Subgroups — C₂×#13092193 #15674987

Order 2944.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃⋊C₁₆	C₂	1	2	yes	maximal
2	#13092193	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₂₃	C₄	1	1	yes	characteristic
7	C₄×C₈×C₂₃	C₄	1	2	yes	—
8	C₄×C₈×C₂₃	C₂²	1	2	yes	—
9	C₂×C₂₃⋊C₁₆	C₄	1	8	yes	complemented
10	C₂×C₂₃⋊C₁₆	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₃	C₈	1	2	yes	—
12	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₈	1	4	yes	—
14	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
18	C₄²×C₂₃	C₈	1	2	yes	—
19	C₄²×C₂₃	C₂×C₄	1	2	yes	—
20	C₂₃⋊C₁₆	C₂×C₄	1	8	yes	complemented
21	C₂³×C₂₃	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄×C₂₃	—	2	4	no	—
23	C₂×C₄×C₂₃	C₄²	1	2	yes	—
24	C₂×C₄×C₂₃	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₂₃	C₄²	1	2	yes	—
29	C₈×C₂₃	C₂×C₈	1	4	yes	—
30	C₈×C₂₃	C₂²×C₄	1	2	yes	—
31	C₂×#346	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	C₄×C₈	1	2	yes	—
33	C₂²×C₂₃	M₃₂	1	4	yes	—
34	C₂²×C₂₃	C₂²×C₈	1	1	yes	characteristic
35	C₄×C₂₃	—	2	4	no	—
36	C₄×C₂₃	C₄×C₈	1	2	yes	—
37	C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
38	C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
39	C₂²×C₁₆	—	23	2	no	—
40	C₂×C₄×C₈	D₂₃	1	1	yes	characteristic
41	#346	—	23	4	no	—
42	C₂×C₂₃	#346	1	4	yes	complemented
43	C₂×C₂₃	C₂×C₄×C₈	1	1	yes	characteristic
44	C₂×C₂₃	C₂×M₃₂	1	2	yes	—
45	C₂²×C₈	Dic₂₃	1	1	yes	characteristic
46	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
47	C₂×C₄²	Dic₂₃	1	1	yes	characteristic
48	C₂×C₁₆	—	23	8	no	—
49	C₂×C₁₆	—	23	4	no	—
50	C₄×C₈	Dic₂₃	1	2	yes	—
51	C₄×C₈	C₂×D₂₃	1	2	yes	—
52	C₂₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	C₂₃⋊C₈	1	2	yes	—
54	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
55	C₂×C₈	C₂₃⋊C₈	1	4	yes	—
56	C₂×C₈	C₄×D₂₃	1	4	yes	—
57	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
58	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
59	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
60	C₄²	C₂₃⋊C₈	1	2	yes	—
61	C₄²	C₂×Dic₂₃	1	2	yes	—
62	C₁₆	—	23	8	no	—
63	C₂³	C₂×C₂₃⋊C₈	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	C₂×C₂₃⋊C₈	1	4	yes	—
66	C₂×C₄	C₂×C₂₃⋊C₈	1	2	yes	—
67	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
68	C₂×C₄	C₄×Dic₂₃	1	2	yes	—
69	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
70	C₈	C₂×C₂₃⋊C₈	1	4	yes	—
71	C₈	C₄×Dic₂₃	1	2	yes	—
72	C₈	C₂×C₄×D₂₃	1	2	yes	—
73	C₂²	C₄×C₂₃⋊C₈	1	2	yes	—
74	C₂²	#10624994	1	4	yes	—
75	C₂²	C₂²×C₂₃⋊C₈	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	C₄×C₂₃⋊C₈	1	2	yes	—
78	C₄	C₂²×C₂₃⋊C₈	1	1	yes	characteristic
79	C₄	C₂×C₄×Dic₂₃	1	1	yes	characteristic
80	C₂	#13092193	1	4	yes	direct product factor
81	C₂	C₂×C₄×C₂₃⋊C₈	1	1	yes	characteristic
82	C₂	C₂×#10624994	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂×C₄×C₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂×C₈
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	C₂×C₄×C₈	D₂₃
hypocenter	C₂₃	C₂×#346
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13092193	C₂	direct (N × H)
9. C₂×C₂₃⋊C₁₆	C₄	semidirect
20. C₂₃⋊C₁₆	C₂×C₄	semidirect
42. C₂×C₂₃	#346	semidirect
52. C₂₃	C₂×#346	semidirect
80. C₂	#13092193	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×C₂₃⋊C₁₆	2
#13092193	2
C₂×C₄×C₈×C₂₃	2
C₂×#346	23

Subgroups — C2×#13092193 #15674987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092193 #15674987