Subgroups — C₂×#13092834 #15686496

Order 2944.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092834	C₂	1	8	yes	maximal, direct product factor
2	C₂×#10624994	C₂	1	3	yes	maximal, complemented
3	C₂²×C₂₃⋊C₁₆	C₂	1	3	yes	maximal, complemented
4	C₂×C₂₃×#131	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃×#131	C₄	1	4	yes	—
7	C₂₃×#131	C₂²	1	4	yes	—
8	C₂×M₁₆×C₂₃	C₄	1	3	yes	—
9	C₂²×C₈×C₂₃	C₂²	1	3	yes	—
10	#10624994	C₂²	1	12	yes	complemented
11	C₂×C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₁₆	C₂²	1	3	yes	—
13	C₂×C₂₃⋊C₁₆	C₂²	1	12	yes	complemented
14	#41×C₂₃	C₈	1	4	yes	—
15	#41×C₂₃	C₂×C₄	1	4	yes	—
16	C₂×Q₈×C₂₃	C₈	1	1	yes	characteristic
17	C₂×D₄×C₂₃	C₈	1	3	yes	—
18	C₂²×C₄×C₂₃	C₂×C₄	1	3	yes	—
19	M₁₆×C₂₃	C₂×C₄	1	12	yes	—
20	C₂×C₈×C₂₃	C₂×C₄	1	3	yes	—
21	C₂×C₈×C₂₃	C₂×C₄	1	6	yes	—
22	C₂×C₈×C₂₃	C₂³	1	6	yes	—
23	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
24	C₂₃⋊C₁₆	C₂³	1	2	yes	—
25	C₂₃⋊C₁₆	C₂³	1	6	yes	—
26	C₂³×C₂₃	C₂×C₈	1	3	yes	—
27	Q₈×C₂₃	C₂×C₈	1	4	yes	—
28	D₄×C₂₃	C₂×C₈	1	12	yes	—
29	C₂×C₄×C₂₃	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₂₃	C₂×C₈	1	6	yes	—
31	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₃	C₂²×C₄	1	6	yes	—
33	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₂₃	C₂²×C₄	1	6	yes	—
35	C₈×C₂₃	C₂⁴	1	1	yes	characteristic
36	C₂×#504	—	23	1	no	maximal, Sylow
37	C₂²×C₂₃	—	2	6	no	—
38	C₂²×C₂₃	C₂²×C₈	1	6	yes	—
39	C₂²×C₂₃	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₂₃	C₂²×C₈	1	6	yes	—
42	C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
43	C₂×#131	D₂₃	1	1	yes	characteristic
44	#504	—	23	8	no	—
45	C₂×M₃₂	—	23	3	no	—
46	C₂²×C₁₆	—	23	3	no	—
47	C₂×C₂₃	—	2	6	no	—
48	C₂×C₂₃	#504	1	2	yes	complemented
49	C₂×C₂₃	C₂³×C₈	1	1	yes	characteristic
50	C₂×#41	Dic₂₃	1	1	yes	characteristic
51	#131	Dic₂₃	1	4	yes	—
52	#131	C₂×D₂₃	1	4	yes	—
53	C₂×M₁₆	Dic₂₃	1	3	yes	—
54	C₂²×C₈	C₂×D₂₃	1	3	yes	—
55	M₃₂	—	23	12	no	—
56	C₂×C₁₆	—	23	12	no	—
57	C₂×C₁₆	—	23	1	no	—
58	C₂×C₁₆	—	23	3	no	—
59	C₂₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
60	#41	C₂₃⋊C₈	1	4	yes	—
61	#41	C₂×Dic₂₃	1	4	yes	—
62	C₂×Q₈	C₂₃⋊C₈	1	1	yes	characteristic
63	C₂×D₄	C₂₃⋊C₈	1	3	yes	—
64	C₂²×C₄	C₂×Dic₂₃	1	3	yes	—
65	M₁₆	C₂×Dic₂₃	1	12	yes	—
66	C₂×C₈	C₂×Dic₂₃	1	3	yes	—
67	C₂×C₈	C₂×Dic₂₃	1	6	yes	—
68	C₂×C₈	C₂²×D₂₃	1	6	yes	—
69	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
70	C₁₆	—	23	2	no	—
71	C₁₆	—	23	6	no	—
72	C₂³	C₂×C₂₃⋊C₈	1	3	yes	—
73	Q₈	C₂×C₂₃⋊C₈	1	4	yes	—
74	D₄	C₂×C₂₃⋊C₈	1	12	yes	—
75	C₂×C₄	C₂×C₂₃⋊C₈	1	3	yes	—
76	C₂×C₄	C₂×C₂₃⋊C₈	1	6	yes	—
77	C₂×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
78	C₂×C₄	C₂²×Dic₂₃	1	6	yes	—
79	C₈	C₂²×Dic₂₃	1	1	yes	characteristic
80	C₈	C₂²×Dic₂₃	1	6	yes	—
81	C₈	C₂³×D₂₃	1	1	yes	characteristic
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×C₂₃⋊C₈	1	6	yes	—
84	C₂²	C₂²×C₂₃⋊C₈	1	1	yes	characteristic
85	C₄	C₂²×C₂₃⋊C₈	1	1	yes	characteristic
86	C₄	C₂²×C₂₃⋊C₈	1	6	yes	—
87	C₄	C₂³×Dic₂₃	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#13092834	1	2	yes	direct product factor
90	C₂	C₂³×C₂₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₂₃
commutator	C₂×C₂₃	C₂³×C₈
Frattini	C₈	C₂³×D₂₃
Fitting	C₂×C₂₃×#131	C₂
socle	C₂²×C₂₃	C₂²×C₈
prime radical	C₂×#41×C₂₃	C₄
cosocle	C₈×C₂₃	C₂⁴
hypercenter	C₂×#131	D₂₃
hypocenter	C₂₃	C₂×#504
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. #13092834	C₂	direct (N × H)
2. C₂×#10624994	C₂	semidirect
3. C₂²×C₂₃⋊C₁₆	C₂	semidirect
10. #10624994	C₂²	semidirect
13. C₂×C₂₃⋊C₁₆	C₂²	semidirect
48. C₂×C₂₃	#504	semidirect
59. C₂₃	C₂×#504	semidirect
89. C₂	#13092834	direct (N × H)

Maximal subgroups

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

subgroup	index
#13092834	2
C₂×#10624994	2
C₂²×C₂₃⋊C₁₆	2
C₂×C₂₃×#131	2
C₂×#504	23

Subgroups — C2×#13092834 #15686496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092834 #15686496