Subgroups — #13092268

Order 1472.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃⋊C₄	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₂₃	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#95	C₂	1	1	yes	maximal, characteristic
5	C₂₃⋊#95	C₂	1	1	yes	maximal, characteristic
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	Dic₂₃⋊C₄	C₄	1	8	yes	complemented
12	C₄×Dic₂₃	—	2	4	no	—
13	C₄×Dic₂₃	C₄	1	4	yes	complemented
14	C₂³×C₂₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₂₃	—	2	2	no	—
16	C₂×C₄×C₂₃	—	2	2	no	—
17	C₂×C₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
20	C₂×Dic₂₃	—	2	2	no	—
21	C₂×Dic₂₃	—	2	2	no	—
22	C₂×Dic₂₃	C₂×C₄	1	4	yes	—
23	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
24	C₂×Dic₂₃	C₂×C₄	1	4	yes	—
25	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
26	C₂×Dic₂₃	D₄	1	2	yes	—
27	C₂×Dic₂₃	Q₈	1	2	yes	—
28	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₂₃	C₂²×C₄	1	2	yes	—
30	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₂₃	#41	1	2	yes	—
33	C₄×C₂₃	—	2	2	no	—
34	C₄×C₂₃	—	2	4	no	—
35	Dic₂₃	—	2	4	no	—
36	Dic₂₃	C₄²	1	4	yes	complemented
37	Dic₂₃	C₄⋊C₄	1	4	yes	complemented
38	C₄×C₄⋊C₄	—	23	1	no	maximal, Sylow
39	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₂₃	#117	1	1	yes	characteristic
42	C₂×C₂₃	C₄×D₄	1	2	yes	—
43	C₂×C₂₃	C₄×Q₈	1	2	yes	—
44	C₂×C₄⋊C₄	—	23	2	no	—
45	C₂×C₄²	—	23	1	no	—
46	C₂×C₄²	—	23	2	no	—
47	#95	—	23	1	no	—
48	#95	D₂₃	1	1	yes	characteristic
49	C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	23	1	no	—
51	C₂²×C₄	—	23	1	no	—
52	C₂²×C₄	—	23	2	no	—
53	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
54	C₂²×C₄	C₂×D₂₃	1	2	yes	—
55	C₄⋊C₄	—	23	8	no	—
56	C₄²	—	23	4	no	—
57	C₄²	—	46	4	no	—
58	C₂³	C₂²×D₂₃	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	23	2	no	—
63	C₂×C₄	—	23	2	no	—
64	C₂×C₄	—	23	4	no	—
65	C₂×C₄	—	23	2	no	—
66	C₂×C₄	—	23	2	no	—
67	C₂×C₄	—	23	4	no	—
68	C₂×C₄	—	46	2	no	—
69	C₂×C₄	—	46	2	no	—
70	C₂×C₄	C₄×D₂₃	1	2	yes	—
71	C₂×C₄	C₄×D₂₃	1	4	yes	—
72	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
73	C₂²	C₂×C₄×D₂₃	1	2	yes	—
74	C₂²	D₄×D₂₃	1	1	yes	characteristic
75	C₂²	#67290	1	2	yes	—
76	C₂²	Q₈×D₂₃	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	4	no	—
79	C₄	—	23	4	no	—
80	C₄	—	23	4	no	—
81	C₄	—	46	4	no	—
82	C₂	C₄²×D₂₃	1	1	yes	characteristic
83	C₂	#10625048	1	1	yes	characteristic
84	C₂	(C₂²⋊D₂₃)⋊C₄	1	2	yes	—
85	C₂	#10625058	1	2	yes	—
86	C₂	C₄⋊C₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₂₃
commutator	C₂×C₂₃	C₂×C₄²
Fitting	C₂₃×#95	C₂
socle, prime radical, cosocle	C₂³×C₂₃	C₂³
hypercenter	#95	D₂₃
hypocenter	C₂₃	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
11. Dic₂₃⋊C₄	C₄	semidirect
13. C₄×Dic₂₃	C₄	semidirect
36. Dic₂₃	C₄²	semidirect
37. Dic₂₃	C₄⋊C₄	semidirect
49. C₂₃	C₄×C₄⋊C₄	semidirect

Maximal subgroups

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

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