Subgroups — C₂×#13092245 #15675177

Order 2944.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625000	C₂	1	2	yes	maximal
2	#13092245	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊Dic₂₃	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₂₃	C₂²	1	2	yes	—
8	#10625000	—	2	2	no	—
9	#10625000	C₂²	1	4	yes	—
10	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
11	C₂²×Dic₂₃	—	4	2	no	—
12	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	Q₈	1	2	yes	—
15	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₂₃	—	2	4	no	—
17	C₄⋊Dic₂₃	—	4	2	no	—
18	C₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
19	C₂³×C₂₃	D₈	1	1	yes	characteristic
20	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₃	Q₁₆	1	2	yes	—
23	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₂₃	—	4	4	no	—
25	C₂×Dic₂₃	—	8	4	no	—
26	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
27	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×#367	—	23	1	no	maximal, Sylow
30	C₂²×C₂₃	#107	1	2	yes	—
31	C₂²×C₂₃	SD₃₂	1	4	yes	—
32	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
33	C₄×C₂₃	#107	1	2	yes	—
34	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₂₃	—	8	4	no	—
37	C₂²×C₁₆	D₂₃	1	1	yes	characteristic
38	C₂×#107	—	23	2	no	—
39	#367	—	23	4	no	—
40	C₂×C₂₃	#367	1	4	yes	complemented
41	C₂×C₂₃	C₂×#107	1	1	yes	characteristic
42	C₂×C₂₃	C₂×SD₃₂	1	2	yes	—
43	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	46	2	no	—
45	C₂×C₁₆	Dic₂₃	1	4	yes	complemented
46	C₂×C₁₆	C₂×D₂₃	1	2	yes	—
47	#107	—	23	4	no	—
48	#107	—	46	2	no	—
49	C₂₃	C₂×#367	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	92	2	no	—
51	C₂²×C₄	D₉₂	1	1	yes	characteristic
52	C₂×C₈	Dic₄₆	1	2	yes	—
53	C₂×C₈	D₉₂	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₂₃	1	2	yes	—
55	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
56	C₄⋊C₄	—	46	4	no	—
57	C₄⋊C₄	—	92	2	no	—
58	C₁₆	C₂×Dic₂₃	1	4	yes	complemented
59	C₂³	D₁₈₄	1	1	yes	characteristic
60	C₂×C₄	—	92	4	no	—
61	C₂×C₄	—	184	4	no	—
62	C₂×C₄	D₁₈₄	1	1	yes	characteristic
63	C₂×C₄	Dic₉₂	1	2	yes	—
64	C₂×C₄	C₄⋊Dic₂₃	1	2	yes	—
65	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
66	C₈	C₄⋊Dic₂₃	1	2	yes	—
67	C₈	C₂×Dic₄₆	1	1	yes	characteristic
68	C₈	C₂²×Dic₂₃	1	1	yes	characteristic
69	C₂²	#10624982	1	4	yes	—
70	C₂²	#10625000	1	2	yes	—
71	C₂²	C₂×D₁₈₄	1	1	yes	characteristic
72	C₄	—	184	4	no	—
73	C₄	#10625000	1	2	yes	—
74	C₄	C₂×Dic₉₂	1	1	yes	characteristic
75	C₄	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic
76	C₂	#13092245	1	4	yes	direct product factor
77	C₂	C₂×#10625000	1	1	yes	characteristic
78	C₂	C₂×#10624982	1	2	yes	—

	subgroup	G/H
center	C₂³	D₁₈₄
commutator	C₈×C₂₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂²×C₁₆×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	D₈
cosocle	C₂×C₈×C₂₃	C₂³
hypercenter	C₂²×C₁₆	D₂₃
hypocenter	C₂₃	C₂×#367
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13092245	C₂	direct (N × H)
6. C₂×C₁₆×C₂₃	C₄	semidirect
18. C₁₆×C₂₃	C₂×C₄	semidirect
40. C₂×C₂₃	#367	semidirect
45. C₂×C₁₆	Dic₂₃	semidirect
49. C₂₃	C₂×#367	semidirect
58. C₁₆	C₂×Dic₂₃	semidirect
76. C₂	#13092245	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×#10625000	2
#13092245	2
C₂²×C₁₆×C₂₃	2
C₂×#367	23

Subgroups — C2×#13092245 #15675177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092245 #15675177