Subgroups — #13092464

Order 1472.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₂₃	C₂	1	2	yes	maximal
2	C₂×#67262	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625004	C₂	1	2	yes	maximal, complemented
5	#10625001	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
7	M₁₆×C₂₃	C₂²	1	2	yes	—
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	#67267	C₂²	1	2	yes	—
10	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
11	#67262	—	2	2	no	—
12	#67262	C₄	1	4	yes	—
13	C₈×D₂₃	—	2	2	no	—
14	C₂²×D₂₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₃	Q₈	1	1	yes	characteristic
17	C₄×D₂₃	C₂×C₄	1	2	yes	—
18	C₄×D₂₃	D₄	1	2	yes	—
19	C₈×C₂₃	—	2	2	no	—
20	C₈×C₂₃	C₂×C₄	1	2	yes	—
21	C₂₃⋊C₈	—	2	2	no	—
22	C₂₃⋊C₈	C₂×C₄	1	2	yes	—
23	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₂₃	—	4	1	no	—
25	C₂×D₂₃	C₄⋊C₄	1	2	yes	—
26	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	Dic₂₃	C₄⋊C₄	1	2	yes	—
29	#430	—	23	1	no	maximal, Sylow
30	C₂×C₂₃	—	2	1	no	—
31	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₂₃	—	2	2	no	—
33	C₂×M₁₆	—	23	1	no	—
34	C₂×M₁₆	—	23	2	no	—
35	#108	—	23	2	no	—
36	#108	—	23	1	no	—
37	#108	D₂₃	1	1	yes	characteristic, complemented
38	C₂₃	#430	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₄	—	23	1	no	—
40	M₁₆	—	23	4	no	—
41	M₁₆	—	23	2	no	—
42	M₁₆	—	46	2	no	—
43	M₁₆	C₂×D₂₃	1	2	yes	—
44	C₂×C₈	—	23	1	no	—
45	C₂×C₈	—	46	2	no	—
46	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
47	C₂³	—	23	1	no	—
48	C₂×C₄	—	23	1	no	—
49	C₂×C₄	—	23	2	no	—
50	C₂×C₄	—	23	2	no	—
51	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	23	2	no	—
54	C₈	—	46	2	no	—
55	C₈	C₄×D₂₃	1	2	yes	—
56	C₂²	—	23	2	no	—
57	C₂²	—	92	1	no	—
58	C₂²	Q₈×D₂₃	1	1	yes	characteristic
59	C₄	—	23	2	no	—
60	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
61	C₄	D₄×D₂₃	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	46	2	no	—
64	C₂	C₄⋊C₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#108	C₂
socle	C₂×C₂₃	C₂×C₄⋊C₄
prime radical	C₂²×D₂₃	Q₈
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#108	D₂₃
hypocenter	C₂₃	#430
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. C₂₃×#108	C₂	semidirect
4. #10625004	C₂	semidirect
5. #10625001	C₂	semidirect
37. #108	D₂₃	semidirect
38. C₂₃	#430	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₂₃	2
C₂×#67262	2
C₂₃×#108	2
#10625004	2
#10625001	2
#430	23