Subgroups — C₂×#10624997 #13092365

Order 1472.

146 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	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10624997	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₃	C₄	1	2	yes	—
7	C₂×C₈×C₂₃	C₄	1	4	yes	complemented
8	C₂×C₈×C₂₃	C₂²	1	2	yes	—
9	C₄×Dic₂₃	C₄	1	2	yes	—
10	C₄×Dic₂₃	C₂²	1	2	yes	—
11	C₂×C₂₃⋊C₈	C₄	1	4	yes	complemented
12	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₂₃	—	2	4	no	—
19	C₂×Dic₂₃	C₂×C₄	1	4	yes	—
20	C₈×C₂₃	C₂×C₄	1	4	yes	complemented
21	C₂₃⋊C₈	C₂×C₄	1	4	yes	complemented
22	C₂²×C₂₃	C₄²	1	2	yes	—
23	C₂²×C₂₃	M₁₆	1	4	yes	—
24	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₂₃	C₄²	1	2	yes	—
26	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	Dic₂₃	—	2	4	no	—
29	C₂×#97	—	23	1	no	maximal, Sylow
30	C₂×C₂₃	#97	1	4	yes	complemented
31	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₂₃	C₂×M₁₆	1	2	yes	—
33	C₂²×C₈	—	23	1	no	—
34	C₂²×C₈	D₂₃	1	1	yes	characteristic
35	C₂×C₄²	—	23	1	no	—
36	#97	—	23	4	no	—
37	C₂₃	C₂×#97	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	—	23	2	no	—
39	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
40	C₂×C₈	—	23	4	no	—
41	C₂×C₈	—	23	2	no	—
42	C₂×C₈	Dic₂₃	1	4	yes	complemented
43	C₂×C₈	C₂×D₂₃	1	2	yes	—
44	C₄²	—	23	2	no	—
45	C₄²	—	23	2	no	—
46	C₂³	C₄×D₂₃	1	1	yes	characteristic
47	C₂×C₄	—	23	4	no	—
48	C₂×C₄	—	46	4	no	—
49	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
50	C₂×C₄	C₄×D₂₃	1	2	yes	—
51	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
52	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
53	C₈	—	23	4	no	—
54	C₈	C₂×Dic₂₃	1	4	yes	complemented
55	C₂²	#67262	1	4	yes	—
56	C₂²	C₄×Dic₂₃	1	2	yes	—
57	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
58	C₄	—	46	4	no	—
59	C₄	C₄×Dic₂₃	1	2	yes	—
60	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
61	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
62	C₂	#10624997	1	4	yes	direct product factor
63	C₂	C₂×#67262	1	2	yes	—
64	C₂	C₂×C₄×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	C₂×#97
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #10624997	C₂	direct (N × H)
7. C₂×C₈×C₂₃	C₄	semidirect
11. C₂×C₂₃⋊C₈	C₄	semidirect
20. C₈×C₂₃	C₂×C₄	semidirect
21. C₂₃⋊C₈	C₂×C₄	semidirect
30. C₂×C₂₃	#97	semidirect
37. C₂₃	C₂×#97	semidirect
42. C₂×C₈	Dic₂₃	semidirect
54. C₈	C₂×Dic₂₃	semidirect
62. C₂	#10624997	direct (N × H)

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
C₂×C₄×Dic₂₃	2
C₂²×C₂₃⋊C₈	2
#10624997	2
C₂×#97	23

Subgroups — C2×#10624997 #13092365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624997 #13092365