Group #16828279 — subgroups

Subgroups — C₂×#14271270 #16828279

Order 3712.

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

normal subgroups only

This group has 480 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×Q₈×Dic₂₉	C₂	1	2	yes	maximal
2	#14271270	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11745165	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745183	C₂	1	2	yes	maximal
5	C₂×#11745163	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₂₉	C₂²	1	2	yes	—
8	C₂×Q₁₆×C₂₉	C₄	1	8	yes	complemented
9	C₂×Q₁₆×C₂₉	C₂²	1	4	yes	—
10	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	Q₈×Dic₂₉	—	2	4	no	—
12	Q₈×Dic₂₉	C₂²	1	8	yes	—
13	C₂×C₄⋊Dic₂₉	—	2	2	no	—
14	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₂₉	—	2	2	no	—
16	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₂²×#6597	C₂²	1	1	yes	characteristic
18	#11745183	C₂²	1	8	yes	—
19	#11745165	C₂²	1	4	yes	—
20	#11745163	C₂²	1	4	yes	—
21	C₂×Q₈×C₂₉	—	2	2	no	—
22	C₂×Q₈×C₂₉	—	2	4	no	—
23	C₂×Q₈×C₂₉	C₂×C₄	1	8	yes	—
24	C₂×Q₈×C₂₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₂₉	—	2	2	no	—
26	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₂₉	—	2	2	no	—
28	C₂²×Dic₂₉	D₄	1	2	yes	—
29	Q₁₆×C₂₉	C₂×C₄	1	16	yes	complemented
30	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
31	C₂×C₈×C₂₉	C₂³	1	2	yes	—
32	C₄⋊Dic₂₉	—	2	2	no	—
33	C₄⋊Dic₂₉	—	2	8	no	—
34	C₄⋊Dic₂₉	C₂³	1	4	yes	—
35	C₄×Dic₂₉	—	2	8	no	—
36	C₄×Dic₂₉	D₄	1	2	yes	—
37	C₄×Dic₂₉	C₂³	1	2	yes	—
38	C₂×#6597	—	2	2	no	—
39	C₂×#6597	C₂³	1	2	yes	—
40	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₂₉	—	2	8	no	—
42	Q₈×C₂₉	—	2	4	no	—
43	Q₈×C₂₉	C₂²×C₄	1	8	yes	—
44	C₂×C₄×C₂₉	—	2	8	no	—
45	C₂×C₄×C₂₉	—	2	4	no	—
46	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	#41	1	2	yes	—
49	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₂₉	—	2	4	no	—
51	C₂×Dic₂₉	—	2	4	no	—
52	C₂×Dic₂₉	—	4	4	no	—
53	C₂×Dic₂₉	C₂×D₄	1	4	yes	—
54	C₈×C₂₉	C₂²×C₄	1	4	yes	—
55	#6597	—	2	2	no	—
56	C₂×#441	—	29	1	no	maximal, Sylow
57	C₂²×C₂₉	C₄×D₄	1	2	yes	—
58	C₂²×C₂₉	#137	1	4	yes	—
59	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
60	C₄×C₂₉	—	2	8	no	—
61	C₄×C₂₉	C₄×D₄	1	2	yes	—
62	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
63	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
64	Dic₂₉	—	2	4	no	—
65	Dic₂₉	—	4	4	no	—
66	C₂²×Q₁₆	D₂₉	1	1	yes	characteristic
67	C₂×C₄×Q₈	—	29	2	no	—
68	#441	—	29	8	no	—
69	C₂×#106	—	29	1	no	—
70	C₂×#103	—	29	2	no	—
71	C₂×#97	—	29	1	no	—
72	C₂×C₂₉	#441	1	4	yes	complemented
73	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
74	C₂×C₂₉	C₂×#137	1	2	yes	—
75	C₂²×Q₈	C₂×D₂₉	1	2	yes	—
76	C₂×Q₁₆	Dic₂₉	1	8	yes	complemented
77	C₂×Q₁₆	C₂×D₂₉	1	4	yes	—
78	C₂²×C₈	—	29	1	no	—
79	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
80	C₄×Q₈	—	29	8	no	—
81	C₄×Q₈	—	58	4	no	—
82	C₂×C₄⋊C₄	—	29	2	no	—
83	C₂×C₄⋊C₄	—	58	2	no	—
84	C₂×C₄²	—	29	1	no	—
85	C₂×C₄²	—	58	2	no	—
86	#106	—	29	4	no	—
87	#103	—	29	8	no	—
88	#97	—	29	4	no	—
89	C₂₉	C₂×#441	1	1	yes	characteristic, complemented, Sylow
90	C₂×Q₈	—	2	2	no	—
91	C₂×Q₈	—	2	4	no	—
92	C₂×Q₈	C₂×Dic₂₉	1	8	yes	—
93	C₂×Q₈	C₂²×D₂₉	1	4	yes	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	—	29	2	no	—
96	C₂²×C₄	—	58	2	no	—
97	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
98	Q₁₆	C₂×Dic₂₉	1	16	yes	complemented
99	C₂×C₈	—	29	2	no	—
100	C₂×C₈	—	58	2	no	—
101	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
102	C₂×C₈	C₂²×D₂₉	1	2	yes	—
103	C₄⋊C₄	—	29	4	no	—
104	C₄⋊C₄	—	58	8	no	—
105	C₄⋊C₄	—	58	2	no	—
106	C₄²	—	29	2	no	—
107	C₄²	—	29	2	no	—
108	C₄²	—	58	8	no	—
109	C₂³	D₄×D₂₉	1	1	yes	characteristic
110	Q₈	—	2	8	no	—
111	Q₈	—	2	4	no	—
112	Q₈	C₂²×Dic₂₉	1	8	yes	—
113	C₂×C₄	—	2	8	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	29	4	no	—
116	C₂×C₄	—	58	4	no	—
117	C₂×C₄	—	58	4	no	—
118	C₂×C₄	—	116	4	no	—
119	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
120	C₂×C₄	#90807	1	2	yes	—
121	C₂×C₄	C₂²×Dic₂₉	1	2	yes	—
122	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
123	C₈	—	58	2	no	—
124	C₈	C₂²×Dic₂₉	1	4	yes	—
125	C₂²	#11745280	1	4	yes	—
126	C₂²	D₄×Dic₂₉	1	2	yes	—
127	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
128	C₄	—	2	8	no	—
129	C₄	—	58	4	no	—
130	C₄	—	116	4	no	—
131	C₄	D₄×Dic₂₉	1	2	yes	—
132	C₄	C₂×#90807	1	1	yes	characteristic
133	C₄	C₂³×Dic₂₉	1	1	yes	characteristic
134	C₂	#14271270	1	4	yes	direct product factor
135	C₂	C₂×D₄×Dic₂₉	1	1	yes	characteristic
136	C₂	C₂×#11745280	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₂₉

C₂

yes

maximal

#14271270

C₂

yes

maximal, direct product factor

C₂×#11745165

C₂

yes

maximal, characteristic

C₂×#11745183

C₂

yes

maximal

C₂×#11745163

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₂₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

—

C₂×Q₁₆×C₂₉

C₄

yes

complemented

C₂×Q₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

Q₈×Dic₂₉

—

Q₈×Dic₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

#11745183

C₂²

yes

—

#11745165

C₂²

yes

—

#11745163

C₂²

yes

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

C₂×Q₈×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

D₄

yes

—

Q₁₆×C₂₉

C₂×C₄

yes

complemented

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂³

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₂×#6597

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

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×D₄

yes

—

C₈×C₂₉

C₂²×C₄

yes

—

#6597

—

C₂×#441

—

maximal, Sylow

C₂²×C₂₉

C₄×D₄

yes

—

C₂²×C₂₉

#137

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₂³×C₄

yes

characteristic

C₄×C₂₉

C₂×#41

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂²×Q₁₆

D₂₉

yes

characteristic

C₂×C₄×Q₈

—

#441

—

C₂×#106

—

C₂×#103

—

C₂×#97

—

C₂×C₂₉

#441

yes

complemented

C₂×C₂₉

C₂×C₄×D₄

yes

characteristic

C₂×C₂₉

C₂×#137

yes

—

C₂²×Q₈

C₂×D₂₉

yes

—

C₂×Q₁₆

Dic₂₉

yes

complemented

C₂×Q₁₆

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

#106

—

#103

—

#97

—

C₂₉

C₂×#441

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₂₉

yes

—

C₂×Q₈

C₂²×D₂₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

Q₁₆

C₂×Dic₂₉

yes

complemented

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂×Dic₂₉

yes

—

102

C₂×C₈

C₂²×D₂₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₂³

D₄×D₂₉

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

C₂²×Dic₂₉

yes

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

116

—

119

C₂×C₄

D₄×D₂₉

yes

characteristic

120

C₂×C₄

#90807

yes

—

121

C₂×C₄

C₂²×Dic₂₉

yes

—

122

C₂×C₄

C₂³×D₂₉

yes

characteristic

123

C₈

—

124

C₈

C₂²×Dic₂₉

yes

—

125

C₂²

#11745280

yes

—

126

C₂²

D₄×Dic₂₉

yes

—

127

C₂²

C₂×D₄×D₂₉

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

116

—

131

C₄

D₄×Dic₂₉

yes

—

132

C₄

C₂×#90807

yes

characteristic

133

C₄

C₂³×Dic₂₉

yes

characteristic

134

C₂

#14271270

yes

direct product factor

135

C₂

C₂×D₄×Dic₂₉

yes

characteristic

136

C₂

C₂×#11745280

yes

—

	subgroup	G/H
center	C₂³	D₄×D₂₉
commutator	C₄×C₂₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂²×Q₁₆×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂²×Q₁₆	D₂₉
hypocenter	C₂₉	C₂×#441
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂³

D₄×D₂₉

commutator

C₄×C₂₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂²×Q₁₆×C₂₉

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂×C₄×C₂₉

C₂⁴

hypercenter

C₂²×Q₁₆

D₂₉

hypocenter

C₂₉

C₂×#441

LCS

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
2. #14271270	C₂	direct (N × H)
8. C₂×Q₁₆×C₂₉	C₄	semidirect
29. Q₁₆×C₂₉	C₂×C₄	semidirect
72. C₂×C₂₉	#441	semidirect
76. C₂×Q₁₆	Dic₂₉	semidirect
89. C₂₉	C₂×#441	semidirect
98. Q₁₆	C₂×Dic₂₉	semidirect
134. C₂	#14271270	direct (N × H)

H ≅ G/N

type

2. #14271270

C₂

direct (N × H)

8. C₂×Q₁₆×C₂₉

C₄

semidirect

29. Q₁₆×C₂₉

C₂×C₄

semidirect

72. C₂×C₂₉

#441

semidirect

76. C₂×Q₁₆

Dic₂₉

semidirect

89. C₂₉

C₂×#441

semidirect

98. Q₁₆

C₂×Dic₂₉

semidirect

134. C₂

#14271270

direct (N × H)

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

subgroup	index
C₂×Q₈×Dic₂₉	2
#14271270	2
C₂×#11745165	2
C₂×#11745183	2
C₂×#11745163	2
C₂²×Q₁₆×C₂₉	2
C₂×#441	29

subgroup

index

C₂×Q₈×Dic₂₉

C₂²×Q₁₆×C₂₉

Subgroups — C₂×#14271270 #16828279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#14271270 #16828279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271270 #16828279