Group #21462185 — subgroups

Subgroups — #21462185

Order 7808.

138 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 64 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	#16840683	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11758187	C₂	1	2	yes	maximal
3	#16840651	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840648	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839720	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758187	C₂²	1	2	yes	—
7	C₂×#11758187	C₂²	1	2	yes	—
8	C₂²×#92418	C₂²	1	1	yes	characteristic
9	#14519736	C₄	1	1	yes	characteristic
10	#14519687	C₄	1	1	yes	characteristic
11	#14519687	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₆₁	—	2	2	no	—
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊Dic₆₁	C₈	1	2	yes	—
20	C₄⋊Dic₆₁	C₈	1	2	yes	—
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	—	2	2	no	—
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	C₂³	1	1	yes	characteristic
26	#11758187	—	2	2	no	—
27	#11758187	—	2	2	no	—
28	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
34	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
35	C₈×C₆₁	—	2	1	no	—
36	C₈×C₆₁	M₁₆	1	2	yes	—
37	#92418	—	2	1	no	—
38	#92418	#41	1	2	yes	—
39	C₂²×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	#117	1	1	yes	characteristic
44	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
45	Dic₆₁	—	2	2	no	—
46	Dic₆₁	—	2	2	no	—
47	#2164	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	4	1	no	—
49	C₂×C₆₁	#431	1	1	yes	characteristic
50	C₂×C₆₁	#504	1	2	yes	—
51	#405	—	61	1	no	—
52	C₄⋊C₁₆	—	61	2	no	—
53	C₂²⋊C₁₆	—	61	2	no	—
54	#346	—	61	1	no	—
55	C₄×C₁₆	—	61	1	no	—
56	C₆₁	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	#6923	1	1	yes	characteristic
58	C₂²×C₈	—	61	1	no	—
59	#117	—	61	1	no	—
60	C₂×C₁₆	—	61	2	no	—
61	C₂×C₁₆	—	61	2	no	—
62	#97	—	61	1	no	—
63	#97	—	61	1	no	—
64	C₄×C₈	—	61	1	no	—
65	C₄×C₈	—	61	1	no	—
66	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	61	1	no	—
69	C₂×C₈	—	61	1	no	—
70	C₂×C₈	—	122	2	no	—
71	C₂×C₈	C₂×#6923	1	1	yes	characteristic
72	C₂×C₈	C₂×#6923	1	1	yes	characteristic
73	C₄⋊C₄	—	61	2	no	—
74	C₂²⋊C₄	—	61	2	no	—
75	C₄²	—	61	1	no	—
76	C₄²	—	61	1	no	—
77	C₁₆	—	122	2	no	—
78	C₁₆	—	122	2	no	—
79	C₂³	D₆₁⋊C₈	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	61	2	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
85	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	61	2	no	—
88	C₈	—	122	1	no	—
89	C₈	#11758217	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	122	2	no	—
95	C₄	—	122	2	no	—
96	C₄	#14519856	1	1	yes	characteristic
97	C₄	C₂×#11758217	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#16840779	1	1	yes	characteristic
100	C₂	#16840821	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840683

C₂

yes

maximal, complemented

C₂²⋊#11758187

C₂

yes

maximal

#16840651

C₂

yes

maximal, characteristic, complemented

#16840648

C₂

yes

maximal, characteristic, complemented

#16839720

C₂

yes

maximal, characteristic

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

#14519736

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

M₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂²⋊Dic₆₁

C₈

yes

—

C₄⋊Dic₆₁

C₈

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

#11758187

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

#92418

—

#92418

#41

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#2164

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#431

yes

characteristic

C₂×C₆₁

#504

yes

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₆₁

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

#6923

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

D₆₁⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₆₁⋊C₈

yes

characteristic

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

#11758217

yes

—

C₂²

—

C₂²

—

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

yes

C₄

yes

C₂

—

C₂

#16840779

yes

characteristic

100

C₂

#16840821

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×M₁₆×C₆₁	C₄
hypercenter	C₂×M₁₆	#6923
hypocenter	C₆₁	#2164
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×M₁₆×C₆₁

C₄

C₂×M₁₆

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. #16840683	C₂	semidirect
3. #16840651	C₂	semidirect
4. #16840648	C₂	semidirect
56. C₆₁	#2164	semidirect

H ≅ G/N

type

1. #16840683

C₂

semidirect

3. #16840651

C₂

semidirect

4. #16840648

C₂

semidirect

56. C₆₁

#2164

semidirect

Subgroups — #21462185

Conjugacy classes of subgroups

Complements