Subgroups — C₂×C₂₃⋊#401 #15676693

Order 2944.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃⋊#401	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₂₃⋊#95	C₂	1	3	yes	maximal
3	C₂×C₂₃⋊#95	C₂	1	3	yes	maximal
4	C₂×C₂₃×#95	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₂₃	C₂²	1	3	yes	—
6	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
7	C₂³×Dic₂₃	C₂²	1	3	yes	—
8	C₂₃×#95	C₂²	1	4	yes	—
9	C₂₃⋊#95	C₂²	1	12	yes	—
10	C₂₃⋊#95	C₂²	1	12	yes	—
11	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₂₃	—	2	6	no	—
13	C₂²×C₄×C₂₃	—	2	12	no	—
14	C₂²×C₄×C₂₃	C₂³	1	6	yes	—
15	C₂²×Dic₂₃	—	2	6	no	—
16	C₂²×Dic₂₃	—	2	6	no	—
17	C₂²×Dic₂₃	—	2	6	no	—
18	C₂²×Dic₂₃	—	2	6	no	—
19	C₂²×Dic₂₃	C₂³	1	2	yes	—
20	C₂²×Dic₂₃	C₂³	1	6	yes	—
21	C₂³×C₂₃	#41	1	6	yes	—
22	C₂³×C₂₃	#41	1	6	yes	—
23	C₂³×C₂₃	#41	1	2	yes	—
24	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₂₃	—	2	6	no	—
26	C₂×C₄×C₂₃	—	2	12	no	—
27	C₂×C₄×C₂₃	—	4	12	no	—
28	C₂×Dic₂₃	—	2	6	no	—
29	C₂×Dic₂₃	—	2	6	no	—
30	C₂×Dic₂₃	—	2	6	no	—
31	C₂×Dic₂₃	—	2	6	no	—
32	C₂×Dic₂₃	—	4	4	no	—
33	C₂×Dic₂₃	—	4	12	no	—
34	C₂×#401	—	23	1	no	maximal, Sylow
35	C₂²×C₂₃	#126	1	4	yes	—
36	C₂²×C₂₃	#126	1	12	yes	—
37	C₂²×C₂₃	#126	1	12	yes	—
38	C₂²×C₂₃	C₂×#41	1	3	yes	—
39	C₂²×C₂₃	C₂×#41	1	3	yes	—
40	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
41	C₄×C₂₃	—	4	6	no	—
42	Dic₂₃	—	4	2	no	—
43	Dic₂₃	—	4	6	no	—
44	#401	—	23	8	no	—
45	C₂×#95	—	23	3	no	—
46	C₂×#95	—	23	3	no	—
47	C₂×#95	D₂₃	1	1	yes	characteristic
48	C₂×C₂₃	#401	1	8	yes	complemented
49	C₂×C₂₃	C₂×#126	1	3	yes	—
50	C₂×C₂₃	C₂×#126	1	1	yes	characteristic
51	C₂×C₂₃	C₂×#126	1	3	yes	—
52	C₂³×C₄	—	23	1	no	—
53	C₂³×C₄	—	23	3	no	—
54	C₂³×C₄	C₂×D₂₃	1	3	yes	—
55	#95	—	23	12	no	—
56	#95	—	23	12	no	—
57	#95	C₂×D₂₃	1	4	yes	—
58	C₂₃	C₂×#401	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
60	C₂²×C₄	—	2	6	no	—
61	C₂²×C₄	—	2	12	no	—
62	C₂²×C₄	—	23	2	no	—
63	C₂²×C₄	—	23	6	no	—
64	C₂²×C₄	—	46	6	no	—
65	C₂²×C₄	—	46	6	no	—
66	C₂²×C₄	—	46	6	no	—
67	C₂²×C₄	—	46	6	no	—
68	C₂²×C₄	C₂²×D₂₃	1	6	yes	—
69	C₂³	#67288	1	6	yes	—
70	C₂³	#67290	1	6	yes	—
71	C₂³	#67292	1	2	yes	—
72	C₂³	C₂³×D₂₃	1	1	yes	characteristic
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	2	12	no	—
75	C₂×C₄	—	4	12	no	—
76	C₂×C₄	—	46	6	no	—
77	C₂×C₄	—	46	6	no	—
78	C₂×C₄	—	46	6	no	—
79	C₂×C₄	—	46	6	no	—
80	C₂×C₄	—	92	4	no	—
81	C₂×C₄	—	92	12	no	—
82	C₂²	#10625047	1	4	yes	—
83	C₂²	#10625050	1	12	yes	—
84	C₂²	#10625069	1	12	yes	—
85	C₂²	C₂×#67288	1	3	yes	—
86	C₂²	C₂×#67290	1	3	yes	—
87	C₂²	C₂×#67292	1	1	yes	characteristic
88	C₄	—	4	6	no	—
89	C₄	—	92	2	no	—
90	C₄	—	92	6	no	—
91	C₂	C₂₃⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#10625050	1	3	yes	—
93	C₂	C₂×#10625047	1	1	yes	characteristic
94	C₂	C₂×#10625069	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₂₃
commutator, cosocle	C₂³×C₂₃	C₂⁴
Frattini	C₂³	C₂³×D₂₃
Fitting	C₂×C₂₃×#95	C₂
socle, prime radical	C₂⁴×C₂₃	C₂³
hypercenter	C₂×#95	D₂₃
hypocenter	C₂₃	C₂×#401
LCS	G ▷ C₂³×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₂₃⋊#401	C₂	direct (N × H)
48. C₂×C₂₃	#401	semidirect
58. C₂₃	C₂×#401	semidirect
91. C₂	C₂₃⋊#401	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⋊#401	2
C₂×C₂₃⋊#95	2
C₂×C₂₃×#95	2
C₂×#401	23

Subgroups — C2×C23⋊#401 #15676693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃⋊#401 #15676693