Subgroups — #13092511

Order 1472.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic
2	#10625058	C₂	1	2	yes	maximal
3	C₂₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic
5	#10624992	C₂	1	2	yes	maximal
6	C₂×Dic₄₆	C₂²	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
9	Dic₂₃⋊C₄	—	2	2	no	—
10	C₄×Dic₂₃	—	2	2	no	—
11	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
13	Dic₉₂	C₄	1	4	yes	complemented
14	C₂×C₄×C₂₃	—	2	2	no	—
15	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₃	—	2	2	no	—
17	C₂×Dic₂₃	D₄	1	1	yes	characteristic
18	C₂×Dic₂₃	D₄	1	1	yes	characteristic
19	Dic₄₆	—	2	2	no	—
20	Dic₄₆	C₂×C₄	1	4	yes	—
21	C₈×C₂₃	C₂×C₄	1	2	yes	—
22	C₂₃⋊C₈	—	2	1	no	—
23	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₂₃	—	4	2	no	—
25	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₂₃	#41	1	1	yes	characteristic
27	Dic₂₃	—	2	4	no	—
28	Dic₂₃	—	2	1	no	—
29	Dic₂₃	Q₁₆	1	2	yes	complemented
30	C₄×Q₁₆	—	23	1	no	maximal, Sylow
31	C₂×C₂₃	C₄×D₄	1	1	yes	characteristic
32	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
33	C₂×C₂₃	#135	1	1	yes	characteristic
34	C₂×Q₁₆	—	23	1	no	—
35	C₄×Q₈	—	23	2	no	—
36	#107	D₂₃	1	1	yes	characteristic
37	#103	—	23	2	no	—
38	C₄×C₈	—	23	1	no	—
39	C₂₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	23	2	no	—
41	Q₁₆	—	23	4	no	—
42	C₂×C₈	—	23	1	no	—
43	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
44	C₄⋊C₄	—	46	2	no	—
45	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
46	C₄²	—	23	1	no	—
47	C₄²	—	46	2	no	—
48	Q₈	—	23	4	no	—
49	Q₈	—	46	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	23	1	no	—
52	C₂×C₄	—	23	1	no	—
53	C₂×C₄	—	46	2	no	—
54	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
55	C₈	—	46	1	no	—
56	C₈	C₄×D₂₃	1	2	yes	—
57	C₂²	D₄×D₂₃	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	23	2	no	—
60	C₄	—	46	4	no	—
61	C₄	—	46	1	no	—
62	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
63	C₄	#67292	1	1	yes	characteristic
64	C₂	#10625064	1	1	yes	characteristic
65	C₂	#10625083	1	1	yes	characteristic
66	C₂	Q₁₆×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#107	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	#107	D₂₃
hypocenter	C₂₃	C₄×Q₁₆
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
13. Dic₉₂	C₄	semidirect
29. Dic₂₃	Q₁₆	semidirect
39. C₂₃	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₉₂	2
#10625058	2
C₂₃×#107	2
C₈×Dic₂₃	2
#10624992	2
C₄×Q₁₆	23