Subgroups — #15671349

Order 2944.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092445	C₂	1	1	yes	maximal, characteristic
2	#13092199	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	#10625097	C₄	1	1	yes	characteristic
6	C₂²×C₂₃⋊C₈	C₄	1	1	yes	characteristic
7	C₂₃×M₃₂	—	2	1	no	—
8	Dic₂₃⋊C₈	—	2	1	no	—
9	Dic₂₃⋊C₈	—	2	1	no	—
10	#10624994	—	2	1	no	—
11	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	M₁₆×C₂₃	—	4	1	no	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₂²⋊Dic₂₃	C₈	1	2	yes	—
16	C₄⋊Dic₂₃	—	2	1	no	—
17	C₄×Dic₂₃	—	2	1	no	—
18	C₂×C₂₃⋊C₈	—	2	1	no	—
19	C₂×C₂₃⋊C₈	—	4	1	no	—
20	C₁₆×C₂₃	—	4	1	no	—
21	C₂₃⋊C₁₆	—	4	1	no	—
22	C₂³×C₂₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₂₃	—	2	1	no	—
24	C₂×C₄×C₂₃	—	2	1	no	—
25	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
27	C₂×Dic₂₃	—	2	2	no	—
28	C₈×C₂₃	—	2	1	no	—
29	C₈×C₂₃	—	2	1	no	—
30	C₂₃⋊C₈	—	4	1	no	—
31	#1328	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	—	2	1	no	—
33	C₂²×C₂₃	—	4	1	no	—
34	C₂²×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
35	C₄×C₂₃	—	2	1	no	—
36	C₄×C₂₃	#99	1	1	yes	characteristic
37	C₄×C₂₃	#101	1	1	yes	characteristic
38	Dic₂₃	—	4	2	no	—
39	#424	—	23	1	no	—
40	#349	—	23	1	no	—
41	#349	D₂₃	1	1	yes	characteristic
42	C₂×C₂₃	—	2	1	no	—
43	C₂×C₂₃	—	4	1	no	—
44	C₂×C₂₃	#324	1	1	yes	characteristic
45	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
46	C₂²×C₈	—	23	1	no	—
47	#117	—	23	1	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	46	1	no	—
50	C₄⋊C₈	—	46	1	no	—
51	C₄⋊C₈	—	46	1	no	—
52	C₂₃	#1328	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	C₄×D₂₃	1	1	yes	characteristic
54	M₁₆	—	4	1	no	—
55	C₂×C₈	—	46	1	no	—
56	C₂×C₈	—	92	1	no	—
57	C₂×C₈	D₉₂	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	46	1	no	—
60	C₂²⋊C₄	—	23	2	no	—
61	C₄²	—	46	1	no	—
62	C₁₆	—	4	1	no	—
63	C₁₆	—	92	1	no	—
64	C₂³	C₈×D₂₃	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	46	2	no	—
68	C₂×C₄	#67262	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₈	—	92	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	92	2	no	—
78	C₄	#10624988	1	1	yes	characteristic
79	C₄	#10625006	1	1	yes	characteristic
80	C₂	—	2	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#13092142	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10624988
commutator, prime radical	C₂³×C₂₃	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₂₃
Fitting	C₂₃×#349	C₂
socle	C₂×C₂₃	#324
cosocle	C₂×M₁₆×C₂₃	C₂²
hypercenter	#349	D₂₃
hypocenter	C₂₃	#1328
LCS	G ▷ C₂³×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
52. C₂₃	#1328	semidirect

Maximal subgroups

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

subgroup	index
#13092445	2
#13092199	2
C₂₃×#349	2
#1328	23