Group #16835296 — subgroups

Subgroups — #16835296

Order 3712.

232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11745212	C₂	1	1	yes	maximal, characteristic
2	#14272128	C₂	1	2	yes	maximal
3	C₂×C₈×#1181	C₂	1	1	yes	maximal, characteristic
4	#14272033	C₂	1	2	yes	maximal
5	#14271200	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#1181	C₂²	1	1	yes	characteristic
7	C₂×#90796	C₂²	1	2	yes	—
8	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
10	#11745254	C₂²	1	2	yes	—
11	#11745218	—	2	2	no	—
12	C₄×#6599	—	2	2	no	—
13	#11745212	C₄	1	4	yes	complemented
14	C₈×#1181	C₄	1	4	yes	complemented
15	C₂₉×#107	C₄	1	1	yes	characteristic, complemented
16	#11745166	C₄	1	1	yes	characteristic, complemented
17	#11745156	C₄	1	2	yes	complemented
18	C₂²×#1181	—	2	1	no	—
19	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
20	C₂×#6599	—	2	2	no	—
21	C₂×#6599	D₄	1	1	yes	characteristic
22	C₂×#6599	D₄	1	1	yes	characteristic
23	C₄×#1181	—	2	1	no	—
24	C₄×#1181	C₂×C₄	1	2	yes	—
25	#90796	—	2	2	no	—
26	#90796	C₂×C₄	1	4	yes	—
27	D₂₉⋊C₈	C₂×C₄	1	2	yes	—
28	D₂₉⋊C₈	Q₈	1	2	yes	—
29	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
31	#90781	—	2	2	no	—
32	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
33	C₄×Dic₂₉	—	2	2	no	—
34	C₂×#6597	C₂×C₄	1	1	yes	characteristic
35	C₈×D₂₉	C₂×C₄	1	2	yes	—
36	C₈×D₂₉	C₂×C₄	1	2	yes	—
37	C₂²×D₂₉	#41	1	1	yes	characteristic
38	C₂×#1181	—	2	2	no	—
39	C₂×#1181	—	2	2	no	—
40	C₂×#1181	—	2	2	no	—
41	C₂×C₄×C₂₉	—	2	2	no	—
42	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
45	C₄×D₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₄×D₂₉	C₂²×C₄	1	1	yes	characteristic
47	C₄×D₂₉	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₂₉	#41	1	1	yes	characteristic
49	#6599	—	2	4	no	—
50	#6599	C₄⋊C₄	1	2	yes	—
51	#6599	C₄⋊C₄	1	2	yes	—
52	C₈×C₂₉	C₄²	1	2	yes	—
53	#6597	C₄²	1	2	yes	—
54	#1772	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
56	C₂×D₂₉	—	2	1	no	—
57	C₂×D₂₉	—	2	1	no	—
58	C₂×D₂₉	#117	1	1	yes	characteristic
59	C₂×D₂₉	C₄×Q₈	1	1	yes	characteristic
60	#1181	—	2	4	no	—
61	C₄×C₂₉	—	4	2	no	—
62	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
63	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
64	Dic₂₉	—	4	2	no	—
65	Dic₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
66	Dic₂₉	C₄×D₄	1	1	yes	characteristic
67	C₂×#108	—	29	1	no	—
68	#427	—	29	1	no	—
69	#405	—	29	2	no	—
70	C₂×C₄×C₈	—	29	1	no	—
71	#339	—	29	2	no	—
72	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₂₉	#443	1	1	yes	characteristic
74	C₂×C₂₉	#443	1	1	yes	characteristic
75	D₂₉	—	2	1	no	—
76	D₂₉	—	2	1	no	—
77	C₂×M₁₆	—	29	2	no	—
78	C₂²×C₈	—	29	1	no	—
79	C₂²×C₈	—	29	1	no	—
80	#117	—	29	2	no	—
81	C₂×C₄²	—	29	1	no	—
82	#108	—	29	4	no	—
83	#107	—	29	1	no	—
84	#107	#1181	1	1	yes	characteristic, complemented
85	#106	—	29	2	no	—
86	#97	—	58	2	no	—
87	C₄×C₈	—	29	4	no	—
88	C₄×C₈	—	58	2	no	—
89	C₂₉	#1772	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	29	1	no	—
91	C₂²×C₄	—	58	1	no	—
92	M₁₆	—	29	4	no	—
93	M₁₆	—	58	2	no	—
94	C₂×C₈	—	29	2	no	—
95	C₂×C₈	—	29	1	no	—
96	C₂×C₈	—	29	1	no	—
97	C₂×C₈	—	29	2	no	—
98	C₂×C₈	—	29	1	no	—
99	C₂×C₈	—	29	2	no	—
100	C₂×C₈	—	29	2	no	—
101	C₂×C₈	—	58	2	no	—
102	C₂×C₈	C₂×#1181	1	1	yes	characteristic
103	C₄⋊C₄	—	29	2	no	—
104	C₄⋊C₄	C₂×#1181	1	2	yes	—
105	C₂²⋊C₄	—	58	2	no	—
106	C₄²	—	29	2	no	—
107	C₄²	—	58	2	no	—
108	C₄²	—	58	1	no	—
109	C₂³	—	29	1	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	29	1	no	—
112	C₂×C₄	—	29	1	no	—
113	C₂×C₄	—	29	1	no	—
114	C₂×C₄	—	29	1	no	—
115	C₂×C₄	—	29	1	no	—
116	C₂×C₄	—	58	2	no	—
117	C₂×C₄	—	58	2	no	—
118	C₂×C₄	—	58	2	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
121	C₈	—	29	2	no	—
122	C₈	—	29	2	no	—
123	C₈	—	29	2	no	—
124	C₈	—	58	4	no	—
125	C₈	C₄×#1181	1	2	yes	—
126	C₂²	—	29	1	no	—
127	C₂²	—	29	1	no	—
128	C₂²	—	58	1	no	—
129	C₂²	—	58	1	no	—
130	C₂²	D₄×#1181	1	1	yes	characteristic
131	C₄	—	4	2	no	—
132	C₄	—	29	1	no	—
133	C₄	—	29	1	no	—
134	C₄	—	58	4	no	—
135	C₄	—	116	2	no	—
136	C₄	C₂×C₄×#1181	1	1	yes	characteristic
137	C₄	Q₈×#1181	1	1	yes	characteristic
138	C₂	—	58	1	no	—
139	C₂	—	58	1	no	—
140	C₂	C₄⋊C₄×#1181	1	1	yes	characteristic
141	C₂	#14272205	1	1	yes	characteristic
142	C₂	#14272207	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745212

C₂

yes

maximal, characteristic

#14272128

C₂

yes

maximal

C₂×C₈×#1181

C₂

yes

maximal, characteristic

#14272033

C₂

yes

maximal

#14271200

C₂

yes

maximal, characteristic

C₂×C₄×#1181

C₂²

yes

characteristic

C₂×#90796

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

#11745254

C₂²

yes

—

#11745218

—

C₄×#6599

—

#11745212

C₄

yes

complemented

C₈×#1181

C₄

yes

complemented

C₂₉×#107

C₄

yes

characteristic, complemented

#11745166

C₄

yes

characteristic, complemented

#11745156

C₄

yes

complemented

C₂²×#1181

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×#6599

—

C₂×#6599

D₄

yes

characteristic

C₂×#6599

D₄

yes

characteristic

C₄×#1181

—

C₄×#1181

C₂×C₄

yes

—

#90796

—

#90796

C₂×C₄

yes

—

D₂₉⋊C₈

C₂×C₄

yes

—

D₂₉⋊C₈

Q₈

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

#90781

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

—

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

—

C₂²×D₂₉

yes

—

—

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

C₂×Q₈

yes

C₄×D₂₉

yes

—

C₄⋊C₄

yes

—

#6599

C₄⋊C₄

yes

—

C₈×C₂₉

C₄²

yes

—

#6597

C₄²

yes

—

#1772

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

#117

yes

characteristic

C₂×D₂₉

C₄×Q₈

yes

characteristic

#1181

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

C₂×C₄⋊C₄

yes

characteristic

Dic₂₉

C₄×D₄

yes

—

—

—

C₂×C₄×C₈

—

#339

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

D₂₉

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#106

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#1772

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂×#1181

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

C₂×#1181

yes

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₂³

—

110

C₂×C₄

—

111

C₂×C₄

—

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

C₂²×#1181

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

C₄×#1181

yes

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

D₄×#1181

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

116

—

136

C₄

C₂×C₄×#1181

yes

characteristic

137

C₄

Q₈×#1181

yes

characteristic

138

C₂

—

139

C₂

—

140

C₂

C₄⋊C₄×#1181

yes

characteristic

141

C₂

#14272205

yes

characteristic

142

C₂

#14272207

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#1181
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#107	C₄
socle	C₂²×C₂₉	C₄×D₄
prime radical	C₂²×D₂₉	#41
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	#107	#1181
hypocenter	C₂₉	#1772
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#1181

commutator

C₄×C₂₉

C₂×C₄²

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#107

C₄

socle

C₂²×C₂₉

C₄×D₄

prime radical

C₂²×D₂₉

#41

cosocle

C₂×C₄×D₂₉

C₂³

C₂₉

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
13. #11745212	C₄	semidirect
14. C₈×#1181	C₄	semidirect
15. C₂₉×#107	C₄	semidirect
16. #11745166	C₄	semidirect
17. #11745156	C₄	semidirect
84. #107	#1181	semidirect
89. C₂₉	#1772	semidirect

H ≅ G/N

type

13. #11745212

C₄

semidirect

14. C₈×#1181

C₄

semidirect

15. C₂₉×#107

C₄

semidirect

16. #11745166

C₄

semidirect

17. #11745156

C₄

semidirect

84. #107

#1181

semidirect

89. C₂₉

#1772

semidirect

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

subgroup	index
C₂×#11745212	2
#14272128	2
C₂×C₈×#1181	2
#14272033	2
#14271200	2
#1772	29

subgroup

index

C₂×C₈×#1181

Subgroups — #16835296

Conjugacy classes of subgroups

Complements

Maximal subgroups