Group #21461926 — subgroups

Subgroups — #21461926

Order 7808.

208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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×#14519847	C₂	1	1	yes	maximal, characteristic
2	#16840769	C₂	1	2	yes	maximal
3	C₂×C₈×#6923	C₂	1	1	yes	maximal, characteristic
4	#16840632	C₂	1	2	yes	maximal
5	#16839797	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₂²	1	2	yes	—
7	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×#6923	C₂²	1	1	yes	characteristic
9	#14519847	—	2	2	no	—
10	#14519844	—	2	2	no	—
11	C₄⋊#92420	—	2	2	no	—
12	C₈×#6923	—	2	2	no	—
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	#14519735	C₂²	1	2	yes	—
15	#14519710	C₄	1	2	yes	complemented
16	#14519709	C₄	1	1	yes	characteristic, complemented
17	#106×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂²×#6923	—	2	1	no	—
19	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
20	C₂×#92420	—	2	2	no	—
21	C₂×#92420	D₄	1	2	yes	—
22	C₄×#6923	—	2	1	no	—
23	C₄×#6923	Q₈	1	2	yes	—
24	#11758213	—	2	2	no	—
25	#11758213	—	2	2	no	—
26	D₆₁⋊C₈	—	2	1	no	—
27	D₆₁⋊C₈	—	2	1	no	—
28	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
30	#11758198	—	2	2	no	—
31	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
32	C₄×Dic₆₁	—	2	2	no	—
33	C₂×#92418	C₂×C₄	1	1	yes	characteristic
34	C₈×D₆₁	D₄	1	2	yes	—
35	C₈×D₆₁	Q₈	1	2	yes	—
36	C₂²×D₆₁	#41	1	1	yes	characteristic
37	C₂×#6923	—	2	4	no	—
38	C₂×#6923	—	2	2	no	—
39	C₂×C₄×C₆₁	—	2	2	no	—
40	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₆₁	—	2	2	no	—
42	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
43	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
44	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
45	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₆₁	#41	1	1	yes	characteristic
47	#92420	—	2	2	no	—
48	#92420	—	4	2	no	—
49	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
50	#92418	C₄⋊C₄	1	2	yes	—
51	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
52	C₂×D₆₁	—	2	2	no	—
53	C₂×D₆₁	C₂²⋊Q₈	1	1	yes	characteristic
54	C₂×D₆₁	#125	1	1	yes	characteristic
55	#6923	—	2	4	no	—
56	C₄×C₆₁	—	4	2	no	—
57	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
59	Dic₆₁	—	4	2	no	—
60	Dic₆₁	#121	1	1	yes	characteristic
61	Dic₆₁	C₄⋊Q₈	1	1	yes	characteristic
62	#1945	—	61	1	no	maximal, Sylow
63	C₂×C₆₁	#389	1	1	yes	characteristic
64	C₂×C₆₁	#443	1	2	yes	—
65	D₆₁	—	2	1	no	—
66	D₆₁	—	2	1	no	—
67	C₂×#108	—	61	1	no	—
68	#427	—	61	1	no	—
69	#424	—	61	2	no	—
70	C₂×C₄×C₈	—	61	1	no	—
71	#339	—	61	2	no	—
72	C₆₁	#1945	1	1	yes	characteristic, complemented, Sylow
73	C₂×M₁₆	—	61	2	no	—
74	C₂²×C₈	—	61	1	no	—
75	C₂²×C₈	—	61	1	no	—
76	#117	—	61	2	no	—
77	C₂×C₄²	—	61	1	no	—
78	#108	—	122	2	no	—
79	#107	—	61	2	no	—
80	#106	—	61	1	no	—
81	#106	#6923	1	1	yes	characteristic, complemented
82	C₄⋊C₈	—	122	2	no	—
83	C₄⋊C₈	—	122	2	no	—
84	C₄×C₈	—	122	2	no	—
85	C₂²×C₄	—	61	1	no	—
86	C₂²×C₄	—	122	1	no	—
87	M₁₆	—	122	2	no	—
88	M₁₆	—	122	2	no	—
89	C₂×C₈	—	61	1	no	—
90	C₂×C₈	—	61	2	no	—
91	C₂×C₈	—	61	2	no	—
92	C₂×C₈	—	61	2	no	—
93	C₂×C₈	—	122	1	no	—
94	C₂×C₈	—	122	1	no	—
95	C₂×C₈	—	122	2	no	—
96	C₂×C₈	C₂×#6923	1	1	yes	characteristic
97	C₄⋊C₄	—	61	2	no	—
98	C₄⋊C₄	C₂×#6923	1	2	yes	—
99	C₂²⋊C₄	—	122	2	no	—
100	C₄²	—	61	2	no	—
101	C₄²	—	122	2	no	—
102	C₄²	—	122	1	no	—
103	C₂³	—	61	1	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	61	1	no	—
106	C₂×C₄	—	61	1	no	—
107	C₂×C₄	—	61	1	no	—
108	C₂×C₄	—	61	1	no	—
109	C₂×C₄	—	61	1	no	—
110	C₂×C₄	—	122	2	no	—
111	C₂×C₄	—	122	4	no	—
112	C₂×C₄	—	122	2	no	—
113	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
114	C₈	—	61	2	no	—
115	C₈	—	122	2	no	—
116	C₈	—	244	2	no	—
117	C₈	C₄⋊#6923	1	2	yes	—
118	C₂²	—	61	1	no	—
119	C₂²	—	61	1	no	—
120	C₂²	—	122	2	no	—
121	C₂²	D₄×#6923	1	1	yes	characteristic
122	C₄	—	4	2	no	—
123	C₄	—	61	1	no	—
124	C₄	—	61	1	no	—
125	C₄	—	122	4	no	—
126	C₄	—	244	2	no	—
127	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
128	C₄	Q₈×#6923	1	1	yes	characteristic
129	C₂	—	122	1	no	—
130	C₂	—	122	1	no	—
131	C₂	#16840713	1	1	yes	characteristic
132	C₂	#16840805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519847

C₂

yes

maximal, characteristic

#16840769

C₂

yes

maximal

C₂×C₈×#6923

C₂

yes

maximal, characteristic

#16840632

C₂

yes

maximal

#16839797

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

C₂×D₆₁⋊C₈

C₂²

yes

characteristic

C₂×C₄×#6923

C₂²

yes

—

—

—

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519735

C₂²

yes

—

#14519710

C₄

yes

complemented

#14519709

C₄

yes

characteristic, complemented

#106×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂×#92420

—

C₂×#92420

D₄

yes

—

C₄×#6923

—

C₄×#6923

Q₈

yes

—

#11758213

—

#11758213

—

D₆₁⋊C₈

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

#11758198

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

—

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

C₂²×D₆₁

yes

—

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

C₄×D₆₁

yes

—

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

C₄⋊C₄

yes

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₂²⋊Q₈

yes

C₂×D₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

characteristic

Dic₆₁

—

Dic₆₁

#121

yes

characteristic

Dic₆₁

C₄⋊Q₈

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

D₆₁

—

C₂×#108

—

#427

—

#424

—

C₂×C₄×C₈

—

#339

—

C₆₁

#1945

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

#108

—

122

—

—

—

yes

characteristic, complemented

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×#6923

yes

—

C₂²⋊C₄

—

122

—

100

C₄²

—

101

C₄²

—

122

—

102

C₄²

—

122

—

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

122

—

111

C₂×C₄

—

122

—

112

C₂×C₄

—

122

—

113

C₂×C₄

C₂²×#6923

yes

characteristic

114

C₈

—

115

C₈

—

122

—

116

C₈

—

244

—

117

C₈

C₄⋊#6923

yes

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

122

—

121

C₂²

D₄×#6923

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

122

—

126

C₄

—

244

—

127

C₄

C₂×C₄⋊#6923

yes

characteristic

128

C₄

Q₈×#6923

yes

characteristic

129

C₂

—

122

—

130

C₂

—

122

—

131

C₂

#16840713

yes

characteristic

132

C₂

#16840805

yes

—

	subgroup	G/H
center	C₂²	D₄×#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#106×C₆₁	C₄
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#106	#6923
hypocenter	C₆₁	#1945
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#106×C₆₁

C₄

socle

C₂²×C₆₁

C₄×D₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
15. #14519710	C₄	semidirect
16. #14519709	C₄	semidirect
17. #106×C₆₁	C₄	semidirect
72. C₆₁	#1945	semidirect
81. #106	#6923	semidirect

H ≅ G/N

type

15. #14519710

C₄

semidirect

16. #14519709

C₄

semidirect

17. #106×C₆₁

C₄

semidirect

72. C₆₁

#1945

semidirect

81. #106

#6923

semidirect

Subgroups — #21461926

Conjugacy classes of subgroups

Complements