Group #21461933 — subgroups

Subgroups — #21461933

Order 7808.

200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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	#16840766	C₂	1	1	yes	maximal, characteristic
3	C₄×#11758213	C₂	1	1	yes	maximal, characteristic
4	#16840638	C₂	1	2	yes	maximal
5	C₄⋊C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₂²	1	2	yes	—
7	C₂×#11758213	C₂²	1	1	yes	characteristic
8	C₂×#11758213	C₂²	1	1	yes	characteristic
9	#14519848	—	2	4	no	—
10	C₄⋊#92420	—	2	1	no	—
11	C₄⋊#92420	—	2	1	no	—
12	#14519832	—	2	1	no	—
13	C₄×#92420	—	2	1	no	—
14	C₂×C₈×D₆₁	C₂²	1	2	yes	—
15	C₄²×D₆₁	C₂²	1	1	yes	characteristic
16	C₄⋊#92418	C₄	1	1	yes	characteristic
17	#14519706	C₄	1	2	yes	—
18	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
22	C₂×#92420	—	2	1	no	—
23	C₂×#92420	—	2	1	no	—
24	C₂×#92420	—	2	2	no	—
25	#11758213	—	2	1	no	—
26	#11758213	—	2	1	no	—
27	#11758213	—	2	2	no	—
28	#11758213	—	2	2	no	—
29	#11758213	D₄	1	2	yes	—
30	#11758213	Q₈	1	2	yes	—
31	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
32	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₆₁	D₄	1	1	yes	characteristic
35	C₄×Dic₆₁	D₄	1	1	yes	characteristic
36	C₂×#92418	C₂×C₄	1	2	yes	—
37	C₈×D₆₁	—	2	2	no	—
38	C₈×D₆₁	—	2	2	no	—
39	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
45	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
46	C₄×D₆₁	—	2	2	no	—
47	C₄×D₆₁	—	4	1	no	—
48	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
49	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
50	C₄×D₆₁	#41	1	1	yes	characteristic
51	C₄×D₆₁	#41	1	1	yes	characteristic
52	#92420	—	2	2	no	—
53	#92420	—	2	2	no	—
54	#92420	—	4	2	no	—
55	C₈×C₆₁	—	2	2	no	—
56	#92418	—	2	2	no	—
57	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×D₆₁	—	2	1	no	—
59	C₂×D₆₁	—	2	1	no	—
60	C₂×D₆₁	#125	1	1	yes	characteristic
61	C₂×D₆₁	C₄⋊Q₈	1	1	yes	characteristic
62	C₄×C₆₁	—	2	1	no	—
63	C₄×C₆₁	#108	1	2	yes	complemented
64	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
65	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
66	Dic₆₁	—	2	1	no	—
67	Dic₆₁	—	2	1	no	—
68	Dic₆₁	#121	1	1	yes	characteristic
69	Dic₆₁	C₂²⋊Q₈	1	1	yes	characteristic
70	#1950	—	61	1	no	maximal, Sylow
71	C₂×C₆₁	#389	1	1	yes	characteristic
72	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
73	C₂×C₆₁	#430	1	1	yes	characteristic
74	D₆₁	—	2	1	no	—
75	D₆₁	—	2	1	no	—
76	C₂×#108	—	61	2	no	—
77	#423	—	61	1	no	—
78	C₂×C₄⋊C₈	—	61	1	no	—
79	C₄×M₁₆	—	61	1	no	—
80	#341	—	61	2	no	—
81	C₆₁	#1950	1	1	yes	characteristic, complemented, Sylow
82	C₂×M₁₆	—	61	1	no	—
83	C₂×M₁₆	—	61	1	no	—
84	C₂×M₁₆	—	61	2	no	—
85	C₂²×C₈	—	61	2	no	—
86	C₂×C₄²	—	61	1	no	—
87	#108	—	122	4	no	—
88	C₄⋊C₈	—	61	2	no	—
89	C₄⋊C₈	—	61	1	no	—
90	C₄⋊C₈	—	122	1	no	—
91	C₄⋊C₈	—	122	1	no	—
92	C₄⋊C₈	#6923	1	1	yes	characteristic
93	#97	—	122	1	no	—
94	C₄×C₈	—	122	1	no	—
95	C₂²×C₄	—	61	1	no	—
96	C₂²×C₄	—	61	1	no	—
97	C₂²×C₄	—	61	1	no	—
98	M₁₆	—	61	2	no	—
99	M₁₆	—	61	2	no	—
100	M₁₆	—	122	1	no	—
101	M₁₆	—	122	1	no	—
102	M₁₆	—	122	2	no	—
103	M₁₆	—	122	2	no	—
104	C₂×C₈	—	61	2	no	—
105	C₂×C₈	—	122	2	no	—
106	C₂×C₈	—	122	2	no	—
107	C₂×C₈	—	122	1	no	—
108	C₂×C₈	—	122	1	no	—
109	C₂×C₈	—	122	2	no	—
110	C₂×C₈	C₂×#6923	1	2	yes	—
111	C₄²	—	61	1	no	—
112	C₄²	—	61	1	no	—
113	C₄²	—	61	1	no	—
114	C₄²	C₂×#6923	1	1	yes	characteristic
115	C₂³	—	61	1	no	—
116	C₂×C₄	—	61	1	no	—
117	C₂×C₄	—	61	1	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	61	1	no	—
120	C₂×C₄	—	61	1	no	—
121	C₂×C₄	—	61	1	no	—
122	C₂×C₄	—	61	1	no	—
123	C₂×C₄	—	122	2	no	—
124	C₂×C₄	—	244	1	no	—
125	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
126	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
127	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
128	C₈	—	2	2	no	—
129	C₈	—	122	2	no	—
130	C₈	—	122	2	no	—
131	C₈	—	122	2	no	—
132	C₈	—	244	2	no	—
133	C₂²	—	61	1	no	—
134	C₂²	—	61	1	no	—
135	C₂²	—	122	1	no	—
136	C₂²	—	122	1	no	—
137	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
138	C₄	—	2	1	no	—
139	C₄	—	61	1	no	—
140	C₄	—	61	1	no	—
141	C₄	—	122	1	no	—
142	C₄	—	122	1	no	—
143	C₄	#14519848	1	2	yes	complemented
144	C₄	D₄×#6923	1	1	yes	characteristic
145	C₄	Q₈×#6923	1	1	yes	characteristic
146	C₂	—	122	1	no	—
147	C₂	—	122	1	no	—
148	C₂	#16840713	1	1	yes	characteristic
149	C₂	C₂×#14519848	1	1	yes	characteristic
150	C₂	#16840777	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519848

C₂

yes

maximal

#16840766

C₂

yes

maximal, characteristic

C₄×#11758213

C₂

yes

maximal, characteristic

#16840638

C₂

yes

maximal

C₄⋊C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

C₂×#11758213

C₂²

yes

characteristic

C₂×#11758213

C₂²

yes

—

—

—

—

—

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic

#14519706

C₄

yes

—

C₄⋊C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×C₄×D₆₁

C₂³

yes

—

—

—

—

—

—

—

D₄

yes

—

#11758213

Q₈

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

—

C₈×D₆₁

—

C₂²×D₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

C₄×D₆₁

yes

C₄×D₆₁

yes

—

—

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#125

yes

characteristic

C₂×D₆₁

C₄⋊Q₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#108

yes

complemented

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#121

yes

characteristic

Dic₆₁

C₂²⋊Q₈

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

D₆₁

—

C₂×#108

—

#423

—

C₂×C₄⋊C₈

—

C₄×M₁₆

—

#341

—

C₆₁

#1950

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

122

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

#6923

yes

characteristic

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

100

M₁₆

—

122

—

101

M₁₆

—

122

—

102

M₁₆

—

122

—

103

M₁₆

—

122

—

104

C₂×C₈

—

105

C₂×C₈

—

122

—

106

C₂×C₈

—

122

—

107

C₂×C₈

—

122

—

108

C₂×C₈

—

122

—

109

C₂×C₈

—

122

—

110

C₂×C₈

C₂×#6923

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂×#6923

yes

characteristic

115

C₂³

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

122

—

124

C₂×C₄

—

244

—

125

C₂×C₄

C₄⋊#6923

yes

characteristic

126

C₂×C₄

C₄⋊#6923

yes

characteristic

127

C₂×C₄

C₂²×#6923

yes

characteristic

128

C₈

—

129

C₈

—

122

—

130

C₈

—

122

—

131

C₈

—

122

—

132

C₈

—

244

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

122

—

136

C₂²

—

122

—

137

C₂²

C₂×C₄⋊#6923

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

122

—

142

C₄

—

122

—

143

C₄

#14519848

yes

complemented

144

C₄

D₄×#6923

yes

characteristic

145

C₄

Q₈×#6923

yes

characteristic

146

C₂

—

122

—

147

C₂

—

122

—

148

C₂

#16840713

yes

characteristic

149

C₂

C₂×#14519848

yes

characteristic

150

C₂

#16840777

yes

characteristic

	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	#1950
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
63. C₄×C₆₁	#108	semidirect
81. C₆₁	#1950	semidirect
143. C₄	#14519848	semidirect

H ≅ G/N

type

63. C₄×C₆₁

#108

semidirect

81. C₆₁

#1950

semidirect

143. C₄

#14519848

semidirect

Subgroups — #21461933

Conjugacy classes of subgroups

Complements