Subgroups — #21460765

Order 7808.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840658	C₂	1	2	yes	maximal
2	#16839786	C₂	1	1	yes	maximal, characteristic
3	#14519851	—	2	2	no	—
4	C₂×#11758194	C₄	1	1	yes	characteristic
5	C₂×#11758194	C₂²	1	1	yes	characteristic
6	C₄⋊#92418	—	2	2	no	—
7	C₂×C₄²×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₆₁	—	2	1	no	—
9	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₆₁	—	2	1	no	—
11	C₄²×C₆₁	C₈	1	1	yes	characteristic
12	C₄²×C₆₁	C₈	1	1	yes	characteristic
13	#11758194	—	4	1	no	—
14	#11758194	—	4	1	no	—
15	C₂×#92418	—	2	1	no	—
16	C₂×#92418	D₄	1	2	yes	—
17	#11758187	—	4	2	no	—
18	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₆₁	—	2	1	no	—
20	C₂×C₄×C₆₁	—	2	1	no	—
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	—	4	2	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
26	#92418	—	2	2	no	—
27	#92418	—	4	1	no	—
28	C₂²×C₆₁	—	2	1	no	—
29	C₂²×C₆₁	—	4	1	no	—
30	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₆₁	—	2	2	no	—
32	C₄×C₆₁	—	2	1	no	—
33	C₄×C₆₁	—	4	1	no	—
34	C₄×C₆₁	#99	1	1	yes	characteristic
35	C₄×C₆₁	#101	1	1	yes	characteristic
36	#1327	—	61	1	no	maximal, Sylow
37	C₂×C₆₁	—	2	1	no	—
38	C₂×C₆₁	—	4	1	no	—
39	C₂×C₆₁	#324	1	1	yes	characteristic
40	#423	—	61	1	no	—
41	#349	—	61	2	no	—
42	C₆₁	#1327	1	1	yes	characteristic, complemented, Sylow
43	C₂×M₁₆	—	61	1	no	—
44	C₂×M₁₆	—	61	1	no	—
45	C₂×C₄²	#6923	1	1	yes	characteristic
46	M₃₂	—	122	2	no	—
47	C₄⋊C₈	—	122	2	no	—
48	C₂²×C₄	—	2	1	no	—
49	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
50	M₁₆	—	244	1	no	—
51	M₁₆	—	244	1	no	—
52	C₂×C₈	—	61	2	no	—
53	C₂×C₈	—	122	1	no	—
54	C₄²	—	2	1	no	—
55	C₄²	#92420	1	1	yes	characteristic
56	C₄²	#92420	1	1	yes	characteristic
57	C₁₆	—	244	2	no	—
58	C₂³	#11758217	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×#92420	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
66	C₈	—	122	2	no	—
67	C₈	—	244	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊#92420	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#14519836	1	1	yes	characteristic
75	C₄	#14519838	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#16840607	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519836
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄²×C₆₁	C₄
socle	C₂×C₆₁	#324
hypercenter	C₂×C₄²	#6923
hypocenter	C₆₁	#1327
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
42. C₆₁	#1327	semidirect