Subgroups — #20297293

Order 7136.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₉₂	C₂	1	1	yes	maximal, characteristic
2	(C₂×D₂₂₃)⋊C₄	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₂₂₃	C₂²	1	2	yes	—
6	D₈₉₂	—	2	2	no	—
7	C₂×Dic₂₂₃	C₂²	1	2	yes	—
8	Q₈×C₂₂₃	—	2	2	no	—
9	C₂×C₄×C₂₂₃	C₂²	1	2	yes	—
10	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
11	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
12	C₂×D₂₂₃	—	2	2	no	—
13	C₂×D₂₂₃	—	2	4	no	—
14	C₄×C₂₂₃	—	2	2	no	—
15	C₄×C₂₂₃	D₄	1	2	yes	—
16	Dic₂₂₃	—	2	2	no	—
17	C₂×C₂₂₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₂₂₃	#41	1	2	yes	—
19	D₂₂₃	—	4	2	no	—
20	C₂₂₃	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	223	1	no	maximal, Sylow
22	C₂×Q₈	D₂₂₃	1	1	yes	characteristic, complemented
23	C₂×D₄	—	223	1	no	—
24	C₂²⋊C₄	—	223	4	no	—
25	C₄²	—	223	1	no	—
26	C₂³	—	223	2	no	—
27	Q₈	—	2	2	no	—
28	D₄	—	446	2	no	—
29	C₂×C₄	—	223	2	no	—
30	C₂×C₄	C₂×D₂₂₃	1	2	yes	—
31	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
32	C₂²	—	446	2	no	—
33	C₂²	—	446	4	no	—
34	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	446	2	no	—
37	C₄	C₂²⋊D₂₂₃	1	2	yes	—
38	C₂	—	892	2	no	—
39	C₂	C₂×C₂²⋊D₂₂₃	1	1	yes	characteristic
40	C₂	#16813171	1	2	yes	—

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