Group #16835592 — subgroups

Subgroups — #16835592

Order 3712.

248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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×C₄⋊#6599	C₂	1	2	yes	maximal
2	C₂×C₄⋊#6599	C₂	1	1	yes	maximal, characteristic
3	C₂×#11745218	C₂	1	1	yes	maximal, characteristic
4	#14272029	C₂	1	2	yes	maximal
5	#14271014	C₂	1	1	yes	maximal, characteristic
6	C₂²×#6599	C₂²	1	2	yes	—
7	C₂²×#6599	C₂²	1	1	yes	characteristic
8	C₂²×#6599	C₂²	1	1	yes	characteristic
9	C₂×#90779	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	#11745218	—	2	2	no	—
13	C₄⋊#6599	—	2	4	no	—
14	C₄⋊#6599	—	2	2	no	—
15	C₂₉×#95	C₄	1	1	yes	characteristic
16	#11745179	C₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
19	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
22	C₂×#6599	—	2	1	no	—
23	C₂×#6599	—	2	1	no	—
24	C₂×#6599	—	2	1	no	—
25	C₂×#6599	—	2	1	no	—
26	C₂×#6599	—	2	2	no	—
27	C₂×#6599	—	2	2	no	—
28	C₂×#6599	—	2	2	no	—
29	C₂×#6599	D₄	1	2	yes	—
30	C₂×#6599	Q₈	1	2	yes	—
31	#90779	—	2	4	no	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₄×Dic₂₉	—	2	2	no	—
34	C₄×Dic₂₉	D₄	1	2	yes	—
35	C₄×Dic₂₉	Q₈	1	2	yes	—
36	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	—	2	2	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₂₉	M₁₆	1	4	yes	—
42	C₂×Dic₂₉	—	2	2	no	—
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	—	2	2	no	—
45	C₂×Dic₂₉	—	2	2	no	—
46	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
47	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×Dic₂₉	#41	1	1	yes	characteristic
52	C₂×Dic₂₉	#41	1	1	yes	characteristic
53	#6599	—	2	2	no	—
54	#6599	—	2	2	no	—
55	#6599	—	4	2	no	—
56	#1940	—	29	1	no	maximal, Sylow
57	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
59	C₂²×C₂₉	C₄×Q₈	1	1	yes	characteristic
60	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
61	C₂²×C₂₉	#131	1	2	yes	—
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	—	2	4	no	—
64	Dic₂₉	—	2	2	no	—
65	Dic₂₉	—	4	2	no	—
66	Dic₂₉	#121	1	1	yes	characteristic
67	Dic₂₉	C₂²⋊Q₈	1	1	yes	characteristic
68	Dic₂₉	#125	1	1	yes	characteristic
69	Dic₂₉	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄⋊C₈	—	29	1	no	—
71	C₂×C₄⋊C₈	—	29	2	no	—
72	C₂×#97	—	29	1	no	—
73	C₄×C₄⋊C₄	—	29	1	no	—
74	#336	—	29	2	no	—
75	C₂×C₂₉	#389	1	1	yes	characteristic
76	C₂×C₂₉	#423	1	1	yes	characteristic
77	C₂×C₂₉	#424	1	1	yes	characteristic
78	C₂×C₂₉	#435	1	2	yes	—
79	C₂×C₂₉	#446	1	2	yes	—
80	C₂²×C₈	—	29	1	no	—
81	C₂²×C₈	—	29	1	no	—
82	C₂²×C₈	—	29	2	no	—
83	C₂×C₄⋊C₄	—	29	2	no	—
84	C₂×C₄²	—	29	1	no	—
85	C₂×C₄²	—	29	2	no	—
86	C₄⋊C₈	—	58	2	no	—
87	C₄⋊C₈	—	58	4	no	—
88	#97	—	58	2	no	—
89	#95	—	29	1	no	—
90	#95	#1181	1	1	yes	characteristic
91	C₂₉	#1940	1	1	yes	characteristic, complemented, Sylow
92	C₂²×C₄	—	29	1	no	—
93	C₂²×C₄	—	29	1	no	—
94	C₂²×C₄	—	29	2	no	—
95	C₂²×C₄	C₂×#1181	1	2	yes	—
96	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
97	C₂×C₈	—	29	2	no	—
98	C₂×C₈	—	29	2	no	—
99	C₂×C₈	—	58	1	no	—
100	C₂×C₈	—	58	1	no	—
101	C₂×C₈	—	58	1	no	—
102	C₂×C₈	—	58	1	no	—
103	C₂×C₈	—	58	2	no	—
104	C₂×C₈	—	58	2	no	—
105	C₂×C₈	—	58	2	no	—
106	C₄⋊C₄	—	58	4	no	—
107	C₄²	—	29	2	no	—
108	C₄²	—	29	2	no	—
109	C₄²	—	58	2	no	—
110	C₄²	—	58	2	no	—
111	C₂³	C₂²×#1181	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	29	1	no	—
116	C₂×C₄	—	29	1	no	—
117	C₂×C₄	—	29	1	no	—
118	C₂×C₄	—	29	1	no	—
119	C₂×C₄	—	29	1	no	—
120	C₂×C₄	—	29	1	no	—
121	C₂×C₄	—	29	2	no	—
122	C₂×C₄	—	58	2	no	—
123	C₂×C₄	—	58	2	no	—
124	C₂×C₄	—	58	2	no	—
125	C₂×C₄	—	58	2	no	—
126	C₂×C₄	#90796	1	4	yes	—
127	C₂×C₄	C₄⋊#1181	1	2	yes	—
128	C₈	—	58	2	no	—
129	C₈	—	58	2	no	—
130	C₈	—	116	2	no	—
131	C₂²	C₂×#90796	1	2	yes	—
132	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
133	C₂²	#11745346	1	2	yes	—
134	C₂²	D₄×#1181	1	1	yes	characteristic
135	C₂²	Q₈×#1181	1	1	yes	characteristic
136	C₄	—	2	2	no	—
137	C₄	—	2	4	no	—
138	C₄	—	29	1	no	—
139	C₄	—	29	1	no	—
140	C₄	—	29	1	no	—
141	C₄	—	29	1	no	—
142	C₄	—	58	2	no	—
143	C₄	—	116	2	no	—
144	C₂	#14272114	1	1	yes	characteristic
145	C₂	#14272167	1	1	yes	characteristic
146	C₂	#14272169	1	1	yes	characteristic
147	C₂	#14272192	1	2	yes	—
148	C₂	#14272213	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6599

C₂

yes

maximal

C₂×C₄⋊#6599

C₂

yes

maximal, characteristic

C₂×#11745218

C₂

yes

maximal, characteristic

#14272029

C₂

yes

maximal

#14271014

C₂

yes

maximal, characteristic

C₂²×#6599

C₂²

yes

—

C₂²×#6599

C₂²

yes

characteristic

C₂²×#6599

C₂²

yes

characteristic

C₂×#90779

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

—

—

C₂₉×#95

C₄

yes

characteristic

#11745179

C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

—

—

—

—

—

—

D₄

yes

—

C₂×#6599

Q₈

yes

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

C₂×Dic₂₉

yes

C₂×Dic₂₉

yes

—

—

—

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

—

C₂²×C₂₉

#131

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#121

yes

characteristic

Dic₂₉

C₂²⋊Q₈

yes

characteristic

Dic₂₉

#125

yes

characteristic

Dic₂₉

C₄⋊Q₈

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₄×C₄⋊C₄

—

#336

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#446

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂₉

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

—

C₂²×C₄

C₂×#1181

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₂³

C₂²×#1181

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#90796

yes

—

127

C₂×C₄

C₄⋊#1181

yes

—

128

C₈

—

129

C₈

—

130

C₈

—

116

—

131

C₂²

C₂×#90796

yes

—

132

C₂²

C₂×C₄⋊#1181

yes

characteristic

133

C₂²

#11745346

yes

—

134

C₂²

D₄×#1181

yes

characteristic

135

C₂²

Q₈×#1181

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

116

—

144

C₂

#14272114

yes

characteristic

145

C₂

#14272167

yes

characteristic

146

C₂

#14272169

yes

characteristic

147

C₂

#14272192

yes

—

148

C₂

#14272213

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂₉×#95	C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	#95	#1181
hypocenter	C₂₉	#1940
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#1181

commutator, socle, prime radical

C₂³×C₂₉

C₂²×C₄

Fitting

C₂₉×#95

C₄

cosocle

C₂²×Dic₂₉

C₂³

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
91. C₂₉	#1940	semidirect

H ≅ G/N

type

91. C₂₉

#1940

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄⋊#6599	2
C₂×#11745218	2
#14272029	2
#14271014	2
#1940	29

subgroup

index

C₂×C₄⋊#6599

Subgroups — #16835592

Conjugacy classes of subgroups

Complements

Maximal subgroups