Subgroups — #13092459

Order 1472.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625097	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₂₃	C₂	1	1	yes	maximal, characteristic
4	#10625000	C₂	1	2	yes	maximal, complemented
5	#10624999	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	—	2	1	no	—
8	M₁₆×C₂₃	C₄	1	4	yes	complemented
9	C₂×C₈×C₂₃	C₂²	1	2	yes	—
10	C₂²⋊Dic₂₃	—	2	1	no	—
11	C₄⋊Dic₂₃	—	2	1	no	—
12	C₄⋊Dic₂₃	C₂²	1	2	yes	—
13	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
15	C₄×Dic₂₃	—	2	1	no	—
16	C₂³×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₃	Q₈	1	2	yes	—
20	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₃	—	2	1	no	—
22	C₂×Dic₂₃	—	2	1	no	—
23	C₂×Dic₂₃	—	2	2	no	—
24	C₂×Dic₂₃	—	4	2	no	—
25	C₈×C₂₃	C₂×C₄	1	4	yes	complemented
26	C₂²×C₂₃	—	2	1	no	—
27	C₂²×C₂₃	—	2	1	no	—
28	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
29	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
31	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
33	Dic₂₃	—	4	1	no	—
34	Dic₂₃	—	4	2	no	—
35	Dic₂₃	—	4	1	no	—
36	#428	—	23	1	no	maximal, Sylow
37	C₂×C₂₃	—	2	2	no	—
38	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₂₃	#137	1	1	yes	characteristic
41	C₂×M₁₆	D₂₃	1	1	yes	characteristic
42	#117	—	23	1	no	—
43	C₂×C₄⋊C₄	—	23	1	no	—
44	#107	—	23	2	no	—
45	#106	—	23	2	no	—
46	C₂₃	#428	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	46	1	no	—
48	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
49	M₁₆	Dic₂₃	1	4	yes	complemented
50	C₂×C₈	C₂×D₂₃	1	2	yes	—
51	C₄⋊C₄	—	23	1	no	—
52	C₄⋊C₄	—	23	2	no	—
53	C₄⋊C₄	—	23	1	no	—
54	C₄⋊C₄	—	46	1	no	—
55	C₂²⋊C₄	—	46	1	no	—
56	C₄²	—	46	1	no	—
57	C₂³	D₉₂	1	1	yes	characteristic
58	C₂×C₄	—	46	1	no	—
59	C₂×C₄	—	46	1	no	—
60	C₂×C₄	—	46	2	no	—
61	C₂×C₄	—	92	2	no	—
62	C₂×C₄	Dic₄₆	1	2	yes	—
63	C₂×C₄	D₉₂	1	1	yes	characteristic
64	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
65	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
66	C₈	C₂×Dic₂₃	1	4	yes	complemented
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	C₄⋊Dic₂₃	1	2	yes	—
70	C₂²	C₂×D₉₂	1	1	yes	characteristic
71	C₄	—	92	2	no	—
72	C₄	—	92	1	no	—
73	C₄	—	92	1	no	—
74	C₄	C₄⋊Dic₂₃	1	2	yes	—
75	C₄	C₂×Dic₄₆	1	1	yes	characteristic
76	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	#10625079	1	1	yes	characteristic
79	C₂	#10625080	1	1	yes	characteristic
80	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂³×C₂₃	D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	#428
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10625000	C₂	semidirect
5. #10624999	C₂	semidirect
8. M₁₆×C₂₃	C₄	semidirect
25. C₈×C₂₃	C₂×C₄	semidirect
46. C₂₃	#428	semidirect
49. M₁₆	Dic₂₃	semidirect
66. C₈	C₂×Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₃	2
#10625097	2
C₂×C₄⋊Dic₂₃	2
#10625000	2
#10624999	2
#428	23