Group #16836405 — subgroups

Subgroups — #16836405

Order 3712.

314 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 144 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	#14272215	C₂	1	4	yes	maximal, complemented
2	#14272213	C₂	1	4	yes	maximal, complemented
3	#14272188	C₂	1	4	yes	maximal
4	#14272185	C₂	1	2	yes	maximal
5	#14271719	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#125	C₄	1	1	yes	characteristic
7	#11745258	C₄	1	4	yes	—
8	#11745254	C₂²	1	2	yes	—
9	#11745250	C₄	1	2	yes	—
10	#11745249	C₂²	1	4	yes	—
11	C₄²×D₂₉	C₂²	1	1	yes	characteristic
12	#11745232	C₄	1	1	yes	characteristic
13	#11745220	C₂²	1	4	yes	—
14	#11745219	C₂²	1	4	yes	—
15	#11745218	C₂²	1	4	yes	—
16	#11745218	C₂²	1	4	yes	—
17	C₄⋊#6599	C₂²	1	2	yes	—
18	C₄⋊#6599	C₂²	1	2	yes	—
19	C₄⋊#6599	C₂²	1	4	yes	—
20	C₄×#6599	C₂²	1	4	yes	—
21	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₅₈	C₂×C₄	1	4	yes	—
24	C₂×#6599	C₂³	1	4	yes	—
25	C₂×#6599	C₂³	1	4	yes	—
26	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
27	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
28	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
29	#90781	C₂×C₄	1	4	yes	—
30	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
31	#90779	C₂×C₄	1	4	yes	—
32	#90779	C₂×C₄	1	4	yes	—
33	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₂₉	C₂³	1	4	yes	—
35	C₄×Dic₂₉	C₂³	1	2	yes	—
36	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
40	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
41	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
42	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
43	C₄×D₂₉	—	2	1	no	—
44	C₄×D₂₉	—	2	1	no	—
45	C₄×D₂₉	—	4	2	no	—
46	Dic₅₈	—	4	4	no	—
47	#6599	—	2	4	no	—
48	#6599	—	2	4	no	—
49	#2987	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
51	C₂×D₂₉	—	2	1	no	—
52	C₂×D₂₉	—	2	2	no	—
53	C₄×C₂₉	—	2	1	no	—
54	C₄×C₂₉	—	2	4	no	—
55	C₄×C₂₉	—	2	2	no	—
56	Dic₂₉	—	2	2	no	—
57	Dic₂₉	—	2	4	no	—
58	Dic₂₉	2₋¹⁺⁴	1	1	yes	characteristic
59	Dic₂₉	2₋¹⁺⁴	1	1	yes	characteristic
60	#533	—	29	1	no	—
61	#446	—	29	4	no	—
62	#446	—	29	4	no	—
63	#433	—	29	4	no	—
64	#432	—	29	2	no	—
65	C₂×C₂₉	#519	1	1	yes	characteristic
66	C₂×C₂₉	#568	1	2	yes	—
67	D₂₉	—	4	1	no	—
68	C₄⋊Q₈	—	29	2	no	—
69	#125	—	29	1	no	—
70	#125	#1181	1	1	yes	characteristic
71	C₂²⋊Q₈	—	29	4	no	—
72	C₄×Q₈	—	29	4	no	—
73	#117	—	29	2	no	—
74	C₂×C₄²	—	29	1	no	—
75	C₄⋊C₈	—	29	2	no	—
76	C₄⋊C₈	—	29	2	no	—
77	C₄⋊C₈	—	29	4	no	—
78	C₄⋊C₈	—	29	4	no	—
79	C₂²⋊C₈	—	29	4	no	—
80	#97	—	29	4	no	—
81	#97	—	29	4	no	—
82	C₄×C₈	—	29	4	no	—
83	C₂₉	#2987	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₈	—	29	4	no	—
85	C₂²×C₄	—	29	1	no	—
86	C₂²×C₄	—	29	2	no	—
87	C₂×C₈	—	29	4	no	—
88	C₂×C₈	—	29	4	no	—
89	C₄⋊C₄	—	29	2	no	—
90	C₄⋊C₄	—	29	4	no	—
91	C₄⋊C₄	—	29	4	no	—
92	C₄⋊C₄	C₂×#1181	1	2	yes	—
93	C₄⋊C₄	C₂×#1181	1	4	yes	—
94	C₂²⋊C₄	—	29	4	no	—
95	C₄²	—	29	4	no	—
96	C₄²	—	29	2	no	—
97	C₄²	—	29	1	no	—
98	C₄²	C₂×#1181	1	1	yes	characteristic
99	C₂³	—	29	1	no	—
100	Q₈	—	116	4	no	—
101	C₂×C₄	—	29	1	no	—
102	C₂×C₄	—	29	2	no	—
103	C₂×C₄	—	29	4	no	—
104	C₂×C₄	—	58	1	no	—
105	C₂×C₄	—	58	1	no	—
106	C₂×C₄	—	116	2	no	—
107	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
108	C₂×C₄	C₂²×#1181	1	2	yes	—
109	C₂×C₄	C₂²×#1181	1	4	yes	—
110	C₈	—	58	4	no	—
111	C₈	—	58	4	no	—
112	C₂²	—	58	1	no	—
113	C₂²	—	58	2	no	—
114	C₂²	C₂³×#1181	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	2	2	no	—
117	C₄	—	2	4	no	—
118	C₄	—	29	1	no	—
119	C₄	—	29	1	no	—
120	C₄	—	58	2	no	—
121	C₄	—	58	4	no	—
122	C₂	—	116	1	no	—
123	C₂	#14272231	1	1	yes	characteristic
124	C₂	#14272242	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272215

C₂

yes

maximal, complemented

#14272213

C₂

yes

maximal, complemented

#14272188

C₂

yes

maximal

#14272185

C₂

yes

maximal

#14271719

C₂

yes

maximal, characteristic

C₂₉×#125

C₄

yes

characteristic

#11745258

C₄

yes

—

#11745254

C₂²

yes

—

#11745250

C₄

yes

—

#11745249

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745232

C₄

yes

characteristic

#11745220

C₂²

yes

—

#11745219

C₂²

yes

—

#11745218

C₂²

yes

—

#11745218

C₂²

yes

—

C₄⋊#6599

C₂²

yes

—

C₄⋊#6599

C₂²

yes

—

C₄⋊#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×#6599

C₂³

yes

—

C₂×#6599

C₂³

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

#90781

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂³

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₂²×D₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂⁴

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

2₋¹⁺⁴

yes

characteristic

Dic₂₉

2₋¹⁺⁴

yes

—

—

—

—

—

C₂×C₂₉

#519

yes

characteristic

C₂×C₂₉

#568

yes

—

D₂₉

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂₉

#2987

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#1181

yes

—

C₄⋊C₄

C₂×#1181

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

100

Q₈

—

116

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

116

—

107

C₂×C₄

C₂²×#1181

yes

characteristic

108

C₂×C₄

C₂²×#1181

yes

—

109

C₂×C₄

C₂²×#1181

yes

—

110

C₈

—

111

C₈

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂³×#1181

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₂

—

116

—

123

C₂

#14272231

yes

characteristic

124

C₂

#14272242

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#125	C₄
prime radical	C₂²×D₂₉	C₂²×C₄
cosocle	C₂×Dic₂₉	C₂⁴
hypercenter	#125	#1181
hypocenter	C₂₉	#2987
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#1181

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting

C₂₉×#125

C₄

prime radical

C₂²×D₂₉

C₂²×C₄

cosocle

C₂×Dic₂₉

C₂⁴

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. #14272215	C₂	semidirect
2. #14272213	C₂	semidirect
83. C₂₉	#2987	semidirect

H ≅ G/N

type

1. #14272215

C₂

semidirect

2. #14272213

C₂

semidirect

83. C₂₉

#2987

semidirect

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

subgroup	index
#14272215	2
#14272213	2
#14272188	2
#14272185	2
#14271719	2
#2987	29

subgroup

index

Subgroups — #16836405

Conjugacy classes of subgroups

Complements

Maximal subgroups