Subgroups — #20297327

Order 7136.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813171	C₂	1	2	yes	maximal, complemented
2	#16813157	C₂	1	2	yes	maximal, complemented
3	D₁₇₈₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈₉₂	—	2	2	no	—
7	D₈₉₂	C₂²	1	2	yes	—
8	C₄×D₂₂₃	—	2	2	no	—
9	C₄×D₂₂₃	C₂²	1	1	yes	characteristic
10	C₂₂₃⋊C₈	C₂²	1	1	yes	characteristic
11	Q₈×C₂₂₃	C₂²	1	2	yes	—
12	C₈×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₂×D₂₂₃	—	2	2	no	—
14	C₂×D₂₂₃	D₄	1	1	yes	characteristic
15	C₄×C₂₂₃	—	2	2	no	—
16	C₄×C₂₂₃	C₂³	1	1	yes	characteristic
17	Dic₂₂₃	D₄	1	1	yes	characteristic
18	C₂×C₂₂₃	C₂×D₄	1	1	yes	characteristic
19	D₂₂₃	—	2	1	no	—
20	D₂₂₃	—	4	2	no	—
21	C₂₂₃	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	223	1	no	maximal, Sylow
23	#41	—	223	2	no	—
24	Q₁₆	D₂₂₃	1	1	yes	characteristic, complemented
25	SD₁₆	—	223	2	no	—
26	D₈	—	223	1	no	—
27	C₂×C₈	—	223	1	no	—
28	Q₈	C₂×D₂₂₃	1	2	yes	—
29	D₄	—	446	2	no	—
30	D₄	—	223	2	no	—
31	C₂×C₄	—	446	2	no	—
32	C₂×C₄	—	223	1	no	—
33	C₈	—	223	1	no	—
34	C₈	C₂×D₂₂₃	1	1	yes	characteristic
35	C₂²	—	446	2	no	—
36	C₂²	—	223	1	no	—
37	C₄	—	2	2	no	—
38	C₄	—	223	1	no	—
39	C₄	C₂²×D₂₂₃	1	1	yes	characteristic
40	C₂	—	892	2	no	—
41	C₂	—	446	1	no	—
42	C₂	D₄×D₂₂₃	1	1	yes	characteristic

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