Subgroups — #13092230

Order 1472.

62 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	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
3	#10624994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₂₃	—	2	1	no	—
5	D₈×C₂₃	—	2	1	no	—
6	D₈×C₂₃	C₄	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	#67267	—	2	1	no	—
9	C₂₃⋊C₁₆	—	2	1	no	—
10	C₂³×C₂₃	—	4	1	no	—
11	D₄×C₂₃	—	2	2	no	—
12	D₄×C₂₃	—	4	1	no	—
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₂₃⋊C₈	—	4	1	no	—
17	C₂²×C₂₃	—	4	2	no	—
18	C₂²×C₂₃	—	8	2	no	—
19	C₂²×C₂₃	SD₁₆	1	1	yes	characteristic
20	C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₃	D₈	1	1	yes	characteristic
22	#361	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	—	2	1	no	—
24	C₂×C₂₃	—	8	2	no	—
25	C₂×C₂₃	#102	1	1	yes	characteristic
26	C₂×D₈	D₂₃	1	1	yes	characteristic
27	M₃₂	—	23	1	no	—
28	#108	—	23	1	no	—
29	C₂₃	#361	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₄	—	2	1	no	—
31	D₈	—	2	1	no	—
32	D₈	Dic₂₃	1	2	yes	—
33	M₁₆	—	46	1	no	—
34	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
35	C₁₆	—	46	1	no	—
36	C₂³	—	4	1	no	—
37	D₄	—	2	2	no	—
38	D₄	—	4	1	no	—
39	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
40	C₈	—	92	1	no	—
41	C₈	C₂×Dic₂₃	1	1	yes	characteristic
42	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
43	C₂²	—	4	2	no	—
44	C₂²	—	8	2	no	—
45	C₂²	#67273	1	1	yes	characteristic
46	C₄	#67272	1	1	yes	characteristic
47	C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	8	2	no	—
50	C₂	#10625014	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10625014
commutator	C₈×C₂₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₃
Fitting, prime radical	C₂×D₈×C₂₃	C₂
socle	C₂×C₂₃	#102
cosocle	C₂×C₈×C₂₃	C₂²
hypercenter	C₂×D₈	D₂₃
hypocenter	C₂₃	#361
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
2. #10625001	C₂	semidirect
3. #10624994	C₂	semidirect
29. C₂₃	#361	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
#10625001	2
#10624994	2
#361	23