Subgroups — #13092168

Order 1472.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₂₃⋊C₈)	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₂₃	C₄	1	1	yes	characteristic
5	C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₈	—	2	2	no	—
7	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
9	C₂×C₄×C₂₃	Q₈	1	1	yes	characteristic
10	C₈×C₂₃	—	2	1	no	—
11	C₈×C₂₃	C₈	1	2	yes	complemented
12	C₂₃⋊C₈	—	4	2	no	—
13	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₂₃	—	2	1	no	—
15	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₂₃	M₁₆	1	1	yes	characteristic
17	C₄×C₂₃	SD₁₆	1	2	yes	—
18	#334	—	23	1	no	maximal, Sylow
19	C₂×C₂₃	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₂₃	#106	1	1	yes	characteristic
21	C₂×C₂₃	#108	1	1	yes	characteristic
22	C₄⋊C₈	—	23	2	no	—
23	C₄×C₈	D₂₃	1	1	yes	characteristic
24	C₂₃	#334	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₈	—	46	2	no	—
26	C₂×C₈	Dic₂₃	1	1	yes	characteristic
27	C₂×C₈	Dic₂₃	1	1	yes	characteristic
28	C₄²	C₂×D₂₃	1	1	yes	characteristic
29	C₂×C₄	Dic₄₆	1	1	yes	characteristic
30	C₂×C₄	D₉₂	1	1	yes	characteristic
31	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	92	2	no	—
34	C₈	C₂₃⋊C₈	1	2	yes	complemented
35	C₂²	C₄⋊Dic₂₃	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#67263	1	2	yes	—
38	C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
39	C₄	#67267	1	1	yes	characteristic
40	C₂	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic
41	C₂	#10624999	1	1	yes	characteristic
42	C₂	#10625001	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator	C₄×C₂₃	C₂×C₈
Frattini	C₄²	C₂×D₂₃
Fitting	C₄×C₈×C₂₃	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
11. C₈×C₂₃	C₈	semidirect
24. C₂₃	#334	semidirect
34. C₈	C₂₃⋊C₈	semidirect

Maximal subgroups

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

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