Subgroups — #13092795

Order 1472.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625115	C₂	1	2	yes	maximal
3	C₂×#67275	C₂	1	2	yes	maximal
4	C₂×Dic₉₂	C₂	1	1	yes	maximal, characteristic
5	C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
7	C₂×Dic₄₆	C₂²	1	2	yes	—
8	Q₁₆×C₂₃	—	2	2	no	—
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	#67275	—	2	4	no	—
11	Dic₂₃⋊C₄	—	2	4	no	—
12	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
14	Dic₉₂	—	2	2	no	—
15	Q₈×C₂₃	—	2	2	no	—
16	Q₈×C₂₃	—	2	2	no	—
17	C₂×C₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₃	—	2	2	no	—
20	C₂×Dic₂₃	D₄	1	2	yes	—
21	Dic₄₆	—	2	2	no	—
22	Dic₄₆	—	2	2	no	—
23	C₈×C₂₃	D₄	1	2	yes	—
24	C₂₃⋊C₈	D₄	1	2	yes	—
25	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₃	—	4	2	no	—
27	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
29	Dic₂₃	—	4	2	no	—
30	Dic₂₃	Q₁₆	1	4	yes	complemented
31	#494	—	23	1	no	maximal, Sylow
32	C₂×C₂₃	#127	1	1	yes	characteristic
33	C₂×C₂₃	C₂×Q₁₆	1	2	yes	—
34	C₂×Q₁₆	—	23	2	no	—
35	C₂×Q₁₆	—	23	1	no	—
36	C₂×Q₁₆	D₂₃	1	1	yes	characteristic
37	C₄⋊Q₈	—	23	2	no	—
38	C₄×C₈	—	23	1	no	—
39	C₂₃	#494	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	23	2	no	—
41	C₂×Q₈	C₂×D₂₃	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	46	4	no	—
44	Q₁₆	—	46	2	no	—
45	C₂×C₈	—	23	1	no	—
46	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
47	C₄⋊C₄	—	46	4	no	—
48	C₄²	—	23	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	46	2	no	—
52	Q₈	—	46	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	23	2	no	—
55	C₂×C₄	—	46	2	no	—
56	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
57	C₈	—	23	2	no	—
58	C₈	C₂²⋊D₂₃	1	2	yes	—
59	C₂²	D₄×D₂₃	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	23	4	no	—
62	C₄	—	92	2	no	—
63	C₄	D₄×D₂₃	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
65	C₂	Q₁₆×D₂₃	1	2	yes	—
66	C₂	#10625111	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×Q₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	C₂×Q₁₆	D₂₃
hypocenter	C₂₃	#494
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₂₃	Q₁₆	semidirect
39. C₂₃	#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₃	2
#10625115	2
C₂×#67275	2
C₂×Dic₉₂	2
C₈×Dic₂₃	2
#494	23