Subgroups — #13092761

Order 1472.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625068	C₂	1	1	yes	maximal, characteristic
2	#10625063	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₂₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#10624998	C₂	1	1	yes	maximal, characteristic, complemented
6	#10624992	C₂	1	1	yes	maximal, characteristic, complemented
7	#10624989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₃	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⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
13	(C₂×D₂₃)⋊C₄	—	2	1	no	—
14	(C₂×D₂₃)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₂₃	—	2	1	no	—
16	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
17	C₄×Dic₂₃	—	2	1	no	—
18	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₂₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₂₃	—	2	1	no	—
24	C₂×Dic₂₃	—	2	1	no	—
25	C₂×Dic₂₃	D₄	1	1	yes	characteristic
26	C₄×D₂₃	—	2	1	no	—
27	C₄×D₂₃	—	2	1	no	—
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	C₂×D₂₃	—	2	1	no	—
34	C₂×D₂₃	—	2	1	no	—
35	C₂×D₂₃	—	2	1	no	—
36	C₄×C₂₃	—	4	1	no	—
37	C₄×C₂₃	—	4	1	no	—
38	C₄×C₂₃	#41	1	1	yes	characteristic
39	C₄×C₂₃	#41	1	1	yes	characteristic
40	Dic₂₃	—	2	1	no	—
41	Dic₂₃	—	4	1	no	—
42	Dic₂₃	—	4	1	no	—
43	#485	—	23	1	no	maximal, Sylow
44	C₂×C₂₃	#123	1	1	yes	characteristic
45	C₂×C₂₃	#135	1	1	yes	characteristic
46	C₂×C₂₃	#137	1	1	yes	characteristic
47	D₂₃	—	4	1	no	—
48	C₂²⋊Q₈	—	23	1	no	—
49	#117	—	23	1	no	—
50	#107	—	23	1	no	—
51	#106	D₂₃	1	1	yes	characteristic, complemented
52	#103	—	23	1	no	—
53	#103	—	23	1	no	—
54	C₂²⋊C₈	—	23	1	no	—
55	C₂₃	#485	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	23	1	no	—
57	C₂²×C₄	—	23	1	no	—
58	C₂×C₈	—	23	1	no	—
59	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
60	C₄⋊C₄	—	23	1	no	—
61	C₄⋊C₄	—	46	1	no	—
62	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
64	C₂²⋊C₄	—	46	1	no	—
65	C₂²⋊C₄	—	46	1	no	—
66	C₄²	—	46	1	no	—
67	C₂³	—	23	1	no	—
68	Q₈	—	46	1	no	—
69	Q₈	—	46	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	23	1	no	—
73	C₂×C₄	—	46	1	no	—
74	C₂×C₄	—	46	1	no	—
75	C₂×C₄	—	46	1	no	—
76	C₂×C₄	—	46	1	no	—
77	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	46	1	no	—
80	C₂²	—	46	1	no	—
81	C₂²	—	46	1	no	—
82	C₂²	—	46	1	no	—
83	C₂²	D₄×D₂₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	46	1	no	—
87	C₄	—	92	1	no	—
88	C₄	—	92	1	no	—
89	C₄	#67288	1	1	yes	characteristic
90	C₄	#67292	1	1	yes	characteristic
91	C₂	—	92	1	no	—
92	C₂	#10625065	1	1	yes	characteristic
93	C₂	#10625086	1	1	yes	characteristic
94	C₂	#10625087	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#106	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂²×D₂₃	D₄
hypercenter	#106	D₂₃
hypocenter	C₂₃	#485
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. C₂₃×#106	C₂	semidirect
5. #10624998	C₂	semidirect
6. #10624992	C₂	semidirect
7. #10624989	C₂	semidirect
51. #106	D₂₃	semidirect
55. C₂₃	#485	semidirect

Maximal subgroups

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

subgroup	index
#10625068	2
#10625063	2
C₂₃×#106	2
(C₂×D₂₃)⋊C₈	2
#10624998	2
#10624992	2
#10624989	2
#485	23