Subgroups — #21460957

Order 7808.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840673	C₂	1	2	yes	maximal
2	#16840142	C₂	1	1	yes	maximal, characteristic
3	#14519838	—	2	2	no	—
4	C₂×Dic₂₄₄	—	2	2	no	—
5	#14519777	C₄	1	1	yes	characteristic
6	#14519777	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
8	C₂×Dic₁₂₂	—	2	1	no	—
9	C₂×Dic₁₂₂	D₄	1	2	yes	—
10	#11758217	—	4	2	no	—
11	C₂×C₈×C₆₁	—	2	1	no	—
12	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₆₁	—	4	1	no	—
14	C₄⋊Dic₆₁	—	4	1	no	—
15	Dic₂₄₄	—	4	4	no	—
16	C₂×C₄×C₆₁	—	2	1	no	—
17	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×Dic₆₁	—	2	2	no	—
19	C₂×Dic₆₁	—	4	1	no	—
20	Dic₁₂₂	—	4	2	no	—
21	Dic₁₂₂	—	4	2	no	—
22	#92420	—	8	2	no	—
23	C₈×C₆₁	—	2	2	no	—
24	C₂²×C₆₁	#99	1	1	yes	characteristic
25	C₄×C₆₁	—	2	2	no	—
26	C₄×C₆₁	—	2	1	no	—
27	Dic₆₁	—	4	2	no	—
28	Dic₆₁	—	8	1	no	—
29	#1411	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	—	2	1	no	—
31	C₂×C₆₁	#353	1	1	yes	characteristic
32	#494	—	61	1	no	—
33	#356	—	61	2	no	—
34	C₆₁	#1411	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	122	2	no	—
36	C₄⋊Q₈	—	61	1	no	—
37	C₄⋊Q₈	—	61	1	no	—
38	#101	—	122	2	no	—
39	C₄×C₈	#6923	1	1	yes	characteristic
40	C₂×Q₈	—	61	2	no	—
41	C₂×Q₈	—	122	1	no	—
42	Q₁₆	—	244	4	no	—
43	M₁₆	—	244	2	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	244	1	no	—
46	C₄⋊C₄	—	244	1	no	—
47	C₄²	C₂×#6923	1	1	yes	characteristic
48	Q₈	—	244	2	no	—
49	Q₈	—	244	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	122	2	no	—
52	C₂×C₄	—	244	1	no	—
53	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	488	2	no	—
56	C₂²	#14519836	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	488	1	no	—
60	C₄	—	244	2	no	—
61	C₂	—	2	1	no	—
62	C₂	#16840667	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16840667
commutator	C₄²×C₆₁	C₂×C₄
Frattini	C₄²	C₂×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂×C₆₁	#353
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1411
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
34. C₆₁	#1411	semidirect