Group #14271709 — subgroups

Subgroups — #14271709

Order 1856.

310 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 115 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×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#90805	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745309	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745306	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745302	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745301	C₂	1	4	yes	maximal, complemented
7	#11745298	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₂²⋊D₂₉	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#41×C₂₉	—	2	4	no	—
11	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₂₉	C₂²	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊D₂₉	C₂²	1	4	yes	—
17	C₂×C₂²⋊D₂₉	C₂²	1	2	yes	—
18	C₂²×Dic₂₉	C₂²	1	2	yes	—
19	#90805	—	2	4	no	—
20	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₂₉	C₂²	1	2	yes	—
22	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
23	C₂²⋊Dic₂₉	C₂²	1	4	yes	—
24	#90781	C₂²	1	4	yes	—
25	#90779	C₂²	1	4	yes	—
26	C₄×Dic₂₉	C₂²	1	2	yes	—
27	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
28	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
29	C₂³×C₂₉	C₂³	1	2	yes	—
30	C₂³×C₂₉	C₂³	1	1	yes	characteristic
31	C₂²×D₂₉	C₂³	1	2	yes	—
32	Q₈×C₂₉	—	2	2	no	—
33	D₄×C₂₉	—	2	4	no	—
34	D₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	—	2	4	no	—
36	C₂×C₄×C₂₉	D₄	1	4	yes	complemented
37	C₂×C₄×C₂₉	C₂³	1	2	yes	—
38	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₂²⋊D₂₉	—	2	4	no	—
41	C₂²⋊D₂₉	—	2	8	no	—
42	C₂×Dic₂₉	—	2	4	no	—
43	C₂×Dic₂₉	C₂³	1	2	yes	—
44	C₂×Dic₂₉	C₂³	1	2	yes	—
45	C₂×Dic₂₉	C₂³	1	2	yes	—
46	D₁₁₆	—	2	2	no	—
47	C₄×D₂₉	—	2	4	no	—
48	Dic₅₈	—	2	2	no	—
49	C₂²×C₂₉	—	2	2	no	—
50	C₂²×C₂₉	—	2	2	no	—
51	C₂²×C₂₉	—	2	4	no	—
52	C₂²×C₂₉	C₂×D₄	1	2	yes	—
53	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
54	C₂×D₂₉	—	2	2	no	—
55	C₂×D₂₉	—	2	4	no	—
56	C₄×C₂₉	—	2	2	no	—
57	C₄×C₂₉	C₂×D₄	1	2	yes	—
58	C₄×C₂₉	C₂×D₄	1	2	yes	—
59	Dic₂₉	—	2	2	no	—
60	Dic₂₉	—	2	2	no	—
61	Dic₂₉	#41	1	4	yes	complemented
62	#532	—	29	1	no	maximal, Sylow
63	C₂×C₂₉	—	2	2	no	—
64	C₂×C₂₉	—	4	2	no	—
65	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
66	C₂×C₂₉	C₂×#41	1	2	yes	—
67	D₂₉	—	4	2	no	—
68	C₂×#41	—	29	1	no	—
69	C₂×#41	D₂₉	1	1	yes	characteristic, complemented
70	C₄⋊Q₈	—	29	1	no	—
71	#127	—	29	1	no	—
72	#124	—	29	1	no	—
73	#124	—	29	1	no	—
74	#121	—	29	4	no	—
75	C₄×D₄	—	29	4	no	—
76	C₂×C₄²	—	29	1	no	—
77	C₂₉	#532	1	1	yes	characteristic, complemented, Sylow
78	#41	—	2	4	no	—
79	#41	—	58	4	no	—
80	C₂×Q₈	—	29	1	no	—
81	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
82	C₂×D₄	—	29	4	no	—
83	C₂×D₄	—	29	2	no	—
84	C₂×D₄	—	29	1	no	—
85	C₂×D₄	C₂×D₂₉	1	2	yes	—
86	C₂×D₄	C₂×D₂₉	1	1	yes	characteristic
87	C₂²×C₄	—	29	2	no	—
88	C₂²×C₄	—	29	2	no	—
89	C₂²×C₄	C₂×D₂₉	1	2	yes	—
90	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
91	C₄⋊C₄	—	29	4	no	—
92	C₂²⋊C₄	—	29	4	no	—
93	C₂²⋊C₄	—	29	4	no	—
94	C₄²	—	29	1	no	—
95	C₄²	—	29	1	no	—
96	C₄²	—	29	2	no	—
97	C₂³	—	29	2	no	—
98	C₂³	C₂²×D₂₉	1	2	yes	—
99	C₂³	C₂²×D₂₉	1	1	yes	characteristic
100	Q₈	—	2	2	no	—
101	Q₈	—	58	2	no	—
102	D₄	—	2	4	no	—
103	D₄	—	2	2	no	—
104	D₄	—	58	8	no	—
105	D₄	—	58	4	no	—
106	D₄	—	58	2	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	29	2	no	—
109	C₂×C₄	—	29	2	no	—
110	C₂×C₄	—	29	2	no	—
111	C₂×C₄	—	58	4	no	—
112	C₂×C₄	—	58	4	no	—
113	C₂×C₄	C₂²⋊D₂₉	1	4	yes	complemented
114	C₂×C₄	C₂²×D₂₉	1	2	yes	—
115	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
116	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
117	C₂²	—	2	2	no	—
118	C₂²	—	2	4	no	—
119	C₂²	—	2	2	no	—
120	C₂²	—	58	4	no	—
121	C₂²	—	58	2	no	—
122	C₂²	C₂×C₂²⋊D₂₉	1	2	yes	—
123	C₂²	C₂³×D₂₉	1	1	yes	characteristic
124	C₄	—	2	2	no	—
125	C₄	—	29	4	no	—
126	C₄	—	58	2	no	—
127	C₄	—	58	2	no	—
128	C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
129	C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
130	C₂	—	2	2	no	—
131	C₂	—	4	2	no	—
132	C₂	—	116	2	no	—
133	C₂	#41×D₂₉	1	2	yes	—
134	C₂	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#41×C₂₉

C₂

yes

maximal, characteristic, complemented

C₂×#90805

C₂

yes

maximal, characteristic, complemented

#11745309

C₂

yes

maximal, characteristic, complemented

#11745306

C₂

yes

maximal, characteristic, complemented

#11745302

C₂

yes

maximal, characteristic, complemented

#11745301

C₂

yes

maximal, complemented

#11745298

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₂₉

C₂

yes

maximal, complemented

C₂×C₄×Dic₂₉

C₂

yes

maximal, characteristic, complemented

#41×C₂₉

—

C₂×Q₈×C₂₉

C₂²

yes

characteristic

C₂×D₄×C₂₉

C₂²

yes

characteristic

C₂×D₄×C₂₉

C₂²

yes

—

C₂²×C₄×C₂₉

C₂²

yes

—

C₂²×C₄×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊D₂₉

C₂²

yes

—

C₂×C₂²⋊D₂₉

C₂²

yes

—

C₂²×Dic₂₉

C₂²

yes

—

#90805

—

C₂×D₁₁₆

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

—

C₂×Dic₅₈

C₂²

yes

characteristic

C₂²⋊Dic₂₉

C₂²

yes

—

#90781

C₂²

yes

—

#90779

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

characteristic

C₂³×C₂₉

C₂³

yes

—

C₂³×C₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂³

yes

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

D₄

yes

complemented

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂²⋊D₂₉

—

C₂²⋊D₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

—

D₁₁₆

—

C₄×D₂₉

—

Dic₅₈

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×D₄

yes

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×D₄

yes

—

C₄×C₂₉

C₂×D₄

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

yes

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂²×D₄

yes

characteristic

C₂×C₂₉

C₂×#41

yes

—

D₂₉

—

C₂×#41

—

C₂×#41

D₂₉

yes

characteristic, complemented

C₄⋊Q₈

—

—

—

—

—

C₄×D₄

—

C₂×C₄²

—

C₂₉

#532

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×Q₈

C₂×D₂₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×D₂₉

yes

—

C₂×D₄

C₂×D₂₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₉

yes

—

C₂²×C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₂³

—

C₂³

C₂²×D₂₉

yes

—

C₂³

C₂²×D₂₉

yes

characteristic

100

Q₈

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

D₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂²⋊D₂₉

yes

complemented

114

C₂×C₄

C₂²×D₂₉

yes

—

115

C₂×C₄

C₂²×D₂₉

yes

characteristic

116

C₂×C₄

C₂²×D₂₉

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₂×C₂²⋊D₂₉

yes

—

123

C₂²

C₂³×D₂₉

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

C₂×C₂²⋊D₂₉

yes

—

129

C₄

C₂×C₂²⋊D₂₉

yes

—

130

C₂

—

131

C₂

—

132

C₂

—

116

—

133

C₂

#41×D₂₉

yes

—

134

C₂

C₂²×C₂²⋊D₂₉

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Frattini	C₂²	C₂³×D₂₉
Fitting	C₂×#41×C₂₉	C₂
hypercenter	C₂×#41	D₂₉
hypocenter	C₂₉	#532
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

subgroup

G/H

center

C₂×C₄

C₂²×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Frattini

C₂²

C₂³×D₂₉

Fitting

C₂×#41×C₂₉

C₂

hypercenter

C₂×#41

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#41×C₂₉	C₂	semidirect
2. C₂×#90805	C₂	semidirect
3. #11745309	C₂	semidirect
4. #11745306	C₂	semidirect
5. #11745302	C₂	semidirect
6. #11745301	C₂	semidirect
7. #11745298	C₂	semidirect
8. C₄×C₂²⋊D₂₉	C₂	semidirect
9. C₂×C₄×Dic₂₉	C₂	semidirect
36. C₂×C₄×C₂₉	D₄	semidirect
61. Dic₂₉	#41	semidirect
69. C₂×#41	D₂₉	semidirect
77. C₂₉	#532	semidirect
113. C₂×C₄	C₂²⋊D₂₉	semidirect

H ≅ G/N

type

1. C₂×#41×C₂₉

C₂

semidirect

2. C₂×#90805

C₂

semidirect

3. #11745309

C₂

semidirect

4. #11745306

C₂

semidirect

5. #11745302

C₂

semidirect

6. #11745301

C₂

semidirect

7. #11745298

C₂

semidirect

8. C₄×C₂²⋊D₂₉

C₂

semidirect

9. C₂×C₄×Dic₂₉

C₂

semidirect

36. C₂×C₄×C₂₉

D₄

semidirect

61. Dic₂₉

#41

semidirect

69. C₂×#41

D₂₉

semidirect

77. C₂₉

#532

semidirect

113. C₂×C₄

C₂²⋊D₂₉

semidirect

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

subgroup	index
C₂×#41×C₂₉	2
C₂×#90805	2
#11745309	2
#11745306	2
#11745302	2
#11745301	2
#11745298	2
C₄×C₂²⋊D₂₉	2
C₂×C₄×Dic₂₉	2
#532	29

subgroup

index

C₂×#41×C₂₉

C₄×C₂²⋊D₂₉

C₂×C₄×Dic₂₉

#532

Subgroups — #14271709

Conjugacy classes of subgroups

Complements

Maximal subgroups