Subgroups — C₂×#10624990 #13092447

Order 1472.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10624990	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	C₄⋊C₄×C₂₃	—	2	1	no	—
9	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
10	C₄⋊Dic₂₃	—	2	1	no	—
11	C₄⋊Dic₂₃	C₂²	1	2	yes	—
12	C₂×C₂₃⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	—	2	2	no	—
16	C₂×C₄×C₂₃	—	4	2	no	—
17	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₃	Q₈	1	2	yes	—
20	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₃	—	2	2	no	—
22	C₂×Dic₂₃	—	4	2	no	—
23	C₂₃⋊C₈	C₂×C₄	1	4	yes	complemented
24	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
25	C₂²×C₂₃	SD₁₆	1	2	yes	—
26	C₂²×C₂₃	SD₁₆	1	2	yes	—
27	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₃	—	4	2	no	—
29	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
30	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
32	Dic₂₃	—	4	2	no	—
33	C₂×#106	—	23	1	no	maximal, Sylow
34	C₂×C₂₃	#106	1	4	yes	complemented
35	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
38	C₂²×C₈	—	23	1	no	—
39	C₂×C₄⋊C₄	—	23	1	no	—
40	C₂×C₄⋊C₄	D₂₃	1	1	yes	characteristic
41	#106	—	23	4	no	—
42	C₂₃	C₂×#106	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	46	1	no	—
45	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
46	C₂×C₈	—	23	4	no	—
47	C₂×C₈	—	23	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	23	2	no	—
50	C₄⋊C₄	—	46	1	no	—
51	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
52	C₂³	C₂²⋊D₂₃	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	46	2	no	—
56	C₂×C₄	—	92	2	no	—
57	C₂×C₄	Dic₄₆	1	2	yes	—
58	C₂×C₄	C₄×D₂₃	1	2	yes	—
59	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
61	C₈	—	23	4	no	—
62	C₂²	Dic₂₃⋊C₄	1	2	yes	—
63	C₂²	#67273	1	2	yes	—
64	C₂²	#67274	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	92	2	no	—
68	C₄	Dic₂₃⋊C₄	1	2	yes	—
69	C₄	C₂×Dic₄₆	1	1	yes	characteristic
70	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
71	C₂	#10624990	1	4	yes	direct product factor
72	C₂	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#67273	1	1	yes	characteristic
74	C₂	C₂×#67274	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×#106
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. #10624990	C₂	direct (N × H)
12. C₂×C₂₃⋊C₈	C₄	semidirect
23. C₂₃⋊C₈	C₂×C₄	semidirect
34. C₂×C₂₃	#106	semidirect
42. C₂₃	C₂×#106	semidirect
71. C₂	#10624990	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×C₄⋊C₄×C₂₃	2
C₂×C₄⋊Dic₂₃	2
C₂²×C₂₃⋊C₈	2
#10624990	2
C₂×#106	23

Subgroups — C2×#10624990 #13092447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624990 #13092447