Group #16828285 — subgroups

Subgroups — C₂×#14271275 #16828285

Order 3712.

608 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 237 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×D₄×Dic₂₉	C₂	1	2	yes	maximal, complemented
2	#14271275	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11745165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11745180	C₂	1	2	yes	maximal, complemented
5	C₂×#11745163	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
8	C₂³×Dic₂₉	—	2	2	no	—
9	C₂×D₈×C₂₉	C₄	1	8	yes	complemented
10	C₂×D₈×C₂₉	C₂²	1	4	yes	—
11	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₂₉	—	2	2	no	—
13	D₄×Dic₂₉	—	2	4	no	—
14	D₄×Dic₂₉	C₂²	1	8	yes	complemented
15	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₂²×#6597	C₂²	1	1	yes	characteristic
18	#11745180	C₂²	1	8	yes	complemented
19	#11745165	C₂²	1	4	yes	complemented
20	#11745163	C₂²	1	4	yes	complemented
21	C₂⁴×C₂₉	—	2	2	no	—
22	C₂×D₄×C₂₉	—	2	2	no	—
23	C₂×D₄×C₂₉	—	2	4	no	—
24	C₂×D₄×C₂₉	C₂×C₄	1	8	yes	complemented
25	C₂×D₄×C₂₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₂₉	—	2	2	no	—
28	C₂²×Dic₂₉	—	2	8	no	—
29	C₂²×Dic₂₉	—	4	8	no	—
30	C₂²×Dic₂₉	D₄	1	2	yes	—
31	D₈×C₂₉	C₂×C₄	1	16	yes	complemented
32	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
33	C₂×C₈×C₂₉	C₂³	1	2	yes	—
34	C₂²⋊Dic₂₉	—	2	8	no	—
35	C₄⋊Dic₂₉	—	2	2	no	—
36	C₄⋊Dic₂₉	C₂³	1	4	yes	—
37	C₄×Dic₂₉	D₄	1	2	yes	—
38	C₄×Dic₂₉	C₂³	1	2	yes	—
39	C₂×#6597	—	2	2	no	—
40	C₂×#6597	C₂³	1	2	yes	—
41	C₂³×C₂₉	—	2	8	no	—
42	C₂³×C₂₉	—	2	4	no	—
43	C₂³×C₂₉	—	4	4	no	—
44	C₂³×C₂₉	—	4	4	no	—
45	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
46	D₄×C₂₉	—	2	8	no	—
47	D₄×C₂₉	—	2	4	no	—
48	D₄×C₂₉	C₂²×C₄	1	8	yes	complemented
49	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₂₉	#41	1	2	yes	—
52	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
53	C₂×Dic₂₉	—	2	4	no	—
54	C₂×Dic₂₉	—	2	4	no	—
55	C₂×Dic₂₉	—	4	16	no	—
56	C₂×Dic₂₉	—	4	4	no	—
57	C₂×Dic₂₉	C₂×D₄	1	4	yes	—
58	C₈×C₂₉	C₂²×C₄	1	4	yes	complemented
59	#6597	—	2	2	no	—
60	C₂×#442	—	29	1	no	maximal, Sylow
61	C₂²×C₂₉	—	2	8	no	—
62	C₂²×C₂₉	—	4	4	no	—
63	C₂²×C₂₉	—	4	4	no	—
64	C₂²×C₂₉	—	4	16	no	—
65	C₂²×C₂₉	C₄×D₄	1	2	yes	—
66	C₂²×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
67	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
68	C₄×C₂₉	C₄×D₄	1	2	yes	—
69	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
70	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
71	Dic₂₉	—	2	4	no	—
72	Dic₂₉	—	4	4	no	—
73	C₂²×D₈	D₂₉	1	1	yes	characteristic
74	C₂×C₄×D₄	—	29	2	no	—
75	#442	—	29	8	no	—
76	C₂×#106	—	29	1	no	—
77	C₂×#102	—	29	2	no	—
78	C₂×#97	—	29	1	no	—
79	C₂×C₂₉	—	4	8	no	—
80	C₂×C₂₉	#442	1	4	yes	complemented
81	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
82	C₂×C₂₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
83	C₂²×D₄	C₂×D₂₉	1	2	yes	—
84	C₂³×C₄	—	58	2	no	—
85	C₂×D₈	Dic₂₉	1	8	yes	complemented
86	C₂×D₈	C₂×D₂₉	1	4	yes	—
87	C₂²×C₈	—	29	1	no	—
88	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
89	C₄×D₄	—	29	8	no	—
90	C₄×D₄	—	58	4	no	—
91	C₂×C₄⋊C₄	—	29	2	no	—
92	C₂×C₂²⋊C₄	—	58	2	no	—
93	C₂×C₄²	—	29	1	no	—
94	#106	—	29	4	no	—
95	#102	—	29	8	no	—
96	#97	—	29	4	no	—
97	C₂₉	C₂×#442	1	1	yes	characteristic, complemented, Sylow
98	C₂⁴	—	2	2	no	—
99	C₂×D₄	—	2	2	no	—
100	C₂×D₄	—	2	4	no	—
101	C₂×D₄	C₂×Dic₂₉	1	8	yes	complemented
102	C₂×D₄	C₂²×D₂₉	1	4	yes	—
103	C₂²×C₄	—	29	2	no	—
104	C₂²×C₄	—	58	8	no	—
105	C₂²×C₄	—	58	2	no	—
106	C₂²×C₄	—	116	8	no	—
107	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
108	D₈	C₂×Dic₂₉	1	16	yes	complemented
109	C₂×C₈	—	29	2	no	—
110	C₂×C₈	—	58	2	no	—
111	C₂×C₈	C₂×Dic₂₉	1	4	yes	complemented
112	C₂×C₈	C₂²×D₂₉	1	2	yes	—
113	C₄⋊C₄	—	29	4	no	—
114	C₄⋊C₄	—	58	2	no	—
115	C₂²⋊C₄	—	58	8	no	—
116	C₄²	—	29	2	no	—
117	C₄²	—	29	2	no	—
118	C₂³	—	2	8	no	—
119	C₂³	—	2	4	no	—
120	C₂³	—	4	4	no	—
121	C₂³	—	4	4	no	—
122	C₂³	D₄×D₂₉	1	1	yes	characteristic
123	D₄	—	2	8	no	—
124	D₄	—	2	4	no	—
125	D₄	C₂²×Dic₂₉	1	8	yes	complemented
126	C₂×C₄	—	29	4	no	—
127	C₂×C₄	—	58	4	no	—
128	C₂×C₄	—	58	4	no	—
129	C₂×C₄	—	116	16	no	—
130	C₂×C₄	—	116	4	no	—
131	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
132	C₂×C₄	#90807	1	2	yes	—
133	C₂×C₄	C₂²×Dic₂₉	1	2	yes	—
134	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
135	C₈	—	58	2	no	—
136	C₈	C₂²×Dic₂₉	1	4	yes	complemented
137	C₂²	—	2	8	no	—
138	C₂²	—	4	16	no	—
139	C₂²	—	4	4	no	—
140	C₂²	—	4	4	no	—
141	C₂²	#11745273	1	4	yes	—
142	C₂²	D₄×Dic₂₉	1	2	yes	—
143	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
144	C₄	—	58	4	no	—
145	C₄	—	116	4	no	—
146	C₄	D₄×Dic₂₉	1	2	yes	—
147	C₄	C₂×#90807	1	1	yes	characteristic
148	C₄	C₂³×Dic₂₉	1	1	yes	characteristic
149	C₂	—	4	8	no	—
150	C₂	#14271275	1	4	yes	direct product factor
151	C₂	C₂×D₄×Dic₂₉	1	1	yes	characteristic
152	C₂	C₂×#11745273	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×Dic₂₉

C₂

yes

maximal, complemented

#14271275

C₂

yes

maximal, direct product factor

C₂×#11745165

C₂

yes

maximal, characteristic, complemented

C₂×#11745180

C₂

yes

maximal, complemented

C₂×#11745163

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₂₉

C₂

yes

maximal, characteristic

C₂²×D₄×C₂₉

C₂²

yes

—

C₂³×Dic₂₉

—

C₂×D₈×C₂₉

C₄

yes

complemented

C₂×D₈×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₂₉

—

D₄×Dic₂₉

—

D₄×Dic₂₉

C₂²

yes

complemented

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

#11745180

C₂²

yes

complemented

#11745165

C₂²

yes

complemented

#11745163

C₂²

yes

complemented

C₂⁴×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂×C₄

yes

complemented

C₂×D₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂²×Dic₂₉

D₄

yes

—

D₈×C₂₉

C₂×C₄

yes

complemented

C₂×C₈×C₂₉

C₂×C₄

yes

complemented

C₂×C₈×C₂₉

C₂³

yes

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₂×#6597

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

C₂²×C₄

yes

complemented

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

—

C₈×C₂₉

C₂²×C₄

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₄×D₄

yes

—

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₂³×C₄

yes

characteristic

C₄×C₂₉

C₂×#41

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂²×D₈

D₂₉

yes

characteristic

C₂×C₄×D₄

—

#442

—

C₂×#106

—

C₂×#102

—

C₂×#97

—

C₂×C₂₉

—

C₂×C₂₉

#442

yes

complemented

C₂×C₂₉

C₂×C₄×D₄

yes

characteristic

C₂×C₂₉

C₂×AGL(1,ℤ/8)

yes

—

C₂²×D₄

C₂×D₂₉

yes

—

C₂³×C₄

—

C₂×D₈

Dic₂₉

yes

complemented

C₂×D₈

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#106

—

#102

—

#97

—

C₂₉

C₂×#442

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

C₂×Dic₂₉

yes

complemented

102

C₂×D₄

C₂²×D₂₉

yes

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

116

—

107

C₂²×C₄

C₂²×D₂₉

yes

characteristic

108

D₈

C₂×Dic₂₉

yes

complemented

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₂×Dic₂₉

yes

complemented

112

C₂×C₈

C₂²×D₂₉

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

D₄×D₂₉

yes

characteristic

123

D₄

—

124

D₄

—

125

D₄

C₂²×Dic₂₉

yes

complemented

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

116

—

130

C₂×C₄

—

116

—

131

C₂×C₄

D₄×D₂₉

yes

characteristic

132

C₂×C₄

#90807

yes

—

133

C₂×C₄

C₂²×Dic₂₉

yes

—

134

C₂×C₄

C₂³×D₂₉

yes

characteristic

135

C₈

—

136

C₈

C₂²×Dic₂₉

yes

complemented

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

#11745273

yes

—

142

C₂²

D₄×Dic₂₉

yes

—

143

C₂²

C₂×D₄×D₂₉

yes

characteristic

144

C₄

—

145

C₄

—

116

—

146

C₄

D₄×Dic₂₉

yes

—

147

C₄

C₂×#90807

yes

characteristic

148

C₄

C₂³×Dic₂₉

yes

characteristic

149

C₂

—

150

C₂

#14271275

yes

direct product factor

151

C₂

C₂×D₄×Dic₂₉

yes

characteristic

152

C₂

C₂×#11745273

yes

—

	subgroup	G/H
center	C₂³	D₄×D₂₉
commutator	C₄×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting, prime radical	C₂²×D₈×C₂₉	C₂
socle	C₂³×C₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂²×D₈	D₂₉
hypocenter	C₂₉	C₂×#442
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₈

subgroup

G/H

center

C₂³

D₄×D₂₉

commutator

C₄×C₂₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₂₉

Fitting, prime radical

C₂²×D₈×C₂₉

C₂

socle

C₂³×C₂₉

C₂×D₄

cosocle

C₂×C₄×C₂₉

C₂⁴

hypercenter

C₂²×D₈

D₂₉

hypocenter

C₂₉

C₂×#442

LCS

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₈

N	H ≅ G/N	type
1. C₂×D₄×Dic₂₉	C₂	semidirect
2. #14271275	C₂	direct (N × H)
3. C₂×#11745165	C₂	semidirect
4. C₂×#11745180	C₂	semidirect
5. C₂×#11745163	C₂	semidirect
9. C₂×D₈×C₂₉	C₄	semidirect
14. D₄×Dic₂₉	C₂²	semidirect
18. #11745180	C₂²	semidirect
19. #11745165	C₂²	semidirect
20. #11745163	C₂²	semidirect
24. C₂×D₄×C₂₉	C₂×C₄	semidirect
31. D₈×C₂₉	C₂×C₄	semidirect
32. C₂×C₈×C₂₉	C₂×C₄	semidirect
48. D₄×C₂₉	C₂²×C₄	semidirect
58. C₈×C₂₉	C₂²×C₄	semidirect
80. C₂×C₂₉	#442	semidirect
85. C₂×D₈	Dic₂₉	semidirect
97. C₂₉	C₂×#442	semidirect
101. C₂×D₄	C₂×Dic₂₉	semidirect
108. D₈	C₂×Dic₂₉	semidirect
111. C₂×C₈	C₂×Dic₂₉	semidirect
125. D₄	C₂²×Dic₂₉	semidirect
136. C₈	C₂²×Dic₂₉	semidirect
150. C₂	#14271275	direct (N × H)

H ≅ G/N

type

1. C₂×D₄×Dic₂₉

C₂

semidirect

2. #14271275

C₂

direct (N × H)

3. C₂×#11745165

C₂

semidirect

4. C₂×#11745180

C₂

semidirect

5. C₂×#11745163

C₂

semidirect

9. C₂×D₈×C₂₉

C₄

semidirect

14. D₄×Dic₂₉

C₂²

semidirect

18. #11745180

C₂²

semidirect

19. #11745165

C₂²

semidirect

20. #11745163

C₂²

semidirect

24. C₂×D₄×C₂₉

C₂×C₄

semidirect

31. D₈×C₂₉

C₂×C₄

semidirect

32. C₂×C₈×C₂₉

C₂×C₄

semidirect

48. D₄×C₂₉

C₂²×C₄

semidirect

58. C₈×C₂₉

C₂²×C₄

semidirect

80. C₂×C₂₉

#442

semidirect

85. C₂×D₈

Dic₂₉

semidirect

97. C₂₉

C₂×#442

semidirect

101. C₂×D₄

C₂×Dic₂₉

semidirect

108. D₈

C₂×Dic₂₉

semidirect

111. C₂×C₈

C₂×Dic₂₉

semidirect

125. D₄

C₂²×Dic₂₉

semidirect

136. C₈

C₂²×Dic₂₉

semidirect

150. C₂

#14271275

direct (N × H)

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

subgroup	index
C₂×D₄×Dic₂₉	2
#14271275	2
C₂×#11745165	2
C₂×#11745180	2
C₂×#11745163	2
C₂²×D₈×C₂₉	2
C₂×#442	29

subgroup

index

C₂×D₄×Dic₂₉

C₂²×D₈×C₂₉

Subgroups — C₂×#14271275 #16828285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#14271275 #16828285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271275 #16828285