Group #21461302 — subgroups

Subgroups — #21461302

Order 7808.

196 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 56 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	#16840784	C₂	1	2	yes	maximal
2	#16840619	C₂	1	4	yes	maximal, complemented
3	#125×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#92420	—	2	2	no	—
5	#14519834	—	2	2	no	—
6	#14519832	C₂²	1	4	yes	—
7	#14519769	C₄	1	1	yes	characteristic
8	#14519768	C₂²	1	2	yes	—
9	#14519767	—	2	2	no	—
10	C₄⋊C₄×D₆₁	—	2	2	no	—
11	C₄⋊C₄×D₆₁	C₄	1	2	yes	—
12	C₄²×D₆₁	C₂²	1	1	yes	characteristic
13	#125×C₆₁	C₄	1	1	yes	characteristic
14	C₂×C₄×D₆₁	—	2	2	no	—
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	D₄	1	2	yes	—
17	C₂×#92420	—	2	4	no	—
18	C₄⋊C₄×C₆₁	—	2	2	no	—
19	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₄⋊Dic₆₁	—	2	2	no	—
22	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
23	#11758196	—	2	2	no	—
24	#11758196	—	2	2	no	—
25	#11758196	—	2	2	no	—
26	C₄×Dic₆₁	D₄	1	2	yes	—
27	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
28	C₂²×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	2	no	—
33	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₂×D₄	1	2	yes	—
35	C₄×D₆₁	—	2	2	no	—
36	C₄×D₆₁	—	4	2	no	—
37	C₄×D₆₁	—	4	4	no	—
38	#92420	—	4	4	no	—
39	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×D₆₁	—	2	2	no	—
41	C₂×D₆₁	#101	1	2	yes	—
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	—	4	2	no	—
45	Dic₆₁	—	2	1	no	—
46	Dic₆₁	—	2	2	no	—
47	Dic₆₁	—	4	2	no	—
48	#1534	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	C₂×#101	1	1	yes	characteristic
50	C₂×C₆₁	#421	1	2	yes	—
51	D₆₁	—	2	2	no	—
52	C₂×#125	—	61	1	no	—
53	#432	—	61	2	no	—
54	#330	—	61	4	no	—
55	C₆₁	#1534	1	1	yes	characteristic, complemented, Sylow
56	#125	—	61	2	no	—
57	#125	—	61	1	no	—
58	#125	—	122	2	no	—
59	#125	#6923	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	61	2	no	—
61	C₂×C₄⋊C₄	—	122	2	no	—
62	C₂×C₄²	—	61	1	no	—
63	C₄⋊C₈	—	122	2	no	—
64	C₂²⋊C₈	—	122	2	no	—
65	#97	—	61	4	no	—
66	C₂²×C₄	—	61	1	no	—
67	C₂²×C₄	—	61	2	no	—
68	C₂²×C₄	—	122	2	no	—
69	C₂×C₈	—	122	4	no	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	61	2	no	—
72	C₄⋊C₄	—	122	2	no	—
73	C₄⋊C₄	—	122	2	no	—
74	C₄⋊C₄	—	122	2	no	—
75	C₄⋊C₄	—	122	2	no	—
76	C₄⋊C₄	C₂×#6923	1	2	yes	—
77	C₄²	—	61	2	no	—
78	C₄²	—	61	1	no	—
79	C₄²	C₂×#6923	1	1	yes	characteristic
80	C₂³	—	61	1	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	61	1	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	—	122	2	no	—
85	C₂×C₄	—	122	2	no	—
86	C₂×C₄	—	244	2	no	—
87	C₂×C₄	—	244	4	no	—
88	C₂×C₄	C₂²⋊#6923	1	2	yes	—
89	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
90	C₈	—	244	4	no	—
91	C₂²	—	61	2	no	—
92	C₂²	—	122	2	no	—
93	C₂²	C₂×C₂²⋊#6923	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	122	1	no	—
98	C₄	—	122	2	no	—
99	C₄	—	244	2	no	—
100	C₂	—	122	2	no	—
101	C₂	D₆₁⋊#101	1	1	yes	characteristic
102	C₂	#16840759	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840784

C₂

yes

maximal

#16840619

C₂

yes

maximal, complemented

#125×D₆₁

C₂

yes

maximal, characteristic

C₄⋊#92420

—

#14519834

—

#14519832

C₂²

yes

—

#14519769

C₄

yes

characteristic

#14519768

C₂²

yes

—

#14519767

—

C₄⋊C₄×D₆₁

—

C₄⋊C₄×D₆₁

C₄

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#125×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

C₂×#92420

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

#11758196

—

#11758196

—

C₄×Dic₆₁

D₄

yes

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂²×D₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#101

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

C₂×#125

—

#432

—

#330

—

C₆₁

#1534

yes

characteristic, complemented, Sylow

#125

—

#125

—

#125

—

122

—

#125

#6923

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂²⋊#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

244

—

C₂²

—

C₂²

—

122

—

C₂²

C₂×C₂²⋊#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

—

244

—

100

C₂

—

122

—

101

C₂

D₆₁⋊#101

yes

characteristic

102

C₂

#16840759

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#125×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₂²⋊C₄
hypercenter	#125	#6923
hypocenter	C₆₁	#1534
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#125×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₂²⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
2. #16840619	C₂	semidirect
55. C₆₁	#1534	semidirect

H ≅ G/N

type

2. #16840619

C₂

semidirect

55. C₆₁

#1534

semidirect

Subgroups — #21461302

Conjugacy classes of subgroups

Complements