Subgroups — #15671308

Order 2944.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092474	C₂	1	2	yes	maximal
2	C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₂₃	C₄	1	2	yes	—
4	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
5	C₂₃×C₄⋊C₈	—	2	2	no	—
6	C₂²⋊(C₂₃⋊C₈)	C₄	1	4	yes	—
7	C₄⋊(C₂₃⋊C₈)	—	2	2	no	—
8	#10624985	—	2	2	no	—
9	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
11	M₁₆×C₂₃	—	4	2	no	—
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₄²×C₂₃	D₄	1	1	yes	characteristic
14	C₄²×C₂₃	D₄	1	2	yes	—
15	C₄²×C₂₃	Q₈	1	1	yes	characteristic
16	C₂×C₂₃⋊C₈	—	2	4	no	—
17	C₂³×C₂₃	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	1	no	—
19	C₂×C₄×C₂₃	—	2	1	no	—
20	C₂×C₄×C₂₃	—	4	2	no	—
21	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
25	C₈×C₂₃	—	4	2	no	—
26	C₂₃⋊C₈	—	4	4	no	—
27	#1307	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	—	2	1	no	—
29	C₂²×C₂₃	—	2	2	no	—
30	C₂²×C₂₃	#95	1	1	yes	characteristic
31	C₄×C₂₃	—	2	1	no	—
32	C₄×C₂₃	—	2	2	no	—
33	C₄×C₂₃	—	2	2	no	—
34	C₄×C₂₃	#100	1	1	yes	characteristic
35	C₄×C₂₃	#101	1	1	yes	characteristic
36	#432	—	23	2	no	—
37	#423	D₂₃	1	1	yes	characteristic
38	C₂×C₂₃	—	4	1	no	—
39	C₂×C₂₃	#343	1	1	yes	characteristic
40	C₂×C₂₃	#344	1	2	yes	—
41	C₂×M₁₆	Dic₂₃	1	2	yes	—
42	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
43	C₄⋊C₈	—	2	2	no	—
44	C₄⋊C₈	—	46	2	no	—
45	C₂²⋊C₈	—	23	4	no	—
46	#97	—	46	2	no	—
47	C₂₃	#1307	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	C₄×D₂₃	1	2	yes	—
49	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
50	M₁₆	—	4	2	no	—
51	C₂×C₈	—	2	2	no	—
52	C₂×C₈	—	46	4	no	—
53	C₄²	Dic₄₆	1	1	yes	characteristic
54	C₄²	D₉₂	1	1	yes	characteristic
55	C₄²	C₂²⋊D₂₃	1	2	yes	—
56	C₂³	C₄×Dic₂₃	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	Dic₂₃⋊C₄	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
62	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
63	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
64	C₈	—	4	2	no	—
65	C₈	—	92	4	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂₃⋊#95	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	2	no	—
72	C₄	#10625015	1	1	yes	characteristic
73	C₄	#10625018	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	#13092186	1	1	yes	characteristic
76	C₂	#13092189	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂₃⋊#95
commutator, prime radical	C₂³×C₂₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₃
Fitting	C₂₃×#423	C₂
socle	C₂²×C₂₃	#95
cosocle	C₂×C₄²×C₂₃	C₂²
hypercenter	#423	D₂₃
hypocenter	C₂₃	#1307
LCS	G ▷ C₂³×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
47. C₂₃	#1307	semidirect

Maximal subgroups

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

subgroup	index
#13092474	2
C₂₃×#423	2
#1307	23