Subgroups — #13092208

Order 1472.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625106	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#100	C₂	1	1	yes	maximal, characteristic
3	#10625016	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂²×Dic₂₃	C₄	1	1	yes	characteristic, complemented
6	M₁₆×C₂₃	—	2	1	no	—
7	C₂²⋊Dic₂₃	—	2	1	no	—
8	C₂²⋊Dic₂₃	—	2	1	no	—
9	C₂²⋊Dic₂₃	C₄	1	1	yes	characteristic, complemented
10	Dic₂₃⋊C₄	—	2	1	no	—
11	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₂₃	D₄	1	1	yes	characteristic
13	D₄×C₂₃	—	4	1	no	—
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	1	no	—
16	C₂×Dic₂₃	—	2	1	no	—
17	C₂×Dic₂₃	—	4	1	no	—
18	C₂×Dic₂₃	—	4	1	no	—
19	C₈×C₂₃	—	4	1	no	—
20	C₂²×C₂₃	—	2	1	no	—
21	C₂²×C₂₃	—	2	1	no	—
22	C₂²×C₂₃	—	4	1	no	—
23	C₂²×C₂₃	—	4	1	no	—
24	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₂₃	—	2	1	no	—
26	Dic₂₃	—	4	1	no	—
27	Dic₂₃	—	4	1	no	—
28	Dic₂₃	—	8	1	no	—
29	#352	—	23	1	no	maximal, Sylow
30	C₂×C₂₃	—	2	1	no	—
31	C₂×C₂₃	—	4	1	no	—
32	C₂×C₂₃	—	4	1	no	—
33	C₂×C₂₃	#99	1	1	yes	characteristic
34	#123	—	23	1	no	—
35	#100	D₂₃	1	1	yes	characteristic
36	#99	—	23	1	no	—
37	C₂₃	#352	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₄	C₂×D₂₃	1	1	yes	characteristic
39	C₂²×C₄	—	23	1	no	—
40	M₁₆	—	2	1	no	—
41	C₄⋊C₄	—	46	1	no	—
42	C₂²⋊C₄	—	23	1	no	—
43	C₂²⋊C₄	—	46	1	no	—
44	C₂²⋊C₄	—	46	1	no	—
45	C₂³	C₄×D₂₃	1	1	yes	characteristic
46	C₂³	D₉₂	1	1	yes	characteristic
47	D₄	—	4	1	no	—
48	C₂×C₄	—	46	1	no	—
49	C₂×C₄	—	46	1	no	—
50	C₂×C₄	—	92	1	no	—
51	C₂×C₄	—	92	1	no	—
52	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
53	C₈	—	4	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	4	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	92	1	no	—
61	C₄	—	92	1	no	—
62	C₄	—	184	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	4	1	no	—
66	C₂	#10624988	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10624988
commutator	C₂³×C₂₃	C₂×C₄
Frattini	C₂×D₄	C₂×D₂₃
Fitting	C₂₃×#100	C₂
socle	C₂×C₂₃	#99
prime radical, cosocle	C₂×D₄×C₂₃	C₂²
hypercenter	#100	D₂₃
hypocenter	C₂₃	#352
LCS	G ▷ C₂³×C₂₃ ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #100

Complements

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

N	H ≅ G/N	type
5. C₂²×Dic₂₃	C₄	semidirect
9. C₂²⋊Dic₂₃	C₄	semidirect
37. C₂₃	#352	semidirect

Maximal subgroups

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

subgroup	index
#10625106	2
C₂₃×#100	2
#10625016	2
#352	23