Group #21461759 — subgroups

Subgroups — #21461759

Order 7808.

220 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14519848	C₂	1	2	yes	maximal
2	C₂×#14519847	C₂	1	2	yes	maximal
3	#16840767	C₂	1	2	yes	maximal
4	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758213	C₂²	1	4	yes	—
6	#14519848	—	2	4	no	—
7	#14519847	—	2	4	no	—
8	#14519844	—	2	4	no	—
9	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
11	C₄²×D₆₁	C₂²	1	1	yes	characteristic
12	C₄×#92418	C₄	1	1	yes	characteristic
13	C₈×Dic₆₁	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₄	1	1	yes	characteristic
15	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	Q₈	1	2	yes	—
17	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
18	C₂×#92420	—	2	4	no	—
19	#11758213	—	2	4	no	—
20	#11758213	—	2	4	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	2	yes	—
26	C₂×#92418	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	C₂×C₄	1	1	yes	characteristic
28	C₈×D₆₁	D₄	1	2	yes	—
29	C₈×D₆₁	D₄	1	2	yes	—
30	C₈×D₆₁	Q₈	1	2	yes	—
31	C₈×D₆₁	Q₈	1	2	yes	—
32	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
36	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
37	C₄×D₆₁	—	2	4	no	—
38	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
39	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
40	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
41	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
42	#92420	—	4	4	no	—
43	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
44	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
45	#92418	C₄⋊C₄	1	2	yes	—
46	#92418	C₄⋊C₄	1	2	yes	—
47	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₆₁	—	2	2	no	—
49	C₂×D₆₁	C₄⋊Q₈	1	1	yes	characteristic
50	C₂×D₆₁	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₆₁	—	2	2	no	—
52	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
54	Dic₆₁	#108	1	4	yes	complemented
55	Dic₆₁	#127	1	1	yes	characteristic
56	Dic₆₁	C₄⋊Q₈	1	1	yes	characteristic
57	#1848	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	#384	1	1	yes	characteristic
59	C₂×C₆₁	C₂×#108	1	2	yes	—
60	D₆₁	—	2	1	no	—
61	D₆₁	—	2	1	no	—
62	C₂×#108	—	61	2	no	—
63	C₂×#108	—	61	2	no	—
64	#423	—	61	2	no	—
65	C₂×C₄×C₈	—	61	1	no	—
66	C₆₁	#1848	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₁₆	—	61	4	no	—
68	C₂²×C₈	—	61	1	no	—
69	C₂²×C₈	—	61	1	no	—
70	C₂×C₄²	—	61	1	no	—
71	#108	—	122	4	no	—
72	#108	—	122	4	no	—
73	C₄⋊C₈	—	122	4	no	—
74	C₄×C₈	—	61	1	no	—
75	C₄×C₈	—	61	1	no	—
76	C₄×C₈	—	61	1	no	—
77	C₄×C₈	#6923	1	1	yes	characteristic
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	61	2	no	—
80	M₁₆	—	122	4	no	—
81	M₁₆	—	122	4	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	61	2	no	—
86	C₂×C₈	—	61	2	no	—
87	C₂×C₈	—	61	2	no	—
88	C₂×C₈	—	122	4	no	—
89	C₂×C₈	C₂×#6923	1	1	yes	characteristic
90	C₂×C₈	C₂×#6923	1	1	yes	characteristic
91	C₄²	—	61	2	no	—
92	C₄²	—	61	1	no	—
93	C₄²	C₂×#6923	1	1	yes	characteristic
94	C₂³	—	61	1	no	—
95	C₂×C₄	—	61	2	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	122	4	no	—
102	C₂×C₄	C₄⋊#6923	1	2	yes	—
103	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
104	C₈	—	61	2	no	—
105	C₈	—	61	2	no	—
106	C₈	—	244	4	no	—
107	C₈	C₄⋊#6923	1	2	yes	—
108	C₈	C₄⋊#6923	1	2	yes	—
109	C₂²	—	61	1	no	—
110	C₂²	—	61	1	no	—
111	C₂²	—	122	2	no	—
112	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	61	1	no	—
115	C₄	—	61	1	no	—
116	C₄	—	61	4	no	—
117	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
118	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
119	C₂	—	122	1	no	—
120	C₂	—	122	1	no	—
121	C₂	#16840708	1	1	yes	characteristic
122	C₂	D₆₁⋊#108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519848

C₂

yes

maximal

C₂×#14519847

C₂

yes

maximal

#16840767

C₂

yes

maximal

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

#14519848

—

#14519847

—

#14519844

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

—

C₂×C₄×D₆₁

C₂³

yes

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

C₈×D₆₁

Q₈

yes

—

C₂²×D₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

characteristic

#92420

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

C₄⋊C₄

yes

—

#92418

C₄⋊C₄

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄⋊Q₈

yes

characteristic

C₂×D₆₁

C₄⋊Q₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

Dic₆₁

yes

Dic₆₁

yes

Dic₆₁

C₄⋊Q₈

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

D₆₁

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

C₆₁

#1848

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

122

—

#108

—

122

—

C₄⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

122

—

102

C₂×C₄

C₄⋊#6923

yes

—

103

C₂×C₄

C₂²×#6923

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

244

—

107

C₈

C₄⋊#6923

yes

—

108

C₈

C₄⋊#6923

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

122

—

112

C₂²

C₂×C₄⋊#6923

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×C₄⋊#6923

yes

characteristic

118

C₄

C₂×C₄⋊#6923

yes

characteristic

119

C₂

—

122

—

120

C₂

—

122

—

121

C₂

#16840708

yes

characteristic

122

C₂

D₆₁⋊#108

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1848
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₄×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
54. Dic₆₁	#108	semidirect
66. C₆₁	#1848	semidirect

H ≅ G/N

type

54. Dic₆₁

#108

semidirect

66. C₆₁

#1848

semidirect

Subgroups — #21461759

Conjugacy classes of subgroups

Complements