Subgroups — C₂×#10625059 #13092960

Order 1472.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₃⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
6	#10625059	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
8	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₃	C₂²	1	2	yes	—
10	C₂²×Dic₂₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₆	—	2	8	no	—
13	C₂×Dic₄₆	C₂²	1	8	yes	—
14	C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
15	C₄⋊Dic₂₃	C₂²	1	4	yes	—
16	Dic₂₃⋊C₄	C₂²	1	8	yes	—
17	C₄×Dic₂₃	C₂²	1	4	yes	—
18	C₂³×C₂₃	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₂₃	—	2	4	no	—
20	C₂×C₄×C₂₃	Q₈	1	4	yes	complemented
21	C₂×C₄×C₂₃	C₂³	1	4	yes	—
22	C₂×C₄×C₂₃	C₂³	1	2	yes	—
23	C₂×Dic₂₃	—	2	4	no	—
24	C₂×Dic₂₃	D₄	1	4	yes	—
25	C₂×Dic₂₃	Q₈	1	4	yes	complemented
26	C₂×Dic₂₃	C₂³	1	4	yes	—
27	C₂×Dic₂₃	C₂³	1	2	yes	—
28	C₂×Dic₂₃	C₂³	1	2	yes	—
29	Dic₄₆	—	2	16	no	—
30	C₂²×C₂₃	C₂×D₄	1	2	yes	—
31	C₂²×C₂₃	C₂×Q₈	1	2	yes	—
32	C₂²×C₂₃	C₂×Q₈	1	2	yes	—
33	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
34	C₄×C₂₃	—	2	4	no	—
35	C₄×C₂₃	C₂×Q₈	1	4	yes	complemented
36	Dic₂₃	—	2	4	no	—
37	Dic₂₃	C₂×D₄	1	4	yes	—
38	Dic₂₃	C₂×Q₈	1	4	yes	complemented
39	C₂×C₄⋊Q₈	—	23	1	no	maximal, Sylow
40	C₂×C₂₃	C₄⋊Q₈	1	4	yes	complemented
41	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
42	C₂×C₂₃	C₂²×Q₈	1	1	yes	characteristic
43	C₂×C₂₃	C₂²×Q₈	1	1	yes	characteristic
44	C₂²×Q₈	—	23	2	no	—
45	C₄⋊Q₈	—	23	8	no	—
46	C₂×C₄⋊C₄	—	23	2	no	—
47	C₂×C₄⋊C₄	—	23	1	no	—
48	C₂×C₄⋊C₄	D₂₃	1	1	yes	characteristic
49	C₂×C₄²	—	23	1	no	—
50	C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	23	8	no	—
52	C₂×Q₈	—	46	8	no	—
53	C₂²×C₄	—	23	1	no	—
54	C₂²×C₄	—	23	1	no	—
55	C₂²×C₄	—	23	2	no	—
56	C₂²×C₄	C₂×D₂₃	1	2	yes	—
57	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
58	C₄⋊C₄	—	23	8	no	—
59	C₄⋊C₄	—	23	4	no	—
60	C₄⋊C₄	C₂×D₂₃	1	4	yes	—
61	C₄²	—	23	4	no	—
62	C₂³	C₂²×D₂₃	1	1	yes	characteristic
63	Q₈	—	46	16	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	23	4	no	—
66	C₂×C₄	—	23	4	no	—
67	C₂×C₄	—	23	2	no	—
68	C₂×C₄	—	23	2	no	—
69	C₂×C₄	—	23	4	no	—
70	C₂×C₄	—	46	4	no	—
71	C₂×C₄	Dic₄₆	1	4	yes	complemented
72	C₂×C₄	C₂²×D₂₃	1	4	yes	—
73	C₂×C₄	C₂²×D₂₃	1	2	yes	—
74	C₂²	C₂×Dic₄₆	1	2	yes	—
75	C₂²	D₄×D₂₃	1	2	yes	—
76	C₂²	Q₈×D₂₃	1	2	yes	—
77	C₂²	C₂³×D₂₃	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	23	4	no	—
80	C₄	—	23	4	no	—
81	C₄	—	46	4	no	—
82	C₄	C₂×Dic₄₆	1	4	yes	complemented
83	C₂	#10625059	1	4	yes	direct product factor
84	C₂	C₂²×Dic₄₆	1	1	yes	characteristic
85	C₂	C₂×D₄×D₂₃	1	1	yes	characteristic
86	C₂	C₂×Q₈×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁴
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂×C₄⋊C₄×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₂₃
hypocenter	C₂₃	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #10625059	C₂	direct (N × H)
20. C₂×C₄×C₂₃	Q₈	semidirect
25. C₂×Dic₂₃	Q₈	semidirect
35. C₄×C₂₃	C₂×Q₈	semidirect
38. Dic₂₃	C₂×Q₈	semidirect
40. C₂×C₂₃	C₄⋊Q₈	semidirect
50. C₂₃	C₂×C₄⋊Q₈	semidirect
71. C₂×C₄	Dic₄₆	semidirect
82. C₄	C₂×Dic₄₆	semidirect
83. C₂	#10625059	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×Dic₄₆	2
C₂×C₄⋊C₄×C₂₃	2
C₂×C₄⋊Dic₂₃	2
C₂×Dic₂₃⋊C₄	2
C₂×C₄×Dic₂₃	2
#10625059	2
C₂×C₄⋊Q₈	23

Subgroups — C2×#10625059 #13092960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625059 #13092960