₂₂₃	1	3	yes	—
24	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
25	C₄	—	446	3	no	—
26	C₄	—	223	2	no	—
27	C₄	C₂×Dic₂₂₃	1	6	yes	—
28	C₂	C₂²×Dic₂₂₃	1	1	yes	characteristic
29	C₂	Q₈×D₂₂₃	1	1	yes	characteristic
30	C₂	#16813171	1	1	yes	characteristic

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