Subgroups — #15671267

Order 2944.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092474	C₂	1	2	yes	maximal
2	C₂×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×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)	—	2	2	no	—
7	C₄⋊(C₂₃⋊C₈)	—	2	2	no	—
8	#10624985	C₄	1	4	yes	—
9	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₃	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₂×C₈×C₂₃	—	4	2	no	—
14	C₄²×C₂₃	C₂×C₄	1	2	yes	—
15	C₄²×C₂₃	D₄	1	2	yes	—
16	C₂×C₂₃⋊C₈	—	2	4	no	—
17	C₂³×C₂₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	2	no	—
19	C₂×C₄×C₂₃	—	2	1	no	—
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	—	4	1	no	—
22	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
26	C₈×C₂₃	—	4	2	no	—
27	C₂₃⋊C₈	—	4	4	no	—
28	#1290	—	23	1	no	maximal, Sylow
29	C₂²×C₂₃	—	2	1	no	—
30	C₂²×C₂₃	—	2	1	no	—
31	C₂²×C₂₃	#95	1	1	yes	characteristic
32	C₂²×C₂₃	#108	1	2	yes	—
33	C₄×C₂₃	—	2	2	no	—
34	C₄×C₂₃	—	2	2	no	—
35	C₄×C₂₃	—	2	1	no	—
36	C₄×C₂₃	#100	1	1	yes	characteristic
37	C₄×C₂₃	#101	1	1	yes	characteristic
38	#432	—	23	2	no	—
39	C₂×C₄⋊C₈	D₂₃	1	1	yes	characteristic
40	C₂×C₂₃	—	2	2	no	—
41	C₂×C₂₃	H(3,ℤ/4)	1	1	yes	characteristic
42	C₂×C₂₃	#341	1	1	yes	characteristic
43	C₂×C₂₃	#343	1	1	yes	characteristic
44	C₂²×C₈	Dic₂₃	1	2	yes	—
45	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
46	C₄⋊C₈	—	2	2	no	—
47	C₄⋊C₈	—	46	2	no	—
48	C₂²⋊C₈	—	46	2	no	—
49	#97	—	23	4	no	—
50	C₂₃	#1290	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	Dic₄₆	1	1	yes	characteristic
52	C₂²×C₄	D₉₂	1	1	yes	characteristic
53	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	—	4	2	no	—
56	C₂×C₈	—	46	4	no	—
57	C₄²	C₄×D₂₃	1	2	yes	—
58	C₄²	C₂²⋊D₂₃	1	2	yes	—
59	C₂³	C₄⋊Dic₂₃	1	1	yes	characteristic
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
65	C₂×C₄	Dic₂₃⋊C₄	1	2	yes	—
66	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
67	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
68	C₈	—	4	2	no	—
69	C₈	—	92	4	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	2	1	no	—
72	C₂²	#10625001	1	2	yes	—
73	C₂²	C₂₃⋊#95	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	#10625015	1	1	yes	characteristic
78	C₄	#10625018	1	1	yes	characteristic
79	C₂	—	2	2	no	—
80	C₂	#13092174	1	1	yes	characteristic
81	C₂	#13092182	1	1	yes	characteristic
82	C₂	#13092186	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂₃⋊#95
commutator	C₂×C₄×C₂₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₃
Fitting	C₂×C₂₃×C₄⋊C₈	C₂
socle	C₂²×C₂₃	#95
prime radical	C₂³×C₂₃	C₄⋊C₄
cosocle	C₂×C₄²×C₂₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₃
hypocenter	C₂₃	#1290
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
50. C₂₃	#1290	semidirect

Maximal subgroups

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

subgroup	index
#13092474	2
C₂×C₂₃×C₄⋊C₈	2
#1290	23