Subgroups — C₄×C₂²⋊Dic₂₃ #13092265

Order 1472.

258 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	C₂×C₂²⋊Dic₂₃	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₂₃	C₂	1	2	yes	maximal, complemented
4	C₂₃⋊#95	C₂	1	2	yes	maximal, complemented
5	C₂⁴×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₃	—	2	4	no	—
7	C₂²×C₄×C₂₃	C₄	1	4	yes	complemented
8	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₂₃	C₂²	1	4	yes	—
11	C₂²⋊Dic₂₃	C₄	1	8	yes	direct product factor
12	C₄×Dic₂₃	—	2	4	no	—
13	C₂³×C₂₃	—	2	2	no	—
14	C₂³×C₂₃	—	2	2	no	—
15	C₂³×C₂₃	C₂×C₄	1	4	yes	—
16	C₂³×C₂₃	C₂×C₄	1	2	yes	—
17	C₂³×C₂₃	C₂³	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	2	no	—
19	C₂×C₄×C₂₃	—	2	8	no	—
20	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₂₃	D₄	1	4	yes	—
23	C₂×Dic₂₃	—	2	4	no	—
24	C₂×Dic₂₃	—	2	4	no	—
25	C₂×Dic₂₃	C₂×C₄	1	8	yes	complemented
26	C₂²×C₂₃	—	2	2	no	—
27	C₂²×C₂₃	—	2	2	no	—
28	C₂²×C₂₃	—	2	8	no	—
29	C₂²×C₂₃	C₄²	1	4	yes	complemented
30	C₂²×C₂₃	C₂²×C₄	1	2	yes	—
31	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₂₃	C₂×D₄	1	2	yes	—
33	C₂²×C₂₃	#41	1	2	yes	—
34	C₄×C₂₃	—	2	2	no	—
35	C₄×C₂₃	C₂²⋊C₄	1	4	yes	complemented
36	Dic₂₃	—	2	8	no	—
37	C₄×C₂²⋊C₄	—	23	1	no	maximal, Sylow
38	C₂×C₂₃	—	2	4	no	—
39	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₂₃	#117	1	1	yes	characteristic
42	C₂×C₂₃	C₄×D₄	1	4	yes	—
43	C₂³×C₄	D₂₃	1	1	yes	characteristic
44	C₂×C₂²⋊C₄	—	23	2	no	—
45	C₂×C₄²	—	23	2	no	—
46	#95	—	23	2	no	—
47	C₂₃	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	C₂×D₂₃	1	1	yes	characteristic
49	C₂²×C₄	—	2	4	no	—
50	C₂²×C₄	—	23	4	no	—
51	C₂²×C₄	Dic₂₃	1	4	yes	complemented
52	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
53	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
54	C₂²⋊C₄	—	23	8	no	—
55	C₄²	—	46	4	no	—
56	C₂³	—	2	2	no	—
57	C₂³	—	2	2	no	—
58	C₂³	C₄×D₂₃	1	4	yes	—
59	C₂³	C₂×Dic₂₃	1	2	yes	—
60	C₂³	C₂²×D₂₃	1	1	yes	characteristic
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	8	no	—
63	C₂×C₄	—	23	8	no	—
64	C₂×C₄	—	46	4	no	—
65	C₂×C₄	—	46	4	no	—
66	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
67	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
68	C₂×C₄	C₂²⋊D₂₃	1	4	yes	—
69	C₂²	—	2	2	no	—
70	C₂²	—	2	8	no	—
71	C₂²	—	2	2	no	—
72	C₂²	C₄×Dic₂₃	1	4	yes	complemented
73	C₂²	C₂×C₄×D₂₃	1	2	yes	—
74	C₂²	#67288	1	2	yes	—
75	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
76	C₂²	C₂×C₂²⋊D₂₃	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	46	8	no	—
79	C₄	C₂²⋊Dic₂₃	1	4	yes	direct product factor
80	C₂	—	2	4	no	—
81	C₂	C₂×C₄×Dic₂₃	1	1	yes	characteristic
82	C₂	#10625097	1	1	yes	characteristic
83	C₂	C₄×C₂²⋊D₂₃	1	4	yes	—
84	C₂	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₂₃	C₂	semidirect
4. C₂₃⋊#95	C₂	semidirect
7. C₂²×C₄×C₂₃	C₄	semidirect
11. C₂²⋊Dic₂₃	C₄	direct (N × H)
25. C₂×Dic₂₃	C₂×C₄	semidirect
29. C₂²×C₂₃	C₄²	semidirect
35. C₄×C₂₃	C₂²⋊C₄	semidirect
47. C₂₃	C₄×C₂²⋊C₄	semidirect
51. C₂²×C₄	Dic₂₃	semidirect
72. C₂²	C₄×Dic₂₃	semidirect
79. C₄	C₂²⋊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
C₂³×C₄×C₂₃	2
C₂×C₂²⋊Dic₂₃	2
C₂×C₄×Dic₂₃	2
C₂₃⋊#95	2
C₄×C₂²⋊C₄	23

Subgroups — C4×C22⋊Dic23 #13092265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂²⋊Dic₂₃ #13092265