Subgroups — #13092626

Order 1472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625115	C₂	1	1	yes	maximal, characteristic
2	C₂×#67275	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic
4	#10625058	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#103	C₂	1	1	yes	maximal, characteristic
6	Dic₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#10624992	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
13	#67275	—	2	2	no	—
14	Dic₂₃⋊C₄	—	2	1	no	—
15	Dic₂₃⋊C₄	—	2	1	no	—
16	Dic₂₃⋊C₄	—	2	1	no	—
17	C₄×Dic₂₃	—	2	1	no	—
18	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
20	Dic₉₂	—	2	2	no	—
21	Q₈×C₂₃	—	2	1	no	—
22	Q₈×C₂₃	—	2	1	no	—
23	C₂×C₄×C₂₃	—	2	1	no	—
24	C₂×C₄×C₂₃	—	2	1	no	—
25	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
26	C₂×Dic₂₃	—	2	1	no	—
27	C₂×Dic₂₃	—	2	1	no	—
28	C₂×Dic₂₃	D₄	1	1	yes	characteristic
29	C₂×Dic₂₃	D₄	1	1	yes	characteristic
30	Dic₄₆	—	2	1	no	—
31	Dic₄₆	—	2	1	no	—
32	Dic₄₆	—	2	1	no	—
33	Dic₄₆	D₄	1	2	yes	—
34	C₈×C₂₃	—	2	1	no	—
35	C₂₃⋊C₈	—	2	1	no	—
36	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
37	C₄×C₂₃	—	4	1	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	2	no	—
42	Dic₂₃	—	2	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	—	23	1	no	—
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	D₂₃	1	1	yes	characteristic
56	C₂₃	#462	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	23	1	no	—
58	C₂×Q₈	—	23	1	no	—
59	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
60	Q₁₆	—	46	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	—	46	1	no	—
65	C₄⋊C₄	—	46	1	no	—
66	C₄⋊C₄	—	46	1	no	—
67	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
68	C₄²	—	23	1	no	—
69	C₄²	—	46	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	23	2	no	—
73	Q₈	—	46	1	no	—
74	Q₈	—	46	1	no	—
75	Q₈	—	46	1	no	—
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	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	23	2	no	—
89	C₄	—	46	2	no	—
90	C₄	—	46	1	no	—
91	C₄	—	92	1	no	—
92	C₄	#67288	1	1	yes	characteristic
93	C₄	D₄×D₂₃	1	1	yes	characteristic
94	C₂	#10625055	1	1	yes	characteristic
95	C₂	#10625086	1	1	yes	characteristic
96	C₂	Q₁₆×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#103	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	#103	D₂₃
hypocenter	C₂₃	#462
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

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
#10625115	2
C₂×#67275	2
C₂×Dic₉₂	2
#10625058	2
C₂₃×#103	2
Dic₂₃⋊C₈	2
#10624992	2
#462	23