Group #14271793 — subgroups

Subgroups — #14271793

Order 1856.

206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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	C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745259	C₂	1	2	yes	maximal
3	#11745258	C₂	1	2	yes	maximal
4	#11745254	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×D₂₉	C₂	1	1	yes	maximal, characteristic
6	#11745252	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745251	C₂	1	2	yes	maximal, complemented
8	#11745250	C₂	1	1	yes	maximal, characteristic, complemented
9	#11745250	C₂	1	2	yes	maximal, complemented
10	#11745234	C₂	1	1	yes	maximal, characteristic
11	#11745231	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₂₉	C₂²	1	2	yes	—
13	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₅₈	C₂²	1	2	yes	—
15	C₂×Dic₅₈	C₂²	1	2	yes	—
16	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
18	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
19	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₄²×C₂₉	C₂²	1	1	yes	characteristic
21	#90781	C₂²	1	1	yes	characteristic
22	#90781	C₂²	1	1	yes	characteristic
23	#90781	C₂²	1	2	yes	—
24	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
25	C₄⋊Dic₂₉	C₂²	1	2	yes	—
26	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
27	C₄⋊Dic₂₉	C₂²	1	2	yes	—
28	#90779	C₂²	1	1	yes	characteristic
29	#90779	C₂²	1	1	yes	characteristic
30	#90779	C₂²	1	2	yes	—
31	#90779	C₂²	1	2	yes	—
32	#90779	C₂²	1	2	yes	—
33	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₉	C₂²	1	2	yes	—
35	C₂²×D₂₉	C₂³	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂³	1	2	yes	—
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	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
41	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
42	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
43	C₂×Dic₂₉	C₂³	1	2	yes	—
44	C₂×Dic₂₉	C₂³	1	2	yes	—
45	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
46	C₄×D₂₉	—	4	2	no	—
47	C₄×D₂₉	Q₈	1	4	yes	complemented
48	Dic₅₈	—	4	2	no	—
49	Dic₅₈	—	4	2	no	—
50	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
51	C₂×D₂₉	—	2	1	no	—
52	C₂×D₂₉	—	2	1	no	—
53	C₂×D₂₉	C₂×Q₈	1	2	yes	—
54	C₄×C₂₉	—	2	1	no	—
55	C₄×C₂₉	—	2	2	no	—
56	C₄×C₂₉	—	2	2	no	—
57	C₄×C₂₉	—	2	1	no	—
58	C₄×C₂₉	C₂×Q₈	1	2	yes	—
59	Dic₂₉	—	2	1	no	—
60	Dic₂₉	—	2	2	no	—
61	Dic₂₉	—	2	2	no	—
62	Dic₂₉	—	2	1	no	—
63	Dic₂₉	C₂×Q₈	1	2	yes	—
64	#544	—	29	1	no	maximal, Sylow
65	C₂×C₂₉	C₂²×Q₈	1	1	yes	characteristic
66	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
67	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
68	D₂₉	—	2	2	no	—
69	C₄⋊Q₈	—	29	2	no	—
70	C₄⋊Q₈	—	29	1	no	—
71	C₄⋊Q₈	—	29	1	no	—
72	#125	—	29	2	no	—
73	#125	—	29	1	no	—
74	#125	D₂₉	1	1	yes	characteristic, complemented
75	C₂²⋊Q₈	—	29	2	no	—
76	C₂²⋊Q₈	—	29	2	no	—
77	#117	—	29	1	no	—
78	#117	—	29	1	no	—
79	C₂×C₄⋊C₄	—	29	1	no	—
80	C₂₉	#544	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₈	—	29	2	no	—
82	C₂×Q₈	—	29	2	no	—
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	29	2	no	—
85	C₄⋊C₄	—	29	2	no	—
86	C₄⋊C₄	—	29	1	no	—
87	C₄⋊C₄	—	29	1	no	—
88	C₄⋊C₄	—	29	1	no	—
89	C₄⋊C₄	—	29	1	no	—
90	C₄⋊C₄	—	29	2	no	—
91	C₄⋊C₄	—	29	2	no	—
92	C₄⋊C₄	—	29	2	no	—
93	C₄⋊C₄	—	29	2	no	—
94	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
95	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
96	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
97	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
98	C₂²⋊C₄	—	29	1	no	—
99	C₂²⋊C₄	—	29	2	no	—
100	C₂²⋊C₄	—	29	1	no	—
101	C₄²	—	29	2	no	—
102	C₄²	—	29	1	no	—
103	C₄²	C₂×D₂₉	1	1	yes	characteristic
104	C₂³	—	29	1	no	—
105	Q₈	—	116	2	no	—
106	Q₈	—	116	2	no	—
107	C₂×C₄	—	29	1	no	—
108	C₂×C₄	—	29	4	no	—
109	C₂×C₄	—	29	1	no	—
110	C₂×C₄	—	29	1	no	—
111	C₂×C₄	—	29	2	no	—
112	C₂×C₄	—	29	2	no	—
113	C₂×C₄	—	116	2	no	—
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	C₂×C₄	C₂²×D₂₉	1	2	yes	—
118	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
119	C₂²	—	29	2	no	—
120	C₂²	—	58	1	no	—
121	C₂²	—	58	1	no	—
122	C₂²	C₂³×D₂₉	1	1	yes	characteristic
123	C₄	—	2	2	no	—
124	C₄	—	2	1	no	—
125	C₄	—	2	2	no	—
126	C₄	—	2	1	no	—
127	C₄	—	29	2	no	—
128	C₄	—	58	2	no	—
129	C₄	—	58	1	no	—
130	C₄	—	58	2	no	—
131	C₄	—	58	1	no	—
132	C₄	Q₈×D₂₉	1	2	yes	—
133	C₂	—	58	2	no	—
134	C₂	C₂×Q₈×D₂₉	1	1	yes	characteristic
135	C₂	#11745364	1	1	yes	characteristic
136	C₂	#11745365	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#125

C₂

yes

maximal, characteristic, complemented

#11745259

C₂

yes

maximal

#11745258

C₂

yes

maximal

#11745254

C₂

yes

maximal, characteristic

C₄⋊C₄×D₂₉

C₂

yes

maximal, characteristic

#11745252

C₂

yes

maximal, characteristic, complemented

#11745251

C₂

yes

maximal, complemented

#11745250

C₂

yes

maximal, characteristic, complemented

#11745250

C₂

yes

maximal, complemented

#11745234

C₂

yes

maximal, characteristic

#11745231

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₂₉

C₂²

yes

—

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×Dic₅₈

C₂²

yes

—

C₂×Dic₅₈

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄²×C₂₉

C₂²

yes

characteristic

#90781

C₂²

yes

characteristic

#90781

C₂²

yes

characteristic

#90781

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

characteristic

C₄⋊Dic₂₉

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

characteristic

C₄⋊Dic₂₉

C₂²

yes

—

#90779

C₂²

yes

characteristic

#90779

C₂²

yes

characteristic

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

—

C₂²×D₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

Q₈

yes

complemented

Dic₅₈

—

Dic₅₈

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

C₂×Q₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

C₂×Q₈

yes

—

#544

—

maximal, Sylow

C₂×C₂₉

C₂²×Q₈

yes

characteristic

C₂×C₂₉

H(5,𝔽₂)

yes

characteristic

C₂×C₂₉

2₋¹⁺⁴

yes

characteristic

D₂₉

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

#125

D₂₉

yes

characteristic, complemented

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂₉

#544

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₄⋊C₄

C₂×D₂₉

yes

—

C₄⋊C₄

C₂×D₂₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₂²⋊C₄

—

101

C₄²

—

102

C₄²

—

103

C₄²

C₂×D₂₉

yes

characteristic

104

C₂³

—

105

Q₈

—

116

—

106

Q₈

—

116

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

116

—

114

C₂×C₄

C₂²×D₂₉

yes

—

115

C₂×C₄

C₂²×D₂₉

yes

characteristic

116

C₂×C₄

C₂²×D₂₉

yes

characteristic

117

C₂×C₄

C₂²×D₂₉

yes

—

118

C₂×C₄

C₂²×D₂₉

yes

characteristic

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₂³×D₂₉

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

Q₈×D₂₉

yes

—

133

C₂

—

134

C₂

C₂×Q₈×D₂₉

yes

characteristic

135

C₂

#11745364

yes

characteristic

136

C₂

#11745365

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#125	C₂
prime radical	C₂²×D₂₉	C₂³
hypercenter	#125	D₂₉
hypocenter	C₂₉	#544
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂₉×#125

C₂

prime radical

C₂²×D₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. C₂₉×#125	C₂	semidirect
6. #11745252	C₂	semidirect
7. #11745251	C₂	semidirect
8. #11745250	C₂	semidirect
9. #11745250	C₂	semidirect
11. #11745231	C₂	semidirect
47. C₄×D₂₉	Q₈	semidirect
74. #125	D₂₉	semidirect
80. C₂₉	#544	semidirect

H ≅ G/N

type

1. C₂₉×#125

C₂

semidirect

6. #11745252

C₂

semidirect

7. #11745251

C₂

semidirect

8. #11745250

C₂

semidirect

9. #11745250

C₂

semidirect

11. #11745231

C₂

semidirect

47. C₄×D₂₉

Q₈

semidirect

74. #125

D₂₉

semidirect

80. C₂₉

#544

semidirect

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

subgroup	index
C₂₉×#125	2
#11745259	2
#11745258	2
#11745254	2
C₄⋊C₄×D₂₉	2
#11745252	2
#11745251	2
#11745250	2
#11745234	2
#11745231	2
#544	29

subgroup

index

C₂₉×#125

C₄⋊C₄×D₂₉

Subgroups — #14271793

Conjugacy classes of subgroups

Complements

Maximal subgroups