Subgroups — #13092165

Order 1472.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625040	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₂₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₆	C₄	1	2	yes	—
5	C₂×C₈×C₂₃	—	2	1	no	—
6	C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₂₃	—	2	1	no	—
8	C₄⋊Dic₂₃	—	2	1	no	—
9	C₂×C₂₃⋊C₈	—	2	1	no	—
10	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
12	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×Dic₂₃	—	2	2	no	—
14	Dic₄₆	—	4	2	no	—
15	C₈×C₂₃	—	4	1	no	—
16	C₂₃⋊C₈	—	4	1	no	—
17	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₂₃	—	2	1	no	—
19	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
20	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₃	Q₁₆	1	1	yes	characteristic
22	C₄×C₂₃	Q₁₆	1	1	yes	characteristic
23	Dic₂₃	—	4	2	no	—
24	#333	—	23	1	no	maximal, Sylow
25	C₂×C₂₃	#100	1	1	yes	characteristic
26	C₂×C₂₃	#103	1	1	yes	characteristic
27	C₂×C₂₃	#103	1	1	yes	characteristic
28	C₄⋊Q₈	—	23	1	no	—
29	C₄⋊C₈	—	23	1	no	—
30	C₄⋊C₈	D₂₃	1	1	yes	characteristic
31	C₂₃	#333	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₈	—	23	2	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	46	1	no	—
35	C₄⋊C₄	—	46	1	no	—
36	C₄⋊C₄	—	46	1	no	—
37	C₄²	C₂×D₂₃	1	1	yes	characteristic
38	Q₈	—	92	2	no	—
39	C₂×C₄	—	46	2	no	—
40	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
41	C₂×C₄	D₉₂	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
43	C₈	—	4	1	no	—
44	C₈	—	92	1	no	—
45	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	92	2	no	—
48	C₄	#67263	1	1	yes	characteristic
49	C₄	Dic₉₂	1	1	yes	characteristic
50	C₄	#67273	1	1	yes	characteristic
51	C₄	#67275	1	1	yes	characteristic
52	C₂	#10624992	1	1	yes	characteristic
53	C₂	#10624998	1	1	yes	characteristic
54	C₂	#10625005	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₂₃)⋊C₄
commutator	C₂×C₄×C₂₃	C₂×C₄
Frattini	C₄²	C₂×D₂₃
Fitting	C₂₃×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₂₃	C₂²⋊C₄
cosocle	C₄²×C₂₃	C₂²
hypercenter	C₄⋊C₈	D₂₃
hypocenter	C₂₃	#333
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
31. C₂₃	#333	semidirect

Maximal subgroups

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

subgroup	index
#10625040	2
C₂₃×C₄⋊C₈	2
C₄⋊(C₂₃⋊C₈)	2
#333	23