Subgroups — #13092800

Order 1472.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625107	C₂	1	2	yes	maximal, complemented
3	C₂×#67273	C₂	1	2	yes	maximal, complemented
4	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₂₃	C₂²	1	2	yes	—
7	C₂×Dic₄₆	C₂²	1	2	yes	—
8	D₈×C₂₃	—	2	2	no	—
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₂₃	—	2	4	no	—
11	#67273	—	2	4	no	—
12	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
14	Dic₉₂	—	2	2	no	—
15	C₂³×C₂₃	—	2	2	no	—
16	D₄×C₂₃	—	2	2	no	—
17	D₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₃	—	2	2	no	—
20	C₂×Dic₂₃	D₄	1	2	yes	—
21	Dic₄₆	—	2	2	no	—
22	Dic₄₆	—	2	2	no	—
23	C₈×C₂₃	D₄	1	2	yes	—
24	C₂₃⋊C₈	D₄	1	2	yes	—
25	C₂²×C₂₃	—	4	2	no	—
26	C₂²×C₂₃	—	4	4	no	—
27	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	Dic₂₃	—	2	2	no	—
31	Dic₂₃	—	4	2	no	—
32	#495	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	—	8	2	no	—
34	C₂×C₂₃	#127	1	1	yes	characteristic
35	C₂×C₂₃	#135	1	2	yes	—
36	C₂×Q₁₆	—	23	1	no	—
37	C₂×SD₁₆	—	23	2	no	—
38	C₂×D₈	D₂₃	1	1	yes	characteristic
39	#124	—	23	2	no	—
40	C₄×C₈	—	23	1	no	—
41	C₂₃	#495	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	23	2	no	—
43	C₂×D₄	C₂×D₂₃	1	2	yes	—
44	Q₁₆	—	46	2	no	—
45	SD₁₆	—	46	4	no	—
46	D₈	—	2	2	no	—
47	C₂×C₈	—	23	1	no	—
48	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
49	C₂²⋊C₄	—	46	4	no	—
50	C₄²	—	23	1	no	—
51	C₂³	—	2	2	no	—
52	Q₈	—	46	2	no	—
53	Q₈	—	46	2	no	—
54	D₄	—	2	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	23	2	no	—
57	C₂×C₄	—	46	2	no	—
58	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
59	C₈	—	23	2	no	—
60	C₈	C₂²⋊D₂₃	1	2	yes	—
61	C₂²	—	4	4	no	—
62	C₂²	—	4	2	no	—
63	C₂²	D₄×D₂₃	1	1	yes	characteristic
64	C₄	—	46	2	no	—
65	C₄	—	92	2	no	—
66	C₄	D₄×D₂₃	1	1	yes	characteristic
67	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
68	C₂	—	8	2	no	—
69	C₂	#10625083	1	2	yes	—
70	C₂	#10625111	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting, prime radical	C₂×D₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
hypercenter	C₂×D₈	D₂₃
hypocenter	C₂₃	#495
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
2. #10625107	C₂	semidirect
3. C₂×#67273	C₂	semidirect
4. C₂×Dic₉₂	C₂	semidirect
5. C₈×Dic₂₃	C₂	semidirect
41. C₂₃	#495	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₂₃	2
#10625107	2
C₂×#67273	2
C₂×Dic₉₂	2
C₈×Dic₂₃	2
#495	23