Subgroups — C₂×#10624992 #13092407

Order 1472.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10624992	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₂₃	—	2	1	no	—
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	—	2	1	no	—
8	C₂×Dic₄₆	—	2	2	no	—
9	C₂×Dic₄₆	—	2	1	no	—
10	C₂×Dic₄₆	C₄	1	4	yes	complemented
11	C₂×Dic₄₆	C₂²	1	2	yes	—
12	C₄⋊C₄×C₂₃	—	2	1	no	—
13	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
14	C₂×C₂₃⋊C₈	—	2	2	no	—
15	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₂₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	—	4	2	no	—
19	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₂₃	D₄	1	2	yes	—
21	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₂₃	—	2	4	no	—
24	C₂×Dic₂₃	—	2	2	no	—
25	Dic₄₆	—	2	4	no	—
26	Dic₄₆	—	2	2	no	—
27	Dic₄₆	C₂×C₄	1	4	yes	complemented
28	C₂₃⋊C₈	—	2	2	no	—
29	C₂²×C₂₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₂₃	SD₁₆	1	2	yes	—
31	C₂²×C₂₃	Q₁₆	1	2	yes	—
32	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₃	—	4	2	no	—
34	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
35	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
37	Dic₂₃	—	2	4	no	—
38	C₂×#103	—	23	1	no	maximal, Sylow
39	C₂×C₂₃	#103	1	4	yes	complemented
40	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
43	C₂²×Q₈	—	23	1	no	—
44	C₂²×C₈	—	23	1	no	—
45	C₂×C₄⋊C₄	D₂₃	1	1	yes	characteristic
46	#103	—	23	4	no	—
47	C₂₃	C₂×#103	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	23	4	no	—
49	C₂×Q₈	—	23	2	no	—
50	C₂×Q₈	—	46	2	no	—
51	C₂×Q₈	—	46	1	no	—
52	C₂²×C₄	—	2	1	no	—
53	C₂²×C₄	—	46	1	no	—
54	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
55	C₂×C₈	—	23	2	no	—
56	C₂×C₈	—	46	2	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
59	C₂³	C₂²⋊D₂₃	1	1	yes	characteristic
60	Q₈	—	23	4	no	—
61	Q₈	—	46	4	no	—
62	Q₈	—	46	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	46	4	no	—
66	C₂×C₄	—	46	2	no	—
67	C₂×C₄	C₄×D₂₃	1	2	yes	—
68	C₂×C₄	D₉₂	1	2	yes	—
69	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
71	C₈	—	46	2	no	—
72	C₂²	(C₂×D₂₃)⋊C₄	1	2	yes	—
73	C₂²	#67273	1	2	yes	—
74	C₂²	#67275	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
76	C₄	—	4	2	no	—
77	C₄	—	46	4	no	—
78	C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
79	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
80	C₄	C₂×D₉₂	1	1	yes	characteristic
81	C₂	#10624992	1	4	yes	direct product factor
82	C₂	C₂×(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
83	C₂	C₂×#67273	1	1	yes	characteristic
84	C₂	C₂×#67275	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₂₃
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂×C₄⋊C₄×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	D₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₂₃
hypocenter	C₂₃	C₂×#103
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #10624992	C₂	direct (N × H)
10. C₂×Dic₄₆	C₄	semidirect
27. Dic₄₆	C₂×C₄	semidirect
39. C₂×C₂₃	#103	semidirect
47. C₂₃	C₂×#103	semidirect
81. C₂	#10624992	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
C₂²×C₂₃⋊C₈	2
#10624992	2
C₂×#103	23

Subgroups — C2×#10624992 #13092407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624992 #13092407