Group #16819604 — subgroups

Subgroups — #16819604

Order 3712.

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

normal subgroups only

This group has 236 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	#14271641	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745184	C₂	1	1	yes	maximal, characteristic
3	#14270935	C₂	1	2	yes	maximal
4	#14270934	C₂	1	2	yes	maximal
5	C₂×C₂₉×#101	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	Q₈×Dic₂₉	—	2	2	no	—
9	Q₈×Dic₂₉	—	2	2	no	—
10	#11745288	C₄	1	4	yes	—
11	#11745288	C₂²	1	1	yes	characteristic
12	#11745288	C₂²	1	1	yes	characteristic
13	C₂×#90777	C₂²	1	2	yes	—
14	C₂₉×#101	—	2	2	no	—
15	#11745184	—	2	2	no	—
16	C₂×Q₈×C₂₉	—	2	2	no	—
17	C₂×Q₈×C₂₉	—	2	2	no	—
18	C₂×Q₈×C₂₉	D₄	1	2	yes	—
19	C₂×Q₈×C₂₉	D₄	1	2	yes	—
20	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₉	—	2	2	no	—
23	M₁₆×C₂₉	—	2	2	no	—
24	C₂×C₈×C₂₉	—	2	2	no	—
25	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
26	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
27	C₄⋊Dic₂₉	—	2	4	no	—
28	C₄⋊Dic₂₉	—	2	1	no	—
29	C₄⋊Dic₂₉	—	2	1	no	—
30	C₄×Dic₂₉	—	2	4	no	—
31	C₄×Dic₂₉	—	2	1	no	—
32	C₄×Dic₂₉	—	2	1	no	—
33	#90777	—	2	2	no	—
34	#90777	—	2	2	no	—
35	C₂×#6597	—	2	2	no	—
36	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₂₉	—	2	4	no	—
38	Q₈×C₂₉	—	2	4	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	—	2	2	no	—
41	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
42	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₂₉	#41	1	2	yes	—
45	C₂×C₄×C₂₉	#41	1	2	yes	—
46	C₂×Dic₂₉	—	2	2	no	—
47	C₂×Dic₂₉	—	2	2	no	—
48	C₈×C₂₉	—	4	2	no	—
49	#6597	—	4	2	no	—
50	#1830	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	4	1	no	—
52	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₂₉	#117	1	1	yes	characteristic
54	C₂²×C₂₉	#117	1	1	yes	characteristic
55	C₄×C₂₉	—	2	4	no	—
56	C₄×C₂₉	#123	1	2	yes	—
57	C₄×C₂₉	#123	1	2	yes	—
58	Dic₂₉	—	4	2	no	—
59	Dic₂₉	—	4	2	no	—
60	#519	—	29	1	no	—
61	C₂×#101	—	29	1	no	—
62	C₂×#101	D₂₉	1	1	yes	characteristic
63	#344	—	29	2	no	—
64	#344	—	29	2	no	—
65	C₂×C₂₉	—	2	1	no	—
66	C₂×C₂₉	—	2	1	no	—
67	C₂×C₂₉	—	2	1	no	—
68	C₂×C₂₉	#381	1	1	yes	characteristic
69	C₂²×Q₈	C₂×D₂₉	1	1	yes	characteristic
70	C₂×M₁₆	—	29	2	no	—
71	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
72	C₄×Q₈	—	58	2	no	—
73	C₄×Q₈	—	58	2	no	—
74	#117	—	29	4	no	—
75	#117	—	29	1	no	—
76	#117	—	29	1	no	—
77	#101	—	2	2	no	—
78	#101	—	58	2	no	—
79	C₂₉	#1830	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	D₁₁₆	1	2	yes	—
83	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
84	C₂²×C₄	C₄×D₂₉	1	2	yes	—
85	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	M₁₆	—	58	2	no	—
89	M₁₆	—	58	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	58	2	no	—
92	C₄⋊C₄	—	58	4	no	—
93	C₄⋊C₄	—	58	1	no	—
94	C₄⋊C₄	—	58	1	no	—
95	C₂²⋊C₄	—	29	2	no	—
96	C₂²⋊C₄	—	29	2	no	—
97	C₄²	—	58	4	no	—
98	C₄²	—	58	1	no	—
99	C₄²	—	58	1	no	—
100	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
101	Q₈	—	2	4	no	—
102	Q₈	—	2	4	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	58	2	no	—
106	C₂×C₄	—	58	2	no	—
107	C₂×C₄	#90781	1	4	yes	—
108	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
109	C₂×C₄	#90807	1	2	yes	—
110	C₂×C₄	#90807	1	2	yes	—
111	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
112	C₈	—	4	2	no	—
113	C₈	—	116	2	no	—
114	C₂²	—	4	1	no	—
115	C₂²	#11745239	1	1	yes	characteristic
116	C₂²	#11745239	1	1	yes	characteristic
117	C₂²	C₂×#90781	1	1	yes	characteristic
118	C₄	—	2	4	no	—
119	C₄	—	116	2	no	—
120	C₄	—	116	2	no	—
121	C₄	#11745248	1	2	yes	—
122	C₄	#11745297	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	—	2	1	no	—
126	C₂	#14271024	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271641

C₂

yes

maximal, characteristic

C₂×#11745184

C₂

yes

maximal, characteristic

#14270935

C₂

yes

maximal

#14270934

C₂

yes

maximal

C₂×C₂₉×#101

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

Q₈×Dic₂₉

—

Q₈×Dic₂₉

—

#11745288

C₄

yes

—

#11745288

C₂²

yes

characteristic

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂₉×#101

—

#11745184

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂²⋊Dic₂₉

C₂×C₄

yes

—

C₂²⋊Dic₂₉

C₂×C₄

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

#90777

—

#90777

—

C₂×#6597

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

#6597

—

#1830

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

#123

yes

—

C₄×C₂₉

#123

yes

—

Dic₂₉

—

Dic₂₉

—

#519

—

C₂×#101

—

C₂×#101

D₂₉

yes

characteristic

#344

—

#344

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#381

yes

characteristic

C₂²×Q₈

C₂×D₂₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

—

—

—

—

—

C₂₉

#1830

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₁₁₆

yes

—

C₂×Q₈

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₄×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

100

C₂³

C₂×C₄×D₂₉

yes

characteristic

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

#90781

yes

—

108

C₂×C₄

C₂×D₁₁₆

yes

characteristic

109

C₂×C₄

#90807

yes

—

110

C₂×C₄

#90807

yes

—

111

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

112

C₈

—

113

C₈

—

116

—

114

C₂²

—

115

C₂²

#11745239

yes

characteristic

116

C₂²

#11745239

yes

characteristic

117

C₂²

C₂×#90781

yes

characteristic

118

C₄

—

119

C₄

—

116

—

120

C₄

—

116

—

121

C₄

#11745248

yes

—

122

C₄

#11745297

yes

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

#14271024

yes

characteristic

	subgroup	G/H
center	C₂	#14271024
commutator, prime radical	C₂³×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#101	C₂
socle	C₂×C₂₉	#381
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#101	D₂₉
hypocenter	C₂₉	#1830
LCS	G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂

#14271024

commutator, prime radical

C₂³×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#101

C₂

socle

C₂×C₂₉

#381

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
79. C₂₉	#1830	semidirect

H ≅ G/N

type

79. C₂₉

#1830

semidirect

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

subgroup	index
#14271641	2
C₂×#11745184	2
#14270935	2
#14270934	2
C₂×C₂₉×#101	2
#1830	29

subgroup

index

C₂×C₂₉×#101

Subgroups — #16819604

Conjugacy classes of subgroups

Complements

Maximal subgroups