Subgroups — #15671385

Order 2944.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092199	C₂	1	1	yes	maximal, characteristic
2	#13092174	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#470	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₃	C₄	1	1	yes	characteristic, complemented
5	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×C₂²⋊Q₈	—	2	1	no	—
7	#10625097	—	2	1	no	—
8	C₂₃×#106	C₄	1	1	yes	characteristic, complemented
9	C₂₃×#103	—	2	1	no	—
10	#10624994	—	2	1	no	—
11	C₂×Q₈×C₂₃	—	2	1	no	—
12	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
13	Q₁₆×C₂₃	—	4	1	no	—
14	M₁₆×C₂₃	—	4	1	no	—
15	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₂₃	—	2	1	no	—
18	C₄⋊C₄×C₂₃	—	4	1	no	—
19	C₂²⋊C₄×C₂₃	—	4	1	no	—
20	C₂²⋊Dic₂₃	—	4	1	no	—
21	C₄⋊Dic₂₃	—	4	1	no	—
22	C₄×Dic₂₃	—	2	2	no	—
23	C₂₃⋊C₁₆	—	4	1	no	—
24	C₂³×C₂₃	D₈	1	1	yes	characteristic
25	Q₈×C₂₃	—	4	1	no	—
26	Q₈×C₂₃	—	4	1	no	—
27	C₂×C₄×C₂₃	—	2	1	no	—
28	C₂×C₄×C₂₃	—	2	1	no	—
29	C₂×C₄×C₂₃	—	4	1	no	—
30	C₂×C₄×C₂₃	—	4	1	no	—
31	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₃	SD₁₆	1	1	yes	characteristic
33	C₂×Dic₂₃	—	4	2	no	—
34	C₈×C₂₃	—	2	1	no	—
35	C₈×C₂₃	—	2	1	no	—
36	#1340	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	1	no	—
38	C₂²×C₂₃	—	4	1	no	—
39	C₂²×C₂₃	#102	1	1	yes	characteristic
40	C₄×C₂₃	—	2	1	no	—
41	C₄×C₂₃	—	8	1	no	—
42	C₄×C₂₃	—	8	1	no	—
43	C₄×C₂₃	#99	1	1	yes	characteristic
44	C₄×C₂₃	#104	1	1	yes	characteristic
45	Dic₂₃	—	8	2	no	—
46	#470	D₂₃	1	1	yes	characteristic
47	#349	—	23	1	no	—
48	H(3,ℤ/4)	—	23	1	no	—
49	C₂×C₂₃	—	2	1	no	—
50	C₂×C₂₃	—	4	1	no	—
51	C₂×C₂₃	#327	1	1	yes	characteristic
52	C₂×Q₁₆	Dic₂₃	1	1	yes	characteristic, complemented
53	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
54	C₂²⋊Q₈	—	2	1	no	—
55	#117	—	46	1	no	—
56	M₃₂	—	46	1	no	—
57	#106	Dic₂₃	1	1	yes	characteristic, complemented
58	#103	—	2	1	no	—
59	C₂₃	#1340	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	92	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	92	1	no	—
71	C₄²	—	46	2	no	—
72	C₁₆	—	92	1	no	—
73	C₂³	#67272	1	1	yes	characteristic
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	92	2	no	—
81	C₂×C₄	#67273	1	1	yes	characteristic
82	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#10625014	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	8	1	no	—
90	C₄	—	8	1	no	—
91	C₄	—	184	2	no	—
92	C₄	#10625016	1	1	yes	characteristic
93	C₄	#10625019	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#13092151	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092151
commutator	C₂×C₈×C₂₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₂₃
Fitting	C₂₃×#470	C₂
socle	C₂×C₂₃	#327
prime radical	C₂³×C₂₃	D₈
cosocle	C₂×M₁₆×C₂₃	C₂²
hypercenter	#470	D₂₃
hypocenter	C₂₃	#1340
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

Complements

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

N	H ≅ G/N	type
4. C₂×Q₁₆×C₂₃	C₄	semidirect
8. C₂₃×#106	C₄	semidirect
52. C₂×Q₁₆	Dic₂₃	semidirect
57. #106	Dic₂₃	semidirect
59. C₂₃	#1340	semidirect

Maximal subgroups

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

subgroup	index
#13092199	2
#13092174	2
C₂₃×#470	2
#1340	23