Subgroups — C₂²×Dic₂₃⋊C₄ #13092867

Order 1472.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₂₃⋊C₄	C₂	direct (N × H)
9. C₂²×Dic₂₃	C₄	semidirect
12. Dic₂₃⋊C₄	C₂²	direct (N × H)
20. C₂×Dic₂₃	C₂×C₄	semidirect
23. C₂²×C₂₃	C₄⋊C₄	semidirect
30. Dic₂₃	C₂²×C₄	semidirect
32. C₂×C₂₃	C₂×C₄⋊C₄	semidirect
40. C₂₃	C₂²×C₄⋊C₄	semidirect
59. C₂²	Dic₂₃⋊C₄	direct (N × H)
67. C₂	C₂×Dic₂₃⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₂₃	2
C₂³×Dic₂₃	2
C₂×Dic₂₃⋊C₄	2
C₂²×C₄⋊C₄	23

Subgroups — C22×Dic23⋊C4 #13092867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₂₃⋊C₄ #13092867