Group #21460752 — subgroups

Subgroups — #21460752

Order 7808.

128 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840658	C₂	1	2	yes	maximal, complemented
2	#16839725	C₂	1	1	yes	maximal, characteristic
3	#14519851	—	2	2	no	—
4	C₂²×C₄×D₆₁	C₄	1	1	yes	characteristic
5	C₂×#11758194	C₂²	1	1	yes	characteristic
6	#14519689	—	2	2	no	—
7	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
8	C₂³×D₆₁	C₈	1	1	yes	characteristic
9	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×Dic₆₁	C₈	1	1	yes	characteristic
11	C₂×C₄×D₆₁	—	2	1	no	—
12	C₂×C₄×D₆₁	—	2	1	no	—
13	C₂×C₄×D₆₁	—	4	1	no	—
14	C₂×C₄×D₆₁	—	4	1	no	—
15	M₁₆×C₆₁	—	4	1	no	—
16	C₂×C₈×C₆₁	—	2	1	no	—
17	#11758194	—	4	1	no	—
18	C₂×#92418	D₄	1	2	yes	—
19	#11758187	—	4	2	no	—
20	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
21	C₂²×D₆₁	—	2	1	no	—
22	C₂²×D₆₁	—	4	2	no	—
23	C₂²×D₆₁	—	4	1	no	—
24	C₂×C₄×C₆₁	—	2	1	no	—
25	C₂×C₄×C₆₁	—	2	1	no	—
26	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
28	C₂×Dic₆₁	—	2	1	no	—
29	C₂×Dic₆₁	—	4	1	no	—
30	C₄×D₆₁	—	4	2	no	—
31	C₄×D₆₁	—	4	1	no	—
32	C₄×D₆₁	—	4	1	no	—
33	C₈×C₆₁	—	4	1	no	—
34	#92418	—	2	2	no	—
35	C₂²×C₆₁	—	2	1	no	—
36	C₂²×C₆₁	—	4	1	no	—
37	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×D₆₁	—	2	2	no	—
39	C₂×D₆₁	—	4	1	no	—
40	C₂×D₆₁	—	4	2	no	—
41	C₂×D₆₁	—	4	1	no	—
42	C₂×D₆₁	—	4	2	no	—
43	C₄×C₆₁	—	2	1	no	—
44	C₄×C₆₁	#99	1	1	yes	characteristic
45	C₄×C₆₁	#100	1	1	yes	characteristic
46	Dic₆₁	—	4	1	no	—
47	#1320	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	1	no	—
49	C₂×C₆₁	—	4	1	no	—
50	C₂×C₆₁	#323	1	1	yes	characteristic
51	D₆₁	—	4	2	no	—
52	#407	—	61	1	no	—
53	#349	—	61	2	no	—
54	C₆₁	#1320	1	1	yes	characteristic, complemented, Sylow
55	C₂³×C₄	—	61	1	no	—
56	C₂×M₁₆	—	61	1	no	—
57	C₂×M₁₆	#6923	1	1	yes	characteristic
58	M₃₂	—	122	2	no	—
59	C₂²⋊C₈	—	122	2	no	—
60	C₂⁴	—	61	1	no	—
61	C₂²×C₄	—	61	1	no	—
62	C₂²×C₄	—	122	1	no	—
63	C₂²×C₄	—	122	1	no	—
64	C₂²×C₄	—	244	1	no	—
65	C₂²×C₄	—	244	1	no	—
66	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
67	M₁₆	—	4	1	no	—
68	M₁₆	—	244	1	no	—
69	C₂×C₈	—	2	1	no	—
70	C₂×C₈	—	61	2	no	—
71	C₁₆	—	244	2	no	—
72	C₂³	—	122	1	no	—
73	C₂³	—	244	1	no	—
74	C₂³	—	244	2	no	—
75	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	122	1	no	—
79	C₂×C₄	—	244	2	no	—
80	C₂×C₄	—	244	1	no	—
81	C₂×C₄	—	244	1	no	—
82	C₂×C₄	—	244	1	no	—
83	C₂×C₄	#11758213	1	1	yes	characteristic
84	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
85	C₈	—	4	1	no	—
86	C₈	—	122	2	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	4	1	no	—
89	C₂²	—	122	2	no	—
90	C₂²	—	244	1	no	—
91	C₂²	—	244	2	no	—
92	C₂²	—	244	2	no	—
93	C₂²	—	244	1	no	—
94	C₂²	#14519834	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	244	1	no	—
97	C₄	#14519836	1	1	yes	characteristic
98	C₄	#14519837	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	244	2	no	—
102	C₂	#16840606	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840658

C₂

yes

maximal, complemented

#16839725

C₂

yes

maximal, characteristic

#14519851

—

C₂²×C₄×D₆₁

C₄

yes

characteristic

C₂×#11758194

C₂²

yes

characteristic

#14519689

—

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂³×D₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

#11758194

—

C₂×#92418

D₄

yes

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

#1320

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#323

yes

characteristic

D₆₁

—

#407

—

#349

—

C₆₁

#1320

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

#6923

yes

characteristic

M₃₂

—

122

—

C₂²⋊C₈

—

122

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

—

244

—

C₂²×C₄

—

244

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₁₆

—

244

—

C₂³

—

122

—

C₂³

—

244

—

C₂³

—

244

—

C₂³

D₆₁⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758213

yes

characteristic

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₂²

—

C₂²

—

C₂²

—

122

—

C₂²

—

244

—

C₂²

—

244

—

C₂²

—

244

—

C₂²

—

244

—

C₂²

#14519834

yes

characteristic

C₄

—

C₄

—

244

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

244

—

102

C₂

#16840606

yes

characteristic

	subgroup	G/H
center	C₄	#14519836
commutator	C₂³×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×M₁₆×C₆₁	C₄
socle	C₂×C₆₁	#323
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#1320
LCS	G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

#14519836

commutator

C₂³×C₆₁

C₂×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×M₁₆×C₆₁

C₄

C₂×C₆₁

C₂×M₁₆

C₆₁

G ▷ C₂³×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. #16840658	C₂	semidirect
54. C₆₁	#1320	semidirect

H ≅ G/N

type

1. #16840658

C₂

semidirect

54. C₆₁

#1320

semidirect

Subgroups — #21460752

Conjugacy classes of subgroups

Complements