Subgroups — #15675002

Order 2944.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10624994	C₂	1	2	yes	maximal
2	#13092195	C₂	1	4	yes	maximal, complemented
3	C₂₃×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×#117	C₄	1	1	yes	characteristic
7	C₂₃×#97	C₂²	1	2	yes	—
8	C₄×C₈×C₂₃	C₄	1	2	yes	—
9	#10624994	C₄	1	4	yes	complemented
10	#10624994	C₂²	1	4	yes	—
11	C₂×C₂₃⋊C₁₆	C₄	1	4	yes	complemented
12	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₂₃	—	2	2	no	—
14	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₂₃	—	2	1	no	—
20	C₂²⋊C₄×C₂₃	—	2	1	no	—
21	C₄²×C₂₃	C₂×C₄	1	2	yes	—
22	C₂₃⋊C₁₆	C₂×C₄	1	8	yes	—
23	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₂₃	—	2	2	no	—
25	C₂×C₄×C₂₃	C₄²	1	2	yes	—
26	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₂₃	M₁₆	1	2	yes	—
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₂₃	—	2	2	no	—
30	C₈×C₂₃	C₄²	1	1	yes	characteristic
31	C₈×C₂₃	C₄²	1	1	yes	characteristic
32	C₈×C₂₃	C₂²×C₄	1	2	yes	—
33	#2110	—	23	1	no	maximal, Sylow
34	C₂²×C₂₃	—	4	1	no	—
35	C₂²×C₂₃	#97	1	2	yes	—
36	C₂²×C₂₃	C₂×M₁₆	1	1	yes	characteristic
37	C₄×C₂₃	—	4	2	no	—
38	C₄×C₂₃	#97	1	2	yes	—
39	C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
41	C₂×M₃₂	—	23	2	no	—
42	#405	D₂₃	1	1	yes	characteristic
43	#347	—	23	4	no	—
44	C₂×C₂₃	—	2	1	no	—
45	C₂×C₂₃	—	2	2	no	—
46	C₂×C₂₃	C₂×#97	1	1	yes	characteristic
47	C₂×M₁₆	Dic₂₃	1	1	yes	characteristic
48	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
49	#117	Dic₂₃	1	1	yes	characteristic
50	M₃₂	—	23	4	no	—
51	M₃₂	—	23	4	no	—
52	C₂×C₁₆	—	23	4	no	—
53	#97	C₂×D₂₃	1	2	yes	—
54	C₄×C₈	Dic₂₃	1	2	yes	—
55	C₂₃	#2110	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
57	M₁₆	—	2	2	no	—
58	C₂×C₈	C₄×D₂₃	1	2	yes	—
59	C₂×C₈	C₄×D₂₃	1	2	yes	—
60	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
61	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
62	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×Dic₂₃	1	2	yes	—
66	C₁₆	—	23	8	no	—
67	C₂³	#67267	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	#67267	1	2	yes	—
70	C₂×C₄	#67267	1	1	yes	characteristic
71	C₂×C₄	C₄×Dic₂₃	1	2	yes	—
72	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₈	C₄×Dic₂₃	1	1	yes	characteristic
75	C₈	C₄×Dic₂₃	1	1	yes	characteristic
76	C₈	C₂×C₄×D₂₃	1	2	yes	—
77	C₂²	—	4	1	no	—
78	C₂²	#10624985	1	2	yes	—
79	C₂²	C₂×#67267	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#10624985	1	2	yes	—
82	C₄	C₂×#67267	1	1	yes	characteristic
83	C₄	C₂×C₄×Dic₂₃	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#10624985	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₂₃
commutator	C₄×C₂₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#405	C₂
socle	C₂×C₂₃	C₂×#97
prime radical	C₂³×C₂₃	M₁₆
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	#405	D₂₃
hypocenter	C₂₃	#2110
LCS	G ▷ C₄×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13092195	C₂	semidirect
9. #10624994	C₄	semidirect
11. C₂×C₂₃⋊C₁₆	C₄	semidirect
55. C₂₃	#2110	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10624994	2
#13092195	2
C₂₃×#405	2
#2110	23