Group #16835704 — subgroups

Subgroups — #16835704

Order 3712.

184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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×D₂₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#14272126	C₂	1	1	yes	maximal, characteristic
3	#14272050	C₂	1	2	yes	maximal, complemented
4	C₁₆×#1181	C₂	1	2	yes	maximal, complemented
5	M₃₂×D₂₉	C₂	1	1	yes	maximal, characteristic
6	#11745345	C₄	1	1	yes	characteristic
7	D₂₉⋊M₁₆	C₄	1	1	yes	characteristic
8	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90770	C₄	1	2	yes	complemented
10	#11745208	C₄	1	2	yes	—
11	C₈×#1181	C₂²	1	2	yes	—
12	D₂₉⋊C₁₆	C₄	1	2	yes	complemented
13	D₂₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	D₂₉⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂₉×M₃₂	C₄	1	1	yes	characteristic, complemented
16	#11745160	C₄	1	1	yes	characteristic, complemented
17	#11745146	C₄	1	2	yes	complemented
18	C₁₆×D₂₉	C₂²	1	2	yes	—
19	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊#1181	C₈	1	2	yes	—
21	#90800	C₈	1	2	yes	—
22	C₄⋊#1181	C₈	1	2	yes	—
23	C₄×#1181	C₂×C₄	1	2	yes	—
24	#90796	C₈	1	2	yes	—
25	D₂₉⋊C₈	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
27	C₂×#6597	C₂×C₄	1	1	yes	characteristic
28	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
29	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
30	C₈×D₂₉	C₂×C₄	1	1	yes	characteristic
31	C₈×D₂₉	C₂³	1	1	yes	characteristic
32	#90770	C₂×C₄	1	2	yes	—
33	#90770	C₂×C₄	1	2	yes	—
34	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
35	#90768	C₂×C₄	1	2	yes	—
36	C₂²×D₂₉	C₂×C₈	1	1	yes	characteristic
37	C₂×#1181	C₂×C₈	1	4	yes	—
38	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
39	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
40	C₄×D₂₉	C₄²	1	1	yes	characteristic
41	C₄×D₂₉	C₂×C₈	1	1	yes	characteristic
42	C₄×D₂₉	C₂×C₈	1	1	yes	characteristic
43	C₄×D₂₉	C₂²×C₄	1	1	yes	characteristic
44	#6599	C₂×C₈	1	4	yes	—
45	C₈×C₂₉	C₄²	1	1	yes	characteristic
46	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
47	#6597	C₄²	1	1	yes	characteristic
48	#6597	C₂²×C₄	1	1	yes	characteristic
49	#2108	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
51	C₂×D₂₉	—	2	2	no	—
52	C₂×D₂₉	C₄×C₈	1	1	yes	characteristic
53	C₂×D₂₉	C₂²×C₈	1	1	yes	characteristic
54	#1181	—	2	4	no	—
55	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
56	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
57	Dic₂₉	C₄×C₈	1	1	yes	characteristic
58	Dic₂₉	C₂²×C₈	1	1	yes	characteristic
59	C₂×M₃₂	—	29	1	no	—
60	C₂²×C₁₆	—	29	1	no	—
61	#405	—	29	1	no	—
62	#346	—	29	2	no	—
63	C₄×C₁₆	—	29	2	no	—
64	C₂×C₂₉	—	2	1	no	—
65	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
66	D₂₉	—	2	1	no	—
67	D₂₉	#504	1	2	yes	—
68	C₂×M₁₆	—	29	1	no	—
69	C₂²×C₈	—	29	1	no	—
70	#117	—	29	1	no	—
71	M₃₂	—	29	1	no	—
72	M₃₂	—	29	2	no	—
73	M₃₂	#1181	1	1	yes	characteristic, complemented
74	C₂×C₁₆	—	29	1	no	—
75	C₂×C₁₆	—	29	1	no	—
76	C₂×C₁₆	—	29	2	no	—
77	C₂×C₁₆	—	29	2	no	—
78	C₂×C₁₆	—	29	2	no	—
79	#97	—	29	2	no	—
80	C₄×C₈	—	29	2	no	—
81	C₂₉	#2108	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₄	—	29	1	no	—
83	M₁₆	—	29	2	no	—
84	M₁₆	—	29	2	no	—
85	C₂×C₈	—	29	2	no	—
86	C₂×C₈	—	29	1	no	—
87	C₂×C₈	—	29	1	no	—
88	C₂×C₈	—	29	1	no	—
89	C₂×C₈	—	29	1	no	—
90	C₂×C₈	—	29	1	no	—
91	C₂×C₈	C₂×#1181	1	1	yes	characteristic
92	C₄⋊C₄	—	29	2	no	—
93	C₂²⋊C₄	—	29	2	no	—
94	C₄²	—	29	2	no	—
95	C₁₆	—	29	2	no	—
96	C₁₆	—	29	2	no	—
97	C₁₆	—	29	2	no	—
98	C₁₆	C₂×#1181	1	2	yes	—
99	C₂³	—	29	1	no	—
100	C₂×C₄	—	29	1	no	—
101	C₂×C₄	—	29	1	no	—
102	C₂×C₄	—	29	1	no	—
103	C₂×C₄	—	29	1	no	—
104	C₂×C₄	—	29	1	no	—
105	C₂×C₄	—	29	4	no	—
106	C₂×C₄	C₄×#1181	1	1	yes	characteristic
107	C₈	—	29	4	no	—
108	C₈	—	29	1	no	—
109	C₈	—	29	1	no	—
110	C₈	C₄×#1181	1	1	yes	characteristic
111	C₈	C₂²×#1181	1	1	yes	characteristic
112	C₂²	—	29	1	no	—
113	C₂²	—	29	1	no	—
114	C₂²	—	58	2	no	—
115	C₂²	C₈×#1181	1	1	yes	characteristic
116	C₄	—	29	1	no	—
117	C₄	—	29	1	no	—
118	C₄	—	58	4	no	—
119	C₄	C₈×#1181	1	1	yes	characteristic
120	C₄	C₂×C₄×#1181	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	29	2	no	—
123	C₂	—	58	1	no	—
124	C₂	C₂×C₈×#1181	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₂₉⋊C₁₆

C₂

yes

maximal, characteristic

#14272126

C₂

yes

maximal, characteristic

#14272050

C₂

yes

maximal, complemented

C₁₆×#1181

C₂

yes

maximal, complemented

M₃₂×D₂₉

C₂

yes

maximal, characteristic

#11745345

C₄

yes

characteristic

D₂₉⋊M₁₆

C₄

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₂×#90770

C₄

yes

complemented

#11745208

C₄

yes

—

C₈×#1181

C₂²

yes

—

D₂₉⋊C₁₆

C₄

yes

complemented

D₂₉⋊C₁₆

C₂²

yes

characteristic

D₂₉⋊C₁₆

C₂²

yes

characteristic

C₂₉×M₃₂

C₄

yes

characteristic, complemented

#11745160

C₄

yes

characteristic, complemented

#11745146

C₄

yes

complemented

C₁₆×D₂₉

C₂²

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂²⋊#1181

C₈

yes

—

#90800

C₈

yes

—

C₄⋊#1181

C₈

yes

—

C₄×#1181

C₂×C₄

yes

—

#90796

C₈

yes

—

D₂₉⋊C₈

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂×C₄

yes

characteristic

C₈×D₂₉

C₂³

yes

characteristic

#90770

C₂×C₄

yes

—

#90770

C₂×C₄

yes

—

C₁₆×C₂₉

C₂×C₄

yes

—

#90768

C₂×C₄

yes

—

C₂²×D₂₉

C₂×C₈

yes

characteristic

C₂×#1181

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₄²

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₄×D₂₉

C₄²

yes

characteristic

C₄×D₂₉

C₂×C₈

yes

characteristic

C₄×D₂₉

C₂×C₈

yes

characteristic

C₄×D₂₉

C₂²×C₄

yes

characteristic

#6599

C₂×C₈

yes

—

C₈×C₂₉

C₄²

yes

characteristic

C₈×C₂₉

C₂²×C₄

yes

characteristic

#6597

C₄²

yes

characteristic

#6597

C₂²×C₄

yes

characteristic

#2108

—

maximal, Sylow

C₂²×C₂₉

C₄×C₈

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

C₄×C₈

yes

characteristic

C₂×D₂₉

C₂²×C₈

yes

characteristic

#1181

—

C₄×C₂₉

C₄×C₈

yes

characteristic

C₄×C₂₉

C₂×C₄²

yes

characteristic

Dic₂₉

C₄×C₈

yes

characteristic

Dic₂₉

C₂²×C₈

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₄×C₈

yes

characteristic

D₂₉

—

D₂₉

#504

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

#1181

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂₉

#2108

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

C₂×#1181

yes

—

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₄×#1181

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

C₄×#1181

yes

characteristic

111

C₈

C₂²×#1181

yes

characteristic

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₈×#1181

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

C₈×#1181

yes

characteristic

120

C₄

C₂×C₄×#1181

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

C₂×C₈×#1181

yes

characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#1181
commutator, socle	C₂×C₂₉	C₂×C₄×C₈
Fitting	C₂₉×M₃₂	C₄
prime radical	C₂²×D₂₉	C₂×C₈
cosocle	C₈×D₂₉	C₂³
hypercenter	M₃₂	#1181
hypocenter	C₂₉	#2108
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ M₃₂

subgroup

G/H

center, Frattini

C₈

C₂²×#1181

commutator, socle

C₂×C₂₉

C₂×C₄×C₈

Fitting

C₂₉×M₃₂

C₄

prime radical

C₂²×D₂₉

C₂×C₈

cosocle

C₈×D₂₉

C₂³

M₃₂

C₂₉

G ▷ C₂×C₂₉ ▷ C₂₉

C₁ ◁ C₈ ◁ M₃₂

N	H ≅ G/N	type
3. #14272050	C₂	semidirect
4. C₁₆×#1181	C₂	semidirect
9. C₂×#90770	C₄	semidirect
12. D₂₉⋊C₁₆	C₄	semidirect
15. C₂₉×M₃₂	C₄	semidirect
16. #11745160	C₄	semidirect
17. #11745146	C₄	semidirect
73. M₃₂	#1181	semidirect
81. C₂₉	#2108	semidirect

H ≅ G/N

type

3. #14272050

C₂

semidirect

4. C₁₆×#1181

C₂

semidirect

9. C₂×#90770

C₄

semidirect

12. D₂₉⋊C₁₆

C₄

semidirect

15. C₂₉×M₃₂

C₄

semidirect

16. #11745160

C₄

semidirect

17. #11745146

C₄

semidirect

73. M₃₂

#1181

semidirect

81. C₂₉

#2108

semidirect

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

subgroup	index
C₂×D₂₉⋊C₁₆	2
#14272126	2
#14272050	2
C₁₆×#1181	2
M₃₂×D₂₉	2
#2108	29

subgroup

index

C₂×D₂₉⋊C₁₆

#14272126

#14272050

C₁₆×#1181

M₃₂×D₂₉

#2108

Subgroups — #16835704

Conjugacy classes of subgroups

Complements

Maximal subgroups