Group #16836461 — subgroups

Subgroups — #16836461

Order 3712.

360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 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	#14272222	C₂	1	8	yes	maximal, complemented
2	D₂₉⋊M₃₂	C₂	1	4	yes	maximal, complemented
3	C₂×#11745214	C₂	1	2	yes	maximal, complemented
4	C₂×#11745269	C₂	1	1	yes	maximal, characteristic
5	C₂×#90805	C₄	1	1	yes	characteristic
6	C₂×M₁₆×C₂₉	C₄	1	1	yes	characteristic
7	C₂²×#6597	C₂²	1	1	yes	characteristic
8	#11745269	C₄	1	4	yes	—
9	#11745269	C₂²	1	4	yes	—
10	C₂×#90772	C₄	1	2	yes	—
11	C₂×C₈×D₂₉	C₂²	1	2	yes	—
12	#11745214	C₂²	1	4	yes	—
13	#11745214	C₂²	1	4	yes	complemented
14	C₂×#90770	C₂²	1	4	yes	complemented
15	#11745206	C₂²	1	8	yes	complemented
16	D₂₉⋊C₁₆	C₂²	1	8	yes	complemented
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₂²⋊D₂₉	C₈	1	2	yes	—
19	#90805	C₈	1	4	yes	—
20	#90805	C₂×C₄	1	4	yes	—
21	C₂×D₁₁₆	C₈	1	1	yes	characteristic
22	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
23	C₂×Dic₅₈	C₈	1	1	yes	characteristic
24	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₂×#6597	C₂×C₄	1	1	yes	characteristic
27	C₂×#6597	C₂×C₄	1	2	yes	—
28	C₂×#6597	C₂³	1	2	yes	—
29	C₂×#6597	C₂³	1	1	yes	characteristic
30	#90772	C₂×C₄	1	8	yes	—
31	C₈×D₂₉	C₂×C₄	1	4	yes	—
32	C₈×D₂₉	C₂³	1	4	yes	—
33	#90770	C₂³	1	8	yes	—
34	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₂₉	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
40	C₂²⋊D₂₉	C₂×C₈	1	8	yes	—
41	C₂×Dic₂₉	C₂×C₈	1	2	yes	—
42	D₁₁₆	C₂×C₈	1	4	yes	—
43	C₄×D₂₉	C₂×C₈	1	4	yes	—
44	C₄×D₂₉	C₂²×C₄	1	4	yes	—
45	Dic₅₈	C₂×C₈	1	4	yes	—
46	C₈×C₂₉	C₂²×C₄	1	4	yes	—
47	#6597	C₂²×C₄	1	1	yes	characteristic
48	#6597	C₂²×C₄	1	2	yes	—
49	#6597	C₂⁴	1	1	yes	characteristic
50	#3407	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	4	1	no	—
52	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
53	C₂²×C₂₉	C₂²×C₈	1	2	yes	—
54	C₂×D₂₉	—	4	2	no	—
55	C₂×D₂₉	C₂²×C₈	1	4	yes	—
56	C₄×C₂₉	C₂²×C₈	1	2	yes	—
57	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
58	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
59	Dic₂₉	C₂²×C₈	1	4	yes	—
60	C₂×#131	—	29	1	no	—
61	#504	—	29	8	no	—
62	C₂×M₃₂	—	29	2	no	—
63	C₂×M₃₂	—	29	4	no	—
64	C₂×C₂₉	—	2	1	no	—
65	C₂×C₂₉	—	2	2	no	—
66	C₂×C₂₉	C₂³×C₈	1	1	yes	characteristic
67	D₂₉	—	2	4	no	—
68	C₂×#41	—	29	1	no	—
69	#131	—	29	4	no	—
70	#131	—	29	4	no	—
71	C₂×M₁₆	—	29	2	no	—
72	C₂×M₁₆	#1181	1	1	yes	characteristic
73	C₂²×C₈	—	29	1	no	—
74	C₂²×C₈	—	29	2	no	—
75	M₃₂	—	29	8	no	—
76	M₃₂	—	29	4	no	—
77	M₃₂	—	29	4	no	—
78	C₂×C₁₆	—	29	8	no	—
79	C₂×C₁₆	—	29	4	no	—
80	C₂₉	#3407	1	1	yes	characteristic, complemented, Sylow
81	#41	—	29	4	no	—
82	#41	—	29	4	no	—
83	C₂×Q₈	—	29	1	no	—
84	C₂×D₄	—	29	2	no	—
85	C₂×D₄	—	29	1	no	—
86	C₂²×C₄	—	29	2	no	—
87	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
88	M₁₆	—	29	8	no	—
89	M₁₆	C₂×#1181	1	4	yes	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	29	1	no	—
92	C₂×C₈	—	29	1	no	—
93	C₂×C₈	—	29	2	no	—
94	C₂×C₈	—	29	4	no	—
95	C₂×C₈	—	29	4	no	—
96	C₂×C₈	C₂×#1181	1	2	yes	—
97	C₁₆	—	29	8	no	—
98	C₂³	—	29	2	no	—
99	C₂³	D₂₉⋊C₈	1	1	yes	characteristic
100	Q₈	—	29	4	no	—
101	D₄	—	29	8	no	—
102	D₄	—	29	4	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	29	4	no	—
105	C₂×C₄	—	29	4	no	—
106	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
107	C₂×C₄	D₂₉⋊C₈	1	2	yes	—
108	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
109	C₂×C₄	C₂²×#1181	1	2	yes	—
110	C₈	—	29	1	no	—
111	C₈	—	29	1	no	—
112	C₈	—	29	2	no	—
113	C₈	C₂²×#1181	1	4	yes	—
114	C₂²	—	4	1	no	—
115	C₂²	—	29	4	no	—
116	C₂²	—	116	2	no	—
117	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
118	C₂²	C₂×D₂₉⋊C₈	1	2	yes	—
119	C₄	—	29	4	no	—
120	C₄	C₂×D₂₉⋊C₈	1	1	yes	characteristic
121	C₄	C₂×D₂₉⋊C₈	1	2	yes	—
122	C₄	C₂³×#1181	1	1	yes	characteristic
123	C₂	—	2	1	no	—
124	C₂	—	2	2	no	—
125	C₂	—	58	4	no	—
126	C₂	C₂²×D₂₉⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272222

C₂

yes

maximal, complemented

D₂₉⋊M₃₂

C₂

yes

maximal, complemented

C₂×#11745214

C₂

yes

maximal, complemented

C₂×#11745269

C₂

yes

maximal, characteristic

C₂×#90805

C₄

yes

characteristic

C₂×M₁₆×C₂₉

C₄

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

#11745269

C₄

yes

—

#11745269

C₂²

yes

—

C₂×#90772

C₄

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

#11745214

C₂²

yes

—

#11745214

C₂²

yes

complemented

C₂×#90770

C₂²

yes

complemented

#11745206

C₂²

yes

complemented

D₂₉⋊C₁₆

C₂²

yes

complemented

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₂₉

C₈

yes

—

#90805

C₈

yes

—

#90805

C₂×C₄

yes

—

C₂×D₁₁₆

C₈

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×Dic₅₈

C₈

yes

characteristic

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂³

yes

—

C₂×#6597

C₂³

yes

characteristic

#90772

C₂×C₄

yes

—

C₈×D₂₉

C₂×C₄

yes

—

C₈×D₂₉

C₂³

yes

—

#90770

C₂³

yes

—

C₂³×C₂₉

C₂×C₈

yes

characteristic

C₂²×D₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂²⋊D₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

D₁₁₆

C₂×C₈

yes

—

C₄×D₂₉

C₂×C₈

yes

—

C₄×D₂₉

C₂²×C₄

yes

—

Dic₅₈

C₂×C₈

yes

—

C₈×C₂₉

C₂²×C₄

yes

—

#6597

C₂²×C₄

yes

characteristic

#6597

C₂²×C₄

yes

—

#6597

C₂⁴

yes

characteristic

#3407

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂²×C₂₉

C₂²×C₈

yes

—

C₂×D₂₉

—

C₂×D₂₉

C₂²×C₈

yes

—

C₄×C₂₉

C₂²×C₈

yes

—

C₄×C₂₉

C₂²×C₈

yes

characteristic

C₄×C₂₉

C₂³×C₄

yes

characteristic

Dic₂₉

C₂²×C₈

yes

—

C₂×#131

—

#504

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂³×C₈

yes

characteristic

D₂₉

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

#1181

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂₉

#3407

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

characteristic

M₁₆

—

M₁₆

C₂×#1181

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₁₆

—

C₂³

—

C₂³

D₂₉⋊C₈

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

D₂₉⋊C₈

yes

characteristic

107

C₂×C₄

D₂₉⋊C₈

yes

—

108

C₂×C₄

C₂²×#1181

yes

characteristic

109

C₂×C₄

C₂²×#1181

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

C₂²×#1181

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

116

—

117

C₂²

C₂×D₂₉⋊C₈

yes

characteristic

118

C₂²

C₂×D₂₉⋊C₈

yes

—

119

C₄

—

120

C₄

C₂×D₂₉⋊C₈

yes

characteristic

121

C₄

C₂×D₂₉⋊C₈

yes

—

122

C₄

C₂³×#1181

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

C₂²×D₂₉⋊C₈

yes

characteristic

	subgroup	G/H
center, Frattini	C₄	C₂³×#1181
commutator, socle	C₂×C₂₉	C₂³×C₈
Fitting	C₂×M₁₆×C₂₉	C₄
prime radical	C₂×#90805	C₄
cosocle	#6597	C₂⁴
hypercenter	C₂×M₁₆	#1181
hypocenter	C₂₉	#3407
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₄

C₂³×#1181

commutator, socle

C₂×C₂₉

C₂³×C₈

Fitting

C₂×M₁₆×C₂₉

C₄

C₄

C₂⁴

C₂×M₁₆

C₂₉

G ▷ C₂×C₂₉ ▷ C₂₉

C₁ ◁ C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. #14272222	C₂	semidirect
2. D₂₉⋊M₃₂	C₂	semidirect
3. C₂×#11745214	C₂	semidirect
13. #11745214	C₂²	semidirect
14. C₂×#90770	C₂²	semidirect
15. #11745206	C₂²	semidirect
16. D₂₉⋊C₁₆	C₂²	semidirect
80. C₂₉	#3407	semidirect

H ≅ G/N

type

1. #14272222

C₂

semidirect

2. D₂₉⋊M₃₂

C₂

semidirect

3. C₂×#11745214

C₂

semidirect

13. #11745214

C₂²

semidirect

14. C₂×#90770

C₂²

semidirect

15. #11745206

C₂²

semidirect

16. D₂₉⋊C₁₆

C₂²

semidirect

80. C₂₉

#3407

semidirect

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

subgroup	index
#14272222	2
D₂₉⋊M₃₂	2
C₂×#11745214	2
C₂×#11745269	2
#3407	29

subgroup

index

D₂₉⋊M₃₂

Subgroups — #16836461

Conjugacy classes of subgroups

Complements

Maximal subgroups