Subgroups — #21462040

Order 7808.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519851	C₂	1	2	yes	maximal
2	#16840654	C₂	1	4	yes	maximal, complemented
3	#16839718	C₂	1	1	yes	maximal, characteristic
4	#14519851	C₄	1	4	yes	complemented
5	#14519851	C₂²	1	4	yes	—
6	C₂×#11758187	C₄	1	4	yes	complemented
7	C₂×#11758194	C₄	1	1	yes	characteristic
8	C₂²×#92418	C₂²	1	1	yes	characteristic
9	#14519688	C₂²	1	2	yes	—
10	C₄×#92418	C₄	1	2	yes	—
11	#117×C₆₁	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₄⋊C₄×C₆₁	—	2	1	no	—
14	C₂²⋊C₄×C₆₁	—	2	1	no	—
15	C₄²×C₆₁	C₂×C₄	1	2	yes	—
16	#11758194	—	2	2	no	—
17	C₂×#92418	C₂×C₄	1	2	yes	—
18	C₂×#92418	C₂×C₄	1	1	yes	characteristic
19	C₂×#92418	C₂×C₄	1	2	yes	—
20	C₂×#92418	C₂×C₄	1	2	yes	—
21	C₂×#92418	C₂³	1	1	yes	characteristic
22	#11758187	C₂×C₄	1	8	yes	—
23	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₆₁	—	2	2	no	—
25	C₂×C₄×C₆₁	C₄²	1	2	yes	—
26	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	#92418	—	2	2	no	—
30	#92418	C₄²	1	1	yes	characteristic
31	#92418	C₄²	1	1	yes	characteristic
32	#92418	C₂²×C₄	1	2	yes	—
33	C₂²×C₆₁	—	4	1	no	—
34	C₂²×C₆₁	#97	1	2	yes	—
35	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₆₁	—	4	2	no	—
37	C₄×C₆₁	#97	1	2	yes	—
38	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
40	#2110	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	—	2	1	no	—
42	C₂×C₆₁	—	2	2	no	—
43	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
44	C₂×M₃₂	—	61	2	no	—
45	#405	—	61	1	no	—
46	#347	—	61	4	no	—
47	C₆₁	#2110	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₁₆	—	61	1	no	—
49	C₂²×C₈	—	61	1	no	—
50	#117	#6923	1	1	yes	characteristic
51	M₃₂	—	61	4	no	—
52	M₃₂	—	61	4	no	—
53	C₂×C₁₆	—	61	4	no	—
54	#97	—	61	2	no	—
55	C₄×C₈	—	61	2	no	—
56	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
57	M₁₆	—	122	2	no	—
58	C₂×C₈	—	61	2	no	—
59	C₂×C₈	—	61	2	no	—
60	C₂×C₈	—	61	1	no	—
61	C₂×C₈	—	61	1	no	—
62	C₂×C₈	—	61	2	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×#6923	1	2	yes	—
66	C₁₆	—	61	8	no	—
67	C₂³	#11758217	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	#11758213	1	2	yes	—
70	C₂×C₄	C₄×#6923	1	2	yes	—
71	C₂×C₄	#11758217	1	1	yes	characteristic
72	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
73	C₈	—	61	1	no	—
74	C₈	—	61	1	no	—
75	C₈	—	61	2	no	—
76	C₈	—	122	2	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#14519832	1	2	yes	—
79	C₂²	C₂×#11758217	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#14519832	1	2	yes	—
82	C₄	C₂×C₄×#6923	1	1	yes	characteristic
83	C₄	C₂×#11758213	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#14519832	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#6923
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×#6923
Fitting	#117×C₆₁	C₄
socle	C₂×C₆₁	C₂×#97
hypercenter	#117	#6923
hypocenter	C₆₁	#2110
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #16840654	C₂	semidirect
4. #14519851	C₄	semidirect
6. C₂×#11758187	C₄	semidirect
47. C₆₁	#2110	semidirect