Subgroups — C₂×#10625040 #13092961

Order 1472.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₆	C₂	1	2	yes	maximal
2	C₂×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₂₃	C₂	1	4	yes	maximal
4	#10625040	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₃	C₂²	1	2	yes	—
7	C₂²×Dic₂₃	C₂²	1	4	yes	—
8	C₂×Dic₄₆	—	2	8	no	—
9	C₂×Dic₄₆	C₂²	1	8	yes	—
10	C₄²×C₂₃	C₂²	1	4	yes	—
11	C₄⋊Dic₂₃	C₂²	1	16	yes	—
12	C₂³×C₂₃	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₂₃	D₄	1	4	yes	—
14	C₂×C₄×C₂₃	Q₈	1	8	yes	complemented
15	C₂×C₄×C₂₃	C₂³	1	2	yes	—
16	C₂×C₄×C₂₃	C₂³	1	4	yes	—
17	C₂×Dic₂₃	—	2	8	no	—
18	C₂×Dic₂₃	C₂³	1	8	yes	—
19	Dic₄₆	—	2	16	no	—
20	C₂²×C₂₃	C₂×D₄	1	2	yes	—
21	C₂²×C₂₃	C₂×Q₈	1	4	yes	—
22	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
23	C₄×C₂₃	C₂×D₄	1	4	yes	—
24	C₄×C₂₃	C₂×Q₈	1	8	yes	complemented
25	Dic₂₃	—	2	8	no	—
26	C₂×C₄⋊Q₈	—	23	1	no	maximal, Sylow
27	C₂×C₂₃	C₄⋊Q₈	1	4	yes	complemented
28	C₂×C₂₃	C₂²×D₄	1	1	yes	characteristic
29	C₂×C₂₃	C₂²×Q₈	1	2	yes	—
30	C₂²×Q₈	—	23	2	no	—
31	C₄⋊Q₈	—	23	8	no	—
32	C₂×C₄⋊C₄	—	23	4	no	—
33	C₂×C₄²	D₂₃	1	1	yes	characteristic
34	C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	23	8	no	—
36	C₂×Q₈	—	46	8	no	—
37	C₂²×C₄	—	23	4	no	—
38	C₂²×C₄	C₂×D₂₃	1	2	yes	—
39	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
40	C₄⋊C₄	—	23	16	no	—
41	C₄²	C₂×D₂₃	1	4	yes	—
42	C₂³	C₂²×D₂₃	1	1	yes	characteristic
43	Q₈	—	46	16	no	—
44	C₂×C₄	—	23	8	no	—
45	C₂×C₄	—	46	8	no	—
46	C₂×C₄	Dic₄₆	1	8	yes	complemented
47	C₂×C₄	D₉₂	1	4	yes	—
48	C₂×C₄	C₂²×D₂₃	1	4	yes	—
49	C₂×C₄	C₂²×D₂₃	1	2	yes	—
50	C₂²	C₂×Dic₄₆	1	4	yes	—
51	C₂²	C₂×D₉₂	1	2	yes	—
52	C₂²	C₂³×D₂₃	1	1	yes	characteristic
53	C₄	—	46	8	no	—
54	C₄	C₂×Dic₄₆	1	8	yes	complemented
55	C₄	C₂×D₉₂	1	4	yes	—
56	C₂	#10625040	1	4	yes	direct product factor
57	C₂	C₂²×Dic₄₆	1	2	yes	—
58	C₂	C₂²×D₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁴
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂×C₄²×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂³
hypercenter	C₂×C₄²	D₂₃
hypocenter	C₂₃	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #10625040	C₂	direct (N × H)
14. C₂×C₄×C₂₃	Q₈	semidirect
24. C₄×C₂₃	C₂×Q₈	semidirect
27. C₂×C₂₃	C₄⋊Q₈	semidirect
34. C₂₃	C₂×C₄⋊Q₈	semidirect
46. C₂×C₄	Dic₄₆	semidirect
54. C₄	C₂×Dic₄₆	semidirect
56. C₂	#10625040	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×C₄²×C₂₃	2
C₂×C₄⋊Dic₂₃	2
#10625040	2
C₂×C₄⋊Q₈	23

Subgroups — C2×#10625040 #13092961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10625040 #13092961