Group #16819340 — subgroups

Subgroups — #16819340

Order 3712.

316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 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×C₈×Dic₂₉	C₂	1	2	yes	maximal
3	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270918	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#336	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	#11745162	C₄	1	8	yes	complemented
14	C₈×Dic₂₉	—	2	4	no	—
15	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	—	2	2	no	—
22	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
23	C₄²×C₂₉	—	2	2	no	—
24	C₄×Dic₂₉	—	2	4	no	—
25	C₄×Dic₂₉	C₈	1	8	yes	complemented
26	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
27	C₄×Dic₂₉	D₄	1	2	yes	—
28	C₄×Dic₂₉	Q₈	1	2	yes	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	C₂×C₄	1	4	yes	—
32	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₂₉	#41	1	2	yes	—
40	C₂×Dic₂₉	—	2	2	no	—
41	C₂×Dic₂₉	C₄²	1	2	yes	—
42	C₂×Dic₂₉	C₄²	1	2	yes	—
43	C₂×Dic₂₉	C₄⋊C₄	1	4	yes	—
44	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
45	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
46	C₂×Dic₂₉	M₁₆	1	4	yes	—
47	C₈×C₂₉	—	2	4	no	—
48	#6597	—	2	4	no	—
49	C₄×C₄⋊C₈	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
51	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₂₉	#117	1	1	yes	characteristic
53	C₂²×C₂₉	C₂²×C₈	1	2	yes	—
54	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
55	C₄×C₂₉	—	2	4	no	—
56	C₄×C₂₉	C₄×D₄	1	2	yes	—
57	C₄×C₂₉	C₄×Q₈	1	2	yes	—
58	Dic₂₉	—	2	2	no	—
59	Dic₂₉	C₄×C₈	1	4	yes	complemented
60	Dic₂₉	C₄⋊C₈	1	8	yes	complemented
61	C₂×C₄⋊C₈	—	29	2	no	—
62	C₂×C₄×C₈	—	29	2	no	—
63	C₄³	—	29	1	no	—
64	#336	—	29	1	no	—
65	#336	D₂₉	1	1	yes	characteristic
66	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
68	C₂×C₂₉	C₄×M₁₆	1	1	yes	characteristic
69	C₂×C₂₉	C₂×C₄⋊C₈	1	2	yes	—
70	C₂×C₂₉	#431	1	2	yes	—
71	C₂²×C₈	—	29	2	no	—
72	C₂²×C₈	C₂×D₂₉	1	2	yes	—
73	C₂×C₄²	—	29	2	no	—
74	C₂×C₄²	—	29	1	no	—
75	C₂×C₄²	—	29	1	no	—
76	C₂×C₄²	—	29	2	no	—
77	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
78	C₄⋊C₈	—	29	8	no	—
79	C₄×C₈	—	58	4	no	—
80	C₂₉	C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	29	1	no	—
82	C₂²×C₄	—	29	2	no	—
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	C₄×D₂₉	1	2	yes	—
85	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	29	4	no	—
89	C₂×C₈	—	58	2	no	—
90	C₂×C₈	—	58	2	no	—
91	C₂×C₈	C₄×D₂₉	1	4	yes	—
92	C₄²	—	2	2	no	—
93	C₄²	—	29	8	no	—
94	C₄²	—	29	4	no	—
95	C₄²	—	29	2	no	—
96	C₄²	—	29	2	no	—
97	C₄²	—	58	4	no	—
98	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	29	2	no	—
102	C₂×C₄	—	29	4	no	—
103	C₂×C₄	—	29	4	no	—
104	C₂×C₄	—	29	4	no	—
105	C₂×C₄	—	29	4	no	—
106	C₂×C₄	—	29	2	no	—
107	C₂×C₄	—	58	2	no	—
108	C₂×C₄	C₈×D₂₉	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
110	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
111	C₂×C₄	#90807	1	2	yes	—
112	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
113	C₈	—	2	4	no	—
114	C₈	—	58	4	no	—
115	C₂²	C₄²×D₂₉	1	1	yes	characteristic
116	C₂²	#11745239	1	1	yes	characteristic
117	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
118	C₂²	C₂×C₈×D₂₉	1	2	yes	—
119	C₂²	M₁₆×D₂₉	1	2	yes	—
120	C₄	—	2	4	no	—
121	C₄	—	29	4	no	—
122	C₄	—	29	8	no	—
123	C₄	—	58	2	no	—
124	C₄	#11745243	1	2	yes	—
125	C₄	#11745249	1	2	yes	—
126	C₂	#14271014	1	1	yes	characteristic
127	C₂	C₄×C₈×D₂₉	1	1	yes	characteristic
128	C₂	#14271115	1	1	yes	characteristic
129	C₂	C₄⋊C₈×D₂₉	1	2	yes	—
130	C₂	#14271213	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745162

C₂

yes

maximal

C₂×C₈×Dic₂₉

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

C₂₉×#336

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

—

#11745162

C₄

yes

complemented

C₈×Dic₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₈

yes

complemented

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

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

C₂×C₈

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

C₄²

yes

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₈×C₂₉

—

#6597

—

C₄×C₄⋊C₈

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

characteristic

C₂²×C₂₉

C₂²×C₈

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₄×Q₈

yes

—

Dic₂₉

—

Dic₂₉

C₄×C₈

yes

complemented

Dic₂₉

C₄⋊C₈

yes

complemented

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₄³

—

#336

—

#336

D₂₉

yes

characteristic

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

C₂×C₄×C₈

yes

characteristic

C₂×C₂₉

C₄×M₁₆

yes

characteristic

C₂×C₂₉

C₂×C₄⋊C₈

yes

—

C₂×C₂₉

#431

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₂₉

C₄×C₄⋊C₈

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

—

C₄²

—

C₂³

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₈×D₂₉

yes

—

109

C₂×C₄

C₂×C₄×D₂₉

yes

—

110

C₂×C₄

D₄×D₂₉

yes

characteristic

111

C₂×C₄

#90807

yes

—

112

C₂×C₄

Q₈×D₂₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₂²

C₄²×D₂₉

yes

characteristic

116

C₂²

#11745239

yes

characteristic

117

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

118

C₂²

C₂×C₈×D₂₉

yes

—

119

C₂²

M₁₆×D₂₉

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#11745243

yes

—

125

C₄

#11745249

yes

—

126

C₂

#14271014

yes

characteristic

127

C₂

C₄×C₈×D₂₉

yes

characteristic

128

C₂

#14271115

yes

characteristic

129

C₂

C₄⋊C₈×D₂₉

yes

—

130

C₂

#14271213

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂×C₄×C₈
Fitting	C₂₉×#336	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#336	D₂₉
hypocenter	C₂₉	C₄×C₄⋊C₈
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator

C₂×C₂₉

C₂×C₄×C₈

Fitting

C₂₉×#336

C₂

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

#336

D₂₉

hypocenter

C₂₉

C₄×C₄⋊C₈

LCS

G ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
13. #11745162	C₄	semidirect
25. C₄×Dic₂₉	C₈	semidirect
59. Dic₂₉	C₄×C₈	semidirect
60. Dic₂₉	C₄⋊C₈	semidirect
80. C₂₉	C₄×C₄⋊C₈	semidirect

H ≅ G/N

type

13. #11745162

C₄

semidirect

25. C₄×Dic₂₉

C₈

semidirect

59. Dic₂₉

C₄×C₈

semidirect

60. Dic₂₉

C₄⋊C₈

semidirect

80. C₂₉

C₄×C₄⋊C₈

semidirect

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

subgroup	index
C₂×#11745162	2
C₂×C₈×Dic₂₉	2
C₄²×Dic₂₉	2
#14270918	2
C₂₉×#336	2
C₄×C₄⋊C₈	29

subgroup

index

C₂×#11745162

C₂×C₈×Dic₂₉

C₄²×Dic₂₉

#14270918

C₂₉×#336

C₄×C₄⋊C₈

Subgroups — #16819340

Conjugacy classes of subgroups

Complements

Maximal subgroups