Group #14271787 — subgroups

Subgroups — #14271787

Order 1856.

216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745309	C₂	1	2	yes	maximal, complemented
3	#11745308	C₂	1	2	yes	maximal, complemented
4	#11745260	C₂	1	2	yes	maximal, complemented
5	#11745259	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745257	C₂	1	1	yes	maximal, characteristic
7	#11745256	C₂	1	2	yes	maximal, complemented
8	#11745255	C₂	1	1	yes	maximal, characteristic, complemented
9	#11745249	C₂	1	1	yes	maximal, characteristic, complemented
10	#11745237	C₂	1	1	yes	maximal, characteristic, complemented
11	#11745234	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
13	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
14	C₂×D₁₁₆	C₂²	1	2	yes	—
15	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₂₉	C₂²	1	2	yes	—
17	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
21	C₄²×C₂₉	C₂²	1	1	yes	characteristic
22	#90781	C₂²	1	2	yes	—
23	#90781	C₂²	1	2	yes	—
24	#90781	C₂²	1	1	yes	characteristic
25	#90781	C₂²	1	2	yes	—
26	#90781	C₂²	1	2	yes	—
27	#90781	C₂²	1	1	yes	characteristic
28	#90781	C₂²	1	2	yes	—
29	C₄⋊Dic₂₉	C₂²	1	2	yes	—
30	#90779	C₂²	1	1	yes	characteristic
31	#90779	C₂²	1	2	yes	—
32	#90779	C₂²	1	1	yes	characteristic
33	C₄×Dic₂₉	C₂²	1	2	yes	—
34	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
35	C₂²×D₂₉	C₂³	1	1	yes	characteristic
36	C₂²×D₂₉	C₂³	1	2	yes	—
37	Q₈×C₂₉	—	4	2	no	—
38	C₂×C₄×C₂₉	C₂³	1	2	yes	—
39	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂³	1	2	yes	—
42	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
43	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
44	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
45	C₂×Dic₂₉	C₂³	1	2	yes	—
46	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
47	D₁₁₆	—	2	2	no	—
48	D₁₁₆	—	4	2	no	—
49	C₄×D₂₉	—	2	2	no	—
50	C₄×D₂₉	—	4	2	no	—
51	Dic₅₈	—	2	2	no	—
52	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
53	C₂×D₂₉	—	2	1	no	—
54	C₂×D₂₉	—	2	2	no	—
55	C₂×D₂₉	—	2	2	no	—
56	C₂×D₂₉	—	2	1	no	—
57	C₂×D₂₉	—	2	1	no	—
58	C₂×D₂₉	—	2	2	no	—
59	C₄×C₂₉	—	2	2	no	—
60	C₄×C₂₉	—	2	2	no	—
61	C₄×C₂₉	—	2	1	no	—
62	C₄×C₂₉	—	2	1	no	—
63	C₄×C₂₉	#41	1	2	yes	—
64	Dic₂₉	—	2	2	no	—
65	Dic₂₉	—	2	1	no	—
66	Dic₂₉	—	2	1	no	—
67	Dic₂₉	—	2	1	no	—
68	#542	—	29	1	no	maximal, Sylow
69	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
70	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
71	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
72	D₂₉	—	4	1	no	—
73	D₂₉	—	4	2	no	—
74	C₄⋊Q₈	D₂₉	1	1	yes	characteristic, complemented
75	#126	—	29	2	no	—
76	#124	—	29	2	no	—
77	#124	—	29	1	no	—
78	#123	—	29	2	no	—
79	C₂²⋊Q₈	—	29	2	no	—
80	C₂²⋊Q₈	—	29	1	no	—
81	#121	—	29	1	no	—
82	C₄×Q₈	—	29	1	no	—
83	C₄×D₄	—	29	1	no	—
84	#117	—	29	1	no	—
85	C₂₉	#542	1	1	yes	characteristic, complemented, Sylow
86	C₂×Q₈	—	29	1	no	—
87	C₂×Q₈	C₂×D₂₉	1	2	yes	—
88	C₂×D₄	—	29	1	no	—
89	C₂×D₄	—	29	2	no	—
90	C₂²×C₄	—	29	1	no	—
91	C₂²×C₄	—	29	2	no	—
92	C₄⋊C₄	—	29	1	no	—
93	C₄⋊C₄	—	29	1	no	—
94	C₄⋊C₄	—	29	2	no	—
95	C₄⋊C₄	—	29	2	no	—
96	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
97	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
98	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
99	C₂²⋊C₄	—	29	1	no	—
100	C₂²⋊C₄	—	29	1	no	—
101	C₂²⋊C₄	—	29	2	no	—
102	C₂²⋊C₄	—	29	2	no	—
103	C₂²⋊C₄	—	29	2	no	—
104	C₂²⋊C₄	—	29	2	no	—
105	C₂²⋊C₄	—	29	2	no	—
106	C₄²	—	29	1	no	—
107	C₄²	—	29	2	no	—
108	C₄²	C₂×D₂₉	1	1	yes	characteristic
109	C₂³	—	29	2	no	—
110	C₂³	—	29	1	no	—
111	Q₈	—	4	2	no	—
112	Q₈	—	58	2	no	—
113	D₄	—	58	2	no	—
114	D₄	—	116	2	no	—
115	C₂×C₄	—	29	1	no	—
116	C₂×C₄	—	29	2	no	—
117	C₂×C₄	—	29	1	no	—
118	C₂×C₄	—	29	1	no	—
119	C₂×C₄	—	58	2	no	—
120	C₂×C₄	—	116	2	no	—
121	C₂×C₄	C₂²×D₂₉	1	2	yes	—
122	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
123	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
124	C₂×C₄	C₂²×D₂₉	1	2	yes	—
125	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
126	C₂²	—	58	2	no	—
127	C₂²	—	58	1	no	—
128	C₂²	—	58	1	no	—
129	C₂²	—	58	2	no	—
130	C₂²	—	58	2	no	—
131	C₂²	—	58	1	no	—
132	C₂²	C₂³×D₂₉	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	2	no	—
135	C₄	—	2	1	no	—
136	C₄	—	2	1	no	—
137	C₄	—	58	1	no	—
138	C₄	—	58	1	no	—
139	C₄	—	58	2	no	—
140	C₄	—	58	1	no	—
141	C₄	#90809	1	2	yes	—
142	C₂	—	116	2	no	—
143	C₂	—	116	1	no	—
144	C₂	#11745359	1	1	yes	characteristic
145	C₂	C₂×#90809	1	1	yes	characteristic
146	C₂	#11745362	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×C₄⋊Q₈

C₂

yes

maximal, characteristic, complemented

#11745309

C₂

yes

maximal, complemented

#11745308

C₂

yes

maximal, complemented

#11745260

C₂

yes

maximal, complemented

#11745259

C₂

yes

maximal, characteristic, complemented

#11745257

C₂

yes

maximal, characteristic

#11745256

C₂

yes

maximal, complemented

#11745255

C₂

yes

maximal, characteristic, complemented

#11745249

C₂

yes

maximal, characteristic, complemented

#11745237

C₂

yes

maximal, characteristic, complemented

#11745234

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×C₂₉

C₂²

yes

—

C₂×D₁₁₆

C₂²

yes

characteristic

C₂×D₁₁₆

C₂²

yes

—

C₂×C₄×D₂₉

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂²

yes

—

C₂×Dic₅₈

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₄⋊C₄×C₂₉

C₂²

yes

—

C₄²×C₂₉

C₂²

yes

characteristic

#90781

C₂²

yes

—

#90781

C₂²

yes

—

#90781

C₂²

yes

characteristic

#90781

C₂²

yes

—

#90781

C₂²

yes

—

#90781

C₂²

yes

characteristic

#90781

C₂²

yes

—

C₄⋊Dic₂₉

C₂²

yes

—

#90779

C₂²

yes

characteristic

#90779

C₂²

yes

—

#90779

C₂²

yes

characteristic

C₄×Dic₂₉

C₂²

yes

—

C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×D₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂³

yes

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₄×C₂₉

C₂³

yes

—

C₂×C₄×C₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₂₉

C₂³

yes

—

C₂×Dic₂₉

C₂³

yes

characteristic

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₂²×C₂₉

C₂⁴

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#41

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

#542

—

maximal, Sylow

C₂×C₂₉

C₂×#41

yes

characteristic

C₂×C₂₉

H(5,𝔽₂)

yes

characteristic

C₂×C₂₉

2₋¹⁺⁴

yes

characteristic

D₂₉

—

D₂₉

—

C₄⋊Q₈

D₂₉

yes

characteristic, complemented

—

—

—

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂₉

#542

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×D₂₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×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

—

C₂²⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

C₂×D₂₉

yes

characteristic

109

C₂³

—

110

C₂³

—

111

Q₈

—

112

Q₈

—

113

D₄

—

114

D₄

—

116

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

116

—

121

C₂×C₄

C₂²×D₂₉

yes

—

122

C₂×C₄

C₂²×D₂₉

yes

characteristic

123

C₂×C₄

C₂²×D₂₉

yes

characteristic

124

C₂×C₄

C₂²×D₂₉

yes

—

125

C₂×C₄

C₂²×D₂₉

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₂³×D₂₉

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

#90809

yes

—

142

C₂

—

116

—

143

C₂

—

116

—

144

C₂

#11745359

yes

characteristic

145

C₂

C₂×#90809

yes

characteristic

146

C₂

#11745362

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×C₄⋊Q₈	C₂
prime radical	#11745257	C₂
hypercenter	C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#542
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₂₉

commutator, socle, cosocle

C₂²×C₂₉

C₂⁴

Fitting

C₂₉×C₄⋊Q₈

C₂

prime radical

#11745257

C₂

hypercenter

C₄⋊Q₈

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ C₄⋊Q₈

N	H ≅ G/N	type
1. C₂₉×C₄⋊Q₈	C₂	semidirect
2. #11745309	C₂	semidirect
3. #11745308	C₂	semidirect
4. #11745260	C₂	semidirect
5. #11745259	C₂	semidirect
7. #11745256	C₂	semidirect
8. #11745255	C₂	semidirect
9. #11745249	C₂	semidirect
10. #11745237	C₂	semidirect
11. #11745234	C₂	semidirect
74. C₄⋊Q₈	D₂₉	semidirect
85. C₂₉	#542	semidirect

H ≅ G/N

type

1. C₂₉×C₄⋊Q₈

C₂

semidirect

2. #11745309

C₂

semidirect

3. #11745308

C₂

semidirect

4. #11745260

C₂

semidirect

5. #11745259

C₂

semidirect

7. #11745256

C₂

semidirect

8. #11745255

C₂

semidirect

9. #11745249

C₂

semidirect

10. #11745237

C₂

semidirect

11. #11745234

C₂

semidirect

74. C₄⋊Q₈

D₂₉

semidirect

85. C₂₉

#542

semidirect

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

subgroup	index
C₂₉×C₄⋊Q₈	2
#11745309	2
#11745308	2
#11745260	2
#11745259	2
#11745257	2
#11745256	2
#11745255	2
#11745249	2
#11745237	2
#11745234	2
#542	29

subgroup

index

C₂₉×C₄⋊Q₈

Subgroups — #14271787

Conjugacy classes of subgroups

Complements

Maximal subgroups