Group #21454925 — subgroups

Subgroups — #21454925

Order 7808.

314 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 197 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	#16839893	C₂	1	8	yes	maximal, complemented
2	#16839823	C₂	1	4	yes	maximal
3	#16839819	C₂	1	2	yes	maximal
4	C₆₁×#533	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#92418	C₂²	1	4	yes	—
6	C₄⋊#92418	C₂²	1	8	yes	—
7	C₂²⋊#92418	C₂²	1	4	yes	—
8	#14519688	C₂²	1	4	yes	—
9	#14519688	C₂²	1	4	yes	—
10	C₄×#92418	C₂²	1	4	yes	—
11	C₄⋊Q₈×C₆₁	C₄	1	2	yes	—
12	#125×C₆₁	C₄	1	2	yes	—
13	C₂²⋊Q₈×C₆₁	C₄	1	4	yes	—
14	C₄×Q₈×C₆₁	C₂²	1	4	yes	—
15	#117×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
21	C₄⋊C₄×C₆₁	C₂×C₄	1	8	yes	—
22	C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
23	C₂²⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
24	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₆₁	C₂³	1	2	yes	—
27	C₄²×C₆₁	C₂³	1	4	yes	—
28	C₂×#92418	C₂³	1	8	yes	—
29	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	Q₈×C₆₁	—	4	4	no	—
31	C₂×C₄×C₆₁	—	2	2	no	—
32	C₂×C₄×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂²×C₄	1	8	yes	—
37	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
38	#92418	—	2	8	no	—
39	C₂²×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	—	2	8	no	—
46	C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
47	#2987	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	4	1	no	—
49	C₂×C₆₁	#519	1	1	yes	characteristic
50	C₂×C₆₁	#568	1	2	yes	—
51	#533	D₆₁	1	1	yes	characteristic
52	#446	—	61	8	no	—
53	#433	—	61	4	no	—
54	#432	—	61	2	no	—
55	C₆₁	#2987	1	1	yes	characteristic, complemented, Sylow
56	C₄⋊Q₈	Dic₆₁	1	2	yes	—
57	#125	Dic₆₁	1	2	yes	—
58	C₂²⋊Q₈	Dic₆₁	1	4	yes	—
59	C₄×Q₈	C₂×D₆₁	1	4	yes	—
60	#117	C₂×D₆₁	1	2	yes	—
61	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
62	C₄⋊C₈	—	61	4	no	—
63	C₄⋊C₈	—	61	8	no	—
64	C₂²⋊C₈	—	61	4	no	—
65	#97	—	61	4	no	—
66	#97	—	61	4	no	—
67	C₄×C₈	—	61	4	no	—
68	C₂×Q₈	C₂×Dic₆₁	1	4	yes	—
69	C₂²×C₄	C₂×Dic₆₁	1	2	yes	—
70	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
71	C₂×C₈	—	61	8	no	—
72	C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
73	C₄⋊C₄	C₂×Dic₆₁	1	8	yes	—
74	C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
75	C₂²⋊C₄	C₂×Dic₆₁	1	4	yes	—
76	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
77	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
78	C₄²	C₂²×D₆₁	1	4	yes	—
79	C₄²	C₂²×D₆₁	1	2	yes	—
80	C₂³	C₂²×Dic₆₁	1	1	yes	characteristic
81	Q₈	—	4	4	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
85	C₂×C₄	C₂²×Dic₆₁	1	2	yes	—
86	C₂×C₄	C₂²×Dic₆₁	1	2	yes	—
87	C₂×C₄	C₂²×Dic₆₁	1	8	yes	—
88	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
89	C₈	—	122	8	no	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂³×Dic₆₁	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	—	2	8	no	—
97	C₄	#14519825	1	2	yes	—
98	C₂	—	4	1	no	—
99	C₂	#16840240	1	1	yes	characteristic
100	C₂	#16840529	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839893

C₂

yes

maximal, complemented

#16839823

C₂

yes

maximal

#16839819

C₂

yes

maximal

C₆₁×#533

C₂

yes

maximal, characteristic

C₄⋊#92418

C₂²

yes

—

C₄⋊#92418

C₂²

yes

—

C₂²⋊#92418

C₂²

yes

—

#14519688

C₂²

yes

—

#14519688

C₂²

yes

—

C₄×#92418

C₂²

yes

—

C₄⋊Q₈×C₆₁

C₄

yes

—

#125×C₆₁

C₄

yes

—

C₂²⋊Q₈×C₆₁

C₄

yes

—

C₄×Q₈×C₆₁

C₂²

yes

—

#117×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₂²⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂³

yes

—

C₄²×C₆₁

C₂³

yes

—

C₂×#92418

C₂³

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂⁴

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂³×C₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

2₋¹⁺⁴

yes

—

#2987

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#519

yes

characteristic

C₂×C₆₁

#568

yes

—

#533

D₆₁

yes

—

—

—

C₆₁

#2987

yes

characteristic, complemented, Sylow

C₄⋊Q₈

Dic₆₁

yes

—

#125

Dic₆₁

yes

—

C₂²⋊Q₈

Dic₆₁

yes

—

C₄×Q₈

C₂×D₆₁

yes

—

#117

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂×Q₈

C₂×Dic₆₁

yes

—

C₂²×C₄

C₂×Dic₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₂²⋊C₄

C₂×Dic₆₁

yes

—

C₄²

C₂×Dic₆₁

yes

characteristic

C₄²

C₂×Dic₆₁

yes

characteristic

C₄²

C₂²×D₆₁

yes

—

C₄²

C₂²×D₆₁

yes

—

C₂³

C₂²×Dic₆₁

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₂×C₄

C₂²×Dic₆₁

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

—

C₂×C₄

C₂³×D₆₁

yes

characteristic

C₈

—

122

—

C₂²

—

C₂²

—

C₂²

C₂³×Dic₆₁

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#14519825

yes

—

C₂

—

C₂

#16840240

yes

characteristic

100

C₂

#16840529

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₄
Fitting	C₆₁×#533	C₂
hypercenter	#533	D₆₁
hypocenter	C₆₁	#2987
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #533

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₆₁

commutator, socle

C₂²×C₆₁

C₂³×C₄

Fitting

C₆₁×#533

C₂

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #533

N	H ≅ G/N	type
1. #16839893	C₂	semidirect
55. C₆₁	#2987	semidirect

H ≅ G/N

type

1. #16839893

C₂

semidirect

55. C₆₁

#2987

semidirect

Subgroups — #21454925

Conjugacy classes of subgroups

Complements