Subgroups — #20297352

Order 7136.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813171	C₂	1	4	yes	maximal, complemented
2	#16813170	C₂	1	6	yes	maximal, complemented
3	Q₈×D₂₂₃	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₄₆	C₂²	1	6	yes	—
6	D₈₉₂	C₂²	1	6	yes	—
7	C₂²⋊D₂₂₃	C₂²	1	4	yes	—
8	C₄×D₂₂₃	C₂²	1	12	yes	—
9	Q₈×C₂₂₃	C₂²	1	4	yes	—
10	C₂×C₄×C₂₂₃	C₂²	1	3	yes	—
11	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
12	C₂×D₂₂₃	C₂³	1	4	yes	—
13	C₄×C₂₂₃	C₂³	1	6	yes	—
14	Dic₂₂₃	C₂³	1	4	yes	—
15	C₂×C₂₂₃	—	2	1	no	—
16	C₂×C₂₂₃	C₂⁴	1	1	yes	characteristic
17	D₂₂₃	—	2	4	no	—
18	C₂₂₃	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
19	2₋¹⁺⁴	—	223	1	no	maximal, Sylow
20	#41	—	223	4	no	—
21	#41	—	223	6	no	—
22	C₂×Q₈	—	223	4	no	—
23	C₂×Q₈	D₂₂₃	1	1	yes	characteristic, complemented
24	Q₈	—	223	6	no	—
25	Q₈	C₂×D₂₂₃	1	4	yes	—
26	D₄	—	223	4	no	—
27	D₄	—	223	6	no	—
28	C₂×C₄	—	223	12	no	—
29	C₂×C₄	C₂×D₂₂₃	1	3	yes	—
30	C₂²	—	223	4	no	—
31	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
32	C₄	—	223	4	no	—
33	C₄	C₂²×D₂₂₃	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	446	4	no	—
36	C₂	C₂³×D₂₂₃	1	1	yes	characteristic

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