Group #16820283 — subgroups

Subgroups — #16820283

Order 3712.

184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14271212	C₂	1	2	yes	maximal
2	C₂×#11745167	C₂	1	1	yes	maximal, characteristic
3	#14271118	C₂	1	1	yes	maximal, characteristic
4	#14270935	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	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂×#90777	C₂²	1	1	yes	characteristic
11	C₂₉×#108	C₄	1	4	yes	complemented
12	#11745167	—	2	1	no	—
13	#11745167	—	2	1	no	—
14	#11745167	—	2	4	no	—
15	#11745163	—	2	1	no	—
16	C₈×Dic₂₉	—	2	1	no	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	M₁₆×C₂₉	—	2	2	no	—
19	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	Q₈	1	2	yes	—
25	C₂²⋊Dic₂₉	Q₈	1	2	yes	—
26	C₄⋊Dic₂₉	—	2	1	no	—
27	C₄×Dic₂₉	—	2	1	no	—
28	#90777	—	2	1	no	—
29	#90777	—	2	2	no	—
30	#90777	—	2	2	no	—
31	#90777	D₄	1	2	yes	—
32	C₂×#6597	—	2	1	no	—
33	C₂×#6597	—	2	2	no	—
34	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
40	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
41	C₂×Dic₂₉	—	2	2	no	—
42	C₈×C₂₉	—	2	4	no	—
43	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
44	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
45	#6597	—	2	2	no	—
46	#6597	—	4	2	no	—
47	#1953	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	—	4	1	no	—
49	C₂²×C₂₉	C₄×Q₈	1	1	yes	characteristic
50	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
52	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
54	C₄×C₂₉	#121	1	1	yes	characteristic
55	C₄×C₂₉	#125	1	1	yes	characteristic
56	Dic₂₉	—	4	2	no	—
57	#430	—	29	2	no	—
58	C₂×#108	—	29	1	no	—
59	C₂×#108	D₂₉	1	1	yes	characteristic
60	#405	—	29	1	no	—
61	#344	—	29	2	no	—
62	C₂×C₂₉	—	2	1	no	—
63	C₂×C₂₉	—	2	1	no	—
64	C₂×C₂₉	—	2	1	no	—
65	C₂×C₂₉	#389	1	1	yes	characteristic
66	C₂×M₁₆	—	29	1	no	—
67	C₂×M₁₆	—	29	2	no	—
68	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
69	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
70	#117	—	29	1	no	—
71	#108	—	58	4	no	—
72	#108	—	58	1	no	—
73	#108	—	58	1	no	—
74	#108	Dic₂₉	1	4	yes	complemented
75	#97	—	58	1	no	—
76	C₄×C₈	—	58	1	no	—
77	C₂₉	#1953	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
79	M₁₆	—	2	2	no	—
80	M₁₆	—	29	2	no	—
81	M₁₆	—	58	1	no	—
82	M₁₆	—	58	2	no	—
83	M₁₆	—	58	2	no	—
84	M₁₆	C₂×Dic₂₉	1	4	yes	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	58	1	no	—
87	C₂×C₈	—	58	2	no	—
88	C₂×C₈	Dic₅₈	1	2	yes	—
89	C₂×C₈	D₁₁₆	1	1	yes	characteristic
90	C₂×C₈	D₁₁₆	1	1	yes	characteristic
91	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
92	C₄⋊C₄	—	58	1	no	—
93	C₂²⋊C₄	—	29	2	no	—
94	C₄²	—	58	1	no	—
95	C₂³	Q₈×D₂₉	1	1	yes	characteristic
96	C₂×C₄	—	58	2	no	—
97	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
98	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
99	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
100	C₂×C₄	#90807	1	1	yes	characteristic
101	C₂×C₄	#90809	1	1	yes	characteristic
102	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₈	—	58	2	no	—
105	C₈	—	116	2	no	—
106	C₈	C₄⋊Dic₂₉	1	2	yes	—
107	C₈	C₄⋊Dic₂₉	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#11745250	1	1	yes	characteristic
110	C₂²	#11745259	1	1	yes	characteristic
111	C₂²	Q₈×Dic₂₉	1	1	yes	characteristic
112	C₄	—	116	2	no	—
113	C₄	#11745252	1	1	yes	characteristic
114	C₄	#11745257	1	1	yes	characteristic
115	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
116	C₄	D₄×Dic₂₉	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#14271062	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271212

C₂

yes

maximal

C₂×#11745167

C₂

yes

maximal, characteristic

#14271118

C₂

yes

maximal, characteristic

#14270935

C₂

yes

maximal

C₂×C₂₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂×#90777

C₂²

yes

characteristic

C₂₉×#108

C₄

yes

—

—

—

—

C₈×Dic₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

Q₈

yes

—

C₂²⋊Dic₂₉

Q₈

yes

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

—

—

—

D₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₈×C₂₉

—

C₈×C₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

C₄⋊C₄

yes

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₄×Q₈

yes

characteristic

C₂²×C₂₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

#430

—

C₂×#108

—

C₂×#108

D₂₉

yes

characteristic

#405

—

#344

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#389

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

C₂×D₂₉

yes

—

—

—

—

Dic₂₉

yes

complemented

#97

—

C₄×C₈

—

C₂₉

#1953

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₂₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

D₁₁₆

yes

characteristic

C₂×C₈

D₁₁₆

yes

characteristic

C₂×C₈

C₂×Dic₂₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

Q₈×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

characteristic

100

C₂×C₄

#90807

yes

characteristic

101

C₂×C₄

#90809

yes

characteristic

102

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

116

—

106

C₈

C₄⋊Dic₂₉

yes

—

107

C₈

C₄⋊Dic₂₉

yes

—

108

C₂²

—

109

C₂²

#11745250

yes

characteristic

110

C₂²

#11745259

yes

characteristic

111

C₂²

Q₈×Dic₂₉

yes

characteristic

112

C₄

—

116

—

113

C₄

#11745252

yes

characteristic

114

C₄

#11745257

yes

characteristic

115

C₄

C₂×C₄⋊Dic₂₉

yes

characteristic

116

C₄

D₄×Dic₂₉

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#14271062

yes

characteristic

	subgroup	G/H
center	C₄	#11745257
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#108	C₂
socle	C₂×C₂₉	#389
prime radical	C₂³×C₂₉	C₂×Q₈
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#108	D₂₉
hypocenter	C₂₉	#1953
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#11745257

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#108

C₂

socle

C₂×C₂₉

#389

prime radical

C₂³×C₂₉

C₂×Q₈

cosocle

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
11. C₂₉×#108	C₄	semidirect
74. #108	Dic₂₉	semidirect
77. C₂₉	#1953	semidirect

H ≅ G/N

type

11. C₂₉×#108

C₄

semidirect

74. #108

Dic₂₉

semidirect

77. C₂₉

#1953

semidirect

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

subgroup	index
#14271212	2
C₂×#11745167	2
#14271118	2
#14270935	2
C₂×C₂₉×#108	2
#1953	29

subgroup

index

C₂×C₂₉×#108

Subgroups — #16820283

Conjugacy classes of subgroups

Complements

Maximal subgroups