Subgroups — #20297326

Order 7136.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813170	C₂	1	2	yes	maximal, complemented
2	Dic₈₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813159	C₂	1	2	yes	maximal, complemented
4	D₁₇₈₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₄₄₆	C₂²	1	2	yes	—
7	D₈₉₂	C₂²	1	2	yes	—
8	C₂²⋊D₂₂₃	—	2	2	no	—
9	C₄×D₂₂₃	—	2	2	no	—
10	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
11	C₈×C₂₂₃	C₂²	1	1	yes	characteristic
12	C₈×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₂²×C₂₂₃	D₄	1	1	yes	characteristic
14	C₂×D₂₂₃	—	2	2	no	—
15	C₄×C₂₂₃	D₄	1	1	yes	characteristic
16	C₄×C₂₂₃	C₂³	1	1	yes	characteristic
17	Dic₂₂₃	—	2	2	no	—
18	C₂×C₂₂₃	—	2	1	no	—
19	C₂×C₂₂₃	C₂×D₄	1	1	yes	characteristic
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	—	223	1	no	—
25	SD₁₆	—	223	2	no	—
26	D₈	—	223	1	no	—
27	C₂×C₈	D₂₂₃	1	1	yes	characteristic, complemented
28	Q₈	—	223	2	no	—
29	D₄	—	446	2	no	—
30	D₄	—	223	2	no	—
31	C₂×C₄	—	446	2	no	—
32	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
33	C₈	C₂×D₂₂₃	1	1	yes	characteristic
34	C₈	C₂×D₂₂₃	1	1	yes	characteristic
35	C₂²	—	446	2	no	—
36	C₂²	D₈₉₂	1	1	yes	characteristic
37	C₄	—	446	2	no	—
38	C₄	D₈₉₂	1	1	yes	characteristic
39	C₄	C₂²×D₂₂₃	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	892	2	no	—
42	C₂	C₂×D₈₉₂	1	1	yes	characteristic

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