Subgroups — C₂²×#14519771 #21459075

Order 7808.

1320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519771	C₂	1	24	yes	maximal, direct product factor
2	C₂²×#11758196	C₂	1	3	yes	maximal, complemented
3	C₂²×#11758198	C₂	1	3	yes	maximal
4	C₂²×C₄²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₆₁	C₂²	1	1	yes	characteristic
6	C₂³×Dic₆₁	C₂²	1	3	yes	—
7	#14519771	C₂²	1	64	yes	direct product factor
8	C₂×#11758196	C₂²	1	36	yes	complemented
9	C₂×#11758198	C₂²	1	36	yes	—
10	C₂³×C₄×C₆₁	C₂²	1	3	yes	—
11	C₂×C₄²×C₆₁	C₂²	1	12	yes	complemented
12	C₂⁴×C₆₁	C₂³	1	1	yes	characteristic
13	C₂³×D₆₁	—	2	12	no	—
14	C₂³×D₆₁	C₂³	1	6	yes	—
15	C₂²×C₄×C₆₁	—	2	12	no	—
16	C₂²×C₄×C₆₁	C₂³	1	18	yes	—
17	C₂²×Dic₆₁	—	2	12	no	—
18	C₂²×Dic₆₁	C₂³	1	18	yes	—
19	C₄²×C₆₁	C₂³	1	16	yes	complemented
20	#11758198	C₂³	1	48	yes	—
21	#11758196	C₂³	1	48	yes	complemented
22	C₂³×C₆₁	#41	1	12	yes	—
23	C₂³×C₆₁	C₂⁴	1	3	yes	—
24	C₂²×D₆₁	—	2	36	no	—
25	C₂²×D₆₁	—	4	16	no	—
26	C₂²×D₆₁	C₂⁴	1	4	yes	—
27	C₂×C₄×C₆₁	—	2	36	no	—
28	C₂×C₄×C₆₁	C₂⁴	1	12	yes	—
29	C₂×Dic₆₁	—	2	36	no	—
30	C₂×Dic₆₁	C₂⁴	1	12	yes	—
31	C₂²×C₆₁	#126	1	16	yes	complemented
32	C₂²×C₆₁	C₂×#41	1	18	yes	—
33	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
34	C₂×D₆₁	—	2	12	no	—
35	C₂×D₆₁	—	4	24	no	—
36	C₄×C₆₁	—	2	12	no	—
37	Dic₆₁	—	2	12	no	—
38	C₂²×#126	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	C₂×#126	1	12	yes	complemented
40	C₂×C₆₁	C₂²×#41	1	3	yes	—
41	D₆₁	—	4	4	no	—
42	C₂×#126	—	61	24	no	—
43	C₂²×C₄⋊C₄	—	61	3	no	—
44	C₂²×C₂²⋊C₄	—	61	3	no	—
45	C₂²×C₄²	D₆₁	1	1	yes	characteristic, complemented
46	C₆₁	C₂²×#126	1	1	yes	characteristic, complemented, Sylow
47	C₂⁵	—	61	1	no	—
48	C₂³×C₄	—	61	3	no	—
49	C₂³×C₄	C₂×D₆₁	1	3	yes	—
50	#126	—	61	64	no	—
51	C₂×C₄⋊C₄	—	61	36	no	—
52	C₂×C₂²⋊C₄	—	61	36	no	—
53	C₂×C₄²	C₂×D₆₁	1	12	yes	complemented
54	C₂⁴	—	61	6	no	—
55	C₂⁴	—	122	12	no	—
56	C₂⁴	C₂²×D₆₁	1	1	yes	characteristic
57	C₂²×C₄	—	2	12	no	—
58	C₂²×C₄	—	61	18	no	—
59	C₂²×C₄	—	122	12	no	—
60	C₂²×C₄	C₂²×D₆₁	1	18	yes	—
61	C₄⋊C₄	—	61	48	no	—
62	C₂²⋊C₄	—	61	48	no	—
63	C₄²	C₂²×D₆₁	1	16	yes	complemented
64	C₂³	—	61	4	no	—
65	C₂³	—	122	36	no	—
66	C₂³	—	244	16	no	—
67	C₂³	#11758222	1	12	yes	—
68	C₂³	C₂³×D₆₁	1	3	yes	—
69	C₂×C₄	—	2	36	no	—
70	C₂×C₄	—	61	12	no	—
71	C₂×C₄	—	122	36	no	—
72	C₂×C₄	C₂³×D₆₁	1	12	yes	—
73	C₂²	—	122	12	no	—
74	C₂²	—	244	24	no	—
75	C₂²	#14519771	1	16	yes	direct product factor
76	C₂²	C₂×#11758222	1	18	yes	—
77	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
78	C₄	—	2	12	no	—
79	C₄	—	122	12	no	—
80	C₂	—	244	4	no	—
81	C₂	C₂×#14519771	1	12	yes	direct product factor
82	C₂	C₂²×#11758222	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₆₁
commutator	C₂²×C₆₁	C₂⁵
Frattini	C₂²	C₂⁴×D₆₁
Fitting	C₂²×C₄²×C₆₁	C₂
socle	C₂⁴×C₆₁	C₂³
hypercenter	C₂²×C₄²	D₆₁
hypocenter	C₆₁	C₂²×#126
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#14519771	C₂	direct (N × H)
2. C₂²×#11758196	C₂	semidirect
4. C₂²×C₄²×C₆₁	C₂	semidirect
7. #14519771	C₂²	direct (N × H)
8. C₂×#11758196	C₂²	semidirect
11. C₂×C₄²×C₆₁	C₂²	semidirect
19. C₄²×C₆₁	C₂³	semidirect
21. #11758196	C₂³	semidirect
31. C₂²×C₆₁	#126	semidirect
39. C₂×C₆₁	C₂×#126	semidirect
45. C₂²×C₄²	D₆₁	semidirect
46. C₆₁	C₂²×#126	semidirect
53. C₂×C₄²	C₂×D₆₁	semidirect
63. C₄²	C₂²×D₆₁	semidirect
75. C₂²	#14519771	direct (N × H)
81. C₂	C₂×#14519771	direct (N × H)

Subgroups — C22×#14519771 #21459075

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14519771 #21459075