Subgroups — #15675163

Order 2944.

152 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	#13092238	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	C₄	1	2	yes	—
8	C₄×C₈×C₂₃	C₂²	1	2	yes	—
9	#10624994	—	2	2	no	—
10	#10624994	C₂²	1	4	yes	—
11	C₂×C₂₃⋊C₁₆	—	2	2	no	—
12	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₂₃	C₈	1	4	yes	—
14	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₂₃	D₄	1	2	yes	—
17	C₂×C₈×C₂₃	Q₈	1	2	yes	—
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	—	2	4	no	—
23	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₂₃	—	2	2	no	—
25	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
30	C₈×C₂₃	C₂×C₈	1	4	yes	—
31	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
32	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
33	#2153	—	23	1	no	maximal, Sylow
34	C₂²×C₂₃	—	4	1	no	—
35	C₂²×C₂₃	C₄⋊C₈	1	2	yes	—
36	C₂²×C₂₃	C₂×M₁₆	1	1	yes	characteristic
37	C₄×C₂₃	—	4	2	no	—
38	C₄×C₂₃	C₄⋊C₈	1	2	yes	—
39	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
41	C₂×M₃₂	—	23	2	no	—
42	#405	D₂₃	1	1	yes	characteristic
43	#364	—	23	4	no	—
44	C₂×C₂₃	—	2	1	no	—
45	C₂×C₂₃	—	2	2	no	—
46	C₂×C₂₃	C₂×C₄⋊C₈	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	—	46	2	no	—
52	C₂×C₁₆	—	46	2	no	—
53	#97	Dic₂₃	1	2	yes	—
54	C₄×C₈	C₂×D₂₃	1	2	yes	—
55	C₂₃	#2153	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
57	M₁₆	C₂₃⋊C₈	1	4	yes	—
58	C₂×C₈	Dic₄₆	1	2	yes	—
59	C₂×C₈	D₉₂	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	—	46	4	no	—
67	C₂³	#67267	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₂×C₂₃⋊C₈	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	C₂×C₂₃⋊C₈	1	4	yes	—
74	C₈	C₄⋊Dic₂₃	1	2	yes	—
75	C₈	C₂×Dic₄₆	1	1	yes	characteristic
76	C₈	C₂×D₉₂	1	1	yes	characteristic
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊(C₂₃⋊C₈)	1	2	yes	—
79	C₂²	C₂×#67267	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	C₄⋊(C₂₃⋊C₈)	1	2	yes	—
82	C₄	C₂²×C₂₃⋊C₈	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×C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₉₂
commutator	C₄×C₂₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#405	C₂
socle	C₂×C₂₃	C₂×C₄⋊C₈
prime radical	C₂³×C₂₃	M₁₆
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	#405	D₂₃
hypocenter	C₂₃	#2153
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13092238	C₂	semidirect
55. C₂₃	#2153	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
#13092238	2
C₂₃×#405	2
#2153	23