Group #21460881 — subgroups

Subgroups — #21460881

Order 7808.

132 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 50 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	D₆₁⋊#108	C₂	1	1	yes	maximal, characteristic
2	#16840772	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
4	D₆₁⋊M₁₆	—	2	1	no	—
5	#14519856	—	2	1	no	—
6	#14519848	C₄	1	2	yes	complemented
7	#14519847	—	2	1	no	—
8	#14519846	C₄	1	2	yes	—
9	#14519845	—	2	1	no	—
10	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
11	C₂×#11758185	C₄	1	1	yes	characteristic, complemented
12	C₁₆×D₆₁	—	2	1	no	—
13	C₁₆×D₆₁	—	2	1	no	—
14	C₂×C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
16	C₂²⋊#6923	—	4	1	no	—
17	#11758217	—	4	1	no	—
18	C₄⋊#6923	—	2	2	no	—
19	C₄×#6923	—	4	1	no	—
20	#11758213	—	2	2	no	—
21	D₆₁⋊C₈	—	4	1	no	—
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	Q₈	1	1	yes	characteristic
24	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
25	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	D₄	1	1	yes	characteristic
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₁₆×C₆₁	—	2	1	no	—
29	#11758185	—	2	1	no	—
30	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
31	C₂×#6923	—	4	2	no	—
32	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
34	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×D₆₁	D₈	1	1	yes	characteristic
37	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
38	#92420	—	4	2	no	—
39	C₈×C₆₁	C₄²	1	1	yes	characteristic
40	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
41	#92418	C₄⋊C₄	1	1	yes	characteristic
42	#92418	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₆₁	#106	1	1	yes	characteristic
44	C₂×D₆₁	—	2	2	no	—
45	C₂×D₆₁	#102	1	1	yes	characteristic
46	C₂×D₆₁	#103	1	1	yes	characteristic
47	#6923	—	8	2	no	—
48	C₄×C₆₁	#95	1	1	yes	characteristic
49	C₄×C₆₁	#107	1	1	yes	characteristic
50	Dic₆₁	#102	1	1	yes	characteristic
51	Dic₆₁	#103	1	1	yes	characteristic
52	#1382	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	#340	1	1	yes	characteristic
55	D₆₁	—	2	1	no	—
56	D₆₁	#359	1	2	yes	—
57	C₂²×C₁₆	—	61	1	no	—
58	C₂×#108	—	61	1	no	—
59	#427	—	61	1	no	—
60	C₆₁	#1382	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	122	1	no	—
62	C₂²×C₈	—	61	1	no	—
63	#117	—	122	1	no	—
64	C₂×C₁₆	—	61	1	no	—
65	C₂×C₁₆	—	122	1	no	—
66	C₂×C₁₆	—	122	1	no	—
67	C₂×C₁₆	#6923	1	1	yes	characteristic, complemented
68	#108	—	61	2	no	—
69	#108	—	122	1	no	—
70	#107	—	61	2	no	—
71	#106	—	122	1	no	—
72	C₂²×C₄	—	61	1	no	—
73	M₁₆	—	122	2	no	—
74	M₁₆	—	244	1	no	—
75	C₂×C₈	—	61	1	no	—
76	C₂×C₈	—	61	1	no	—
77	C₂×C₈	—	61	1	no	—
78	C₂×C₈	—	61	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	244	1	no	—
81	C₂×C₈	C₂×#6923	1	1	yes	characteristic
82	C₄⋊C₄	—	122	2	no	—
83	C₂²⋊C₄	—	244	1	no	—
84	C₄²	—	244	1	no	—
85	C₁₆	—	2	1	no	—
86	C₁₆	—	122	1	no	—
87	C₂³	—	61	1	no	—
88	C₂×C₄	—	61	1	no	—
89	C₂×C₄	—	61	1	no	—
90	C₂×C₄	—	61	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	244	2	no	—
94	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
95	C₈	—	61	1	no	—
96	C₈	—	61	1	no	—
97	C₈	—	244	2	no	—
98	C₈	C₄×#6923	1	1	yes	characteristic
99	C₈	C₂²⋊#6923	1	1	yes	characteristic
100	C₂²	—	61	1	no	—
101	C₂²	—	61	1	no	—
102	C₂²	—	122	2	no	—
103	C₂²	#14519845	1	1	yes	characteristic
104	C₄	—	61	1	no	—
105	C₄	—	61	1	no	—
106	C₄	—	488	2	no	—
107	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
108	C₄	#14519846	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	61	2	no	—
111	C₂	—	122	1	no	—
112	C₂	#16840636	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊#108

C₂

yes

maximal, characteristic

#16840772

C₂

yes

maximal, characteristic

C₂×C₁₆×D₆₁

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

—

#14519856

—

#14519848

C₄

yes

complemented

#14519847

—

#14519846

C₄

yes

—

#14519845

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×#11758185

C₄

yes

characteristic, complemented

C₁₆×D₆₁

—

C₁₆×D₆₁

—

C₂×C₁₆×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂²⋊#6923

—

—

—

—

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

Q₈

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

SD₁₆

yes

characteristic

C₂×#6923

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

D₈

yes

characteristic

C₄×D₆₁

Q₁₆

yes

characteristic

#92420

—

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₂²⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#106

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

#340

yes

characteristic

D₆₁

—

D₆₁

#359

yes

—

C₂²×C₁₆

—

C₂×#108

—

#427

—

C₆₁

#1382

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

#117

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

—

122

—

C₂×C₁₆

#6923

yes

characteristic, complemented

#108

—

#108

—

122

—

#107

—

#106

—

122

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

244

—

C₈

C₄×#6923

yes

characteristic

C₈

C₂²⋊#6923

yes

characteristic

100

C₂²

—

101

C₂²

—

102

C₂²

—

122

—

103

C₂²

#14519845

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

488

—

107

C₄

(C₂×#6923)⋊C₄

yes

characteristic

108

C₄

#14519846

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

122

—

112

C₂

#16840636

yes

characteristic

	subgroup	G/H
center	C₄	#14519846
commutator	C₈×C₆₁	C₄²
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×C₁₆×C₆₁	C₄
socle	C₂×C₆₁	#340
hypercenter	C₂×C₁₆	#6923
hypocenter	C₆₁	#1382
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₄

#14519846

commutator

C₈×C₆₁

C₄²

Frattini

C₂×C₈

C₂×#6923

Fitting

C₂×C₁₆×C₆₁

C₄

C₂×C₆₁

C₂×C₁₆

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
6. #14519848	C₄	semidirect
11. C₂×#11758185	C₄	semidirect
14. C₂×C₁₆×C₆₁	C₄	semidirect
60. C₆₁	#1382	semidirect
67. C₂×C₁₆	#6923	semidirect

H ≅ G/N

type

6. #14519848

C₄

semidirect

11. C₂×#11758185

C₄

semidirect

14. C₂×C₁₆×C₆₁

C₄

semidirect

60. C₆₁

#1382

semidirect

67. C₂×C₁₆

#6923

semidirect

Subgroups — #21460881

Conjugacy classes of subgroups

Complements