Subgroups — #13092147

Order 1472.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₄₆	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	1	yes	characteristic
5	C₂×C₈×C₂₃	—	2	1	no	—
6	C₄²×C₂₃	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₂₃	C₄	1	1	yes	characteristic
8	Dic₂₃⋊C₄	—	2	1	no	—
9	C₄×Dic₂₃	—	2	1	no	—
10	C₂×C₂₃⋊C₈	—	2	1	no	—
11	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₂×Dic₂₃	—	2	1	no	—
15	C₂×Dic₂₃	—	2	1	no	—
16	Dic₄₆	—	2	1	no	—
17	Dic₄₆	C₈	1	2	yes	complemented
18	C₈×C₂₃	—	4	1	no	—
19	C₂₃⋊C₈	—	2	2	no	—
20	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₃	—	2	1	no	—
22	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
23	C₄×C₂₃	M₁₆	1	1	yes	characteristic
24	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
25	C₄×C₂₃	Q₁₆	1	1	yes	characteristic
26	Dic₂₃	—	2	2	no	—
27	Dic₂₃	—	4	1	no	—
28	Q₈⋊C₈	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₂×C₂₃	#103	1	1	yes	characteristic
31	C₂×C₂₃	#104	1	1	yes	characteristic
32	C₄×Q₈	—	23	1	no	—
33	C₄⋊C₈	D₂₃	1	1	yes	characteristic
34	C₄×C₈	—	23	1	no	—
35	C₂₃	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	23	1	no	—
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	—	46	1	no	—
39	C₄⋊C₄	—	23	1	no	—
40	C₄⋊C₄	—	46	1	no	—
41	C₄²	—	46	1	no	—
42	C₄²	C₂×D₂₃	1	1	yes	characteristic
43	Q₈	—	23	2	no	—
44	Q₈	—	46	1	no	—
45	C₂×C₄	—	46	1	no	—
46	C₂×C₄	—	46	1	no	—
47	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
48	C₂×C₄	D₉₂	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	46	2	no	—
52	C₂²	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	46	2	no	—
55	C₄	—	92	1	no	—
56	C₄	C₈×D₂₃	1	1	yes	characteristic
57	C₄	#67262	1	1	yes	characteristic
58	C₄	#67273	1	1	yes	characteristic
59	C₄	#67275	1	1	yes	characteristic
60	C₂	#10624992	1	1	yes	characteristic
61	C₂	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
62	C₂	#10625007	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	C₂²⋊C₄
cosocle	C₄²×C₂₃	C₂²
hypercenter	C₄⋊C₈	D₂₃
hypocenter	C₂₃	Q₈⋊C₈
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
17. Dic₄₆	C₈	semidirect
35. C₂₃	Q₈⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₄₆	2
C₂₃×C₄⋊C₈	2
C₄×C₂₃⋊C₈	2
Q₈⋊C₈	23