Subgroups — C₄×C₄⋊Dic₂₃ #13092269

Order 1472.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₃	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₂₃	C₂	1	2	yes	maximal
4	C₂₃⋊#95	C₂	1	2	yes	maximal
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
8	C₂²×Dic₂₃	C₂²	1	4	yes	—
9	C₄²×C₂₃	C₄	1	4	yes	complemented
10	C₄⋊Dic₂₃	C₄	1	8	yes	direct product factor
11	C₄×Dic₂₃	—	2	4	no	—
12	C₂³×C₂₃	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	2	2	no	—
14	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₃	D₄	1	2	yes	—
19	C₂×C₄×C₂₃	Q₈	1	2	yes	—
20	C₂×Dic₂₃	—	2	4	no	—
21	C₂×Dic₂₃	—	2	4	no	—
22	C₂×Dic₂₃	C₂×C₄	1	8	yes	—
23	C₂²×C₂₃	C₂²×C₄	1	2	yes	—
24	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
27	C₂²×C₂₃	#41	1	2	yes	—
28	C₄×C₂₃	—	2	2	no	—
29	C₄×C₂₃	C₄²	1	4	yes	complemented
30	C₄×C₂₃	C₄⋊C₄	1	4	yes	complemented
31	Dic₂₃	—	2	8	no	—
32	C₄×C₄⋊C₄	—	23	1	no	maximal, Sylow
33	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
34	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₂₃	#117	1	1	yes	characteristic
36	C₂×C₂₃	C₄×D₄	1	2	yes	—
37	C₂×C₂₃	C₄×Q₈	1	2	yes	—
38	C₂×C₄⋊C₄	—	23	2	no	—
39	C₂×C₄²	—	23	2	no	—
40	C₂×C₄²	D₂₃	1	1	yes	characteristic
41	#95	—	23	2	no	—
42	C₂₃	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	23	4	no	—
44	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
45	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
46	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
47	C₄⋊C₄	—	23	8	no	—
48	C₄²	—	46	4	no	—
49	C₄²	Dic₂₃	1	4	yes	complemented
50	C₂³	C₂²×D₂₃	1	1	yes	characteristic
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	23	8	no	—
53	C₂×C₄	—	46	4	no	—
54	C₂×C₄	—	46	4	no	—
55	C₂×C₄	Dic₄₆	1	2	yes	—
56	C₂×C₄	C₄×D₂₃	1	4	yes	—
57	C₂×C₄	D₉₂	1	2	yes	—
58	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
59	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
60	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
61	C₂²	C₂×Dic₄₆	1	1	yes	characteristic
62	C₂²	C₂×C₄×D₂₃	1	2	yes	—
63	C₂²	C₂×D₉₂	1	1	yes	characteristic
64	C₂²	#67288	1	2	yes	—
65	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	46	8	no	—
68	C₄	C₄×Dic₂₃	1	4	yes	complemented
69	C₄	C₄⋊Dic₂₃	1	4	yes	direct product factor
70	C₂	C₄×Dic₄₆	1	2	yes	—
71	C₂	C₄×D₉₂	1	2	yes	—
72	C₂	C₂×C₄×Dic₂₃	1	1	yes	characteristic
73	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
74	C₂	#10625097	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
9. C₄²×C₂₃	C₄	semidirect
10. C₄⋊Dic₂₃	C₄	direct (N × H)
29. C₄×C₂₃	C₄²	semidirect
30. C₄×C₂₃	C₄⋊C₄	semidirect
42. C₂₃	C₄×C₄⋊C₄	semidirect
49. C₄²	Dic₂₃	semidirect
68. C₄	C₄×Dic₂₃	semidirect
69. C₄	C₄⋊Dic₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₂₃	2
C₂×C₄⋊Dic₂₃	2
C₂×C₄×Dic₂₃	2
C₂₃⋊#95	2
C₄×C₄⋊C₄	23

Subgroups — C4×C4⋊Dic23 #13092269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊Dic₂₃ #13092269