Group #16835148 — subgroups

Subgroups — #16835148

Order 3712.

328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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	#14272122	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745208	C₂	1	2	yes	maximal
3	C₂×C₈×#1181	C₂	1	2	yes	maximal
4	#14272099	C₂	1	1	yes	maximal, characteristic
5	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#1181	C₂²	1	2	yes	—
7	C₂×D₂₉⋊C₈	C₂²	1	2	yes	—
8	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
10	C₄²×D₂₉	C₂²	1	1	yes	characteristic
11	(C₂×#1181)⋊C₄	C₄	1	4	yes	—
12	#11745218	C₄	1	4	yes	complemented
13	#11745208	C₄	1	8	yes	complemented
14	C₈×#1181	C₄	1	8	yes	complemented
15	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic, complemented
16	C₈×Dic₂₉	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₂₉	C₄	1	1	yes	characteristic, complemented
18	C₄×#6597	C₄	1	1	yes	characteristic, complemented
19	C₂²×#1181	C₂×C₄	1	4	yes	—
20	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
22	C₂×#6599	C₂×C₄	1	4	yes	—
23	C₄×#1181	C₂×C₄	1	4	yes	—
24	C₄×#1181	C₂×C₄	1	4	yes	—
25	D₂₉⋊C₈	C₂×C₄	1	4	yes	—
26	D₂₉⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
32	C₂×#6597	C₂×C₄	1	1	yes	characteristic
33	C₂×#6597	C₂×C₄	1	1	yes	characteristic
34	C₈×D₂₉	C₂×C₄	1	4	yes	—
35	C₈×D₂₉	C₂×C₄	1	4	yes	—
36	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×#1181	—	2	8	no	—
38	C₂×#1181	C₄²	1	8	yes	—
39	C₂×C₄×C₂₉	C₄²	1	2	yes	—
40	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₂₉	C₄²	1	2	yes	—
42	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
43	C₄×D₂₉	—	2	4	no	—
44	C₄×D₂₉	C₂²×C₄	1	2	yes	—
45	C₄×D₂₉	C₂²×C₄	1	2	yes	—
46	#6599	C₄²	1	8	yes	—
47	C₈×C₂₉	C₄²	1	2	yes	—
48	C₈×C₂₉	C₄²	1	2	yes	—
49	#6597	C₄²	1	2	yes	—
50	#6597	C₄²	1	2	yes	—
51	#1726	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
53	C₂×D₂₉	C₂×C₄²	1	2	yes	—
54	C₂×D₂₉	#131	1	4	yes	—
55	#1181	—	2	8	no	—
56	C₄×C₂₉	—	2	2	no	—
57	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
58	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
59	Dic₂₉	—	2	2	no	—
60	Dic₂₉	C₂×C₄²	1	2	yes	—
61	C₂×#97	—	29	2	no	—
62	C₂×#97	—	29	1	no	—
63	C₂×C₄×C₈	—	29	2	no	—
64	C₂×C₄×C₈	—	29	1	no	—
65	#376	—	29	1	no	—
66	C₂×C₂₉	C₄³	1	1	yes	characteristic
67	C₂×C₂₉	#405	1	2	yes	—
68	D₂₉	#405	1	4	yes	—
69	C₂²×C₈	—	29	2	no	—
70	C₂²×C₈	—	29	1	no	—
71	C₂²×C₈	—	29	1	no	—
72	C₂×C₄²	—	29	2	no	—
73	C₂×C₄²	—	29	1	no	—
74	#97	—	29	8	no	—
75	#97	—	29	4	no	—
76	C₄×C₈	—	29	8	no	—
77	C₄×C₈	—	29	1	no	—
78	C₄×C₈	—	29	1	no	—
79	C₄×C₈	—	29	1	no	—
80	C₄×C₈	#1181	1	1	yes	characteristic, complemented
81	#95	—	29	4	no	—
82	C₂₉	#1726	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	29	4	no	—
85	C₂²×C₄	—	29	2	no	—
86	C₂×C₈	—	29	4	no	—
87	C₂×C₈	—	29	4	no	—
88	C₂×C₈	—	29	4	no	—
89	C₂×C₈	—	29	1	no	—
90	C₂×C₈	—	29	1	no	—
91	C₂×C₈	—	29	4	no	—
92	C₂×C₈	—	29	4	no	—
93	C₂×C₈	C₂×#1181	1	1	yes	characteristic
94	C₂×C₈	C₂×#1181	1	1	yes	characteristic
95	C₄²	—	29	4	no	—
96	C₄²	—	29	4	no	—
97	C₄²	—	29	2	no	—
98	C₄²	—	29	1	no	—
99	C₄²	C₂×#1181	1	1	yes	characteristic
100	C₂³	—	29	1	no	—
101	C₂×C₄	—	29	1	no	—
102	C₂×C₄	—	29	2	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	29	8	no	—
105	C₂×C₄	—	29	2	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	—	58	8	no	—
108	C₂×C₄	C₄×#1181	1	2	yes	—
109	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
110	C₈	—	29	8	no	—
111	C₈	—	29	2	no	—
112	C₈	—	29	2	no	—
113	C₈	C₄×#1181	1	2	yes	—
114	C₈	C₄×#1181	1	2	yes	—
115	C₂²	—	29	2	no	—
116	C₂²	—	29	4	no	—
117	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	29	2	no	—
120	C₄	—	58	8	no	—
121	C₄	—	58	2	no	—
122	C₄	C₂×C₄×#1181	1	1	yes	characteristic
123	C₄	C₂×C₄×#1181	1	1	yes	characteristic
124	C₂	—	29	4	no	—
125	C₂	C₄²×#1181	1	1	yes	characteristic
126	C₂	#14272126	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272122

C₂

yes

maximal, characteristic

C₂×#11745208

C₂

yes

maximal

C₂×C₈×#1181

C₂

yes

maximal

#14272099

C₂

yes

maximal, characteristic

C₄×C₈×D₂₉

C₂

yes

maximal, characteristic

C₂×C₄×#1181

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₄²×D₂₉

C₂²

yes

characteristic

(C₂×#1181)⋊C₄

C₄

yes

—

#11745218

C₄

yes

complemented

#11745208

C₄

yes

complemented

C₈×#1181

C₄

yes

complemented

C₄×C₈×C₂₉

C₄

yes

characteristic, complemented

C₈×Dic₂₉

C₄

yes

characteristic, complemented

C₈×Dic₂₉

C₄

yes

characteristic, complemented

C₄×#6597

C₄

yes

characteristic, complemented

C₂²×#1181

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×#6599

C₂×C₄

yes

—

C₄×#1181

C₂×C₄

yes

—

C₄×#1181

C₂×C₄

yes

—

D₂₉⋊C₈

C₂×C₄

yes

—

D₂₉⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

—

C₂²×D₂₉

C₂²×C₄

yes

characteristic

C₂×#1181

—

C₂×#1181

C₄²

yes

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

C₂²×C₄

yes

—

C₄×D₂₉

C₂²×C₄

yes

—

#6599

C₄²

yes

—

C₈×C₂₉

C₄²

yes

—

C₈×C₂₉

C₄²

yes

—

#6597

C₄²

yes

—

#6597

C₄²

yes

—

#1726

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

C₂×C₄²

yes

—

C₂×D₂₉

#131

yes

—

#1181

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

C₂×C₄²

yes

characteristic

Dic₂₉

—

Dic₂₉

C₂×C₄²

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₂×C₂₉

C₄³

yes

characteristic

C₂×C₂₉

#405

yes

—

D₂₉

#405

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#1181

yes

characteristic, complemented

#95

—

C₂₉

#1726

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

100

C₂³

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₄×#1181

yes

—

109

C₂×C₄

C₂²×#1181

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

C₄×#1181

yes

—

114

C₈

C₄×#1181

yes

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×C₄×#1181

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

C₂×C₄×#1181

yes

characteristic

123

C₄

C₂×C₄×#1181

yes

characteristic

124

C₂

—

125

C₂

C₄²×#1181

yes

characteristic

126

C₂

#14272126

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#1181
commutator	C₂×C₂₉	C₄³
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₄²
prime radical	C₂²×D₂₉	C₂²×C₄
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1726
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#1181

commutator

C₂×C₂₉

C₄³

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₄×C₈×C₂₉

C₄

socle

C₂²×C₂₉

C₂×C₄²

prime radical

C₂²×D₂₉

C₂²×C₄

cosocle

C₂×C₄×D₂₉

C₂³

C₄×C₈

C₂₉

G ▷ C₂×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
12. #11745218	C₄	semidirect
13. #11745208	C₄	semidirect
14. C₈×#1181	C₄	semidirect
15. C₄×C₈×C₂₉	C₄	semidirect
16. C₈×Dic₂₉	C₄	semidirect
17. C₈×Dic₂₉	C₄	semidirect
18. C₄×#6597	C₄	semidirect
80. C₄×C₈	#1181	semidirect
82. C₂₉	#1726	semidirect

H ≅ G/N

type

12. #11745218

C₄

semidirect

13. #11745208

C₄

semidirect

14. C₈×#1181

C₄

semidirect

15. C₄×C₈×C₂₉

C₄

semidirect

16. C₈×Dic₂₉

C₄

semidirect

17. C₈×Dic₂₉

C₄

semidirect

18. C₄×#6597

C₄

semidirect

80. C₄×C₈

#1181

semidirect

82. C₂₉

#1726

semidirect

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

subgroup	index
#14272122	2
C₂×#11745208	2
C₂×C₈×#1181	2
#14272099	2
C₄×C₈×D₂₉	2
#1726	29

subgroup

index

C₂×C₈×#1181

C₄×C₈×D₂₉

Subgroups — #16835148

Conjugacy classes of subgroups

Complements

Maximal subgroups