Subgroups — #13092768

Order 1472.

98 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	#10625040	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	#10624998	C₂	1	4	yes	maximal
5	C₂×Dic₄₆	—	2	1	no	—
6	C₂×Dic₄₆	C₂²	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	2	yes	—
8	C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₃	—	2	1	no	—
10	C₄⋊Dic₂₃	—	2	1	no	—
11	C₄⋊Dic₂₃	—	2	1	no	—
12	C₄⋊Dic₂₃	C₂²	1	2	yes	—
13	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₃	—	2	2	no	—
17	C₂×Dic₂₃	—	2	2	no	—
18	Dic₄₆	—	2	4	no	—
19	Dic₄₆	—	4	2	no	—
20	C₈×C₂₃	—	2	2	no	—
21	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₂₃	SD₁₆	1	2	yes	—
23	C₄×C₂₃	Q₁₆	1	2	yes	—
24	C₄×C₂₃	#41	1	2	yes	—
25	Dic₂₃	—	4	2	no	—
26	Dic₂₃	—	4	2	no	—
27	#487	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	#124	1	1	yes	characteristic
29	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
30	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
31	C₄⋊Q₈	—	23	1	no	—
32	C₄⋊Q₈	—	23	1	no	—
33	#103	—	23	4	no	—
34	C₄×C₈	D₂₃	1	1	yes	characteristic
35	C₂₃	#487	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	23	2	no	—
37	C₂×Q₈	—	46	1	no	—
38	C₂×C₈	C₂×D₂₃	1	2	yes	—
39	C₄⋊C₄	—	23	2	no	—
40	C₄⋊C₄	—	46	1	no	—
41	C₄⋊C₄	—	46	1	no	—
42	C₄⋊C₄	—	46	1	no	—
43	C₄²	C₂×D₂₃	1	1	yes	characteristic
44	Q₈	—	46	4	no	—
45	Q₈	—	92	2	no	—
46	C₂×C₄	—	46	2	no	—
47	C₂×C₄	—	46	2	no	—
48	C₂×C₄	D₉₂	1	1	yes	characteristic
49	C₂×C₄	D₉₂	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₂²	C₂×D₉₂	1	1	yes	characteristic
53	C₄	—	92	2	no	—
54	C₄	—	92	2	no	—
55	C₄	#67263	1	2	yes	—
56	C₄	Dic₉₂	1	2	yes	—
57	C₄	#67288	1	2	yes	—
58	C₂	#10625046	1	1	yes	characteristic
59	C₂	C₂×#67263	1	1	yes	characteristic
60	C₂	C₂×Dic₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₄×C₈×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	C₄×C₈	D₂₃
hypocenter	C₂₃	#487
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
35. C₂₃	#487	semidirect

Maximal subgroups

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

subgroup	index
#10625040	2
C₄×C₈×C₂₃	2
#10624998	2
#487	23