Subgroups — #21454211

Order 7808.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839653	C₂	1	7	yes	maximal
2	#16839646	C₂	1	7	yes	maximal, complemented
3	C₄³×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11758196	C₂²	1	7	yes	—
5	C₂×#11758198	C₂²	1	7	yes	—
6	#14519684	C₂²	1	14	yes	—
7	C₂×C₄²×C₆₁	C₂²	1	7	yes	—
8	C₂³×D₆₁	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₆₁	C₂³	1	7	yes	—
10	C₂²×Dic₆₁	C₂³	1	7	yes	—
11	C₄²×C₆₁	—	2	14	no	—
12	#11758198	—	2	14	no	—
13	#11758196	—	2	14	no	—
14	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
15	C₂²×D₆₁	—	2	7	no	—
16	C₂×C₄×C₆₁	—	2	14	no	—
17	C₂×C₄×C₆₁	#41	1	14	yes	—
18	C₂×Dic₆₁	—	2	14	no	—
19	C₂×Dic₆₁	—	2	7	no	—
20	C₂²×C₆₁	C₂×#41	1	7	yes	—
21	C₂×D₆₁	—	4	7	no	—
22	C₄×C₆₁	—	2	14	no	—
23	Dic₆₁	—	4	7	no	—
24	#2866	—	61	1	no	maximal, Sylow
25	C₂×C₆₁	#529	1	7	yes	—
26	D₆₁	—	8	1	no	—
27	#388	—	61	7	no	—
28	#387	—	61	7	no	—
29	C₄³	D₆₁	1	1	yes	characteristic, complemented
30	C₆₁	#2866	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄⋊C₄	—	61	7	no	—
32	C₂×C₂²⋊C₄	—	61	7	no	—
33	C₂×C₄²	C₂×D₆₁	1	7	yes	—
34	#95	—	61	14	no	—
35	C₂⁴	—	61	1	no	—
36	C₂²×C₄	—	61	7	no	—
37	C₂²×C₄	C₂²×D₆₁	1	7	yes	—
38	C₄⋊C₄	—	122	14	no	—
39	C₂²⋊C₄	—	122	14	no	—
40	C₄²	—	2	14	no	—
41	C₂³	—	122	7	no	—
42	C₂³	C₂³×D₆₁	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	122	7	no	—
45	C₂×C₄	—	122	14	no	—
46	C₂×C₄	#11758222	1	14	yes	—
47	C₂²	—	244	7	no	—
48	C₂²	C₂×#11758222	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	244	7	no	—
51	C₂	—	488	1	no	—
52	C₂	#16840296	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂⁴
Fitting	C₄³×C₆₁	C₂
hypercenter	C₄³	D₆₁
hypocenter	C₆₁	#2866
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. #16839646	C₂	semidirect
3. C₄³×C₆₁	C₂	semidirect
29. C₄³	D₆₁	semidirect
30. C₆₁	#2866	semidirect