Group #21460689 — subgroups

Subgroups — #21460689

Order 7808.

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

normal subgroups only

This group has 152 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	#16840765	C₂	1	2	yes	maximal
2	C₂×#14519706	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758217	—	2	2	no	—
4	#14519844	C₄	1	4	yes	—
5	C₄⋊#92420	—	2	2	no	—
6	C₂²×#92418	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	#14519706	—	2	2	no	—
9	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
12	C₂²×Dic₆₁	Q₈	1	1	yes	characteristic
13	#11758217	—	4	2	no	—
14	#11758217	—	4	2	no	—
15	C₂×#92420	—	2	4	no	—
16	C₂×C₈×C₆₁	—	2	1	no	—
17	C₂×C₈×C₆₁	—	4	1	no	—
18	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
19	C₄×Dic₆₁	D₄	1	2	yes	—
20	C₂×#92418	—	2	1	no	—
21	C₂×#92418	—	4	1	no	—
22	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	—	2	1	no	—
25	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	4	1	no	—
28	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
30	C₂×Dic₆₁	D₈	1	1	yes	characteristic
31	C₂×Dic₆₁	SD₁₆	1	2	yes	—
32	C₂×Dic₆₁	Q₁₆	1	1	yes	characteristic
33	#92420	—	4	4	no	—
34	C₈×C₆₁	—	4	1	no	—
35	#92418	—	4	1	no	—
36	C₂²×C₆₁	—	2	1	no	—
37	C₂²×C₆₁	—	2	1	no	—
38	C₂²×C₆₁	#95	1	1	yes	characteristic
39	C₂²×C₆₁	#106	1	1	yes	characteristic
40	C₂²×C₆₁	#107	1	1	yes	characteristic
41	C₄×C₆₁	—	2	1	no	—
42	C₄×C₆₁	#100	1	1	yes	characteristic
43	C₄×C₆₁	#101	1	1	yes	characteristic
44	Dic₆₁	—	2	2	no	—
45	Dic₆₁	#102	1	2	yes	—
46	Dic₆₁	#103	1	2	yes	—
47	#1292	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	1	no	—
49	C₂×C₆₁	—	2	1	no	—
50	C₂×C₆₁	#338	1	1	yes	characteristic
51	C₂×C₆₁	#340	1	1	yes	characteristic
52	C₂×C₆₁	#343	1	1	yes	characteristic
53	#423	—	61	2	no	—
54	C₂×C₄⋊C₈	—	61	1	no	—
55	C₆₁	#1292	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	122	2	no	—
57	C₂²×C₈	—	61	1	no	—
58	C₂²×C₈	#6923	1	1	yes	characteristic
59	C₂×C₄²	—	61	1	no	—
60	C₄⋊C₈	—	61	4	no	—
61	C₄⋊C₈	—	122	2	no	—
62	C₄⋊C₈	—	122	2	no	—
63	C₂²×C₄	—	61	1	no	—
64	C₂²×C₄	—	61	1	no	—
65	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
66	M₁₆	—	244	2	no	—
67	M₁₆	—	244	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	4	1	no	—
70	C₂×C₈	—	122	4	no	—
71	C₂×C₈	—	122	1	no	—
72	C₂×C₈	—	244	1	no	—
73	C₄²	—	61	2	no	—
74	C₄²	—	61	2	no	—
75	C₂³	C₄⋊#6923	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	61	2	no	—
79	C₂×C₄	—	61	2	no	—
80	C₂×C₄	—	61	1	no	—
81	C₂×C₄	—	61	1	no	—
82	C₂×C₄	—	61	2	no	—
83	C₂×C₄	—	244	1	no	—
84	C₂×C₄	C₄×#6923	1	1	yes	characteristic
85	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
86	C₈	—	4	1	no	—
87	C₈	—	244	4	no	—
88	C₈	—	244	1	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	2	1	no	—
91	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
92	C₂²	#14519845	1	1	yes	characteristic
93	C₂²	#14519846	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	61	2	no	—
96	C₄	—	61	2	no	—
97	C₄	—	122	2	no	—
98	C₄	#14519837	1	1	yes	characteristic
99	C₄	#14519838	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	2	1	no	—
102	C₂	#16840631	1	1	yes	characteristic
103	C₂	#16840636	1	1	yes	characteristic
104	C₂	#16840642	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840765

C₂

yes

maximal

C₂×#14519706

C₂

yes

maximal, characteristic

C₂×#11758217

—

#14519844

C₄

yes

—

C₄⋊#92420

—

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

—

—

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

D₄

yes

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

D₈

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

—

C₂×Dic₆₁

Q₁₆

yes

characteristic

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

#102

yes

—

Dic₆₁

#103

yes

—

#1292

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₄⋊C₈

—

C₆₁

#1292

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

244

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₄²

—

C₄²

—

C₂³

C₄⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₄×#6923

yes

characteristic

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

244

—

C₈

—

244

—

C₂²

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

122

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#16840631

yes

characteristic

103

C₂

#16840636

yes

characteristic

104

C₂

#16840642

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1292
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²

(C₂×#6923)⋊C₄

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂²×C₈×C₆₁

C₄

C₂²×C₆₁

C₂²×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
55. C₆₁	#1292	semidirect

H ≅ G/N

type

55. C₆₁

#1292

semidirect

Subgroups — #21460689

Conjugacy classes of subgroups

Complements