Subgroups — #13092695

Order 1472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625059	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#102	C₂	1	1	yes	maximal, characteristic
4	#10625014	C₂	1	1	yes	maximal, characteristic
5	#10625000	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#10624989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₃	—	2	1	no	—
10	C₂×Dic₄₆	—	2	1	no	—
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₂₃	—	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	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₂₃	—	2	1	no	—
20	D₄×C₂₃	—	2	1	no	—
21	D₄×C₂₃	Q₈	1	2	yes	complemented
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	—	4	2	no	—
27	C₂×Dic₂₃	D₄	1	1	yes	characteristic
28	C₂×Dic₂₃	D₄	1	1	yes	characteristic
29	Dic₄₆	—	4	2	no	—
30	C₈×C₂₃	—	2	1	no	—
31	C₂₃⋊C₈	—	2	1	no	—
32	C₂²×C₂₃	—	2	2	no	—
33	C₂²×C₂₃	—	4	1	no	—
34	C₂²×C₂₃	—	4	1	no	—
35	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
36	C₄×C₂₃	—	4	1	no	—
37	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₂₃	#41	1	1	yes	characteristic
39	Dic₂₃	—	2	1	no	—
40	Dic₂₃	—	4	1	no	—
41	Dic₂₃	—	4	1	no	—
42	Dic₂₃	D₈	1	2	yes	—
43	#474	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	—	4	2	no	—
45	C₂×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
46	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
47	C₂×C₂₃	#137	1	1	yes	characteristic
48	C₄⋊Q₈	—	23	1	no	—
49	C₄×D₄	—	23	1	no	—
50	#107	—	23	1	no	—
51	#107	—	23	1	no	—
52	C₄⋊C₈	—	23	1	no	—
53	#102	—	23	1	no	—
54	#102	D₂₃	1	1	yes	characteristic
55	C₂₃	#474	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	46	1	no	—
57	C₂×D₄	C₂×D₂₃	1	1	yes	characteristic
58	C₂²×C₄	—	46	1	no	—
59	C₂×C₈	—	23	1	no	—
60	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
61	C₄⋊C₄	—	23	1	no	—
62	C₄⋊C₄	—	23	1	no	—
63	C₄⋊C₄	—	46	1	no	—
64	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
65	C₂²⋊C₄	—	46	1	no	—
66	C₄²	—	23	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	92	2	no	—
69	D₄	—	2	1	no	—
70	D₄	Dic₄₆	1	2	yes	complemented
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	23	1	no	—
73	C₂×C₄	—	23	1	no	—
74	C₂×C₄	—	46	1	no	—
75	C₂×C₄	—	46	1	no	—
76	C₂×C₄	—	92	2	no	—
77	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	46	1	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₂₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	23	2	no	—
86	C₄	—	46	1	no	—
87	C₄	—	92	1	no	—
88	C₄	—	92	1	no	—
89	C₄	C₂×Dic₄₆	1	1	yes	characteristic
90	C₄	#67290	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	#10625049	1	1	yes	characteristic
93	C₂	D₈×D₂₃	1	1	yes	characteristic
94	C₂	#10625086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#102	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂×D₄×C₂₃	C₂²
hypercenter	#102	D₂₃
hypocenter	C₂₃	#474
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
2. #10625059	C₂	semidirect
5. #10625000	C₂	semidirect
6. Dic₂₃⋊C₈	C₂	semidirect
7. #10624989	C₂	semidirect
21. D₄×C₂₃	Q₈	semidirect
55. C₂₃	#474	semidirect
70. D₄	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₂₃	2
#10625059	2
C₂₃×#102	2
#10625014	2
#10625000	2
Dic₂₃⋊C₈	2
#10624989	2
#474	23