Subgroups — #13092558

Order 1472.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#10625101	C₂	1	1	yes	maximal, characteristic
3	C₂×#67263	C₂	1	2	yes	maximal, complemented
4	C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10624998	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₂₃	—	2	1	no	—
8	C₂²×Dic₂₃	—	2	1	no	—
9	C₂×D₉₂	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₆	—	2	1	no	—
11	C₂×Dic₄₆	—	2	4	no	—
12	C₂×Dic₄₆	C₂²	1	2	yes	—
13	C₂×C₈×C₂₃	C₂²	1	2	yes	—
14	(C₂×D₂₃)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
16	#67263	—	2	4	no	—
17	C₂³×C₂₃	D₄	1	1	yes	characteristic
18	C₂²×D₂₃	—	2	1	no	—
19	C₂×C₄×C₂₃	—	2	2	no	—
20	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
22	C₂²⋊D₂₃	—	4	2	no	—
23	C₂×Dic₂₃	—	2	4	no	—
24	C₂×Dic₂₃	—	2	2	no	—
25	C₂×Dic₂₃	—	2	1	no	—
26	D₉₂	—	2	2	no	—
27	Dic₄₆	—	2	4	no	—
28	Dic₄₆	—	2	2	no	—
29	Dic₄₆	D₄	1	4	yes	complemented
30	C₈×C₂₃	—	2	2	no	—
31	C₂²×C₂₃	—	2	1	no	—
32	C₂²×C₂₃	—	2	1	no	—
33	C₂²×C₂₃	SD₁₆	1	2	yes	complemented
34	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
35	C₂×D₂₃	—	4	1	no	—
36	C₂×D₂₃	—	4	1	no	—
37	C₂×D₂₃	—	4	1	no	—
38	C₄×C₂₃	—	2	1	no	—
39	C₄×C₂₃	C₂×D₄	1	2	yes	—
40	Dic₂₃	—	2	4	no	—
41	Dic₂₃	—	4	1	no	—
42	#448	—	23	1	no	maximal, Sylow
43	C₂×C₂₃	—	2	2	no	—
44	C₂×C₂₃	#120	1	1	yes	characteristic
45	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
46	C₂×C₂₃	#137	1	1	yes	characteristic
47	D₂₃	—	8	1	no	—
48	C₂²×Q₈	—	23	1	no	—
49	C₂×SD₁₆	—	23	2	no	—
50	#121	—	23	1	no	—
51	#103	—	23	2	no	—
52	C₂²⋊C₈	D₂₃	1	1	yes	characteristic, complemented
53	C₂₃	#448	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	23	2	no	—
55	C₂×Q₈	—	46	4	no	—
56	C₂×Q₈	—	46	1	no	—
57	C₂×D₄	—	23	1	no	—
58	C₂×D₄	—	46	1	no	—
59	C₂²×C₄	—	46	1	no	—
60	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
61	SD₁₆	—	46	4	no	—
62	C₂×C₈	C₂×D₂₃	1	2	yes	—
63	C₄⋊C₄	—	23	1	no	—
64	C₂²⋊C₄	—	46	1	no	—
65	C₂³	—	46	1	no	—
66	C₂³	D₉₂	1	1	yes	characteristic
67	Q₈	—	23	4	no	—
68	Q₈	—	46	4	no	—
69	Q₈	—	46	2	no	—
70	D₄	—	46	2	no	—
71	D₄	—	92	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	46	4	no	—
74	C₂×C₄	—	46	2	no	—
75	C₂×C₄	—	46	1	no	—
76	C₂×C₄	D₉₂	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₂²	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	92	1	no	—
82	C₂²	—	92	1	no	—
83	C₂²	—	92	1	no	—
84	C₂²	#67263	1	2	yes	complemented
85	C₂²	C₂×D₉₂	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	46	4	no	—
88	C₄	—	92	1	no	—
89	C₄	D₄×D₂₃	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	—	184	1	no	—
92	C₂	#10625053	1	1	yes	characteristic
93	C₂	C₂×#67263	1	1	yes	characteristic
94	C₂	#10625080	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×C₂²⋊C₈	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	#10625101	C₂
hypercenter	C₂²⋊C₈	D₂₃
hypocenter	C₂₃	#448
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₄₆	C₂	semidirect
3. C₂×#67263	C₂	semidirect
4. C₂₃×C₂²⋊C₈	C₂	semidirect
5. #10624998	C₂	semidirect
29. Dic₄₆	D₄	semidirect
33. C₂²×C₂₃	SD₁₆	semidirect
52. C₂²⋊C₈	D₂₃	semidirect
53. C₂₃	#448	semidirect
84. C₂²	#67263	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₆	2
#10625101	2
C₂×#67263	2
C₂₃×C₂²⋊C₈	2
#10624998	2
#448	23