Subgroups — #15671348

Order 2944.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092199	C₂	1	2	yes	maximal
2	C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₂₃	C₄	1	1	yes	characteristic
4	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃×C₄⋊C₈	—	2	2	no	—
7	#10624994	—	2	2	no	—
8	C₂²×C₄×C₂₃	—	2	1	no	—
9	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
10	M₁₆×C₂₃	—	4	1	no	—
11	M₁₆×C₂₃	—	4	1	no	—
12	C₂×C₈×C₂₃	—	2	1	no	—
13	C₂×C₈×C₂₃	D₄	1	2	yes	—
14	C₄²×C₂₃	—	2	1	no	—
15	C₄²×C₂₃	C₈	1	1	yes	characteristic
16	C₄²×C₂₃	C₈	1	1	yes	characteristic
17	C₂₃⋊C₁₆	—	4	2	no	—
18	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₃	—	2	1	no	—
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	—	2	1	no	—
23	C₂×C₄×C₂₃	—	4	2	no	—
24	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
26	C₈×C₂₃	—	2	2	no	—
27	C₈×C₂₃	—	4	1	no	—
28	#1327	—	23	1	no	maximal, Sylow
29	C₂²×C₂₃	—	2	1	no	—
30	C₂²×C₂₃	—	4	1	no	—
31	C₂²×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₂₃	—	2	2	no	—
33	C₄×C₂₃	—	2	1	no	—
34	C₄×C₂₃	—	4	1	no	—
35	C₄×C₂₃	#99	1	1	yes	characteristic
36	C₄×C₂₃	#101	1	1	yes	characteristic
37	#423	D₂₃	1	1	yes	characteristic
38	#349	—	23	2	no	—
39	C₂×C₂₃	—	2	1	no	—
40	C₂×C₂₃	—	4	1	no	—
41	C₂×C₂₃	#324	1	1	yes	characteristic
42	C₂×M₁₆	Dic₂₃	1	1	yes	characteristic
43	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
44	C₂×C₄²	Dic₂₃	1	1	yes	characteristic
45	M₃₂	—	46	2	no	—
46	C₄⋊C₈	—	2	2	no	—
47	C₂₃	#1327	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	2	1	no	—
49	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
50	M₁₆	—	4	1	no	—
51	M₁₆	—	4	1	no	—
52	C₂×C₈	—	2	1	no	—
53	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
54	C₄²	—	2	1	no	—
55	C₄²	C₂₃⋊C₈	1	1	yes	characteristic
56	C₄²	C₂₃⋊C₈	1	1	yes	characteristic
57	C₁₆	—	92	2	no	—
58	C₂³	#67267	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	4	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#10625016	1	1	yes	characteristic
75	C₄	#10625018	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#13092143	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10625016
commutator	C₂×C₄×C₂₃	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₂₃
Fitting	C₂₃×#423	C₂
socle	C₂×C₂₃	#324
prime radical	C₂³×C₂₃	M₁₆
cosocle	C₂×M₁₆×C₂₃	C₂²
hypercenter	#423	D₂₃
hypocenter	C₂₃	#1327
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #423

Complements

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

N	H ≅ G/N	type
47. C₂₃	#1327	semidirect

Maximal subgroups

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

subgroup	index
#13092199	2
C₂₃×#423	2
#1327	23