Subgroups — C₂×#13092287 #15675798

Order 2944.

888 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₂₃	C₂	1	6	yes	maximal
2	#13092287	C₂	1	8	yes	maximal, direct product factor
3	C₂²×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₂₃	C₂²	1	3	yes	—
5	C₂³×Dic₂₃	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₃	C₄	1	8	yes	complemented
7	C₂×C₄²×C₂₃	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₂₃	—	2	24	no	—
9	C₂×C₄⋊Dic₂₃	C₂²	1	24	yes	—
10	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
11	C₂²×C₄×C₂₃	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₂₃	D₄	1	12	yes	—
13	C₂²×C₄×C₂₃	Q₈	1	12	yes	—
14	C₂²×C₄×C₂₃	C₂³	1	6	yes	—
15	C₂²×Dic₂₃	—	2	24	no	—
16	C₂²×Dic₂₃	C₂³	1	8	yes	—
17	C₄²×C₂₃	C₂×C₄	1	16	yes	complemented
18	C₄⋊Dic₂₃	—	2	48	no	—
19	C₂³×C₂₃	C₂²×C₄	1	2	yes	—
20	C₂³×C₂₃	C₂×D₄	1	6	yes	—
21	C₂³×C₂₃	C₂×Q₈	1	6	yes	—
22	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
23	C₂×C₄×C₂₃	C₄⋊C₄	1	48	yes	complemented
24	C₂×C₄×C₂₃	C₂²×C₄	1	12	yes	—
25	C₂×C₄×C₂₃	C₂×D₄	1	12	yes	—
26	C₂×C₄×C₂₃	C₂×Q₈	1	12	yes	—
27	C₂×Dic₂₃	—	2	24	no	—
28	C₂×Dic₂₃	—	4	16	no	—
29	C₂×#384	—	23	1	no	maximal, Sylow
30	C₂²×C₂₃	C₂×C₄⋊C₄	1	12	yes	—
31	C₂²×C₂₃	#127	1	4	yes	—
32	C₂²×C₂₃	C₄⋊Q₈	1	12	yes	—
33	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
34	C₂²×C₂₃	C₂²×D₄	1	3	yes	—
35	C₂²×C₂₃	C₂²×Q₈	1	3	yes	—
36	C₄×C₂₃	C₂×C₄⋊C₄	1	24	yes	complemented
37	Dic₂₃	—	4	8	no	—
38	C₂²×C₄⋊C₄	—	23	6	no	—
39	C₂²×C₄²	D₂₃	1	1	yes	characteristic
40	#384	—	23	8	no	—
41	C₂×C₂₃	#384	1	8	yes	complemented
42	C₂×C₂₃	C₂²×C₄⋊C₄	1	3	yes	—
43	C₂×C₂₃	C₂×#127	1	1	yes	characteristic
44	C₂×C₂₃	C₂×C₄⋊Q₈	1	3	yes	—
45	C₂³×C₄	—	23	4	no	—
46	C₂³×C₄	C₂×D₂₃	1	3	yes	—
47	C₂×C₄⋊C₄	—	23	24	no	—
48	C₂×C₄⋊C₄	—	46	24	no	—
49	C₂×C₄²	Dic₂₃	1	8	yes	complemented
50	C₂×C₄²	C₂×D₂₃	1	4	yes	—
51	C₂₃	C₂×#384	1	1	yes	characteristic, complemented, Sylow
52	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
53	C₂²×C₄	—	23	8	no	—
54	C₂²×C₄	—	46	24	no	—
55	C₂²×C₄	Dic₄₆	1	12	yes	—
56	C₂²×C₄	D₉₂	1	12	yes	—
57	C₂²×C₄	C₂×Dic₂₃	1	12	yes	—
58	C₂²×C₄	C₂²×D₂₃	1	6	yes	—
59	C₄⋊C₄	—	46	48	no	—
60	C₄²	C₂×Dic₂₃	1	16	yes	complemented
61	C₂³	C₂×Dic₄₆	1	6	yes	—
62	C₂³	C₂×D₉₂	1	6	yes	—
63	C₂³	C₂²×Dic₂₃	1	2	yes	—
64	C₂³	C₂³×D₂₃	1	1	yes	characteristic
65	C₂×C₄	—	46	24	no	—
66	C₂×C₄	—	92	16	no	—
67	C₂×C₄	C₄⋊Dic₂₃	1	48	yes	complemented
68	C₂×C₄	C₂×Dic₄₆	1	12	yes	—
69	C₂×C₄	C₂×D₉₂	1	12	yes	—
70	C₂×C₄	C₂²×Dic₂₃	1	12	yes	—
71	C₂²	#10625040	1	12	yes	—
72	C₂²	#10625045	1	4	yes	—
73	C₂²	C₂×C₄⋊Dic₂₃	1	12	yes	—
74	C₂²	C₂²×Dic₄₆	1	3	yes	—
75	C₂²	C₂²×D₉₂	1	3	yes	—
76	C₂²	C₂³×Dic₂₃	1	1	yes	characteristic
77	C₄	—	92	8	no	—
78	C₄	C₂×C₄⋊Dic₂₃	1	24	yes	complemented
79	C₂	#13092287	1	8	yes	direct product factor
80	C₂	C₂²×C₄⋊Dic₂₃	1	3	yes	—
81	C₂	C₂×#10625045	1	1	yes	characteristic
82	C₂	C₂×#10625040	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂³×C₄
Frattini	C₂³	C₂³×D₂₃
Fitting	C₂²×C₄²×C₂₃	C₂
socle, prime radical	C₂⁴×C₂₃	C₂³
cosocle	C₂³×C₂₃	C₂⁴
hypercenter	C₂²×C₄²	D₂₃
hypocenter	C₂₃	C₂×#384
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. #13092287	C₂	direct (N × H)
6. C₂×C₄²×C₂₃	C₄	semidirect
17. C₄²×C₂₃	C₂×C₄	semidirect
23. C₂×C₄×C₂₃	C₄⋊C₄	semidirect
36. C₄×C₂₃	C₂×C₄⋊C₄	semidirect
41. C₂×C₂₃	#384	semidirect
49. C₂×C₄²	Dic₂₃	semidirect
51. C₂₃	C₂×#384	semidirect
60. C₄²	C₂×Dic₂₃	semidirect
67. C₂×C₄	C₄⋊Dic₂₃	semidirect
78. C₄	C₂×C₄⋊Dic₂₃	semidirect
79. C₂	#13092287	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×C₄⋊Dic₂₃	2
#13092287	2
C₂²×C₄²×C₂₃	2
C₂×#384	23

Subgroups — C2×#13092287 #15675798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092287 #15675798