Subgroups — C₂×#10625018 #13092397

Order 1472.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	2	yes	maximal
3	#10625018	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₈×C₂₃	—	2	2	no	—
5	C₂×Q₈×C₂₃	—	2	2	no	—
6	C₂×Q₈×C₂₃	C₄	1	2	yes	—
7	C₂×Q₈×C₂₃	C₂²	1	2	yes	—
8	C₂²×C₄×C₂₃	C₄	1	2	yes	—
9	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	#67267	—	2	2	no	—
11	#67267	C₂²	1	4	yes	—
12	C₂×C₂₃⋊C₈	—	2	2	no	—
13	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
14	Q₈×C₂₃	—	2	4	no	—
15	Q₈×C₂₃	—	2	4	no	—
16	C₂×C₄×C₂₃	—	2	2	no	—
17	C₂×C₄×C₂₃	—	2	2	no	—
18	C₂×C₄×C₂₃	C₂×C₄	1	4	yes	—
19	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₃	D₄	1	2	yes	—
21	C₂×C₄×C₂₃	D₄	1	2	yes	—
22	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
23	C₂₃⋊C₈	—	2	4	no	—
24	C₂²×C₂₃	—	2	2	no	—
25	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₃	—	2	4	no	—
29	C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
30	C₄×C₂₃	C₂×D₄	1	2	yes	—
31	C₂×#101	—	23	1	no	maximal, Sylow
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	—	2	1	no	—
34	C₂×C₂₃	#101	1	2	yes	complemented
35	C₂×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×Q₈	D₂₃	1	1	yes	characteristic
37	C₂×M₁₆	—	23	2	no	—
38	#101	—	23	4	no	—
39	C₂₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	2	2	no	—
41	C₂×Q₈	—	2	2	no	—
42	C₂×Q₈	Dic₂₃	1	2	yes	—
43	C₂×Q₈	C₂×D₂₃	1	2	yes	—
44	C₂²×C₄	Dic₂₃	1	2	yes	—
45	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
46	M₁₆	—	23	4	no	—
47	M₁₆	—	46	2	no	—
48	C₂×C₈	—	46	2	no	—
49	C₂³	C₂×Dic₂₃	1	1	yes	characteristic
50	Q₈	—	2	4	no	—
51	Q₈	—	2	4	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	C₂×Dic₂₃	1	4	yes	—
55	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
57	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
58	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
59	C₈	—	46	4	no	—
60	C₂²	—	2	2	no	—
61	C₂²	C₂²⋊Dic₂₃	1	1	yes	characteristic
62	C₂²	C₂²⋊Dic₂₃	1	1	yes	characteristic
63	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	C₂²⋊Dic₂₃	1	2	yes	—
66	C₄	C₂×C₂²⋊D₂₃	1	2	yes	—
67	C₂	—	2	1	no	—
68	C₂	—	2	1	no	—
69	C₂	#10625018	1	2	yes	direct product factor
70	C₂	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊Dic₂₃
commutator	C₂²×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×Q₈×C₂₃	C₂
socle	C₂²×C₂₃	C₂²⋊C₄
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×Q₈	D₂₃
hypocenter	C₂₃	C₂×#101
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
3. #10625018	C₂	direct (N × H)
34. C₂×C₂₃	#101	semidirect
39. C₂₃	C₂×#101	semidirect
69. C₂	#10625018	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×Q₈×C₂₃	2
C₂×#67267	2
#10625018	2
C₂×#101	23

Subgroups — C2×#10625018 #13092397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625018 #13092397