Group #14271847 — subgroups

Subgroups — #14271847

Order 1856.

214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745308	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂²⋊D₂₉	C₂	1	1	yes	maximal, characteristic
5	#11745288	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745254	C₂	1	2	yes	maximal, complemented
7	C₄⋊C₄×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11745252	C₂	1	1	yes	maximal, characteristic, complemented
9	#11745251	C₂	1	2	yes	maximal, complemented
10	#11745245	C₂	1	2	yes	maximal
11	#11745241	C₂	1	2	yes	maximal, complemented
12	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₂₉	C₂²	1	2	yes	—
17	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
18	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
20	C₂²⋊Dic₂₉	C₂²	1	2	yes	—
21	C₂²⋊Dic₂₉	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	1	yes	characteristic
26	C₄⋊Dic₂₉	C₂²	1	2	yes	—
27	C₄⋊Dic₂₉	C₂²	1	2	yes	—
28	#90779	C₂²	1	1	yes	characteristic
29	#90779	C₂²	1	2	yes	—
30	#90779	C₂²	1	2	yes	—
31	#90779	C₂²	1	2	yes	—
32	C₄×Dic₂₉	C₂²	1	2	yes	—
33	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₉	C₂²	1	2	yes	—
35	C₂³×C₂₉	C₂³	1	1	yes	characteristic
36	C₂²×D₂₉	C₂³	1	1	yes	characteristic
37	Q₈×C₂₉	—	2	2	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂³	1	2	yes	—
41	C₂×C₄×C₂₉	C₂³	1	2	yes	—
42	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
43	C₂²⋊D₂₉	—	2	2	no	—
44	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
45	C₂×Dic₂₉	C₂³	1	2	yes	—
46	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
47	C₂×Dic₂₉	C₂³	1	2	yes	—
48	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
49	C₄×D₂₉	—	2	4	no	—
50	C₄×D₂₉	—	2	2	no	—
51	C₂²×C₂₉	—	2	1	no	—
52	C₂²×C₂₉	—	2	1	no	—
53	C₂²×C₂₉	—	2	1	no	—
54	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
55	C₂×D₂₉	—	2	1	no	—
56	C₂×D₂₉	—	2	1	no	—
57	C₂×D₂₉	#41	1	2	yes	—
58	C₄×C₂₉	—	2	2	no	—
59	C₄×C₂₉	—	2	1	no	—
60	C₄×C₂₉	—	2	2	no	—
61	C₄×C₂₉	#41	1	2	yes	—
62	Dic₂₉	—	2	1	no	—
63	Dic₂₉	—	2	2	no	—
64	Dic₂₉	—	2	1	no	—
65	Dic₂₉	—	2	1	no	—
66	Dic₂₉	—	2	2	no	—
67	#552	—	29	1	no	maximal, Sylow
68	C₂×C₂₉	—	4	1	no	—
69	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
70	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
71	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
72	D₂₉	—	2	2	no	—
73	#126	—	29	2	no	—
74	#125	—	29	2	no	—
75	#125	—	29	1	no	—
76	#123	—	29	2	no	—
77	C₂²⋊Q₈	—	29	1	no	—
78	C₂²⋊Q₈	D₂₉	1	1	yes	characteristic, complemented
79	C₄×Q₈	—	29	1	no	—
80	C₄×D₄	—	29	1	no	—
81	#117	—	29	1	no	—
82	#117	—	29	2	no	—
83	C₂×C₄⋊C₄	—	29	1	no	—
84	C₂₉	#552	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
86	C₂×D₄	—	29	1	no	—
87	C₂²×C₄	—	29	2	no	—
88	C₂²×C₄	—	29	1	no	—
89	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
90	C₄⋊C₄	—	29	1	no	—
91	C₄⋊C₄	—	29	2	no	—
92	C₄⋊C₄	—	29	1	no	—
93	C₄⋊C₄	—	29	2	no	—
94	C₄⋊C₄	—	29	1	no	—
95	C₄⋊C₄	—	29	2	no	—
96	C₄⋊C₄	—	29	2	no	—
97	C₄⋊C₄	—	29	2	no	—
98	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
99	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
100	C₂²⋊C₄	—	29	2	no	—
101	C₂²⋊C₄	—	29	1	no	—
102	C₂²⋊C₄	—	29	1	no	—
103	C₂²⋊C₄	—	29	2	no	—
104	C₂²⋊C₄	C₂×D₂₉	1	2	yes	—
105	C₄²	—	29	2	no	—
106	C₄²	—	29	2	no	—
107	C₄²	—	29	1	no	—
108	C₂³	—	29	1	no	—
109	C₂³	C₂²×D₂₉	1	1	yes	characteristic
110	Q₈	—	2	2	no	—
111	D₄	—	58	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	29	1	no	—
114	C₂×C₄	—	29	2	no	—
115	C₂×C₄	—	29	2	no	—
116	C₂×C₄	—	29	1	no	—
117	C₂×C₄	—	29	1	no	—
118	C₂×C₄	—	58	4	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
121	C₂×C₄	C₂²×D₂₉	1	2	yes	—
122	C₂×C₄	C₂²×D₂₉	1	2	yes	—
123	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
124	C₂²	—	2	1	no	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	1	no	—
127	C₂²	—	29	2	no	—
128	C₂²	—	58	1	no	—
129	C₂²	—	58	1	no	—
130	C₂²	C₂³×D₂₉	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	2	2	no	—
133	C₄	—	2	2	no	—
134	C₄	—	58	1	no	—
135	C₄	—	58	1	no	—
136	C₄	—	58	2	no	—
137	C₄	—	58	2	no	—
138	C₄	—	58	1	no	—
139	C₄	#90807	1	2	yes	—
140	C₂	—	4	1	no	—
141	C₂	—	58	2	no	—
142	C₂	C₂×#90807	1	1	yes	characteristic
143	C₂	#11745362	1	1	yes	characteristic
144	C₂	#41×D₂₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×C₂²⋊Q₈

C₂

yes

maximal, characteristic, complemented

#11745308

C₂

yes

maximal, characteristic, complemented

Q₈×Dic₂₉

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₂₉

C₂

yes

maximal, characteristic

#11745288

C₂

yes

maximal, characteristic, complemented

#11745254

C₂

yes

maximal, complemented

C₄⋊C₄×D₂₉

C₂

yes

maximal, characteristic, complemented

#11745252

C₂

yes

maximal, characteristic, complemented

#11745251

C₂

yes

maximal, complemented

#11745245

C₂

yes

maximal

#11745241

C₂

yes

maximal, complemented

C₂×Q₈×C₂₉

C₂²

yes

characteristic

C₂²×C₄×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂²⋊C₄×C₂₉

C₂²

yes

—

C₂²⋊Dic₂₉

C₂²

yes

—

C₂²⋊Dic₂₉

C₂²

yes

characteristic

#90781

C₂²

yes

characteristic

#90781

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

characteristic

C₄⋊Dic₂₉

C₂²

yes

characteristic

C₄⋊Dic₂₉

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

—

#90779

C₂²

yes

characteristic

#90779

C₂²

yes

—

#90779

C₂²

yes

—

#90779

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

—

C₂³×C₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂³

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂²⋊D₂₉

—

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

#41

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#41

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

#552

—

maximal, Sylow

C₂×C₂₉

—

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

2₋¹⁺⁴

yes

characteristic

D₂₉

—

—

—

—

—

C₂²⋊Q₈

—

C₂²⋊Q₈

D₂₉

yes

characteristic, complemented

C₄×Q₈

—

C₄×D₄

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂₉

#552

yes

characteristic, complemented, Sylow

C₂×Q₈

C₂×D₂₉

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₂₉

yes

characteristic

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

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

C₂×D₂₉

yes

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₂³

—

109

C₂³

C₂²×D₂₉

yes

characteristic

110

Q₈

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₂²×D₂₉

yes

characteristic

121

C₂×C₄

C₂²×D₂₉

yes

—

122

C₂×C₄

C₂²×D₂₉

yes

—

123

C₂×C₄

C₂²×D₂₉

yes

characteristic

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

C₂³×D₂₉

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

#90807

yes

—

140

C₂

—

141

C₂

—

142

C₂

C₂×#90807

yes

characteristic

143

C₂

#11745362

yes

characteristic

144

C₂

#41×D₂₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×C₂²⋊Q₈	C₂
prime radical	C₂×C₂²⋊D₂₉	C₂²
hypercenter	C₂²⋊Q₈	D₂₉
hypocenter	C₂₉	#552
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂₉×C₂²⋊Q₈

C₂

prime radical

C₂×C₂²⋊D₂₉

C₂²

hypercenter

C₂²⋊Q₈

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ C₂²⋊Q₈

N	H ≅ G/N	type
1. C₂₉×C₂²⋊Q₈	C₂	semidirect
2. #11745308	C₂	semidirect
3. Q₈×Dic₂₉	C₂	semidirect
5. #11745288	C₂	semidirect
6. #11745254	C₂	semidirect
7. C₄⋊C₄×D₂₉	C₂	semidirect
8. #11745252	C₂	semidirect
9. #11745251	C₂	semidirect
11. #11745241	C₂	semidirect
78. C₂²⋊Q₈	D₂₉	semidirect
84. C₂₉	#552	semidirect

H ≅ G/N

type

1. C₂₉×C₂²⋊Q₈

C₂

semidirect

2. #11745308

C₂

semidirect

3. Q₈×Dic₂₉

C₂

semidirect

5. #11745288

C₂

semidirect

6. #11745254

C₂

semidirect

7. C₄⋊C₄×D₂₉

C₂

semidirect

8. #11745252

C₂

semidirect

9. #11745251

C₂

semidirect

11. #11745241

C₂

semidirect

78. C₂²⋊Q₈

D₂₉

semidirect

84. C₂₉

#552

semidirect

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

subgroup	index
C₂₉×C₂²⋊Q₈	2
#11745308	2
Q₈×Dic₂₉	2
C₄×C₂²⋊D₂₉	2
#11745288	2
#11745254	2
C₄⋊C₄×D₂₉	2
#11745252	2
#11745251	2
#11745245	2
#11745241	2
#552	29

subgroup

index

C₂₉×C₂²⋊Q₈

#11745308

Q₈×Dic₂₉

C₄×C₂²⋊D₂₉

C₄⋊C₄×D₂₉

Subgroups — #14271847

Conjugacy classes of subgroups

Complements

Maximal subgroups