Subgroups — #13092167

Order 1472.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₂₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₂₃	—	2	1	no	—
5	C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₈	—	2	1	no	—
7	C₂×C₂₃⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₂₃⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
11	C₂×C₄×C₂₃	Q₈	1	1	yes	characteristic
12	C₈×C₂₃	—	4	1	no	—
13	C₂₃⋊C₈	—	2	1	no	—
14	C₂₃⋊C₈	—	4	1	no	—
15	C₂₃⋊C₈	C₈	1	2	yes	complemented
16	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₃	—	2	1	no	—
18	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
19	C₄×C₂₃	M₁₆	1	1	yes	characteristic
20	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
22	#334	—	23	1	no	maximal, Sylow
23	C₂×C₂₃	C₄⋊C₈	1	1	yes	characteristic
24	C₂×C₂₃	#106	1	1	yes	characteristic
25	C₂×C₂₃	#108	1	1	yes	characteristic
26	C₄⋊C₈	—	23	1	no	—
27	C₄⋊C₈	D₂₃	1	1	yes	characteristic
28	C₄×C₈	—	23	1	no	—
29	C₂₃	#334	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	23	1	no	—
32	C₂×C₈	—	23	1	no	—
33	C₂×C₈	—	46	1	no	—
34	C₄²	C₂×D₂₃	1	1	yes	characteristic
35	C₂×C₄	Dic₄₆	1	1	yes	characteristic
36	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
37	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	—	23	2	no	—
40	C₈	—	46	1	no	—
41	C₈	—	92	1	no	—
42	C₂²	Dic₂₃⋊C₄	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₈×D₂₃	1	1	yes	characteristic
45	C₄	#67262	1	1	yes	characteristic
46	C₄	#67273	1	1	yes	characteristic
47	C₄	#67274	1	1	yes	characteristic
48	C₂	#10624990	1	1	yes	characteristic
49	C₂	Dic₂₃⋊C₈	1	1	yes	characteristic
50	C₂	#10625004	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₂₃
commutator	C₄×C₂₃	C₂×C₈
Frattini	C₄²	C₂×D₂₃
Fitting	C₂₃×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₂₃	C₄⋊C₄
cosocle	C₄²×C₂₃	C₂²
hypercenter	C₄⋊C₈	D₂₃
hypocenter	C₂₃	#334
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
15. C₂₃⋊C₈	C₈	semidirect
29. C₂₃	#334	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×C₄⋊C₈	2
C₄⋊(C₂₃⋊C₈)	2
C₄×C₂₃⋊C₈	2
#334	23