Group #16819346 — subgroups

Subgroups — #16819346

Order 3712.

292 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11745162	C₂	1	2	yes	maximal
2	C₂×#11745151	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270917	C₂	1	2	yes	maximal
5	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂²×#6597	C₂²	1	2	yes	—
13	C₂₉×#97	—	2	2	no	—
14	#11745162	C₄	1	8	yes	complemented
15	#11745151	—	2	2	no	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₂₉	—	2	2	no	—
22	C₂×C₈×C₂₉	—	2	2	no	—
23	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
24	C₄²×C₂₉	D₄	1	2	yes	—
25	C₄²×C₂₉	Q₈	1	2	yes	—
26	C₄×Dic₂₉	—	2	2	no	—
27	C₄×Dic₂₉	—	2	4	no	—
28	C₄×Dic₂₉	—	2	4	no	—
29	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂×#6597	C₂×C₄	1	4	yes	—
33	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	—	2	2	no	—
36	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₂₉	#41	1	2	yes	—
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	—	2	2	no	—
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	C₄²	1	2	yes	—
45	C₂×Dic₂₉	C₄²	1	2	yes	—
46	C₂×Dic₂₉	M₁₆	1	4	yes	—
47	C₂×Dic₂₉	M₁₆	1	4	yes	—
48	C₈×C₂₉	—	2	4	no	—
49	#6597	—	2	4	no	—
50	#1767	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
52	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₂₉	#117	1	1	yes	characteristic
54	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
55	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
56	C₄×C₂₉	—	2	4	no	—
57	C₄×C₂₉	C₄×D₄	1	2	yes	—
58	C₄×C₂₉	C₄×Q₈	1	2	yes	—
59	Dic₂₉	—	2	2	no	—
60	Dic₂₉	—	2	4	no	—
61	Dic₂₉	#97	1	4	yes	complemented
62	C₂×C₄⋊C₈	—	29	2	no	—
63	C₂×#97	—	29	1	no	—
64	C₂×#97	D₂₉	1	1	yes	characteristic
65	C₄³	—	29	1	no	—
66	#336	—	29	2	no	—
67	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
69	C₂×C₂₉	C₄×M₁₆	1	1	yes	characteristic
70	C₂×C₂₉	#423	1	2	yes	—
71	C₂×C₂₉	#432	1	2	yes	—
72	C₂²×C₈	—	29	2	no	—
73	C₂²×C₈	C₂×D₂₉	1	2	yes	—
74	C₂×C₄²	—	29	1	no	—
75	C₂×C₄²	—	29	2	no	—
76	C₂×C₄²	—	29	2	no	—
77	C₂×C₄²	—	29	1	no	—
78	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
79	C₄⋊C₈	—	29	8	no	—
80	#97	—	2	2	no	—
81	#97	—	58	2	no	—
82	C₂₉	#1767	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	29	1	no	—
85	C₂²×C₄	—	29	2	no	—
86	C₂²×C₄	C₄×D₂₉	1	2	yes	—
87	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	29	4	no	—
91	C₂×C₈	—	58	2	no	—
92	C₂×C₈	—	58	2	no	—
93	C₂×C₈	C₄×D₂₉	1	4	yes	—
94	C₄²	—	29	4	no	—
95	C₄²	—	58	4	no	—
96	C₄²	—	58	4	no	—
97	C₄²	—	58	2	no	—
98	C₄²	Dic₅₈	1	2	yes	—
99	C₄²	C₂²⋊D₂₉	1	2	yes	—
100	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	29	4	no	—
105	C₂×C₄	—	29	2	no	—
106	C₂×C₄	—	29	4	no	—
107	C₂×C₄	—	58	2	no	—
108	C₂×C₄	—	58	2	no	—
109	C₂×C₄	—	58	2	no	—
110	C₂×C₄	#90779	1	4	yes	—
111	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
113	C₂×C₄	#90805	1	2	yes	—
114	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
115	C₈	—	2	4	no	—
116	C₈	—	58	4	no	—
117	C₂²	C₄²×D₂₉	1	1	yes	characteristic
118	C₂²	#11745234	1	1	yes	characteristic
119	C₂²	M₁₆×D₂₉	1	2	yes	—
120	C₂²	M₁₆×D₂₉	1	2	yes	—
121	C₂²	C₂×#90779	1	1	yes	characteristic
122	C₄	—	2	4	no	—
123	C₄	—	29	4	no	—
124	C₄	—	58	2	no	—
125	C₄	—	58	4	no	—
126	C₄	C₄×Dic₅₈	1	2	yes	—
127	C₄	C₄×C₂²⋊D₂₉	1	2	yes	—
128	C₂	C₄×#90779	1	1	yes	characteristic
129	C₂	#97×D₂₉	1	1	yes	characteristic
130	C₂	#14271115	1	1	yes	characteristic
131	C₂	#14271186	1	2	yes	—
132	C₂	#14271218	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745162

C₂

yes

maximal

C₂×#11745151

C₂

yes

maximal, characteristic

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal

C₂×C₂₉×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

—

C₂₉×#97

—

#11745162

C₄

yes

complemented

#11745151

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₈×C₂₉

—

#6597

—

#1767

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₄×Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#97

yes

complemented

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×#97

D₂₉

yes

characteristic

C₄³

—

#336

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

C₂×#97

yes

characteristic

C₂×C₂₉

C₄×M₁₆

yes

characteristic

C₂×C₂₉

#423

yes

—

C₂×C₂₉

#432

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

#97

—

#97

—

C₂₉

#1767

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₅₈

yes

—

C₄²

C₂²⋊D₂₉

yes

—

100

C₂³

C₂×C₄×D₂₉

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

#90779

yes

—

111

C₂×C₄

C₂×Dic₅₈

yes

characteristic

112

C₂×C₄

C₂×C₄×D₂₉

yes

—

113

C₂×C₄

#90805

yes

—

114

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

115

C₈

—

116

C₈

—

117

C₂²

C₄²×D₂₉

yes

characteristic

118

C₂²

#11745234

yes

characteristic

119

C₂²

M₁₆×D₂₉

yes

—

120

C₂²

M₁₆×D₂₉

yes

—

121

C₂²

C₂×#90779

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

C₄×Dic₅₈

yes

—

127

C₄

C₄×C₂²⋊D₂₉

yes

—

128

C₂

C₄×#90779

yes

characteristic

129

C₂

#97×D₂₉

yes

characteristic

130

C₂

#14271115

yes

characteristic

131

C₂

#14271186

yes

—

132

C₂

#14271218

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂×C₄²
Fitting	C₂×C₂₉×#97	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#97	D₂₉
hypocenter	C₂₉	#1767
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator

C₂²×C₂₉

C₂×C₄²

Fitting

C₂×C₂₉×#97

C₂

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×#97

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
14. #11745162	C₄	semidirect
61. Dic₂₉	#97	semidirect
82. C₂₉	#1767	semidirect

H ≅ G/N

type

14. #11745162

C₄

semidirect

61. Dic₂₉

#97

semidirect

82. C₂₉

#1767

semidirect

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

subgroup	index
C₂×#11745162	2
C₂×#11745151	2
C₄²×Dic₂₉	2
#14270917	2
C₂×C₂₉×#97	2
#1767	29

subgroup

index

C₄²×Dic₂₉

C₂×C₂₉×#97

Subgroups — #16819346

Conjugacy classes of subgroups

Complements

Maximal subgroups