Group #21460880 — subgroups

Subgroups — #21460880

Order 7808.

132 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 52 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×D₆₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519848	C₂	1	1	yes	maximal, characteristic
3	#16839799	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758213	—	2	1	no	—
5	D₆₁⋊C₁₆	—	2	1	no	—
6	D₆₁⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×#11758187	—	2	1	no	—
8	#14519848	—	2	1	no	—
9	#14519848	C₄	1	2	yes	complemented
10	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
11	#14519735	—	2	1	no	—
12	#14519711	C₄	1	1	yes	characteristic
13	#14519708	—	2	1	no	—
14	#107×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
16	C₂×#92420	—	4	1	no	—
17	#11758213	—	2	2	no	—
18	#11758213	—	4	1	no	—
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₆₁	—	2	1	no	—
21	#11758198	—	4	1	no	—
22	C₄⋊Dic₆₁	—	2	1	no	—
23	C₄×Dic₆₁	—	4	1	no	—
24	C₂×#92418	D₄	1	1	yes	characteristic
25	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₈×D₆₁	Q₈	1	1	yes	characteristic
29	#11758187	—	2	2	no	—
30	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
31	C₂×C₄×C₆₁	—	4	1	no	—
32	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	—	4	1	no	—
34	C₂×Dic₆₁	D₈	1	1	yes	characteristic
35	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
38	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
39	#92420	—	4	2	no	—
40	C₈×C₆₁	C₄²	1	1	yes	characteristic
41	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	#92418	C₂²⋊C₄	1	1	yes	characteristic
43	#92418	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₆₁	#102	1	1	yes	characteristic
45	C₂×D₆₁	—	2	1	no	—
46	C₂×D₆₁	—	2	1	no	—
47	C₂×D₆₁	#103	1	1	yes	characteristic
48	C₂×D₆₁	#106	1	1	yes	characteristic
49	C₄×C₆₁	—	8	1	no	—
50	C₄×C₆₁	#95	1	1	yes	characteristic
51	C₄×C₆₁	#103	1	1	yes	characteristic
52	Dic₆₁	—	8	1	no	—
53	Dic₆₁	#102	1	1	yes	characteristic
54	Dic₆₁	#107	1	1	yes	characteristic
55	#1382	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	#340	1	1	yes	characteristic
57	C₂×C₆₁	#359	1	1	yes	characteristic
58	C₂×C₆₁	#359	1	1	yes	characteristic
59	D₆₁	—	2	1	no	—
60	D₆₁	—	2	1	no	—
61	C₂²×C₁₆	—	61	1	no	—
62	C₂×#108	—	61	1	no	—
63	#427	—	61	1	no	—
64	C₆₁	#1382	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	122	1	no	—
66	C₂²×C₈	—	61	1	no	—
67	#117	—	122	1	no	—
68	C₂×C₁₆	—	61	2	no	—
69	C₂×C₁₆	—	122	1	no	—
70	C₂×C₁₆	—	122	1	no	—
71	#108	—	61	2	no	—
72	#108	—	122	1	no	—
73	#107	—	61	1	no	—
74	#107	#6923	1	1	yes	characteristic
75	#106	—	122	1	no	—
76	C₂²×C₄	—	61	1	no	—
77	M₁₆	—	122	2	no	—
78	M₁₆	—	244	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	244	1	no	—
85	C₂×C₈	C₂×#6923	1	1	yes	characteristic
86	C₄⋊C₄	—	2	1	no	—
87	C₄⋊C₄	—	122	1	no	—
88	C₂²⋊C₄	—	244	1	no	—
89	C₄²	—	244	1	no	—
90	C₁₆	—	122	2	no	—
91	C₂³	—	61	1	no	—
92	C₂×C₄	—	4	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	244	1	no	—
99	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
100	C₈	—	61	1	no	—
101	C₈	—	61	1	no	—
102	C₈	—	244	2	no	—
103	C₈	C₄×#6923	1	1	yes	characteristic
104	C₈	C₄⋊#6923	1	1	yes	characteristic
105	C₂²	—	61	1	no	—
106	C₂²	—	61	1	no	—
107	C₂²	—	122	1	no	—
108	C₂²	—	122	1	no	—
109	C₂²	#14519839	1	1	yes	characteristic
110	C₄	—	8	1	no	—
111	C₄	—	61	1	no	—
112	C₄	—	61	1	no	—
113	C₄	—	488	1	no	—
114	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
115	C₄	#14519840	1	1	yes	characteristic
116	C₂	—	122	1	no	—
117	C₂	—	122	1	no	—
118	C₂	#16840635	1	1	yes	characteristic
119	C₂	#16840676	1	1	yes	characteristic
120	C₂	#16840677	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₆₁⋊C₁₆

C₂

yes

maximal, characteristic

C₂×#14519848

C₂

yes

maximal, characteristic

#16839799

C₂

yes

maximal, characteristic

C₂×#11758213

—

D₆₁⋊C₁₆

—

D₆₁⋊C₁₆

C₄

yes

—

—

C₄

yes

complemented

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519735

—

#14519711

C₄

yes

characteristic

#14519708

—

#107×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

—

#11758198

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

D₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

#11758187

—

C₂²×D₆₁

SD₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

D₈

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

Q₁₆

yes

characteristic

#92420

—

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#102

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

D₆₁

—

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

—

#108

—

#108

—

122

—

—

yes

—

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

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₂²⋊#6923

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

244

—

103

C₈

C₄×#6923

yes

characteristic

104

C₈

C₄⋊#6923

yes

characteristic

105

C₂²

—

106

C₂²

—

107

C₂²

—

122

—

108

C₂²

—

122

—

109

C₂²

#14519839

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

488

—

114

C₄

(C₂×#6923)⋊C₄

yes

characteristic

115

C₄

#14519840

yes

characteristic

116

C₂

—

122

—

117

C₂

—

122

—

118

C₂

#16840635

yes

characteristic

119

C₂

#16840676

yes

characteristic

120

C₂

#16840677

yes

characteristic

	subgroup	G/H
center	C₂²	#14519839
commutator	C₈×C₆₁	C₄²
Frattini	C₂×C₈	C₂×#6923
Fitting	#107×C₆₁	C₄
socle	C₂²×C₆₁	#102
hypercenter	#107	#6923
hypocenter	C₆₁	#1382
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

subgroup

G/H

center

C₂²

#14519839

commutator

C₈×C₆₁

C₄²

Frattini

C₂×C₈

C₂×#6923

Fitting

#107×C₆₁

C₄

C₂²×C₆₁

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

N	H ≅ G/N	type
6. D₆₁⋊C₁₆	C₄	semidirect
9. #14519848	C₄	semidirect
64. C₆₁	#1382	semidirect

H ≅ G/N

type

6. D₆₁⋊C₁₆

C₄

semidirect

9. #14519848

C₄

semidirect

64. C₆₁

#1382

semidirect

Subgroups — #21460880

Conjugacy classes of subgroups

Complements