Subgroups — #13092746

Order 1472.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625117	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625017	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₂₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#10624999	C₂	1	1	yes	maximal, characteristic, complemented
7	#10624990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₂₃	—	2	1	no	—
10	C₂×C₄×D₂₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
13	(C₂×D₂₃)⋊C₄	—	2	1	no	—
14	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
16	Dic₂₃⋊C₄	—	2	1	no	—
17	Dic₂₃⋊C₄	—	2	1	no	—
18	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₂₃	D₄	1	1	yes	characteristic
20	Q₈×C₂₃	—	2	1	no	—
21	Q₈×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	—	2	1	no	—
23	C₂×C₄×C₂₃	—	2	1	no	—
24	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₂₃	—	2	1	no	—
26	C₂×Dic₂₃	—	2	1	no	—
27	C₂×Dic₂₃	D₄	1	1	yes	characteristic
28	C₄×D₂₃	—	2	1	no	—
29	C₄×D₂₃	—	2	1	no	—
30	C₄×D₂₃	—	4	2	no	—
31	C₈×C₂₃	—	2	1	no	—
32	C₂₃⋊C₈	—	2	1	no	—
33	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
34	C₂×D₂₃	—	2	1	no	—
35	C₂×D₂₃	—	2	1	no	—
36	C₂×D₂₃	SD₁₆	1	2	yes	—
37	C₄×C₂₃	—	4	1	no	—
38	C₄×C₂₃	—	4	1	no	—
39	C₄×C₂₃	#41	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	#483	—	23	1	no	maximal, Sylow
45	C₂×C₂₃	#123	1	1	yes	characteristic
46	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
47	C₂×C₂₃	#137	1	1	yes	characteristic
48	D₂₃	—	2	2	no	—
49	C₂²⋊Q₈	—	23	1	no	—
50	C₂×C₄⋊C₄	—	23	1	no	—
51	#106	—	23	1	no	—
52	#106	—	23	1	no	—
53	#103	—	23	1	no	—
54	#103	D₂₃	1	1	yes	characteristic, complemented
55	C₂²⋊C₈	—	23	1	no	—
56	C₂₃	#483	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
58	C₂²×C₄	—	23	1	no	—
59	C₂²×C₄	—	46	1	no	—
60	C₂×C₈	—	23	1	no	—
61	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
62	C₄⋊C₄	—	23	1	no	—
63	C₄⋊C₄	—	23	1	no	—
64	C₄⋊C₄	—	46	1	no	—
65	C₄⋊C₄	—	46	1	no	—
66	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
67	C₂²⋊C₄	—	46	1	no	—
68	C₂³	—	23	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	23	1	no	—
74	C₂×C₄	—	46	1	no	—
75	C₂×C₄	—	46	1	no	—
76	C₂×C₄	—	46	1	no	—
77	C₂×C₄	—	46	1	no	—
78	C₂×C₄	—	92	2	no	—
79	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	46	1	no	—
82	C₂²	—	23	2	no	—
83	C₂²	—	46	1	no	—
84	C₂²	—	46	1	no	—
85	C₂²	D₄×D₂₃	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	46	1	no	—
89	C₄	—	92	1	no	—
90	C₄	—	92	1	no	—
91	C₄	#67288	1	1	yes	characteristic
92	C₄	#67290	1	1	yes	characteristic
93	C₂	—	46	2	no	—
94	C₂	#10625054	1	1	yes	characteristic
95	C₂	SD₁₆×D₂₃	1	1	yes	characteristic
96	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	C₂²×C₂₃	C₂×D₄
prime radical	C₂²×D₂₃	D₄
hypercenter	#103	D₂₃
hypocenter	C₂₃	#483
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
3. C₂₃×#103	C₂	semidirect
4. #10625017	C₂	semidirect
6. #10624999	C₂	semidirect
7. #10624990	C₂	semidirect
54. #103	D₂₃	semidirect
56. C₂₃	#483	semidirect

Maximal subgroups

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

subgroup	index
#10625117	2
C₄⋊C₄×D₂₃	2
C₂₃×#103	2
#10625017	2
(C₂×D₂₃)⋊C₈	2
#10624999	2
#10624990	2
#483	23