Group #16821029 — subgroups

Subgroups — #16821029

Order 3712.

254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11745166	C₂	1	2	yes	maximal
2	C₂×#11745164	C₂	1	2	yes	maximal
3	#14271069	C₂	1	1	yes	maximal, characteristic
4	#14271033	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₂₉	—	2	2	no	—
10	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
12	#11745179	—	2	2	no	—
13	#11745166	—	2	4	no	—
14	#11745164	—	2	4	no	—
15	C₂²×C₄×C₂₉	D₄	1	2	yes	—
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₉	—	2	1	no	—
18	C₂²×Dic₂₉	—	2	2	no	—
19	C₂²×Dic₂₉	—	2	1	no	—
20	C₂×Dic₅₈	—	2	2	no	—
21	C₂×Dic₅₈	—	2	2	no	—
22	C₂×Dic₅₈	—	2	1	no	—
23	C₂×Dic₅₈	Q₈	1	2	yes	—
24	C₂×C₈×C₂₉	—	2	2	no	—
25	C₂×C₈×C₂₉	—	2	2	no	—
26	C₂×C₈×C₂₉	D₄	1	4	yes	—
27	C₄²×C₂₉	—	2	2	no	—
28	C₄⋊Dic₂₉	—	2	2	no	—
29	C₄⋊Dic₂₉	—	2	2	no	—
30	C₄⋊Dic₂₉	—	2	2	no	—
31	C₄⋊Dic₂₉	—	4	4	no	—
32	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	Q₁₆	1	4	yes	—
36	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₂₉	#41	1	2	yes	—
39	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
40	C₂×Dic₂₉	—	2	2	no	—
41	C₂×Dic₂₉	—	4	1	no	—
42	C₂×Dic₂₉	—	4	1	no	—
43	C₂×Dic₂₉	—	4	2	no	—
44	C₂×Dic₂₉	—	4	1	no	—
45	C₂×Dic₂₉	—	4	4	no	—
46	C₂×Dic₂₉	—	4	2	no	—
47	Dic₅₈	—	2	4	no	—
48	Dic₅₈	—	4	2	no	—
49	C₈×C₂₉	—	2	4	no	—
50	#2095	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₂²×C₂₉	#123	1	1	yes	characteristic
53	C₂²×C₂₉	#127	1	1	yes	characteristic
54	C₂²×C₂₉	C₂×Q₁₆	1	2	yes	—
55	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
56	C₄×C₂₉	—	2	4	no	—
57	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
58	C₄×C₂₉	#123	1	2	yes	—
59	Dic₂₉	—	4	2	no	—
60	Dic₂₉	—	8	2	no	—
61	Dic₂₉	—	8	1	no	—
62	C₂×#107	—	29	2	no	—
63	C₂×#103	—	29	2	no	—
64	#391	—	29	1	no	—
65	#384	—	29	1	no	—
66	#336	D₂₉	1	1	yes	characteristic
67	C₂×C₂₉	#399	1	1	yes	characteristic
68	C₂×C₂₉	#477	1	2	yes	—
69	C₂×C₂₉	#484	1	2	yes	—
70	C₂×C₂₉	#494	1	1	yes	characteristic
71	C₂×C₂₉	#496	1	1	yes	characteristic
72	C₂²×Q₈	—	29	1	no	—
73	C₂²×C₈	C₂×D₂₉	1	2	yes	—
74	C₂×C₄⋊C₄	—	29	2	no	—
75	C₂×C₄⋊C₄	—	29	1	no	—
76	C₂×C₄⋊C₄	—	58	2	no	—
77	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
78	#107	—	58	4	no	—
79	#103	—	58	4	no	—
80	#95	—	58	2	no	—
81	C₂₉	#2095	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₈	—	29	2	no	—
83	C₂×Q₈	—	58	1	no	—
84	C₂×Q₈	—	58	2	no	—
85	C₂×Q₈	—	58	2	no	—
86	C₂²×C₄	—	58	1	no	—
87	C₂²×C₄	—	58	1	no	—
88	C₂²×C₄	—	58	2	no	—
89	C₂²×C₄	D₁₁₆	1	2	yes	—
90	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	D₁₁₆	1	4	yes	—
94	C₄⋊C₄	—	58	2	no	—
95	C₄⋊C₄	—	58	2	no	—
96	C₄⋊C₄	—	58	2	no	—
97	C₄⋊C₄	—	116	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
100	Q₈	—	58	4	no	—
101	Q₈	—	116	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	—	116	1	no	—
106	C₂×C₄	—	116	1	no	—
107	C₂×C₄	—	116	2	no	—
108	C₂×C₄	—	116	1	no	—
109	C₂×C₄	—	116	4	no	—
110	C₂×C₄	—	116	2	no	—
111	C₂×C₄	Dic₁₁₆	1	4	yes	—
112	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
113	C₂×C₄	#90807	1	1	yes	characteristic
114	C₂×C₄	#90807	1	2	yes	—
115	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₂²	#11745236	1	1	yes	characteristic
118	C₂²	#11745248	1	1	yes	characteristic
119	C₂²	#11745259	1	1	yes	characteristic
120	C₂²	C₂×Dic₁₁₆	1	2	yes	—
121	C₂²	#11745270	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	116	2	no	—
124	C₄	—	232	2	no	—
125	C₄	—	232	1	no	—
126	C₄	#11745248	1	2	yes	—
127	C₄	#11745259	1	2	yes	—
128	C₂	#14271100	1	1	yes	characteristic
129	C₂	#14271459	1	2	yes	—
130	C₂	#14271499	1	2	yes	—
131	C₂	#14271543	1	1	yes	characteristic
132	C₂	#14271552	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745166

C₂

yes

maximal

C₂×#11745164

C₂

yes

maximal

#14271069

C₂

yes

maximal, characteristic

#14271033

C₂

yes

maximal, characteristic

C₂₉×#336

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

—

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂²×Dic₂₉

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

Q₈

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₄²×C₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

Q₁₆

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

#2095

—

maximal, Sylow

C₂²×C₂₉

C₂²⋊Q₈

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

C₂×Q₁₆

yes

—

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#123

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#484

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

C₂₉

#2095

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

116

—

C₄²

—

C₂³

C₂×D₁₁₆

yes

characteristic

100

Q₈

—

101

Q₈

—

116

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

116

—

106

C₂×C₄

—

116

—

107

C₂×C₄

—

116

—

108

C₂×C₄

—

116

—

109

C₂×C₄

—

116

—

110

C₂×C₄

—

116

—

111

C₂×C₄

Dic₁₁₆

yes

—

112

C₂×C₄

C₂×D₁₁₆

yes

—

113

C₂×C₄

#90807

yes

characteristic

114

C₂×C₄

#90807

yes

—

115

C₂×C₄

Q₈×D₂₉

yes

characteristic

116

C₈

—

117

C₂²

#11745236

yes

characteristic

118

C₂²

#11745248

yes

characteristic

119

C₂²

#11745259

yes

characteristic

120

C₂²

C₂×Dic₁₁₆

yes

—

121

C₂²

#11745270

yes

—

122

C₄

—

123

C₄

—

116

—

124

C₄

—

232

—

125

C₄

—

232

—

126

C₄

#11745248

yes

—

127

C₄

#11745259

yes

—

128

C₂

#14271100

yes

characteristic

129

C₂

#14271459

yes

—

130

C₂

#14271499

yes

—

131

C₂

#14271543

yes

characteristic

132

C₂

#14271552

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₁₆
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#336	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
hypercenter	#336	D₂₉
hypocenter	C₂₉	#2095
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₁₆

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#336

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

D₂₉

C₂₉

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
81. C₂₉	#2095	semidirect

H ≅ G/N

type

81. C₂₉

#2095

semidirect

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

subgroup	index
C₂×#11745166	2
C₂×#11745164	2
#14271069	2
#14271033	2
C₂₉×#336	2
#2095	29

subgroup

index

C₂₉×#336

Subgroups — #16821029

Conjugacy classes of subgroups

Complements

Maximal subgroups