Subgroups — #13092455

Order 1472.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625097	C₂	1	2	yes	maximal
3	#10625000	C₂	1	2	yes	maximal, complemented
4	#10624999	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₃	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²⋊Dic₂₃	—	2	2	no	—
10	C₄⋊Dic₂₃	C₂²	1	4	yes	—
11	C₄×Dic₂₃	—	2	2	no	—
12	C₂³×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	Q₈	1	2	yes	—
16	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₃	—	2	4	no	—
18	C₈×C₂₃	C₂×C₄	1	2	yes	—
19	C₈×C₂₃	C₂×C₄	1	2	yes	—
20	C₂²×C₂₃	—	2	2	no	—
21	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
22	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
23	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
24	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
26	Dic₂₃	—	4	4	no	—
27	#427	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	—	2	2	no	—
29	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₂₃	#135	1	2	yes	—
31	C₂²×C₈	D₂₃	1	1	yes	characteristic
32	#117	—	23	2	no	—
33	#107	—	23	2	no	—
34	#106	—	23	2	no	—
35	C₂₃	#427	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
37	C₂×C₈	Dic₂₃	1	4	yes	complemented
38	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
39	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
40	C₄⋊C₄	—	23	4	no	—
41	C₂²⋊C₄	—	46	2	no	—
42	C₄²	—	46	2	no	—
43	C₂³	D₉₂	1	1	yes	characteristic
44	C₂×C₄	—	46	4	no	—
45	C₂×C₄	Dic₄₆	1	2	yes	—
46	C₂×C₄	D₉₂	1	1	yes	characteristic
47	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
48	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
49	C₈	C₂×Dic₂₃	1	2	yes	—
50	C₈	C₂×Dic₂₃	1	2	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄⋊Dic₂₃	1	2	yes	—
53	C₂²	C₂×D₉₂	1	1	yes	characteristic
54	C₄	—	92	4	no	—
55	C₄	C₄⋊Dic₂₃	1	2	yes	—
56	C₄	C₂×Dic₄₆	1	1	yes	characteristic
57	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
58	C₂	—	2	2	no	—
59	C₂	#10625075	1	2	yes	—
60	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂×D₄
prime radical	C₂³×C₂₃	D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	#427
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #10625000	C₂	semidirect
4. #10624999	C₂	semidirect
6. C₂×C₈×C₂₃	C₄	semidirect
35. C₂₃	#427	semidirect
37. C₂×C₈	Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₃	2
#10625097	2
#10625000	2
#10624999	2
#427	23