Subgroups — #28383324

Order 14272.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₂₂₃⋊C₈)	C₂	1	2	yes	maximal, complemented
2	#127×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₂₃⋊C₈	—	2	2	no	—
4	C₂×D₄×C₂₂₃	—	2	2	no	—
5	C₂×D₄×C₂₂₃	C₄	1	2	yes	—
6	C₄²×C₂₂₃	C₂²	1	1	yes	characteristic
7	C₂₂₃⋊C₈	—	4	2	no	—
8	C₂³×C₂₂₃	—	2	2	no	—
9	D₄×C₂₂₃	—	4	2	no	—
10	D₄×C₂₂₃	—	4	2	no	—
11	D₄×C₂₂₃	—	4	2	no	—
12	C₂×C₄×C₂₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₂₃	D₄	1	2	yes	—
14	C₂²×C₂₂₃	—	4	2	no	—
15	C₂²×C₂₂₃	—	4	4	no	—
16	C₂²×C₂₂₃	C₂²⋊C₄	1	1	yes	characteristic
17	C₄×C₂₂₃	—	2	1	no	—
18	C₄×C₂₂₃	D₈	1	2	yes	—
19	C₄×C₂₂₃	SD₁₆	1	2	yes	—
20	C₂×C₂₂₃	—	8	2	no	—
21	C₂×C₂₂₃	#100	1	1	yes	characteristic
22	C₂×C₂₂₃	#102	1	2	yes	—
23	C₂₂₃	#331	1	1	yes	characteristic, complemented, Sylow
24	#331	—	223	1	no	maximal, Sylow
25	#127	D₂₂₃	1	1	yes	characteristic
26	C₄⋊C₈	—	223	2	no	—
27	C₂×D₄	—	2	2	no	—
28	C₂×D₄	Dic₂₂₃	1	2	yes	—
29	C₂×C₈	—	446	2	no	—
30	C₄²	C₂×D₂₂₃	1	1	yes	characteristic
31	C₂³	—	2	2	no	—
32	D₄	—	4	2	no	—
33	D₄	—	4	2	no	—
34	D₄	—	4	2	no	—
35	C₂×C₄	C₂×Dic₂₂₃	1	1	yes	characteristic
36	C₂×C₄	C₂²⋊D₂₂₃	1	2	yes	—
37	C₈	—	892	2	no	—
38	C₂²	—	4	2	no	—
39	C₂²	—	4	4	no	—
40	C₂²	C₂²⋊Dic₂₂₃	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	#16813155	1	2	yes	—
43	C₄	#16813158	1	2	yes	—
44	C₂	—	8	2	no	—
45	C₂	#20297221	1	1	yes	characteristic
46	C₂	#20297225	1	2	yes	—

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

N	H ≅ G/N	type
1. C₄⋊(C₂₂₃⋊C₈)	C₂	semidirect
23. C₂₂₃	#331	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.