Group #21461939 — subgroups

Subgroups — #21461939

Order 7808.

184 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 66 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	#16840777	C₂	1	2	yes	maximal
2	C₂×#14519848	C₂	1	1	yes	maximal, characteristic
3	#16840725	C₂	1	1	yes	maximal, characteristic
4	#16840645	C₂	1	2	yes	maximal
5	#108×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₂²	1	2	yes	—
7	D₆₁⋊M₁₆	C₂²	1	1	yes	characteristic
8	#14519856	C₂²	1	1	yes	characteristic
9	#14519848	—	2	2	no	—
10	#14519848	—	2	1	no	—
11	#14519848	—	2	1	no	—
12	#14519847	—	2	2	no	—
13	#14519831	—	2	1	no	—
14	C₈×#6923	—	2	1	no	—
15	M₁₆×D₆₁	C₂²	1	2	yes	—
16	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
17	#14519713	C₄	1	1	yes	characteristic, complemented
18	#14519712	C₄	1	2	yes	complemented
19	#108×C₆₁	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
21	C₂²⋊#6923	Q₈	1	2	yes	—
22	#11758217	—	2	1	no	—
23	C₂×#92420	—	2	2	no	—
24	C₄⋊#6923	—	2	1	no	—
25	C₄×#6923	—	2	1	no	—
26	#11758213	—	2	2	no	—
27	#11758213	—	2	2	no	—
28	#11758213	D₄	1	1	yes	characteristic
29	#11758213	D₄	1	1	yes	characteristic
30	D₆₁⋊C₈	—	2	1	no	—
31	M₁₆×C₆₁	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
33	#11758194	C₂×C₄	1	2	yes	—
34	C₂×#92418	C₂×C₄	1	1	yes	characteristic
35	#11758189	—	2	2	no	—
36	C₈×D₆₁	—	2	2	no	—
37	C₈×D₆₁	D₄	1	1	yes	characteristic
38	C₈×D₆₁	D₄	1	1	yes	characteristic
39	C₈×D₆₁	Q₈	1	1	yes	characteristic
40	C₈×D₆₁	Q₈	1	1	yes	characteristic
41	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×#6923	—	2	2	no	—
43	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×Dic₆₁	#41	1	1	yes	characteristic
45	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
46	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
47	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₆₁	#41	1	1	yes	characteristic
49	#92420	—	2	1	no	—
50	#92420	—	2	1	no	—
51	#92420	—	4	2	no	—
52	C₈×C₆₁	—	2	2	no	—
53	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
54	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
55	#92418	—	2	2	no	—
56	#92418	C₄⋊C₄	1	1	yes	characteristic
57	#92418	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₆₁	C₄×Q₈	1	1	yes	characteristic
59	C₂×D₆₁	—	4	1	no	—
60	C₂×D₆₁	C₂²⋊Q₈	1	1	yes	characteristic
61	C₂×D₆₁	C₄⋊Q₈	1	1	yes	characteristic
62	#6923	—	4	2	no	—
63	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
65	Dic₆₁	#121	1	1	yes	characteristic
66	Dic₆₁	#125	1	1	yes	characteristic
67	#1953	—	61	1	no	maximal, Sylow
68	C₂×C₆₁	—	2	1	no	—
69	C₂×C₆₁	#389	1	1	yes	characteristic
70	D₆₁	—	2	1	no	—
71	D₆₁	—	2	1	no	—
72	#430	—	61	2	no	—
73	C₂×#108	—	61	1	no	—
74	C₂×#108	—	61	1	no	—
75	#405	—	61	1	no	—
76	#344	—	61	2	no	—
77	C₆₁	#1953	1	1	yes	characteristic, complemented, Sylow
78	C₂×M₁₆	—	61	1	no	—
79	C₂×M₁₆	—	61	2	no	—
80	C₂×M₁₆	—	61	2	no	—
81	C₂²×C₈	—	61	1	no	—
82	#117	—	61	1	no	—
83	#108	—	61	2	no	—
84	#108	—	61	1	no	—
85	#108	—	122	1	no	—
86	#108	—	122	1	no	—
87	#108	—	122	2	no	—
88	#108	—	122	2	no	—
89	#108	#6923	1	1	yes	characteristic, complemented
90	#97	—	122	1	no	—
91	C₄×C₈	—	122	1	no	—
92	C₂²×C₄	—	61	1	no	—
93	M₁₆	—	61	1	no	—
94	M₁₆	—	61	1	no	—
95	M₁₆	—	61	2	no	—
96	M₁₆	—	122	2	no	—
97	M₁₆	—	122	1	no	—
98	M₁₆	—	122	2	no	—
99	M₁₆	—	122	2	no	—
100	M₁₆	C₂×#6923	1	2	yes	—
101	C₂×C₈	—	61	1	no	—
102	C₂×C₈	—	61	1	no	—
103	C₂×C₈	—	61	1	no	—
104	C₂×C₈	—	61	1	no	—
105	C₂×C₈	—	61	1	no	—
106	C₂×C₈	—	122	2	no	—
107	C₂×C₈	—	122	1	no	—
108	C₂×C₈	—	122	2	no	—
109	C₂×C₈	C₂×#6923	1	1	yes	characteristic
110	C₄⋊C₄	—	122	1	no	—
111	C₂²⋊C₄	—	61	2	no	—
112	C₄²	—	122	1	no	—
113	C₂³	—	61	1	no	—
114	C₂×C₄	—	61	1	no	—
115	C₂×C₄	—	61	1	no	—
116	C₂×C₄	—	61	1	no	—
117	C₂×C₄	—	61	1	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	122	2	no	—
120	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	—	61	1	no	—
123	C₈	—	61	1	no	—
124	C₈	—	122	1	no	—
125	C₈	—	122	1	no	—
126	C₈	—	122	2	no	—
127	C₈	—	244	2	no	—
128	C₈	C₄⋊#6923	1	1	yes	characteristic
129	C₈	C₄⋊#6923	1	1	yes	characteristic
130	C₂²	—	61	1	no	—
131	C₂²	—	61	1	no	—
132	C₂²	—	244	1	no	—
133	C₂²	Q₈×#6923	1	1	yes	characteristic
134	C₄	—	61	1	no	—
135	C₄	—	61	1	no	—
136	C₄	—	244	2	no	—
137	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
138	C₄	D₄×#6923	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	122	1	no	—
141	C₂	—	122	1	no	—
142	C₂	#16840713	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840777

C₂

yes

maximal

C₂×#14519848

C₂

yes

maximal, characteristic

#16840725

C₂

yes

maximal, characteristic

#16840645

C₂

yes

maximal

#108×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

D₆₁⋊M₁₆

C₂²

yes

characteristic

#14519856

C₂²

yes

—

—

—

—

—

—

M₁₆×D₆₁

C₂²

yes

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519713

C₄

yes

characteristic, complemented

#14519712

C₄

yes

complemented

#108×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂²⋊#6923

Q₈

yes

—

—

—

—

—

—

—

D₄

yes

characteristic

#11758213

D₄

yes

characteristic

D₆₁⋊C₈

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

#11758194

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

C₂²×D₆₁

C₂×Q₈

yes

characteristic

C₂×#6923

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

#41

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

C₄×D₆₁

yes

—

—

—

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

—

#92418

C₄⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×Q₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₂²⋊Q₈

yes

characteristic

C₂×D₆₁

C₄⋊Q₈

yes

characteristic

#6923

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

#389

yes

characteristic

D₆₁

—

D₆₁

—

—

—

—

—

—

C₆₁

#1953

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

122

—

#108

—

122

—

#108

—

122

—

#108

—

122

—

#108

#6923

yes

characteristic, complemented

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

100

M₁₆

C₂×#6923

yes

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

122

—

107

C₂×C₈

—

122

—

108

C₂×C₈

—

122

—

109

C₂×C₈

C₂×#6923

yes

characteristic

110

C₄⋊C₄

—

122

—

111

C₂²⋊C₄

—

112

C₄²

—

122

—

113

C₂³

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

122

—

120

C₂×C₄

C₂²×#6923

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

122

—

125

C₈

—

122

—

126

C₈

—

122

—

127

C₈

—

244

—

128

C₈

C₄⋊#6923

yes

characteristic

129

C₈

C₄⋊#6923

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

244

—

133

C₂²

Q₈×#6923

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

244

—

137

C₄

C₂×C₄⋊#6923

yes

characteristic

138

C₄

D₄×#6923

yes

characteristic

139

C₂

—

140

C₂

—

122

—

141

C₂

—

122

—

142

C₂

#16840713

yes

characteristic

	subgroup	G/H
center	C₂	#16840713
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#108×C₆₁	C₄
socle	C₂×C₆₁	#389
hypercenter	#108	#6923
hypocenter	C₆₁	#1953
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

subgroup

G/H

center

C₂

#16840713

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#108×C₆₁

C₄

C₂×C₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

N	H ≅ G/N	type
17. #14519713	C₄	semidirect
18. #14519712	C₄	semidirect
19. #108×C₆₁	C₄	semidirect
77. C₆₁	#1953	semidirect
89. #108	#6923	semidirect

H ≅ G/N

type

17. #14519713

C₄

semidirect

18. #14519712

C₄

semidirect

19. #108×C₆₁

C₄

semidirect

77. C₆₁

#1953

semidirect

89. #108

#6923

semidirect

Subgroups — #21461939

Conjugacy classes of subgroups

Complements