Subgroups — #13092602

Order 1472.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625158	C₂	1	1	yes	maximal, characteristic
2	#10625115	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625080	C₂	1	2	yes	maximal, complemented
4	C₂₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625007	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
7	#67292	—	2	2	no	—
8	Q₈×D₂₃	—	2	2	no	—
9	#67288	—	2	2	no	—
10	#67288	C₂²	1	2	yes	—
11	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
12	M₁₆×C₂₃	C₂²	1	2	yes	—
13	Dic₂₃⋊C₄	—	2	2	no	—
14	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
15	Dic₉₂	—	2	2	no	—
16	#67263	—	2	2	no	—
17	Q₈×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	D₄	1	2	yes	—
19	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂²⋊D₂₃	—	2	2	no	—
21	C₂×Dic₂₃	—	2	1	no	—
22	C₂×Dic₂₃	—	2	1	no	—
23	D₉₂	—	2	2	no	—
24	D₉₂	D₄	1	2	yes	—
25	C₄×D₂₃	—	2	4	no	—
26	C₄×D₂₃	—	2	2	no	—
27	Dic₄₆	—	2	2	no	—
28	Dic₄₆	—	2	2	no	—
29	Dic₄₆	D₄	1	2	yes	—
30	C₈×C₂₃	—	2	2	no	—
31	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₂×D₂₃	—	2	2	no	—
33	C₄×C₂₃	—	2	2	no	—
34	C₄×C₂₃	C₂×D₄	1	2	yes	—
35	Dic₂₃	—	2	2	no	—
36	Dic₂₃	—	2	2	no	—
37	Dic₂₃	—	4	1	no	—
38	#456	—	23	1	no	maximal, Sylow
39	C₂×C₂₃	—	2	1	no	—
40	C₂×C₂₃	#120	1	1	yes	characteristic
41	D₂₃	—	4	2	no	—
42	2₋¹⁺⁴	—	23	1	no	—
43	#137	—	23	2	no	—
44	C₄⋊Q₈	—	23	1	no	—
45	#104	—	23	2	no	—
46	#101	D₂₃	1	1	yes	characteristic, complemented
47	C₂₃	#456	1	1	yes	characteristic, complemented, Sylow
48	#41	—	23	2	no	—
49	#41	—	46	2	no	—
50	#41	—	46	2	no	—
51	C₂×Q₈	—	23	1	no	—
52	C₂×Q₈	—	46	2	no	—
53	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
54	Q₁₆	—	46	2	no	—
55	SD₁₆	—	46	2	no	—
56	M₁₆	C₂×D₂₃	1	2	yes	—
57	C₄⋊C₄	—	46	2	no	—
58	C₄²	—	23	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	23	2	no	—
61	Q₈	—	46	2	no	—
62	Q₈	—	46	2	no	—
63	D₄	—	23	2	no	—
64	D₄	—	46	2	no	—
65	D₄	—	46	2	no	—
66	C₂×C₄	—	46	4	no	—
67	C₂×C₄	—	46	1	no	—
68	C₂×C₄	—	46	2	no	—
69	C₂×C₄	—	46	1	no	—
70	C₂×C₄	D₉₂	1	2	yes	—
71	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	46	2	no	—
74	C₂²	C₂×D₉₂	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	46	2	no	—
77	C₄	—	46	2	no	—
78	C₄	—	92	1	no	—
79	C₄	D₄×D₂₃	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	92	2	no	—
82	C₂	#10625053	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10625053
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#101	C₂
socle	C₂×C₂₃	#120
prime radical	#10625158	C₂
hypercenter	#101	D₂₃
hypocenter	C₂₃	#456
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #10625115	C₂	semidirect
3. #10625080	C₂	semidirect
4. C₂₃×#101	C₂	semidirect
5. #10625007	C₂	semidirect
46. #101	D₂₃	semidirect
47. C₂₃	#456	semidirect

Maximal subgroups

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

subgroup	index
#10625158	2
#10625115	2
#10625080	2
C₂₃×#101	2
#10625007	2
#456	23