Group #16835623 — subgroups

Subgroups — #16835623

Order 3712.

308 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 78 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×#11745225	C₂	1	4	yes	maximal
2	#14272122	C₂	1	1	yes	maximal, characteristic
3	#14272107	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×D₂₉	C₂²	1	2	yes	—
6	C₂×C₄⋊#1181	C₂²	1	2	yes	—
7	C₂×D₂₉⋊C₈	C₂²	1	2	yes	—
8	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
9	#11745306	C₄	1	2	yes	complemented
10	C₄⋊C₄×D₂₉	—	2	2	no	—
11	#11745250	—	2	2	no	—
12	C₄²×D₂₉	C₂²	1	1	yes	characteristic
13	#11745231	C₄	1	1	yes	characteristic, complemented
14	#11745225	—	2	8	no	—
15	(C₂×#1181)⋊C₄	—	2	2	no	—
16	#11745218	—	2	2	no	—
17	C₂²×#1181	—	2	2	no	—
18	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
19	Q₈×D₂₉	—	2	4	no	—
20	Q₈×D₂₉	—	2	4	no	—
21	C₂×C₄×D₂₉	—	2	2	no	—
22	C₂×C₄×D₂₉	D₄	1	2	yes	—
23	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₅₈	—	2	2	no	—
25	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
26	C₂×#6599	—	2	2	no	—
27	C₄⋊#1181	—	2	4	no	—
28	D₂₉⋊C₈	—	2	2	no	—
29	D₂₉⋊C₈	D₄	1	4	yes	—
30	C₄⋊C₄×C₂₉	—	2	2	no	—
31	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
32	C₄⋊Dic₂₉	—	2	2	no	—
33	#90779	—	2	4	no	—
34	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
35	C₄×Dic₂₉	D₄	1	2	yes	—
36	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×#1181	—	4	2	no	—
38	C₂×#1181	—	4	4	no	—
39	Q₈×C₂₉	—	2	4	no	—
40	C₂×C₄×C₂₉	—	2	2	no	—
41	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
45	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
46	C₄×D₂₉	—	2	4	no	—
47	C₄×D₂₉	—	4	2	no	—
48	C₄×D₂₉	—	4	2	no	—
49	C₄×D₂₉	C₂×D₄	1	2	yes	—
50	C₄×D₂₉	#41	1	2	yes	—
51	Dic₅₈	—	2	4	no	—
52	Dic₅₈	—	4	4	no	—
53	#6599	—	2	4	no	—
54	#1960	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂×D₂₉	#124	1	1	yes	characteristic
57	C₂×D₂₉	#127	1	1	yes	characteristic
58	C₂×D₂₉	#137	1	4	yes	—
59	#1181	—	8	2	no	—
60	C₄×C₂₉	—	2	2	no	—
61	C₄×C₂₉	—	4	2	no	—
62	C₄×C₂₉	C₄×D₄	1	2	yes	—
63	Dic₂₉	—	2	2	no	—
64	Dic₂₉	—	4	2	no	—
65	Dic₂₉	#121	1	2	yes	—
66	C₂×C₄⋊Q₈	—	29	1	no	—
67	C₂×#103	—	29	4	no	—
68	C₂×#97	—	29	1	no	—
69	#382	—	29	1	no	—
70	C₂×C₂₉	#390	1	1	yes	characteristic
71	C₂×C₂₉	#419	1	2	yes	—
72	D₂₉	#491	1	2	yes	—
73	D₂₉	#497	1	2	yes	—
74	C₂²×Q₈	—	29	2	no	—
75	C₂²×C₈	—	29	2	no	—
76	C₄⋊Q₈	—	29	2	no	—
77	C₄⋊Q₈	—	29	1	no	—
78	C₄⋊Q₈	—	58	2	no	—
79	C₄⋊Q₈	#1181	1	1	yes	characteristic, complemented
80	C₂×C₄⋊C₄	—	29	2	no	—
81	C₂×C₄⋊C₄	—	58	2	no	—
82	C₂×C₄²	—	29	1	no	—
83	#103	—	58	8	no	—
84	#97	—	58	2	no	—
85	#95	—	58	2	no	—
86	C₂₉	#1960	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	29	2	no	—
88	C₂×Q₈	—	58	2	no	—
89	C₂×Q₈	—	58	4	no	—
90	C₂×Q₈	—	58	4	no	—
91	C₂×Q₈	C₂×#1181	1	2	yes	—
92	C₂²×C₄	—	29	1	no	—
93	C₂²×C₄	—	29	2	no	—
94	C₂²×C₄	—	58	2	no	—
95	C₂²×C₄	—	58	2	no	—
96	C₂×C₈	—	29	4	no	—
97	C₂×C₈	—	58	2	no	—
98	C₂×C₈	—	58	2	no	—
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	58	4	no	—
101	C₄⋊C₄	—	58	4	no	—
102	C₄⋊C₄	—	58	2	no	—
103	C₄²	—	29	2	no	—
104	C₄²	—	29	1	no	—
105	C₄²	C₂×#1181	1	1	yes	characteristic
106	C₂³	—	29	1	no	—
107	Q₈	—	2	4	no	—
108	Q₈	—	58	4	no	—
109	Q₈	—	116	4	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	29	1	no	—
112	C₂×C₄	—	29	2	no	—
113	C₂×C₄	—	29	2	no	—
114	C₂×C₄	—	29	2	no	—
115	C₂×C₄	—	58	4	no	—
116	C₂×C₄	—	58	2	no	—
117	C₂×C₄	—	116	2	no	—
118	C₂×C₄	—	116	2	no	—
119	C₂×C₄	—	116	2	no	—
120	C₂×C₄	—	116	4	no	—
121	C₂×C₄	C₂²⋊#1181	1	2	yes	—
122	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
123	C₈	—	58	4	no	—
124	C₂²	—	29	1	no	—
125	C₂²	—	29	1	no	—
126	C₂²	—	29	4	no	—
127	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
128	C₄	—	2	2	no	—
129	C₄	—	4	2	no	—
130	C₄	—	29	2	no	—
131	C₄	—	58	2	no	—
132	C₄	—	116	2	no	—
133	C₄	—	232	2	no	—
134	C₄	D₄×#1181	1	2	yes	—
135	C₂	—	29	2	no	—
136	C₂	—	29	2	no	—
137	C₂	#14272115	1	1	yes	characteristic
138	C₂	#14272156	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745225

C₂

yes

maximal

#14272122

C₂

yes

maximal, characteristic

#14272107

C₂

yes

maximal, characteristic

C₄⋊Q₈×D₂₉

C₂

yes

maximal, characteristic

C₂×Q₈×D₂₉

C₂²

yes

—

C₂×C₄⋊#1181

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₄

yes

characteristic, complemented

#11745306

C₄

yes

complemented

C₄⋊C₄×D₂₉

—

#11745250

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745231

C₄

yes

characteristic, complemented

#11745225

—

(C₂×#1181)⋊C₄

—

#11745218

—

C₂²×#1181

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

Q₈×D₂₉

—

Q₈×D₂₉

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

D₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×#6599

—

C₄⋊#1181

—

D₂₉⋊C₈

—

D₂₉⋊C₈

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄⋊Dic₂₉

—

#90779

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂²×D₂₉

C₂×D₄

yes

characteristic

C₂×#1181

—

C₂×#1181

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

C₂×D₄

yes

—

C₄×D₂₉

#41

yes

—

Dic₅₈

—

Dic₅₈

—

#6599

—

#1960

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

C₂×D₂₉

yes

C₂×D₂₉

yes

C₂×D₂₉

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×D₄

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#121

yes

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

—

#382

—

C₂×C₂₉

#390

yes

characteristic

C₂×C₂₉

#419

yes

—

D₂₉

#491

yes

—

D₂₉

#497

yes

—

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

#1181

yes

characteristic, complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#103

—

#97

—

#95

—

C₂₉

#1960

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×#1181

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

C₂×#1181

yes

characteristic

106

C₂³

—

107

Q₈

—

108

Q₈

—

109

Q₈

—

116

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

116

—

118

C₂×C₄

—

116

—

119

C₂×C₄

—

116

—

120

C₂×C₄

—

116

—

121

C₂×C₄

C₂²⋊#1181

yes

—

122

C₂×C₄

C₂²×#1181

yes

characteristic

123

C₈

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂×C₂²⋊#1181

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

116

—

133

C₄

—

232

—

134

C₄

D₄×#1181

yes

—

135

C₂

—

136

C₂

—

137

C₂

#14272115

yes

characteristic

138

C₂

#14272156

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×C₄⋊Q₈	C₄
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂×D₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	#1960
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×C₄⋊Q₈

C₄

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂×D₄

cosocle

C₂×C₄×D₂₉

C₂³

C₄⋊Q₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
8. C₂₉×C₄⋊Q₈	C₄	semidirect
9. #11745306	C₄	semidirect
13. #11745231	C₄	semidirect
79. C₄⋊Q₈	#1181	semidirect
86. C₂₉	#1960	semidirect

H ≅ G/N

type

8. C₂₉×C₄⋊Q₈

C₄

semidirect

9. #11745306

C₄

semidirect

13. #11745231

C₄

semidirect

79. C₄⋊Q₈

#1181

semidirect

86. C₂₉

#1960

semidirect

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

subgroup	index
C₂×#11745225	2
#14272122	2
#14272107	2
C₄⋊Q₈×D₂₉	2
#1960	29

subgroup

index

C₄⋊Q₈×D₂₉

Subgroups — #16835623

Conjugacy classes of subgroups

Complements

Maximal subgroups