Group #16819087 — subgroups

Subgroups — #16819087

Order 3712.

180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 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	#14271566	C₂	1	1	yes	maximal, characteristic
2	#14271561	C₂	1	1	yes	maximal, characteristic
3	#14271542	C₂	1	1	yes	maximal, characteristic
4	#14271515	C₂	1	1	yes	maximal, characteristic
5	#14271513	C₂	1	1	yes	maximal, characteristic
6	C₈×#6597	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#498	C₂	1	1	yes	maximal, characteristic
8	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×#90785	—	2	2	no	—
11	#11745231	C₂²	1	1	yes	characteristic
12	#11745231	C₂²	1	1	yes	characteristic
13	C₂₉×#106	—	2	2	no	—
14	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	#11745183	—	2	2	no	—
16	#11745165	—	2	2	no	—
17	#11745158	—	2	2	no	—
18	#11745155	—	2	2	no	—
19	C₄×#6597	C₂²	1	1	yes	characteristic
20	C₄×#6597	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₂₉	—	2	1	no	—
22	C₂×Q₈×C₂₉	—	2	1	no	—
23	C₂×Dic₅₈	—	2	1	no	—
24	C₂×Dic₅₈	—	2	1	no	—
25	C₂×C₈×C₂₉	D₄	1	2	yes	—
26	C₄⋊C₄×C₂₉	—	2	1	no	—
27	C₄⋊C₄×C₂₉	—	2	1	no	—
28	C₄⋊C₄×C₂₉	—	2	1	no	—
29	C₄⋊C₄×C₂₉	—	2	1	no	—
30	C₄²×C₂₉	C₂³	1	1	yes	characteristic
31	#90785	—	4	4	no	—
32	C₄⋊Dic₂₉	—	2	1	no	—
33	C₄⋊Dic₂₉	—	2	1	no	—
34	C₄⋊Dic₂₉	—	2	1	no	—
35	C₄⋊Dic₂₉	—	2	1	no	—
36	C₂×#6597	D₄	1	2	yes	—
37	C₂×#6597	D₄	1	2	yes	—
38	Q₈×C₂₉	—	4	2	no	—
39	Q₈×C₂₉	—	4	2	no	—
40	C₂×C₄×C₂₉	—	4	1	no	—
41	C₂×C₄×C₂₉	—	4	1	no	—
42	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₂₉	—	4	1	no	—
46	C₂×Dic₂₉	—	4	1	no	—
47	Dic₅₈	—	4	2	no	—
48	Dic₅₈	—	4	2	no	—
49	C₈×C₂₉	Q₁₆	1	4	yes	complemented
50	#6597	—	2	2	no	—
51	#6597	SD₁₆	1	4	yes	—
52	#1707	—	29	1	no	maximal, Sylow
53	C₂²×C₂₉	#127	1	1	yes	characteristic
54	C₄×C₂₉	—	8	1	no	—
55	C₄×C₂₉	—	8	1	no	—
56	C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
57	C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
58	C₄×C₂₉	#135	1	2	yes	—
59	Dic₂₉	—	8	1	no	—
60	Dic₂₉	—	8	1	no	—
61	#500	—	29	1	no	—
62	#498	—	29	1	no	—
63	#498	D₂₉	1	1	yes	characteristic
64	#494	—	29	1	no	—
65	#487	—	29	1	no	—
66	#487	—	29	1	no	—
67	C₈²	—	29	1	no	—
68	C₂×C₂₉	#492	1	1	yes	characteristic
69	C₂×C₂₉	#494	1	1	yes	characteristic
70	C₂×C₂₉	#495	1	1	yes	characteristic
71	C₂×Q₁₆	—	58	2	no	—
72	C₄⋊Q₈	—	29	1	no	—
73	C₄⋊Q₈	—	29	1	no	—
74	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
75	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
76	#107	—	58	2	no	—
77	#106	—	2	2	no	—
78	#106	—	58	2	no	—
79	#103	—	58	2	no	—
80	#103	—	58	2	no	—
81	C₄×C₈	—	29	1	no	—
82	C₄×C₈	—	29	1	no	—
83	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
84	C₂₉	#1707	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₈	—	2	1	no	—
86	C₂×Q₈	—	2	1	no	—
87	C₂×Q₈	—	58	1	no	—
88	C₂×Q₈	—	58	1	no	—
89	Q₁₆	—	116	4	no	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	29	2	no	—
92	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
93	C₄⋊C₄	—	2	1	no	—
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	2	1	no	—
97	C₄⋊C₄	—	58	1	no	—
98	C₄⋊C₄	—	58	1	no	—
99	C₄⋊C₄	—	58	1	no	—
100	C₄⋊C₄	—	58	1	no	—
101	C₄²	C₂²×D₂₉	1	1	yes	characteristic
102	Q₈	—	4	2	no	—
103	Q₈	—	4	2	no	—
104	Q₈	—	116	2	no	—
105	Q₈	—	116	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	116	1	no	—
109	C₂×C₄	—	116	1	no	—
110	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
111	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
112	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
113	C₈	—	29	4	no	—
114	C₈	—	58	2	no	—
115	C₈	#90785	1	4	yes	complemented
116	C₂²	#11745302	1	1	yes	characteristic
117	C₄	—	8	1	no	—
118	C₄	—	8	1	no	—
119	C₄	—	232	1	no	—
120	C₄	—	232	1	no	—
121	C₄	SD₁₆×D₂₉	1	2	yes	—
122	C₄	#11745278	1	2	yes	—
123	C₄	C₂×#90785	1	2	yes	—
124	C₂	#14271534	1	1	yes	characteristic
125	C₂	#14271542	1	1	yes	characteristic
126	C₂	#14271544	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271566

C₂

yes

maximal, characteristic

#14271561

C₂

yes

maximal, characteristic

#14271542

C₂

yes

maximal, characteristic

#14271515

C₂

yes

maximal, characteristic

#14271513

C₂

yes

maximal, characteristic

C₈×#6597

C₂

yes

maximal, characteristic

C₂₉×#498

C₂

yes

maximal, characteristic

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#90785

—

#11745231

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

C₂₉×#106

—

C₄×C₈×C₂₉

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₄×#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90785

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

Q₁₆

yes

complemented

#6597

—

#6597

SD₁₆

yes

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×SD₁₆

yes

—

C₄×C₂₉

C₂×Q₁₆

yes

—

C₄×C₂₉

#135

yes

—

Dic₂₉

—

Dic₂₉

—

#500

—

#498

—

#498

D₂₉

yes

—

—

—

C₈²

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

C₄⋊Q₈

C₂×D₂₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1707

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

C₂²×D₂₉

yes

characteristic

102

Q₈

—

103

Q₈

—

104

Q₈

—

116

—

105

Q₈

—

116

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

116

—

109

C₂×C₄

—

116

—

110

C₂×C₄

D₄×D₂₉

yes

characteristic

111

C₂×C₄

D₄×D₂₉

yes

characteristic

112

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

#90785

yes

complemented

116

C₂²

#11745302

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

232

—

120

C₄

—

232

—

121

C₄

SD₁₆×D₂₉

yes

—

122

C₄

#11745278

yes

—

123

C₄

C₂×#90785

yes

—

124

C₂

#14271534

yes

characteristic

125

C₂

#14271542

yes

characteristic

126

C₂

#14271544

yes

characteristic

	subgroup	G/H
center	C₂²	#11745302
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#498	C₂
socle, prime radical	C₂²×C₂₉	#127
hypercenter	#498	D₂₉
hypocenter	C₂₉	#1707
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

#11745302

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#498

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
49. C₈×C₂₉	Q₁₆	semidirect
84. C₂₉	#1707	semidirect
115. C₈	#90785	semidirect

H ≅ G/N

type

49. C₈×C₂₉

Q₁₆

semidirect

84. C₂₉

#1707

semidirect

115. C₈

#90785

semidirect

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

subgroup	index
#14271566	2
#14271561	2
#14271542	2
#14271515	2
#14271513	2
C₈×#6597	2
C₂₉×#498	2
#1707	29

subgroup

index

C₂₉×#498

Subgroups — #16819087

Conjugacy classes of subgroups

Complements

Maximal subgroups