Group #16835069 — subgroups

Subgroups — #16835069

Order 3712.

158 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 64 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	#14272182	C₂	1	1	yes	maximal, characteristic
2	#14272167	C₂	1	1	yes	maximal, characteristic
3	#14272027	C₂	1	2	yes	maximal, complemented
4	#14272024	C₂	1	2	yes	maximal, complemented
5	#14271215	C₂	1	1	yes	maximal, characteristic
6	C₂×#90796	—	2	1	no	—
7	C₄²×D₂₉	C₂²	1	1	yes	characteristic
8	#11745219	—	2	1	no	—
9	C₄⋊#6599	—	2	1	no	—
10	C₄⋊#6599	C₂²	1	1	yes	characteristic
11	C₄⋊#6599	C₂²	1	2	yes	—
12	C₄⋊#6599	C₂²	1	1	yes	characteristic
13	C₄×#6599	—	2	1	no	—
14	C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic
15	#11745168	C₄	1	2	yes	—
16	C₈×Dic₂₉	C₂²	1	2	yes	—
17	C₄⋊#6597	C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×D₂₉	Q₈	1	1	yes	characteristic
21	C₂×#6599	—	2	2	no	—
22	C₂×#6599	—	2	1	no	—
23	C₂×#6599	—	2	1	no	—
24	#90796	—	4	2	no	—
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₂₉	D₄	1	1	yes	characteristic
28	C₄×Dic₂₉	Q₈	1	1	yes	characteristic
29	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
30	C₂×#6597	C₂×C₄	1	2	yes	—
31	C₂²×D₂₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₄×D₂₉	—	2	2	no	—
39	C₄×D₂₉	—	2	1	no	—
40	C₄×D₂₉	—	2	1	no	—
41	C₄×D₂₉	—	2	1	no	—
42	C₄×D₂₉	—	2	1	no	—
43	#6599	—	4	2	no	—
44	#6599	—	4	1	no	—
45	#6599	—	4	1	no	—
46	C₈×C₂₉	—	2	2	no	—
47	#6597	—	2	2	no	—
48	#1574	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×D₂₉	—	2	1	no	—
51	C₂×D₂₉	—	2	1	no	—
52	C₂×D₂₉	—	2	1	no	—
53	C₄×C₂₉	—	2	1	no	—
54	C₄×C₂₉	#108	1	2	yes	—
55	C₄×C₂₉	#131	1	1	yes	characteristic
56	C₄×C₂₉	#131	1	1	yes	characteristic
57	Dic₂₉	—	2	1	no	—
58	Dic₂₉	—	2	1	no	—
59	Dic₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
60	Dic₂₉	#137	1	1	yes	characteristic
61	#431	—	29	1	no	—
62	#431	—	29	1	no	—
63	#423	—	29	1	no	—
64	#335	—	29	2	no	—
65	#334	—	29	2	no	—
66	C₂×C₂₉	#424	1	1	yes	characteristic
67	C₂×C₂₉	#428	1	1	yes	characteristic
68	C₂×C₂₉	C₂×#108	1	1	yes	characteristic
69	D₂₉	—	4	1	no	—
70	C₂×M₁₆	—	58	1	no	—
71	C₂×C₄²	—	29	1	no	—
72	C₄⋊C₈	—	29	1	no	—
73	C₄⋊C₈	—	29	2	no	—
74	C₄⋊C₈	—	29	1	no	—
75	C₄⋊C₈	—	29	1	no	—
76	C₄⋊C₈	—	58	1	no	—
77	C₄⋊C₈	#1181	1	1	yes	characteristic
78	C₂²⋊C₈	—	29	2	no	—
79	C₂²⋊C₈	—	58	1	no	—
80	C₄×C₈	—	29	2	no	—
81	C₄×C₈	—	58	1	no	—
82	C₂₉	#1574	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	29	1	no	—
85	C₂²×C₄	—	29	1	no	—
86	M₁₆	—	116	2	no	—
87	C₂×C₈	—	29	2	no	—
88	C₂×C₈	—	58	1	no	—
89	C₂×C₈	—	58	1	no	—
90	C₂×C₈	—	58	2	no	—
91	C₂×C₈	C₂×#1181	1	2	yes	—
92	C₄²	—	29	1	no	—
93	C₄²	—	29	1	no	—
94	C₄²	—	29	1	no	—
95	C₄²	C₂×#1181	1	1	yes	characteristic
96	C₂³	—	29	1	no	—
97	C₂×C₄	—	29	1	no	—
98	C₂×C₄	—	29	1	no	—
99	C₂×C₄	—	29	1	no	—
100	C₂×C₄	—	58	1	no	—
101	C₂×C₄	—	58	1	no	—
102	C₂×C₄	—	58	1	no	—
103	C₂×C₄	—	58	1	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
106	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
107	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	58	2	no	—
110	C₈	—	116	2	no	—
111	C₈	—	116	1	no	—
112	C₈	—	116	1	no	—
113	C₂²	—	58	1	no	—
114	C₂²	—	58	1	no	—
115	C₂²	—	58	1	no	—
116	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
117	C₄	—	2	1	no	—
118	C₄	—	29	1	no	—
119	C₄	—	29	1	no	—
120	C₄	—	58	1	no	—
121	C₄	—	58	1	no	—
122	C₄	#11745211	1	2	yes	—
123	C₄	#11745346	1	1	yes	characteristic
124	C₄	#11745348	1	1	yes	characteristic
125	C₂	—	116	1	no	—
126	C₂	#14272170	1	1	yes	characteristic
127	C₂	#14272174	1	1	yes	characteristic
128	C₂	C₂×#11745211	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272182

C₂

yes

maximal, characteristic

#14272167

C₂

yes

maximal, characteristic

#14272027

C₂

yes

maximal, complemented

#14272024

C₂

yes

maximal, complemented

#14271215

C₂

yes

maximal, characteristic

C₂×#90796

—

C₄²×D₂₉

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊#6599

C₂²

yes

—

C₄⋊#6599

C₂²

yes

characteristic

C₄×#6599

—

C₂₉×C₄⋊C₈

C₄

yes

characteristic

#11745168

C₄

yes

—

C₈×Dic₂₉

C₂²

yes

—

C₄⋊#6597

C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂×C₄×D₂₉

Q₈

yes

—

—

—

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

Q₈

yes

characteristic

C₄×Dic₂₉

C₂³

yes

characteristic

C₂×#6597

C₂×C₄

yes

—

C₂²×D₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

#6599

—

#6599

—

#6599

—

C₈×C₂₉

—

#6597

—

#1574

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#108

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

Dic₂₉

yes

Dic₂₉

yes

—

—

—

—

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₂×M₁₆

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#1181

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#1574

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₄⋊#1181

yes

characteristic

106

C₂×C₄

C₄⋊#1181

yes

characteristic

107

C₂×C₄

C₂²×#1181

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

116

—

111

C₈

—

116

—

112

C₈

—

116

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

C₂×C₄⋊#1181

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11745211

yes

—

123

C₄

#11745346

yes

characteristic

124

C₄

#11745348

yes

characteristic

125

C₂

—

116

—

126

C₂

#14272170

yes

characteristic

127

C₂

#14272174

yes

characteristic

128

C₂

C₂×#11745211

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×C₄⋊C₈	C₄
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	C₄⋊C₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₄⋊C₈	#1181
hypocenter	C₂₉	#1574
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×C₄⋊C₈

C₄

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂²×D₂₉

C₄⋊C₄

cosocle

C₄×Dic₂₉

C₂³

C₄⋊C₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
3. #14272027	C₂	semidirect
4. #14272024	C₂	semidirect
82. C₂₉	#1574	semidirect

H ≅ G/N

type

3. #14272027

C₂

semidirect

4. #14272024

C₂

semidirect

82. C₂₉

#1574

semidirect

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

subgroup	index
#14272182	2
#14272167	2
#14272027	2
#14272024	2
#14271215	2
#1574	29

subgroup

index

Subgroups — #16835069

Conjugacy classes of subgroups

Complements

Maximal subgroups