Group #16819138 — subgroups

Subgroups — #16819138

Order 3712.

164 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14271568	C₂	1	1	yes	maximal, characteristic
2	#14271561	C₂	1	1	yes	maximal, characteristic
3	#14271514	C₂	1	1	yes	maximal, characteristic
4	#14271514	C₂	1	1	yes	maximal, characteristic
5	#14271514	C₂	1	1	yes	maximal, characteristic
6	#14271514	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#322	C₂	1	1	yes	maximal, characteristic
8	#11745231	C₂²	1	1	yes	characteristic
9	#11745231	C₂²	1	1	yes	characteristic
10	#11745231	C₂²	1	1	yes	characteristic
11	#11745231	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	#11745166	—	2	2	no	—
16	#11745165	—	2	2	no	—
17	#11745164	—	2	2	no	—
18	#11745164	—	2	2	no	—
19	#11745164	—	2	2	no	—
20	#11745164	—	2	2	no	—
21	C₂×Dic₅₈	—	2	1	no	—
22	C₂×Dic₅₈	—	2	1	no	—
23	C₂×Dic₅₈	—	2	1	no	—
24	C₂×Dic₅₈	—	2	1	no	—
25	C₂×C₈×C₂₉	D₄	1	2	yes	—
26	C₂×C₈×C₂₉	D₄	1	2	yes	—
27	C₂×C₈×C₂₉	D₄	1	2	yes	—
28	C₄²×C₂₉	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₂₉	—	2	1	no	—
30	C₄⋊Dic₂₉	—	2	1	no	—
31	C₄⋊Dic₂₉	—	2	1	no	—
32	C₄⋊Dic₂₉	—	2	1	no	—
33	C₄⋊Dic₂₉	—	2	1	no	—
34	C₄⋊Dic₂₉	—	2	1	no	—
35	C₄⋊Dic₂₉	—	2	1	no	—
36	C₄⋊Dic₂₉	—	2	1	no	—
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₂₉	—	4	1	no	—
41	C₂×Dic₂₉	—	4	1	no	—
42	C₂×Dic₂₉	—	4	1	no	—
43	C₂×Dic₂₉	—	4	1	no	—
44	Dic₅₈	—	4	2	no	—
45	Dic₅₈	—	4	2	no	—
46	Dic₅₈	—	4	2	no	—
47	Dic₅₈	—	4	2	no	—
48	C₈×C₂₉	—	2	2	no	—
49	C₈×C₂₉	—	2	2	no	—
50	C₈×C₂₉	—	2	2	no	—
51	#1718	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	#127	1	1	yes	characteristic
53	C₄×C₂₉	#135	1	2	yes	—
54	C₄×C₂₉	#137	1	2	yes	—
55	C₄×C₂₉	#137	1	2	yes	—
56	Dic₂₉	—	8	1	no	—
57	Dic₂₉	—	8	1	no	—
58	Dic₂₉	—	8	1	no	—
59	Dic₂₉	—	8	1	no	—
60	#500	—	29	1	no	—
61	#498	—	29	1	no	—
62	#487	—	29	1	no	—
63	#487	—	29	1	no	—
64	#487	—	29	1	no	—
65	#487	—	29	1	no	—
66	#322	D₂₉	1	1	yes	characteristic
67	C₂×C₂₉	#495	1	1	yes	characteristic
68	C₂×C₂₉	#497	1	1	yes	characteristic
69	C₂×C₂₉	#497	1	1	yes	characteristic
70	C₄⋊Q₈	—	29	1	no	—
71	C₄⋊Q₈	—	29	1	no	—
72	C₄⋊Q₈	—	29	1	no	—
73	C₄⋊Q₈	—	29	1	no	—
74	#107	—	58	2	no	—
75	#106	—	58	2	no	—
76	#103	—	58	2	no	—
77	#103	—	58	2	no	—
78	#103	—	58	2	no	—
79	#103	—	58	2	no	—
80	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
81	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
82	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
83	C₂₉	#1718	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₈	—	58	1	no	—
85	C₂×Q₈	—	58	1	no	—
86	C₂×Q₈	—	58	1	no	—
87	C₂×Q₈	—	58	1	no	—
88	C₂×C₈	D₁₁₆	1	2	yes	—
89	C₂×C₈	D₁₁₆	1	2	yes	—
90	C₂×C₈	D₁₁₆	1	2	yes	—
91	C₄⋊C₄	—	58	1	no	—
92	C₄⋊C₄	—	58	1	no	—
93	C₄⋊C₄	—	58	1	no	—
94	C₄⋊C₄	—	58	1	no	—
95	C₄⋊C₄	—	58	1	no	—
96	C₄⋊C₄	—	58	1	no	—
97	C₄⋊C₄	—	58	1	no	—
98	C₄⋊C₄	—	58	1	no	—
99	C₄²	C₂²×D₂₉	1	1	yes	characteristic
100	Q₈	—	116	2	no	—
101	Q₈	—	116	2	no	—
102	Q₈	—	116	2	no	—
103	Q₈	—	116	2	no	—
104	C₂×C₄	—	116	1	no	—
105	C₂×C₄	—	116	1	no	—
106	C₂×C₄	—	116	1	no	—
107	C₂×C₄	—	116	1	no	—
108	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
109	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
110	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	2	2	no	—
113	C₈	—	2	2	no	—
114	C₂²	#11745236	1	1	yes	characteristic
115	C₄	—	232	1	no	—
116	C₄	—	232	1	no	—
117	C₄	—	232	1	no	—
118	C₄	—	232	1	no	—
119	C₄	#11745266	1	2	yes	—
120	C₄	#11745271	1	2	yes	—
121	C₄	#11745271	1	2	yes	—
122	C₂	#14271547	1	1	yes	characteristic
123	C₂	#14271557	1	1	yes	characteristic
124	C₂	#14271557	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271568

C₂

yes

maximal, characteristic

#14271561

C₂

yes

maximal, characteristic

#14271514

C₂

yes

maximal, characteristic

#14271514

C₂

yes

maximal, characteristic

#14271514

C₂

yes

maximal, characteristic

#14271514

C₂

yes

maximal, characteristic

C₂₉×#322

C₂

yes

maximal, characteristic

#11745231

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

—

—

—

—

—

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

—

C₂²×C₂₉

yes

C₄×C₂₉

yes

—

C₄×C₂₉

#137

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

—

—

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₄×C₈

C₂×D₂₉

yes

characteristic

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1718

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

D₁₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₂₉

yes

characteristic

100

Q₈

—

116

—

101

Q₈

—

116

—

102

Q₈

—

116

—

103

Q₈

—

116

—

104

C₂×C₄

—

116

—

105

C₂×C₄

—

116

—

106

C₂×C₄

—

116

—

107

C₂×C₄

—

116

—

108

C₂×C₄

C₂×D₁₁₆

yes

characteristic

109

C₂×C₄

C₂×D₁₁₆

yes

characteristic

110

C₂×C₄

C₂×D₁₁₆

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

#11745236

yes

characteristic

115

C₄

—

232

—

116

C₄

—

232

—

117

C₄

—

232

—

118

C₄

—

232

—

119

C₄

#11745266

yes

—

120

C₄

#11745271

yes

—

121

C₄

#11745271

yes

—

122

C₂

#14271547

yes

characteristic

123

C₂

#14271557

yes

characteristic

124

C₂

#14271557

yes

characteristic

	subgroup	G/H
center	C₂²	#11745236
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#322	C₂
socle, prime radical	C₂²×C₂₉	#127
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1718
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#11745236

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#322

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
83. C₂₉	#1718	semidirect

H ≅ G/N

type

83. C₂₉

#1718

semidirect

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

subgroup	index
#14271568	2
#14271561	2
#14271514	2
C₂₉×#322	2
#1718	29

subgroup

index

C₂₉×#322

Subgroups — #16819138

Conjugacy classes of subgroups

Complements

Maximal subgroups