Subgroups — C₂×#10625001 #13092463

Order 1472.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#67267	C₂	1	2	yes	maximal
3	#10625001	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₂₃	C₄	1	2	yes	—
6	C₂×C₈×C₂₃	C₄	1	2	yes	—
7	C₂×C₈×C₂₃	C₂²	1	2	yes	—
8	#67267	—	2	2	no	—
9	#67267	C₂²	1	4	yes	—
10	C₂×C₂₃⋊C₈	—	2	2	no	—
11	C₂³×C₂₃	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	Q₈	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
18	C₈×C₂₃	C₂×C₄	1	4	yes	—
19	C₂₃⋊C₈	—	2	4	no	—
20	C₂²×C₂₃	—	2	2	no	—
21	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₂₃	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
26	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₂×#108	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	—	2	1	no	—
30	C₂×C₂₃	—	2	1	no	—
31	C₂×C₂₃	#108	1	2	yes	complemented
32	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×M₁₆	—	23	2	no	—
34	C₂²×C₈	D₂₃	1	1	yes	characteristic
35	#108	—	23	4	no	—
36	C₂₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
38	M₁₆	—	23	4	no	—
39	M₁₆	—	46	2	no	—
40	C₂×C₈	—	46	2	no	—
41	C₂×C₈	Dic₂₃	1	2	yes	—
42	C₂×C₈	Dic₂₃	1	2	yes	—
43	C₂×C₈	C₂×D₂₃	1	2	yes	—
44	C₂³	Dic₄₆	1	1	yes	characteristic
45	C₂×C₄	Dic₄₆	1	1	yes	characteristic
46	C₂×C₄	D₉₂	1	1	yes	characteristic
47	C₂×C₄	D₉₂	1	1	yes	characteristic
48	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
49	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
51	C₈	—	46	4	no	—
52	C₈	C₂×Dic₂₃	1	4	yes	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₂₃	1	1	yes	characteristic
55	C₂²	C₄⋊Dic₂₃	1	1	yes	characteristic
56	C₂²	C₂×Dic₄₆	1	1	yes	characteristic
57	C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
58	C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
59	C₄	C₂×D₉₂	1	1	yes	characteristic
60	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	—	2	1	no	—
63	C₂	#10625001	1	2	yes	direct product factor
64	C₂	C₂×C₄⋊Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₂
commutator	C₄×C₂₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂²×C₂₃	C₄⋊C₄
prime radical	C₂³×C₂₃	Q₈
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂²×C₈	D₂₃
hypocenter	C₂₃	C₂×#108
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #10625001	C₂	direct (N × H)
31. C₂×C₂₃	#108	semidirect
36. C₂₃	C₂×#108	semidirect
63. C₂	#10625001	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×C₈×C₂₃	2
C₂×#67267	2
#10625001	2
C₂×#108	23

Subgroups — C2×#10625001 #13092463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625001 #13092463