Subgroups — #13092284

Order 1472.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#95	C₂	1	1	yes	maximal, characteristic
3	C₂₃⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂₃⋊#95	C₂	1	2	yes	maximal
5	C₂₃⋊#95	C₂	1	2	yes	maximal
6	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
7	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
8	C₂²×Dic₂₃	C₂²	1	2	yes	—
9	C₂²×Dic₂₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₂₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₂₃	C₄	1	4	yes	complemented
12	C₂³×C₂₃	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	2	2	no	—
14	C₂×C₄×C₂₃	—	2	2	no	—
15	C₂×C₄×C₂₃	—	2	2	no	—
16	C₂×C₄×C₂₃	—	2	2	no	—
17	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×Dic₂₃	—	2	2	no	—
19	C₂×Dic₂₃	—	2	1	no	—
20	C₂×Dic₂₃	—	2	1	no	—
21	C₂×Dic₂₃	—	2	2	no	—
22	C₂×Dic₂₃	—	2	2	no	—
23	C₂×Dic₂₃	—	2	2	no	—
24	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
25	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
26	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₂₃	#41	1	2	yes	—
28	C₂²×C₂₃	#41	1	2	yes	—
29	C₂²×C₂₃	#41	1	1	yes	characteristic
30	C₂²×C₂₃	#41	1	1	yes	characteristic
31	C₄×C₂₃	—	2	2	no	—
32	C₄×C₂₃	—	4	2	no	—
33	Dic₂₃	—	2	2	no	—
34	Dic₂₃	—	2	2	no	—
35	Dic₂₃	—	4	2	no	—
36	#383	—	23	1	no	maximal, Sylow
37	C₂×C₂₃	#117	1	1	yes	characteristic
38	C₂×C₂₃	#117	1	1	yes	characteristic
39	C₂×C₂₃	#117	1	1	yes	characteristic
40	C₂×C₂₃	#126	1	2	yes	—
41	C₂×C₂₃	#126	1	2	yes	—
42	C₂×C₄²	—	23	1	no	—
43	#95	—	23	2	no	—
44	#95	—	23	2	no	—
45	#95	—	23	1	no	—
46	#95	D₂₃	1	1	yes	characteristic
47	C₂₃	#383	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	23	1	no	—
49	C₂²×C₄	—	23	1	no	—
50	C₂²×C₄	—	23	2	no	—
51	C₂²×C₄	C₂×D₂₃	1	2	yes	—
52	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
53	C₄²	—	23	4	no	—
54	C₂³	C₂²×D₂₃	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	23	2	no	—
60	C₂×C₄	—	23	2	no	—
61	C₂×C₄	—	46	2	no	—
62	C₂×C₄	—	46	1	no	—
63	C₂×C₄	—	46	1	no	—
64	C₂×C₄	—	46	2	no	—
65	C₂×C₄	—	46	2	no	—
66	C₂×C₄	—	46	2	no	—
67	C₂×C₄	C₄×D₂₃	1	2	yes	—
68	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
69	C₂²	#67288	1	2	yes	—
70	C₂²	#67290	1	2	yes	—
71	C₂²	#67290	1	1	yes	characteristic
72	C₂²	#67292	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	4	2	no	—
75	C₄	—	46	2	no	—
76	C₄	—	46	2	no	—
77	C₄	—	92	2	no	—
78	C₂	#10625043	1	1	yes	characteristic
79	C₂	#10625048	1	1	yes	characteristic
80	C₂	#10625050	1	2	yes	—
81	C₂	#10625063	1	1	yes	characteristic
82	C₂	#10625069	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂²×C₄
Fitting	C₂₃×#95	C₂
socle, prime radical, cosocle	C₂³×C₂₃	C₂³
hypercenter	#95	D₂₃
hypocenter	C₂₃	#383
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
11. C₄×Dic₂₃	C₄	semidirect
47. C₂₃	#383	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₂₃	2
C₂₃×#95	2
C₂₃⋊#95	2
#383	23