Group #16835662 — subgroups

Subgroups — #16835662

Order 3712.

292 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 110 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×C₄⋊#6599	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6599	C₂	1	1	yes	maximal, characteristic
3	#14272029	C₂	1	4	yes	maximal
4	C₂×#11745249	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₅₈	C₄	1	1	yes	characteristic
6	C₂²×#6599	C₂²	1	2	yes	—
7	C₂²×#6599	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
9	C₂×#90779	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	#11745249	—	2	2	no	—
13	#11745249	—	2	2	no	—
14	C₄⋊#6599	—	2	2	no	—
15	C₄×#6599	—	2	2	no	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₅₈	—	2	2	no	—
22	C₂×Dic₅₈	—	2	2	no	—
23	C₂×Dic₅₈	C₈	1	4	yes	complemented
24	C₂×#6599	—	2	2	no	—
25	C₂×#6599	—	2	2	no	—
26	C₂×#6599	—	2	2	no	—
27	C₂×#6599	—	2	4	no	—
28	C₂×#6599	Q₈	1	4	yes	complemented
29	C₄⋊C₄×C₂₉	—	2	2	no	—
30	#90779	—	2	4	no	—
31	C₄×Dic₂₉	—	2	2	no	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₄×Dic₂₉	D₄	1	2	yes	—
34	C₄×Dic₂₉	D₄	1	2	yes	—
35	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	—	2	2	no	—
37	C₂×C₄×C₂₉	—	2	4	no	—
38	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
40	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	—	2	2	no	—
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
45	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
46	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₂₉	C₂×Q₈	1	2	yes	—
49	C₂×Dic₂₉	#41	1	2	yes	—
50	Dic₅₈	—	2	8	no	—
51	#6599	—	2	4	no	—
52	#6599	—	4	2	no	—
53	#1984	—	29	1	no	maximal, Sylow
54	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₂₉	C₄×Q₈	1	2	yes	—
56	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
57	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
58	C₂²×C₂₉	#131	1	2	yes	—
59	C₄×C₂₉	—	4	2	no	—
60	C₄×C₂₉	C₂²⋊C₈	1	4	yes	—
61	Dic₂₉	—	2	4	no	—
62	Dic₂₉	—	2	2	no	—
63	Dic₂₉	C₂²⋊Q₈	1	2	yes	—
64	Dic₂₉	#124	1	1	yes	characteristic
65	Dic₂₉	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×Q₈	—	29	1	no	—
67	C₂×C₄⋊C₈	—	29	1	no	—
68	C₂×C₄×C₈	—	29	1	no	—
69	#336	—	29	4	no	—
70	C₂×C₂₉	#391	1	1	yes	characteristic
71	C₂×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
72	C₂×C₂₉	#408	1	1	yes	characteristic
73	C₂×C₂₉	C₈×Q₈	1	2	yes	—
74	C₂×C₂₉	#446	1	2	yes	—
75	C₂²×Q₈	—	29	1	no	—
76	C₂²×C₈	—	29	2	no	—
77	C₂²×C₈	—	29	2	no	—
78	C₄×Q₈	—	58	2	no	—
79	C₄×Q₈	—	58	2	no	—
80	C₂×C₄⋊C₄	—	29	2	no	—
81	C₂×C₄⋊C₄	#1181	1	1	yes	characteristic
82	C₂×C₄²	—	29	1	no	—
83	C₂×C₄²	—	29	2	no	—
84	C₄⋊C₈	—	58	2	no	—
85	C₄×C₈	—	58	2	no	—
86	C₂₉	#1984	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	29	4	no	—
88	C₂×Q₈	—	58	2	no	—
89	C₂×Q₈	—	58	2	no	—
90	C₂²×C₄	—	29	1	no	—
91	C₂²×C₄	—	29	1	no	—
92	C₂²×C₄	—	29	2	no	—
93	C₂²×C₄	C₂×#1181	1	2	yes	—
94	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
95	C₂×C₈	—	29	4	no	—
96	C₂×C₈	—	58	2	no	—
97	C₂×C₈	—	58	2	no	—
98	C₂×C₈	—	58	2	no	—
99	C₂×C₈	—	58	4	no	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	—	58	4	no	—
102	C₄²	—	29	2	no	—
103	C₄²	—	29	2	no	—
104	C₄²	—	58	2	no	—
105	C₄²	—	58	2	no	—
106	C₂³	C₂²×#1181	1	1	yes	characteristic
107	Q₈	—	58	8	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	29	2	no	—
111	C₂×C₄	—	29	2	no	—
112	C₂×C₄	—	29	1	no	—
113	C₂×C₄	—	29	1	no	—
114	C₂×C₄	—	29	4	no	—
115	C₂×C₄	—	29	2	no	—
116	C₂×C₄	—	58	2	no	—
117	C₂×C₄	—	58	2	no	—
118	C₂×C₄	—	58	2	no	—
119	C₂×C₄	D₂₉⋊C₈	1	2	yes	—
120	C₂×C₄	#90796	1	2	yes	—
121	C₂×C₄	C₂²⋊#1181	1	2	yes	—
122	C₈	—	58	4	no	—
123	C₈	—	116	2	no	—
124	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
125	C₂²	C₂×#90796	1	1	yes	characteristic
126	C₂²	#11745346	1	2	yes	—
127	C₂²	Q₈×#1181	1	2	yes	—
128	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
129	C₄	—	4	2	no	—
130	C₄	—	29	2	no	—
131	C₄	—	29	1	no	—
132	C₄	—	29	1	no	—
133	C₄	—	58	4	no	—
134	C₄	—	58	2	no	—
135	C₄	#11745219	1	4	yes	—
136	C₂	(C₂×#1181)⋊Q₈	1	1	yes	characteristic
137	C₂	C₂×#11745219	1	1	yes	characteristic
138	C₂	#14272137	1	1	yes	characteristic
139	C₂	#14272212	1	2	yes	—
140	C₂	#14272213	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6599

C₂

yes

maximal, characteristic

C₂×C₄×#6599

C₂

yes

maximal, characteristic

#14272029

C₂

yes

maximal

C₂×#11745249

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₄

yes

characteristic

C₂²×#6599

C₂²

yes

—

C₂²×#6599

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₄

yes

characteristic

C₂×#90779

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

—

—

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

C₈

yes

—

—

—

—

Q₈

yes

complemented

C₄⋊C₄×C₂₉

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

D₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

—

C₂×Dic₂₉

#41

yes

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₂²×C₂₉

#131

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊C₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

#124

yes

characteristic

Dic₂₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×Q₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

#336

—

C₂×C₂₉

#391

yes

characteristic

C₂×C₂₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₂₉

#408

yes

characteristic

C₂×C₂₉

C₈×Q₈

yes

—

C₂×C₂₉

#446

yes

—

C₂²×Q₈

—

C₂²×C₈

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#1181

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄×C₈

—

C₂₉

#1984

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

—

C₂²×C₄

C₂×#1181

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₂³

C₂²×#1181

yes

characteristic

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

D₂₉⋊C₈

yes

—

120

C₂×C₄

#90796

yes

—

121

C₂×C₄

C₂²⋊#1181

yes

—

122

C₈

—

123

C₈

—

116

—

124

C₂²

C₂×D₂₉⋊C₈

yes

characteristic

125

C₂²

C₂×#90796

yes

characteristic

126

C₂²

#11745346

yes

—

127

C₂²

Q₈×#1181

yes

—

128

C₂²

C₂×C₂²⋊#1181

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

#11745219

yes

—

136

C₂

(C₂×#1181)⋊Q₈

yes

characteristic

137

C₂

C₂×#11745219

yes

characteristic

138

C₂

#14272137

yes

characteristic

139

C₂

#14272212

yes

—

140

C₂

#14272213

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₄⋊C₄×C₂₉	C₄
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	C₂×C₄⋊C₄	#1181
hypocenter	C₂₉	#1984
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×#1181

commutator

C₂²×C₂₉

C₂²×C₈

Fitting

C₂×C₄⋊C₄×C₂₉

C₄

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×Dic₂₉

C₂³

C₂×C₄⋊C₄

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
23. C₂×Dic₅₈	C₈	semidirect
28. C₂×#6599	Q₈	semidirect
86. C₂₉	#1984	semidirect

H ≅ G/N

type

23. C₂×Dic₅₈

C₈

semidirect

28. C₂×#6599

Q₈

semidirect

86. C₂₉

#1984

semidirect

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

subgroup	index
C₂×C₄⋊#6599	2
C₂×C₄×#6599	2
#14272029	2
C₂×#11745249	2
#1984	29

subgroup

index

C₂×C₄⋊#6599

C₂×C₄×#6599

#14272029

C₂×#11745249

#1984

Subgroups — #16835662

Conjugacy classes of subgroups

Complements

Maximal subgroups