Subgroups — #13092784

Order 1472.

90 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	#10625061	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#103	C₂	1	1	yes	maximal, characteristic
4	#10625017	C₂	1	1	yes	maximal, characteristic
5	#10624998	C₂	1	1	yes	maximal, characteristic
6	#10624997	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×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₃	—	2	1	no	—
13	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
14	Dic₂₃⋊C₄	—	2	1	no	—
15	Dic₂₃⋊C₄	—	2	1	no	—
16	Dic₂₃⋊C₄	—	2	1	no	—
17	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₂₃	—	2	1	no	—
20	Q₈×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	—	2	1	no	—
23	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₂₃	—	2	1	no	—
25	C₂×Dic₂₃	—	2	1	no	—
26	C₂×Dic₂₃	D₄	1	1	yes	characteristic
27	C₂×Dic₂₃	D₄	1	1	yes	characteristic
28	Dic₄₆	—	2	1	no	—
29	Dic₄₆	—	2	1	no	—
30	C₈×C₂₃	—	2	1	no	—
31	C₂₃⋊C₈	—	2	1	no	—
32	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₃	—	4	1	no	—
34	C₄×C₂₃	—	4	1	no	—
35	C₄×C₂₃	#41	1	1	yes	characteristic
36	C₄×C₂₃	#41	1	1	yes	characteristic
37	Dic₂₃	—	2	1	no	—
38	Dic₂₃	—	2	1	no	—
39	Dic₂₃	—	4	1	no	—
40	Dic₂₃	—	4	1	no	—
41	#491	—	23	1	no	maximal, Sylow
42	C₂×C₂₃	#124	1	1	yes	characteristic
43	C₂×C₂₃	#137	1	1	yes	characteristic
44	C₂×C₂₃	#137	1	1	yes	characteristic
45	C₄⋊Q₈	—	23	1	no	—
46	#125	—	23	1	no	—
47	#103	—	23	1	no	—
48	#103	—	23	1	no	—
49	#103	—	23	1	no	—
50	#103	D₂₃	1	1	yes	characteristic
51	#97	—	23	1	no	—
52	C₂₃	#491	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	23	1	no	—
54	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
55	C₂×C₈	—	23	1	no	—
56	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
57	C₄⋊C₄	—	23	1	no	—
58	C₄⋊C₄	—	46	1	no	—
59	C₄⋊C₄	—	46	1	no	—
60	C₄⋊C₄	—	46	1	no	—
61	C₄⋊C₄	—	46	1	no	—
62	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
63	C₄²	—	23	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	46	1	no	—
67	Q₈	—	46	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	23	1	no	—
71	C₂×C₄	—	23	1	no	—
72	C₂×C₄	—	46	1	no	—
73	C₂×C₄	—	46	1	no	—
74	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	46	1	no	—
77	C₂²	D₄×D₂₃	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	46	1	no	—
81	C₄	—	46	1	no	—
82	C₄	—	92	1	no	—
83	C₄	—	92	1	no	—
84	C₄	#67288	1	1	yes	characteristic
85	C₄	#67290	1	1	yes	characteristic
86	C₂	#10625056	1	1	yes	characteristic
87	C₂	#10625086	1	1	yes	characteristic
88	C₂	#10625089	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	#491
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
52. C₂₃	#491	semidirect

Maximal subgroups

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

subgroup	index
#10625115	2
#10625061	2
C₂₃×#103	2
#10625017	2
#10624998	2
#10624997	2
#10624992	2
#491	23