Subgroups — #21448094

Order 7808.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840167	C₂	1	2	yes	maximal
2	#16839588	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	#14519777	—	2	2	no	—
5	#14519711	—	2	2	no	—
6	#14519711	C₂²	1	4	yes	—
7	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
8	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₂₂	—	4	2	no	—
10	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
12	C₄²×C₆₁	D₄	1	1	yes	characteristic
13	C₄⋊Dic₆₁	—	2	4	no	—
14	C₄⋊Dic₆₁	—	4	2	no	—
15	C₁₆×C₆₁	Q₈	1	4	yes	complemented
16	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
17	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
18	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₆₁	—	4	4	no	—
20	Dic₁₂₂	—	8	4	no	—
21	C₈×C₆₁	Q₁₆	1	2	yes	—
22	C₈×C₆₁	C₂×Q₈	1	2	yes	—
23	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
24	C₄×C₆₁	D₁₆	1	2	yes	—
25	C₄×C₆₁	Q₃₂	1	2	yes	—
26	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₆₁	—	8	4	no	—
29	#2252	—	61	1	no	maximal, Sylow
30	C₂×C₆₁	#500	1	1	yes	characteristic
31	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
32	C₂×C₆₁	C₂×Q₃₂	1	1	yes	characteristic
33	#500	—	61	2	no	—
34	#366	—	61	4	no	—
35	C₄×C₁₆	D₆₁	1	1	yes	characteristic
36	C₆₁	#2252	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊Q₈	—	122	2	no	—
38	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
39	#107	—	61	4	no	—
40	#107	—	122	2	no	—
41	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
42	C₂×Q₈	—	244	2	no	—
43	C₂×C₈	D₂₄₄	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
45	C₄⋊C₄	—	122	4	no	—
46	C₄⋊C₄	—	244	2	no	—
47	C₄²	D₂₄₄	1	1	yes	characteristic
48	C₁₆	Dic₁₂₂	1	4	yes	complemented
49	Q₈	—	488	4	no	—
50	C₂×C₄	—	244	4	no	—
51	C₂×C₄	D₄₈₈	1	1	yes	characteristic
52	C₂×C₄	D₄₈₈	1	1	yes	characteristic
53	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
54	C₈	Dic₂₄₄	1	2	yes	—
55	C₈	C₂×Dic₁₂₂	1	2	yes	—
56	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
57	C₄	—	488	4	no	—
58	C₄	D₉₇₆	1	2	yes	—
59	C₄	Dic₄₈₈	1	2	yes	—
60	C₄	#14519777	1	1	yes	characteristic
61	C₄	C₂×Dic₂₄₄	1	1	yes	characteristic
62	C₂	#16840167	1	1	yes	characteristic
63	C₂	C₂×D₉₇₆	1	1	yes	characteristic
64	C₂	C₂×Dic₄₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	#2252
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₆₁	Q₈	semidirect
36. C₆₁	#2252	semidirect
48. C₁₆	Dic₁₂₂	semidirect