Group #16819617 — subgroups

Subgroups — #16819617

Order 3712.

172 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 81 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	#14271201	C₂	1	1	yes	maximal, characteristic
2	#14271118	C₂	1	1	yes	maximal, characteristic
3	#14270935	C₂	1	2	yes	maximal
4	#14270920	C₂	1	2	yes	maximal
5	C₂×C₂₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745288	C₂²	1	2	yes	—
9	#11745288	C₂²	1	1	yes	characteristic
10	C₂×#90777	C₂²	1	1	yes	characteristic
11	C₂₉×#108	—	2	1	no	—
12	C₂₉×#108	—	2	1	no	—
13	#11745166	—	2	1	no	—
14	#11745165	—	2	1	no	—
15	#11745163	C₄	1	2	yes	complemented
16	C₈×Dic₂₉	C₄	1	2	yes	complemented
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	M₁₆×C₂₉	—	2	2	no	—
19	M₁₆×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
27	C₂²⋊Dic₂₉	—	2	1	no	—
28	C₂²⋊Dic₂₉	—	2	2	no	—
29	C₄⋊Dic₂₉	—	2	1	no	—
30	C₄⋊Dic₂₉	—	2	2	no	—
31	C₄×Dic₂₉	—	2	2	no	—
32	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
33	#90777	—	2	1	no	—
34	#90777	—	2	1	no	—
35	C₂×#6597	C₂×C₄	1	2	yes	—
36	C₂³×C₂₉	#41	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
42	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	—	4	2	no	—
45	C₈×C₂₉	—	4	2	no	—
46	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
47	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
48	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
50	#6597	—	2	2	no	—
51	#1833	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	—	4	1	no	—
53	C₂²×C₂₉	#117	1	1	yes	characteristic
54	C₂²×C₂₉	#124	1	1	yes	characteristic
55	C₂²×C₂₉	#125	1	1	yes	characteristic
56	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₄×C₂₉	#117	1	1	yes	characteristic
58	C₄×C₂₉	#124	1	1	yes	characteristic
59	C₄×C₂₉	#125	1	1	yes	characteristic
60	Dic₂₉	—	4	2	no	—
61	Dic₂₉	—	8	2	no	—
62	C₂×#108	D₂₉	1	1	yes	characteristic
63	#427	—	29	1	no	—
64	#405	—	29	1	no	—
65	#344	—	29	2	no	—
66	H(3,ℤ/4)	—	29	2	no	—
67	C₂×C₂₉	—	2	1	no	—
68	C₂×C₂₉	—	2	1	no	—
69	C₂×C₂₉	—	2	1	no	—
70	C₂×C₂₉	#382	1	1	yes	characteristic
71	C₂×M₁₆	—	29	1	no	—
72	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
73	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
74	#117	—	29	1	no	—
75	#117	—	29	2	no	—
76	#108	—	2	1	no	—
77	#108	—	2	1	no	—
78	#107	—	58	1	no	—
79	#106	—	58	1	no	—
80	#97	—	29	2	no	—
81	C₄×C₈	—	29	2	no	—
82	C₂₉	#1833	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	2	2	no	—
86	M₁₆	—	58	1	no	—
87	M₁₆	—	58	1	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	29	2	no	—
90	C₂×C₈	Dic₅₈	1	1	yes	characteristic
91	C₂×C₈	Dic₅₈	1	1	yes	characteristic
92	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
93	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
94	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
95	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
96	C₄⋊C₄	—	58	1	no	—
97	C₄⋊C₄	—	58	2	no	—
98	C₂²⋊C₄	—	58	1	no	—
99	C₂²⋊C₄	—	58	2	no	—
100	C₄²	—	29	2	no	—
101	C₄²	—	58	2	no	—
102	C₂³	#90809	1	1	yes	characteristic
103	C₂×C₄	—	58	2	no	—
104	C₂×C₄	—	116	2	no	—
105	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
106	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
107	C₂×C₄	#90807	1	1	yes	characteristic
108	C₂×C₄	#90807	1	1	yes	characteristic
109	C₂×C₄	#90809	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
111	C₈	—	4	2	no	—
112	C₈	—	58	2	no	—
113	C₈	#90779	1	1	yes	characteristic
114	C₈	#90779	1	1	yes	characteristic
115	C₈	#90779	1	1	yes	characteristic
116	C₈	#90779	1	1	yes	characteristic
117	C₂²	—	4	1	no	—
118	C₂²	#11745252	1	1	yes	characteristic
119	C₂²	#11745254	1	1	yes	characteristic
120	C₂²	#11745309	1	1	yes	characteristic
121	C₄	—	116	2	no	—
122	C₄	—	232	2	no	—
123	C₄	#11745252	1	1	yes	characteristic
124	C₄	#11745254	1	1	yes	characteristic
125	C₄	C₂×#90779	1	1	yes	characteristic
126	C₄	#11745298	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#14271028	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271201

C₂

yes

maximal, characteristic

#14271118

C₂

yes

maximal, characteristic

#14270935

C₂

yes

maximal

#14270920

C₂

yes

maximal

C₂×C₂₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

—

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

characteristic

C₂₉×#108

—

C₂₉×#108

—

#11745166

—

#11745165

—

#11745163

C₄

yes

complemented

C₈×Dic₂₉

C₄

yes

complemented

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

Q₈

yes

characteristic

C₂×C₈×C₂₉

Q₈

yes

characteristic

C₂²⋊Dic₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

#90777

—

#90777

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

C₈×C₂₉

C₄⋊C₄

yes

characteristic

C₈×C₂₉

C₄⋊C₄

yes

characteristic

C₈×C₂₉

C₄⋊C₄

yes

characteristic

C₈×C₂₉

C₄⋊C₄

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

C₂×C₄⋊C₄

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

C₂×#108

D₂₉

yes

—

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#382

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

C₂×D₂₉

yes

—

—

—

—

—

—

—

C₄×C₈

—

C₂₉

#1833

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

characteristic

C₂×C₈

Dic₅₈

yes

characteristic

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

—

102

C₂³

#90809

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

116

—

105

C₂×C₄

C₂×Dic₅₈

yes

characteristic

106

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

107

C₂×C₄

#90807

yes

characteristic

108

C₂×C₄

#90807

yes

characteristic

109

C₂×C₄

#90809

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

#90779

yes

characteristic

114

C₈

#90779

yes

characteristic

115

C₈

#90779

yes

characteristic

116

C₈

#90779

yes

characteristic

117

C₂²

—

118

C₂²

#11745252

yes

characteristic

119

C₂²

#11745254

yes

characteristic

120

C₂²

#11745309

yes

characteristic

121

C₄

—

116

—

122

C₄

—

232

—

123

C₄

#11745252

yes

characteristic

124

C₄

#11745254

yes

characteristic

125

C₄

C₂×#90779

yes

characteristic

126

C₄

#11745298

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#14271028

yes

characteristic

	subgroup	G/H
center	C₄	#11745254
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#108	C₂
socle	C₂×C₂₉	#382
prime radical	C₂³×C₂₉	#41
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#108	D₂₉
hypocenter	C₂₉	#1833
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#11745254

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#108

C₂

C₂×C₂₉

C₂³×C₂₉

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
15. #11745163	C₄	semidirect
16. C₈×Dic₂₉	C₄	semidirect
82. C₂₉	#1833	semidirect

H ≅ G/N

type

15. #11745163

C₄

semidirect

16. C₈×Dic₂₉

C₄

semidirect

82. C₂₉

#1833

semidirect

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

subgroup	index
#14271201	2
#14271118	2
#14270935	2
#14270920	2
C₂×C₂₉×#108	2
#1833	29

subgroup

index

C₂×C₂₉×#108

Subgroups — #16819617

Conjugacy classes of subgroups

Complements

Maximal subgroups