Subgroups — #15675178

Order 2944.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic
2	#13092454	C₂	1	2	yes	maximal
3	#13092244	C₂	1	2	yes	maximal, complemented
4	#13092243	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
7	#10625063	—	2	2	no	—
8	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#107	C₂²	1	2	yes	—
10	#10625000	C₂²	1	2	yes	—
11	C₂×C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	#10624990	—	2	2	no	—
13	C₁₆×D₂₃	C₄	1	4	yes	complemented
14	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₂₃	—	2	2	no	—
17	(C₂×D₂₃)⋊C₄	—	4	2	no	—
18	C₄⋊Dic₂₃	—	2	2	no	—
19	C₄×Dic₂₃	—	4	2	no	—
20	C₂×C₂₃⋊C₈	D₄	1	1	yes	characteristic
21	C₈×D₂₃	C₂×C₄	1	2	yes	—
22	C₈×D₂₃	Q₈	1	2	yes	—
23	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
24	C₂₃⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂²×D₂₃	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₃	—	4	2	no	—
27	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₂₃	—	4	2	no	—
29	C₂×Dic₂₃	D₈	1	1	yes	characteristic
30	C₄×D₂₃	C₄⋊C₄	1	2	yes	—
31	C₄×D₂₃	Q₁₆	1	2	yes	—
32	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
34	C₂₃⋊C₈	C₄⋊C₄	1	2	yes	—
35	#2158	—	23	1	no	maximal, Sylow
36	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
37	C₂×D₂₃	—	2	1	no	—
38	C₂×D₂₃	—	2	1	no	—
39	C₂×D₂₃	#107	1	2	yes	—
40	C₄×C₂₃	—	8	2	no	—
41	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
43	Dic₂₃	—	8	2	no	—
44	Dic₂₃	#107	1	2	yes	—
45	C₂²×C₁₆	—	23	1	no	—
46	#427	—	23	2	no	—
47	#367	—	23	2	no	—
48	#366	—	23	1	no	—
49	#366	D₂₃	1	1	yes	characteristic, complemented
50	C₂×C₂₃	C₂×#107	1	1	yes	characteristic
51	C₂×C₂₃	#508	1	1	yes	characteristic
52	C₂×C₂₃	#508	1	1	yes	characteristic
53	D₂₃	—	2	2	no	—
54	C₂²×C₈	—	23	1	no	—
55	#117	—	46	2	no	—
56	C₂×C₁₆	—	23	1	no	—
57	C₂×C₁₆	—	23	4	no	—
58	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
59	#107	—	23	2	no	—
60	#107	C₂×D₂₃	1	2	yes	—
61	#106	—	46	2	no	—
62	C₂₃	#2158	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₄	—	23	1	no	—
64	C₂×C₈	—	23	1	no	—
65	C₂×C₈	—	23	2	no	—
66	C₂×C₈	—	23	2	no	—
67	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
68	C₄⋊C₄	—	2	2	no	—
69	C₄⋊C₄	—	46	2	no	—
70	C₂²⋊C₄	—	92	2	no	—
71	C₄²	—	92	2	no	—
72	C₁₆	—	23	2	no	—
73	C₁₆	C₄×D₂₃	1	2	yes	—
74	C₂³	—	23	1	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	23	1	no	—
77	C₂×C₄	—	23	2	no	—
78	C₂×C₄	—	23	2	no	—
79	C₂×C₄	—	92	2	no	—
80	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
81	C₈	—	23	2	no	—
82	C₈	C₂×C₄×D₂₃	1	1	yes	characteristic
83	C₈	Q₈×D₂₃	1	1	yes	characteristic
84	C₂²	—	23	2	no	—
85	C₂²	—	46	1	no	—
86	C₂²	—	46	1	no	—
87	C₂²	D₈×D₂₃	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	23	2	no	—
90	C₄	—	184	2	no	—
91	C₄	C₄⋊C₄×D₂₃	1	1	yes	characteristic
92	C₄	Q₁₆×D₂₃	1	1	yes	characteristic
93	C₂	—	46	2	no	—
94	C₂	#107×D₂₃	1	1	yes	characteristic
95	C₂	#13092846	1	1	yes	characteristic
96	C₂	#13092850	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₂₃
commutator	C₈×C₂₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#366	C₂
socle	C₂²×C₂₃	C₂×D₈
prime radical	C₂²×D₂₃	D₈
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	#366	D₂₃
hypocenter	C₂₃	#2158
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
3. #13092244	C₂	semidirect
4. #13092243	C₂	semidirect
5. C₂₃×#366	C₂	semidirect
13. C₁₆×D₂₃	C₄	semidirect
49. #366	D₂₃	semidirect
62. C₂₃	#2158	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₂₃	2
#13092454	2
#13092244	2
#13092243	2
C₂₃×#366	2
#2158	23