Subgroups — #21443853

Order 7808.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840131	C₂	1	1	yes	maximal, characteristic
2	#16839540	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#347	C₂	1	1	yes	maximal, characteristic
4	#14519777	C₄	1	1	yes	characteristic
5	#14519769	C₄	1	1	yes	characteristic
6	#14519717	—	2	1	no	—
7	#14519702	—	2	1	no	—
8	#14519702	—	2	1	no	—
9	M₃₂×C₆₁	—	2	1	no	—
10	#97×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₂₂	—	2	1	no	—
12	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₆₁	—	2	1	no	—
16	C₄⋊Dic₆₁	—	4	1	no	—
17	#11758196	—	4	1	no	—
18	C₁₆×C₆₁	—	2	2	no	—
19	#11758185	—	2	2	no	—
20	C₂×C₄×C₆₁	—	2	1	no	—
21	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₆₁	—	4	1	no	—
23	C₂×Dic₆₁	—	4	1	no	—
24	Dic₁₂₂	—	4	1	no	—
25	Dic₁₂₂	—	4	1	no	—
26	C₈×C₆₁	—	2	1	no	—
27	C₈×C₆₁	—	2	1	no	—
28	C₂²×C₆₁	#100	1	1	yes	characteristic
29	C₄×C₆₁	—	4	1	no	—
30	C₄×C₆₁	#104	1	1	yes	characteristic
31	C₄×C₆₁	#104	1	1	yes	characteristic
32	Dic₆₁	—	8	1	no	—
33	Dic₆₁	—	8	1	no	—
34	#1356	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	—	2	1	no	—
36	C₂×C₆₁	#329	1	1	yes	characteristic
37	#491	—	61	1	no	—
38	#347	—	61	1	no	—
39	#347	D₆₁	1	1	yes	characteristic
40	C₆₁	#1356	1	1	yes	characteristic, complemented, Sylow
41	C₄⋊Q₈	—	61	1	no	—
42	#125	—	61	1	no	—
43	M₃₂	—	2	1	no	—
44	M₃₂	—	122	1	no	—
45	#103	—	122	1	no	—
46	#103	—	122	1	no	—
47	#97	C₂×D₆₁	1	1	yes	characteristic
48	C₂×Q₈	—	122	1	no	—
49	C₂×C₈	D₂₄₄	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
51	C₄⋊C₄	—	122	1	no	—
52	C₄⋊C₄	—	244	1	no	—
53	C₄⋊C₄	—	244	1	no	—
54	C₄²	C₄×D₆₁	1	1	yes	characteristic
55	C₁₆	—	2	2	no	—
56	C₁₆	—	122	2	no	—
57	Q₈	—	244	1	no	—
58	Q₈	—	244	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	244	1	no	—
61	C₂×C₄	—	244	1	no	—
62	C₂×C₄	#11758198	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	2	1	no	—
65	C₂²	#14519693	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	488	1	no	—
68	C₄	—	488	1	no	—
69	C₄	#14519703	1	1	yes	characteristic
70	C₄	#14519705	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#16839501	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16839501
commutator	C₄²×C₆₁	C₂×C₄
Frattini	#97	C₂×D₆₁
Fitting	C₆₁×#347	C₂
socle	C₂×C₆₁	#329
hypercenter	#347	D₆₁
hypocenter	C₆₁	#1356
LCS	G ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
40. C₆₁	#1356	semidirect