Group #16819665 — subgroups

Subgroups — #16819665

Order 3712.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11745167	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745170	C₂	1	2	yes	maximal
3	#14271186	C₂	1	2	yes	maximal
4	C₂×#11745163	C₂	1	1	yes	maximal, characteristic
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	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	C₂₉×#108	—	2	2	no	—
12	#11745170	—	2	4	no	—
13	#11745167	—	2	2	no	—
14	#11745163	C₄	1	4	yes	—
15	#11745162	—	2	4	no	—
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₉	Q₈	1	2	yes	—
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	2	yes	—
22	C₂×C₈×C₂₉	D₄	1	2	yes	—
23	C₂×C₈×C₂₉	Q₈	1	2	yes	—
24	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
25	C₄×Dic₂₉	D₄	1	2	yes	—
26	#90777	—	2	2	no	—
27	#90777	—	2	2	no	—
28	C₂×#6597	—	2	2	no	—
29	C₂×#6597	C₂×C₄	1	2	yes	—
30	C₂×#6597	D₄	1	2	yes	—
31	C₂×#6597	Q₈	1	2	yes	—
32	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×Dic₂₉	—	4	2	no	—
40	C₂×Dic₂₉	C₄⋊C₄	1	4	yes	—
41	C₈×C₂₉	—	4	2	no	—
42	C₈×C₂₉	C₄⋊C₄	1	4	yes	—
43	#6597	—	4	2	no	—
44	#6597	C₄⋊C₄	1	4	yes	—
45	#1849	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	—	2	2	no	—
47	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
49	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
50	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₂₉	#127	1	1	yes	characteristic
53	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₂₉	—	2	4	no	—
55	C₂×#108	—	29	2	no	—
56	C₂×#108	—	29	1	no	—
57	C₂×#108	D₂₉	1	1	yes	characteristic
58	#423	—	29	2	no	—
59	C₂×#97	—	29	1	no	—
60	C₂×C₂₉	—	2	1	no	—
61	C₂×C₂₉	—	2	1	no	—
62	C₂×C₂₉	#384	1	1	yes	characteristic
63	C₂×C₂₉	#430	1	2	yes	—
64	C₂×M₁₆	—	29	2	no	—
65	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
66	C₂²×C₈	—	29	1	no	—
67	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
68	C₂×C₄²	—	29	1	no	—
69	#108	—	2	2	no	—
70	#108	—	58	4	no	—
71	#108	—	58	2	no	—
72	C₄⋊C₈	—	58	4	no	—
73	#97	—	29	4	no	—
74	C₂₉	#1849	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	29	2	no	—
76	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	58	2	no	—
80	M₁₆	—	58	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	29	2	no	—
83	C₂×C₈	—	29	2	no	—
84	C₂×C₈	—	29	2	no	—
85	C₂×C₈	—	58	2	no	—
86	C₂×C₈	Dic₅₈	1	2	yes	—
87	C₂×C₈	C₄×D₂₉	1	2	yes	—
88	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
89	C₄²	—	29	2	no	—
90	C₄²	—	29	2	no	—
91	C₂³	Q₈×D₂₉	1	1	yes	characteristic
92	C₂×C₄	—	29	4	no	—
93	C₂×C₄	—	116	2	no	—
94	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
96	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
97	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	29	4	no	—
102	C₈	—	116	2	no	—
103	C₈	#90779	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#11745250	1	1	yes	characteristic
106	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
107	C₂²	#11745306	1	1	yes	characteristic
108	C₄	—	58	4	no	—
109	C₄	#11745250	1	1	yes	characteristic
110	C₄	C₄⋊C₄×D₂₉	1	1	yes	characteristic
111	C₄	C₂×#90779	1	1	yes	characteristic
112	C₄	#11745302	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#14271032	1	1	yes	characteristic
116	C₂	#14271210	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745167

C₂

yes

maximal, characteristic

C₂×#11745170

C₂

yes

maximal

#14271186

C₂

yes

maximal

C₂×#11745163

C₂

yes

maximal, characteristic

C₂×C₂₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#108

—

#11745170

—

#11745167

—

#11745163

C₄

yes

—

#11745162

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

Q₈

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

Q₈

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#6597

D₄

yes

—

C₂×#6597

Q₈

yes

—

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×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

—

C₈×C₂₉

C₄⋊C₄

yes

—

#6597

—

#6597

C₄⋊C₄

yes

—

#1849

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

#127

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

C₂×#108

—

C₂×#108

—

C₂×#108

D₂₉

yes

characteristic

#423

—

C₂×#97

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#384

yes

characteristic

C₂×C₂₉

#430

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

#108

—

C₄⋊C₈

—

#97

—

C₂₉

#1849

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

C₄×D₂₉

yes

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

D₄×D₂₉

yes

characteristic

C₂×C₄

Q₈×D₂₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

116

—

103

C₈

#90779

yes

—

104

C₂²

—

105

C₂²

#11745250

yes

characteristic

106

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

107

C₂²

#11745306

yes

characteristic

108

C₄

—

109

C₄

#11745250

yes

characteristic

110

C₄

C₄⋊C₄×D₂₉

yes

characteristic

111

C₄

C₂×#90779

yes

characteristic

112

C₄

#11745302

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#14271032

yes

characteristic

116

C₂

#14271210

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#108	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₉	C₂×Q₈
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#108	D₂₉
hypocenter	C₂₉	#1849
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#108

C₂

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂³×C₂₉

C₂×Q₈

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
74. C₂₉	#1849	semidirect

H ≅ G/N

type

74. C₂₉

#1849

semidirect

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

subgroup	index
C₂×#11745167	2
C₂×#11745170	2
#14271186	2
C₂×#11745163	2
C₂×C₂₉×#108	2
#1849	29

subgroup

index

C₂×C₂₉×#108

Subgroups — #16819665

Conjugacy classes of subgroups

Complements

Maximal subgroups