Group #21460695 — subgroups

Subgroups — #21460695

Order 7808.

180 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 60 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	C₂×#14519832	C₂	1	2	yes	maximal
2	#16839627	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92420	—	2	2	no	—
4	#14519832	—	2	2	no	—
5	#14519832	C₄	1	4	yes	complemented
6	C₂×C₄⋊Dic₆₁	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	#14519684	—	2	2	no	—
9	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	—	2	1	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₆₁	—	2	1	no	—
13	C₂²×Dic₆₁	D₄	1	2	yes	—
14	C₂×#92420	—	2	4	no	—
15	C₂×#92420	—	2	4	no	—
16	C₂×#92420	—	2	4	no	—
17	C₄⋊C₄×C₆₁	—	4	1	no	—
18	C₄⋊Dic₆₁	—	4	1	no	—
19	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
20	C₄×Dic₆₁	D₄	1	1	yes	characteristic
21	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
22	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	—	2	1	no	—
25	C₂×C₄×C₆₁	—	4	1	no	—
26	C₂×C₄×C₆₁	—	4	2	no	—
27	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×Dic₆₁	—	2	2	no	—
30	C₂×Dic₆₁	—	2	2	no	—
31	C₂×Dic₆₁	—	4	1	no	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
34	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
35	#92420	—	2	8	no	—
36	C₂²×C₆₁	#95	1	1	yes	characteristic
37	C₂²×C₆₁	#100	1	1	yes	characteristic
38	C₂²×C₆₁	#101	1	1	yes	characteristic
39	C₂²×C₆₁	#104	1	2	yes	—
40	C₂²×C₆₁	#104	1	2	yes	—
41	C₄×C₆₁	—	2	1	no	—
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	8	1	no	—
44	Dic₆₁	—	2	2	no	—
45	Dic₆₁	—	2	2	no	—
46	Dic₆₁	—	8	1	no	—
47	#1295	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#329	1	1	yes	characteristic
49	C₂×C₆₁	#329	1	1	yes	characteristic
50	C₂×C₆₁	#330	1	2	yes	—
51	C₂×C₆₁	#339	1	2	yes	—
52	C₂×C₆₁	#343	1	1	yes	characteristic
53	C₂×#97	—	61	2	no	—
54	#382	—	61	1	no	—
55	C₆₁	#1295	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	122	2	no	—
57	C₂×C₄⋊C₄	—	61	1	no	—
58	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
59	C₂×C₄²	—	61	1	no	—
60	#97	—	61	4	no	—
61	#97	—	122	2	no	—
62	#95	—	122	2	no	—
63	C₂²×C₄	—	2	1	no	—
64	C₂²×C₄	—	61	2	no	—
65	C₂²×C₄	—	122	1	no	—
66	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
67	C₂×C₈	—	122	4	no	—
68	C₂×C₈	—	122	4	no	—
69	C₂×C₈	—	122	4	no	—
70	C₄⋊C₄	—	4	1	no	—
71	C₄⋊C₄	—	244	1	no	—
72	C₄²	—	61	2	no	—
73	C₄²	—	61	1	no	—
74	C₄²	—	61	1	no	—
75	C₂³	C₂²⋊#6923	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	—	61	2	no	—
81	C₂×C₄	—	61	2	no	—
82	C₂×C₄	—	122	2	no	—
83	C₂×C₄	—	122	2	no	—
84	C₂×C₄	—	244	1	no	—
85	C₂×C₄	—	244	2	no	—
86	C₂×C₄	C₄×#6923	1	1	yes	characteristic
87	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
88	C₈	—	122	8	no	—
89	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
90	C₂²	#14519837	1	1	yes	characteristic
91	C₂²	#14519838	1	1	yes	characteristic
92	C₂²	#14519841	1	2	yes	—
93	C₂²	#14519842	1	2	yes	—
94	C₄	—	2	1	no	—
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	—	122	2	no	—
98	C₄	—	122	2	no	—
99	C₄	—	488	1	no	—
100	C₂	#16840617	1	1	yes	characteristic
101	C₂	#16840618	1	1	yes	characteristic
102	C₂	#16840619	1	2	yes	—
103	C₂	#16840632	1	2	yes	—
104	C₂	#16840642	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519832

C₂

yes

maximal

#16839627

C₂

yes

maximal, characteristic

C₂²×#92420

—

#14519832

—

#14519832

C₄

yes

complemented

C₂×C₄⋊Dic₆₁

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519684

—

C₂×C₄⋊C₄×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×#92420

—

C₂×#92420

—

C₂×#92420

—

C₄⋊C₄×C₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

#92420

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

—

C₂²×C₆₁

#104

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#339

yes

—

C₂×C₆₁

#343

yes

characteristic

C₂×#97

—

#382

—

C₆₁

#1295

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#6923

yes

characteristic

C₂×C₄²

—

#97

—

#97

—

122

—

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

244

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

122

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#14519842

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

—

488

—

100

C₂

#16840617

yes

characteristic

101

C₂

#16840618

yes

characteristic

102

C₂

#16840619

yes

—

103

C₂

#16840632

yes

—

104

C₂

#16840642

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂³×C₆₁	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1295
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂×C₄⋊C₄×C₆₁

C₄

socle

C₂³×C₆₁

C₂²⋊C₄

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
5. #14519832	C₄	semidirect
55. C₆₁	#1295	semidirect

H ≅ G/N

type

5. #14519832

C₄

semidirect

55. C₆₁

#1295

semidirect

Subgroups — #21460695

Conjugacy classes of subgroups

Complements