Subgroups — C₂×#10625119 #13093180

Order 1472.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625119	C₂	1	8	yes	maximal, direct product factor
3	C₂×#67267	C₂	1	3	yes	maximal, complemented
4	C₂²×C₂₃⋊C₈	C₂	1	3	yes	maximal, complemented
5	#41×C₂₃	C₄	1	4	yes	—
6	#41×C₂₃	C₂²	1	4	yes	—
7	C₂×Q₈×C₂₃	C₄	1	1	yes	characteristic
8	C₂×D₄×C₂₃	C₄	1	3	yes	—
9	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
10	#67267	C₂²	1	12	yes	complemented
11	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₂²	1	3	yes	—
13	C₂×C₂₃⋊C₈	C₂²	1	12	yes	complemented
14	C₂³×C₂₃	C₂×C₄	1	3	yes	—
15	Q₈×C₂₃	C₂×C₄	1	4	yes	—
16	D₄×C₂₃	C₂×C₄	1	12	yes	—
17	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
18	C₂×C₄×C₂₃	C₂×C₄	1	6	yes	—
19	C₂×C₄×C₂₃	C₂³	1	6	yes	—
20	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
21	C₂₃⋊C₈	C₂³	1	2	yes	—
22	C₂₃⋊C₈	C₂³	1	6	yes	—
23	C₂²×C₂₃	—	2	6	no	—
24	C₂²×C₂₃	C₂²×C₄	1	6	yes	—
25	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₃	C₂²×C₄	1	6	yes	—
28	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
29	C₂×#131	—	23	1	no	maximal, Sylow
30	C₂×C₂₃	—	2	6	no	—
31	C₂×C₂₃	#131	1	2	yes	complemented
32	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
33	C₂×#41	D₂₃	1	1	yes	characteristic
34	#131	—	23	8	no	—
35	C₂×M₁₆	—	23	3	no	—
36	C₂²×C₈	—	23	3	no	—
37	C₂₃	C₂×#131	1	1	yes	characteristic, complemented, Sylow
38	#41	Dic₂₃	1	4	yes	—
39	#41	C₂×D₂₃	1	4	yes	—
40	C₂×Q₈	Dic₂₃	1	1	yes	characteristic
41	C₂×D₄	Dic₂₃	1	3	yes	—
42	C₂²×C₄	C₂×D₂₃	1	3	yes	—
43	M₁₆	—	23	12	no	—
44	C₂×C₈	—	23	12	no	—
45	C₂×C₈	—	23	1	no	—
46	C₂×C₈	—	23	3	no	—
47	C₂³	C₂×Dic₂₃	1	3	yes	—
48	Q₈	C₂×Dic₂₃	1	4	yes	—
49	D₄	C₂×Dic₂₃	1	12	yes	—
50	C₂×C₄	C₂×Dic₂₃	1	3	yes	—
51	C₂×C₄	C₂×Dic₂₃	1	6	yes	—
52	C₂×C₄	C₂²×D₂₃	1	6	yes	—
53	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
54	C₈	—	23	2	no	—
55	C₈	—	23	6	no	—
56	C₂²	—	2	6	no	—
57	C₂²	C₂²×Dic₂₃	1	6	yes	—
58	C₂²	C₂²×Dic₂₃	1	1	yes	characteristic
59	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
60	C₄	C₂²×Dic₂₃	1	6	yes	—
61	C₄	C₂³×D₂₃	1	1	yes	characteristic
62	C₂	—	2	6	no	—
63	C₂	#10625119	1	2	yes	direct product factor
64	C₂	C₂³×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂³×C₄
Frattini	C₄	C₂³×D₂₃
Fitting, prime radical	C₂×#41×C₂₃	C₂
socle	C₂²×C₂₃	C₂²×C₄
cosocle	C₄×C₂₃	C₂⁴
hypercenter	C₂×#41	D₂₃
hypocenter	C₂₃	C₂×#131
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #10625119	C₂	direct (N × H)
3. C₂×#67267	C₂	semidirect
4. C₂²×C₂₃⋊C₈	C₂	semidirect
10. #67267	C₂²	semidirect
13. C₂×C₂₃⋊C₈	C₂²	semidirect
31. C₂×C₂₃	#131	semidirect
37. C₂₃	C₂×#131	semidirect
63. C₂	#10625119	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×#41×C₂₃	2
#10625119	2
C₂×#67267	2
C₂²×C₂₃⋊C₈	2
C₂×#131	23

Subgroups — C2×#10625119 #13093180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625119 #13093180