Subgroups — #13092625

Order 1472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	#10625115	C₂	1	1	yes	maximal, characteristic
4	C₂×#67275	C₂	1	1	yes	maximal, characteristic
5	#10625017	C₂	1	1	yes	maximal, characteristic
6	#10624998	C₂	1	1	yes	maximal, characteristic
7	Dic₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₂₃	—	2	2	no	—
12	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	#67275	—	2	2	no	—
14	C₄⋊Dic₂₃	—	2	1	no	—
15	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
16	Dic₂₃⋊C₄	—	2	1	no	—
17	Dic₂₃⋊C₄	—	2	1	no	—
18	C₄×Dic₂₃	—	2	1	no	—
19	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
21	Q₈×C₂₃	—	2	1	no	—
22	Q₈×C₂₃	—	2	1	no	—
23	Q₈×C₂₃	—	2	1	no	—
24	Q₈×C₂₃	D₄	1	2	yes	—
25	C₂×C₄×C₂₃	—	2	1	no	—
26	C₂×C₄×C₂₃	—	2	1	no	—
27	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
28	C₂×Dic₂₃	—	2	1	no	—
29	C₂×Dic₂₃	—	2	1	no	—
30	C₂×Dic₂₃	D₄	1	1	yes	characteristic
31	C₂×Dic₂₃	D₄	1	1	yes	characteristic
32	Dic₄₆	—	2	1	no	—
33	Dic₄₆	—	2	1	no	—
34	C₈×C₂₃	—	2	1	no	—
35	C₂₃⋊C₈	—	2	1	no	—
36	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
37	C₄×C₂₃	—	2	2	no	—
38	C₄×C₂₃	—	4	1	no	—
39	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
40	C₄×C₂₃	#41	1	1	yes	characteristic
41	Dic₂₃	—	2	1	no	—
42	Dic₂₃	—	4	1	no	—
43	Dic₂₃	—	4	1	no	—
44	Dic₂₃	Q₁₆	1	2	yes	complemented
45	#462	—	23	1	no	maximal, Sylow
46	C₂×C₂₃	#121	1	1	yes	characteristic
47	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₂×C₂₃	#137	1	1	yes	characteristic
49	C₂×Q₁₆	—	23	1	no	—
50	C₂×Q₁₆	D₂₃	1	1	yes	characteristic
51	C₄⋊Q₈	—	23	1	no	—
52	C₄×Q₈	—	23	1	no	—
53	C₄⋊C₈	—	23	1	no	—
54	#103	—	23	1	no	—
55	#103	—	23	1	no	—
56	C₂₃	#462	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	23	1	no	—
58	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
59	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
60	Q₁₆	—	2	2	no	—
61	Q₁₆	—	46	2	no	—
62	C₂×C₈	—	23	1	no	—
63	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
64	C₄⋊C₄	—	23	1	no	—
65	C₄⋊C₄	—	46	1	no	—
66	C₄⋊C₄	—	46	1	no	—
67	C₄⋊C₄	—	46	1	no	—
68	C₄²	—	23	1	no	—
69	C₄²	—	46	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	2	1	no	—
73	Q₈	—	46	1	no	—
74	Q₈	—	46	1	no	—
75	Q₈	C₂²⋊D₂₃	1	2	yes	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	23	1	no	—
79	C₂×C₄	—	23	1	no	—
80	C₂×C₄	—	46	1	no	—
81	C₂×C₄	—	46	1	no	—
82	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	46	1	no	—
85	C₂²	D₄×D₂₃	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	4	1	no	—
88	C₄	—	23	2	no	—
89	C₄	—	46	1	no	—
90	C₄	—	92	1	no	—
91	C₄	—	92	1	no	—
92	C₄	#67290	1	1	yes	characteristic
93	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
94	C₂	Q₁₆×D₂₃	1	1	yes	characteristic
95	C₂	#10625089	1	1	yes	characteristic
96	C₂	#10625110	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	#462
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
44. Dic₂₃	Q₁₆	semidirect
56. C₂₃	#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₃	2
Q₈×Dic₂₃	2
#10625115	2
C₂×#67275	2
#10625017	2
#10624998	2
Dic₂₃⋊C₈	2
#462	23