Subgroups — C₂×#10622548 #13071017

Order 1408.

888 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₁	C₂	1	6	yes	maximal
3	#10622548	C₂	1	8	yes	maximal, direct product factor
4	C₂³×C₄×C₁₁	C₂²	1	3	yes	—
5	C₂³×Dic₁₁	C₂²	1	4	yes	—
6	C₂×C₄²×C₁₁	C₄	1	8	yes	complemented
7	C₂×C₄²×C₁₁	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₁₁	—	2	24	no	—
9	C₂×C₄⋊Dic₁₁	C₂²	1	24	yes	—
10	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
11	C₂²×C₄×C₁₁	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₁₁	D₄	1	12	yes	—
13	C₂²×C₄×C₁₁	Q₈	1	12	yes	—
14	C₂²×C₄×C₁₁	C₂³	1	6	yes	—
15	C₂²×Dic₁₁	—	2	24	no	—
16	C₂²×Dic₁₁	C₂³	1	8	yes	—
17	C₄²×C₁₁	C₂×C₄	1	16	yes	complemented
18	C₄⋊Dic₁₁	—	2	48	no	—
19	C₂×#384	—	11	1	no	maximal, Sylow
20	C₂³×C₁₁	C₂²×C₄	1	2	yes	—
21	C₂³×C₁₁	C₂×D₄	1	6	yes	—
22	C₂³×C₁₁	C₂×Q₈	1	6	yes	—
23	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
24	C₂×C₄×C₁₁	C₄⋊C₄	1	48	yes	complemented
25	C₂×C₄×C₁₁	C₂²×C₄	1	12	yes	—
26	C₂×C₄×C₁₁	C₂×D₄	1	12	yes	—
27	C₂×C₄×C₁₁	C₂×Q₈	1	12	yes	—
28	C₂×Dic₁₁	—	2	24	no	—
29	C₂×Dic₁₁	—	4	16	no	—
30	C₂²×C₄⋊C₄	—	11	6	no	—
31	C₂²×C₄²	D₁₁	1	1	yes	characteristic
32	#384	—	11	8	no	—
33	C₂²×C₁₁	C₂×C₄⋊C₄	1	12	yes	—
34	C₂²×C₁₁	#127	1	4	yes	—
35	C₂²×C₁₁	C₄⋊Q₈	1	12	yes	—
36	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
37	C₂²×C₁₁	C₂²×D₄	1	3	yes	—
38	C₂²×C₁₁	C₂²×Q₈	1	3	yes	—
39	C₄×C₁₁	C₂×C₄⋊C₄	1	24	yes	complemented
40	Dic₁₁	—	4	8	no	—
41	C₂³×C₄	—	11	4	no	—
42	C₂³×C₄	C₂×D₁₁	1	3	yes	—
43	C₂×C₄⋊C₄	—	11	24	no	—
44	C₂×C₄⋊C₄	—	22	24	no	—
45	C₂×C₄²	Dic₁₁	1	8	yes	complemented
46	C₂×C₄²	C₂×D₁₁	1	4	yes	—
47	C₂×C₁₁	#384	1	8	yes	complemented
48	C₂×C₁₁	C₂²×C₄⋊C₄	1	3	yes	—
49	C₂×C₁₁	C₂×#127	1	1	yes	characteristic
50	C₂×C₁₁	C₂×C₄⋊Q₈	1	3	yes	—
51	C₂⁴	C₂²×D₁₁	1	1	yes	characteristic
52	C₂²×C₄	—	11	8	no	—
53	C₂²×C₄	—	22	24	no	—
54	C₂²×C₄	Dic₂₂	1	12	yes	—
55	C₂²×C₄	D₄₄	1	12	yes	—
56	C₂²×C₄	C₂×Dic₁₁	1	12	yes	—
57	C₂²×C₄	C₂²×D₁₁	1	6	yes	—
58	C₄⋊C₄	—	22	48	no	—
59	C₄²	C₂×Dic₁₁	1	16	yes	complemented
60	C₁₁	C₂×#384	1	1	yes	characteristic, complemented, Sylow
61	C₂³	C₂×Dic₂₂	1	6	yes	—
62	C₂³	C₂×D₄₄	1	6	yes	—
63	C₂³	C₂²×Dic₁₁	1	2	yes	—
64	C₂³	C₂³×D₁₁	1	1	yes	characteristic
65	C₂×C₄	—	22	24	no	—
66	C₂×C₄	—	44	16	no	—
67	C₂×C₄	C₄⋊Dic₁₁	1	48	yes	complemented
68	C₂×C₄	C₂×Dic₂₂	1	12	yes	—
69	C₂×C₄	C₂×D₄₄	1	12	yes	—
70	C₂×C₄	C₂²×Dic₁₁	1	12	yes	—
71	C₂²	#66922	1	12	yes	—
72	C₂²	#66927	1	4	yes	—
73	C₂²	C₂×C₄⋊Dic₁₁	1	12	yes	—
74	C₂²	C₂²×Dic₂₂	1	3	yes	—
75	C₂²	C₂²×D₄₄	1	3	yes	—
76	C₂²	C₂³×Dic₁₁	1	1	yes	characteristic
77	C₄	—	44	8	no	—
78	C₄	C₂×C₄⋊Dic₁₁	1	24	yes	complemented
79	C₂	#10622548	1	8	yes	direct product factor
80	C₂	C₂×#66922	1	3	yes	—
81	C₂	C₂×#66927	1	1	yes	characteristic
82	C₂	C₂²×C₄⋊Dic₁₁	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂³×C₄
Frattini	C₂³	C₂³×D₁₁
Fitting	C₂²×C₄²×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	C₂³
cosocle	C₂³×C₁₁	C₂⁴
hypercenter	C₂²×C₄²	D₁₁
hypocenter	C₁₁	C₂×#384
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. #10622548	C₂	direct (N × H)
6. C₂×C₄²×C₁₁	C₄	semidirect
17. C₄²×C₁₁	C₂×C₄	semidirect
24. C₂×C₄×C₁₁	C₄⋊C₄	semidirect
39. C₄×C₁₁	C₂×C₄⋊C₄	semidirect
45. C₂×C₄²	Dic₁₁	semidirect
47. C₂×C₁₁	#384	semidirect
59. C₄²	C₂×Dic₁₁	semidirect
60. C₁₁	C₂×#384	semidirect
67. C₂×C₄	C₄⋊Dic₁₁	semidirect
78. C₄	C₂×C₄⋊Dic₁₁	semidirect
79. C₂	#10622548	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×C₄²×C₁₁	2
C₂²×C₄⋊Dic₁₁	2
#10622548	2
C₂×#384	11

Subgroups — C2×#10622548 #13071017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10622548 #13071017