Group #16828141 — subgroups

Subgroups — #16828141

Order 3712.

384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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	C₄×#90805	C₂	1	1	yes	maximal, characteristic
2	#14271225	C₂	1	4	yes	maximal, complemented
3	#14271218	C₂	1	4	yes	maximal, complemented
4	#14271189	C₂	1	2	yes	maximal, complemented
5	#14271129	C₂	1	2	yes	maximal
6	C₄×#90777	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#90805	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₄×C₂²⋊D₂₉	C₄	1	4	yes	—
12	#11745288	C₂²	1	1	yes	characteristic
13	C₂×#90777	C₂²	1	2	yes	—
14	C₄×D₁₁₆	C₄	1	2	yes	—
15	#11745234	C₂²	1	2	yes	—
16	C₄²×D₂₉	C₂²	1	2	yes	—
17	C₄×Dic₅₈	C₄	1	2	yes	—
18	C₂₉×#97	C₂²	1	2	yes	—
19	C₂₉×#97	C₂²	1	2	yes	—
20	#11745168	C₂²	1	8	yes	—
21	#11745162	C₂²	1	8	yes	—
22	#11745151	C₂²	1	2	yes	—
23	C₄×#6597	C₂²	1	2	yes	—
24	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂×C₂²⋊D₂₉	C₂×C₄	1	2	yes	—
27	#90805	—	2	4	no	—
28	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
30	C₂×C₄×D₂₉	C₂³	1	2	yes	—
31	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×C₂₉	—	2	4	no	—
33	C₂×C₈×C₂₉	C₂³	1	4	yes	—
34	C₄²×C₂₉	C₂×C₄	1	2	yes	—
35	C₄²×C₂₉	C₂³	1	1	yes	characteristic
36	C₄²×C₂₉	C₂³	1	1	yes	characteristic
37	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
38	#90781	C₂×C₄	1	4	yes	—
39	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
40	#90779	C₂×C₄	1	4	yes	—
41	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
42	C₄×Dic₂₉	C₂³	1	2	yes	—
43	#90777	—	2	4	no	—
44	C₂×#6597	C₂³	1	4	yes	—
45	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₂₉	—	4	2	no	—
48	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₂₉	#41	1	4	yes	—
52	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
53	C₂²⋊D₂₉	—	2	4	no	—
54	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
55	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
56	D₁₁₆	—	2	2	no	—
57	C₄×D₂₉	—	2	4	no	—
58	C₄×D₂₉	—	4	4	no	—
59	Dic₅₈	—	2	2	no	—
60	C₈×C₂₉	—	2	4	no	—
61	#6597	—	2	4	no	—
62	#2923	—	29	1	no	maximal, Sylow
63	C₂²×C₂₉	—	2	2	no	—
64	C₂²×C₂₉	#117	1	2	yes	—
65	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
66	C₂×D₂₉	—	2	2	no	—
67	C₂×D₂₉	—	2	4	no	—
68	C₄×C₂₉	—	2	2	no	—
69	C₄×C₂₉	—	2	2	no	—
70	C₄×C₂₉	#117	1	2	yes	—
71	C₄×C₂₉	C₂×#41	1	2	yes	—
72	Dic₂₉	—	2	2	no	—
73	Dic₂₉	—	2	4	no	—
74	C₄×#41	—	29	1	no	—
75	#433	—	29	4	no	—
76	#432	—	29	4	no	—
77	#424	—	29	2	no	—
78	#408	—	29	2	no	—
79	C₄×M₁₆	—	29	1	no	—
80	C₂×#97	D₂₉	1	1	yes	characteristic, complemented
81	C₂×C₂₉	—	2	2	no	—
82	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
83	C₂×C₂₉	#568	1	2	yes	—
84	D₂₉	—	4	2	no	—
85	C₂×#41	—	29	1	no	—
86	C₂×M₁₆	—	29	2	no	—
87	C₂²×C₈	C₂×D₂₉	1	2	yes	—
88	C₄×Q₈	—	29	2	no	—
89	C₄×D₄	—	29	4	no	—
90	C₄×D₄	—	29	2	no	—
91	#117	—	29	1	no	—
92	#117	—	29	2	no	—
93	C₂×C₄²	—	29	2	no	—
94	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
95	C₄⋊C₈	—	29	8	no	—
96	C₂²⋊C₈	—	29	8	no	—
97	#97	—	29	2	no	—
98	#97	C₂×D₂₉	1	2	yes	—
99	#97	C₂×D₂₉	1	2	yes	—
100	C₄×C₈	—	29	2	no	—
101	C₂₉	#2923	1	1	yes	characteristic, complemented, Sylow
102	#41	—	58	4	no	—
103	C₂×Q₈	—	29	1	no	—
104	C₂×D₄	—	29	2	no	—
105	C₂×D₄	—	29	1	no	—
106	C₂²×C₄	—	29	2	no	—
107	C₂²×C₄	—	29	4	no	—
108	C₂²×C₄	C₄×D₂₉	1	2	yes	—
109	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
110	M₁₆	—	58	4	no	—
111	C₂×C₈	—	2	4	no	—
112	C₂×C₈	—	29	4	no	—
113	C₂×C₈	C₂²×D₂₉	1	4	yes	—
114	C₄⋊C₄	—	29	4	no	—
115	C₄⋊C₄	—	29	2	no	—
116	C₂²⋊C₄	—	29	2	no	—
117	C₂²⋊C₄	—	29	4	no	—
118	C₄²	—	29	4	no	—
119	C₄²	—	29	2	no	—
120	C₄²	C₄×D₂₉	1	2	yes	—
121	C₄²	C₂²×D₂₉	1	1	yes	characteristic
122	C₄²	C₂²×D₂₉	1	1	yes	characteristic
123	C₂³	—	29	2	no	—
124	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
125	Q₈	—	58	2	no	—
126	D₄	—	58	4	no	—
127	D₄	—	58	2	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	29	4	no	—
130	C₂×C₄	—	29	2	no	—
131	C₂×C₄	—	58	4	no	—
132	C₂×C₄	—	116	4	no	—
133	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
134	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
135	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
136	C₂×C₄	#90805	1	4	yes	—
137	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
138	C₈	—	2	4	no	—
139	C₈	—	58	4	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	58	2	no	—
142	C₂²	—	58	4	no	—
143	C₂²	#11745234	1	2	yes	—
144	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	58	2	no	—
148	C₄	—	58	4	no	—
149	C₄	#11745234	1	2	yes	—
150	C₄	C₂×#90805	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	116	2	no	—
153	C₂	C₂×#11745234	1	1	yes	characteristic
154	C₂	#14271929	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#90805

C₂

yes

maximal, characteristic

#14271225

C₂

yes

maximal, complemented

#14271218

C₂

yes

maximal, complemented

#14271189

C₂

yes

maximal, complemented

#14271129

C₂

yes

maximal

C₄×#90777

C₂

yes

maximal, characteristic, complemented

C₂×C₂₉×#97

C₂

yes

maximal, characteristic, complemented

C₂×#90805

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₄×C₂²⋊D₂₉

C₄

yes

—

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₄×D₁₁₆

C₄

yes

—

#11745234

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

—

C₄×Dic₅₈

C₄

yes

—

C₂₉×#97

C₂²

yes

—

C₂₉×#97

C₂²

yes

—

#11745168

C₂²

yes

—

#11745162

C₂²

yes

—

#11745151

C₂²

yes

—

C₄×#6597

C₂²

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₂²⋊D₂₉

C₂×C₄

yes

—

#90805

—

C₂×D₁₁₆

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

C₂×Dic₅₈

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂³

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

C₂×C₄

yes

—

#90781

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂³

yes

—

#90777

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂²×D₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂²⋊D₂₉

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#2923

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

#117

yes

—

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

C₄×C₂₉

C₂×#41

yes

—

Dic₂₉

—

Dic₂₉

—

C₄×#41

—

—

—

—

—

C₄×M₁₆

—

C₂×#97

D₂₉

yes

characteristic, complemented

C₂×C₂₉

—

C₂×C₂₉

C₂×#117

yes

characteristic

C₂×C₂₉

#568

yes

—

D₂₉

—

C₂×#41

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₂×D₂₉

yes

—

#97

C₂×D₂₉

yes

—

100

C₄×C₈

—

101

C₂₉

#2923

yes

characteristic, complemented, Sylow

102

#41

—

103

C₂×Q₈

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₄×D₂₉

yes

—

109

C₂²×C₄

C₂²×D₂₉

yes

characteristic

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₂₉

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₄×D₂₉

yes

—

121

C₄²

C₂²×D₂₉

yes

characteristic

122

C₄²

C₂²×D₂₉

yes

characteristic

123

C₂³

—

124

C₂³

C₂×C₄×D₂₉

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

116

—

133

C₂×C₄

C₂×C₄×D₂₉

yes

—

134

C₂×C₄

C₂×C₄×D₂₉

yes

—

135

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

136

C₂×C₄

#90805

yes

—

137

C₂×C₄

C₂³×D₂₉

yes

characteristic

138

C₈

—

139

C₈

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#11745234

yes

—

144

C₂²

C₂²×C₄×D₂₉

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

#11745234

yes

—

150

C₄

C₂×#90805

yes

—

151

C₂

—

152

C₂

—

116

—

153

C₂

C₂×#11745234

yes

characteristic

154

C₂

#14271929

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₉
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂×C₂₉×#97	C₂
prime radical	C₂×#90805	C₂²
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂×#97	D₂₉
hypocenter	C₂₉	#2923
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₂₉

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting

C₂×C₂₉×#97

C₂

prime radical

C₂×#90805

C₂²

cosocle

C₂×C₄×C₂₉

C₂⁴

hypercenter

C₂×#97

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₂×#97

N	H ≅ G/N	type
2. #14271225	C₂	semidirect
3. #14271218	C₂	semidirect
4. #14271189	C₂	semidirect
6. C₄×#90777	C₂	semidirect
7. C₂×C₂₉×#97	C₂	semidirect
80. C₂×#97	D₂₉	semidirect
101. C₂₉	#2923	semidirect

H ≅ G/N

type

2. #14271225

C₂

semidirect

3. #14271218

C₂

semidirect

4. #14271189

C₂

semidirect

6. C₄×#90777

C₂

semidirect

7. C₂×C₂₉×#97

C₂

semidirect

80. C₂×#97

D₂₉

semidirect

101. C₂₉

#2923

semidirect

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

subgroup	index
C₄×#90805	2
#14271225	2
#14271218	2
#14271189	2
#14271129	2
C₄×#90777	2
C₂×C₂₉×#97	2
#2923	29

subgroup

index

C₂×C₂₉×#97

Subgroups — #16828141

Conjugacy classes of subgroups

Complements

Maximal subgroups