Group #16817793 — subgroups

Subgroups — #16817793

Order 3712.

178 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14271214	C₂	1	1	yes	maximal, characteristic
2	#14271214	C₂	1	1	yes	maximal, characteristic
3	#14271214	C₂	1	1	yes	maximal, characteristic
4	#14270885	C₂	1	1	yes	maximal, characteristic, complemented
5	#14270884	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#6597	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×D₂₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745168	C₄	1	2	yes	—
13	#11745168	C₄	1	2	yes	—
14	#11745168	C₄	1	2	yes	—
15	#11745162	C₄	1	2	yes	—
16	#11745162	C₄	1	2	yes	—
17	#11745162	C₄	1	2	yes	—
18	C₄×#6597	C₂²	1	1	yes	characteristic
19	C₄×#6597	C₂²	1	1	yes	characteristic
20	C₄×#6597	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
27	C₄²×C₂₉	C₂³	1	1	yes	characteristic
28	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
31	C₂×#6597	C₂×C₄	1	2	yes	—
32	C₂×#6597	C₂×C₄	1	2	yes	—
33	C₂×#6597	C₂×C₄	1	2	yes	—
34	C₂²×D₂₉	C₄²	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
39	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
40	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
41	C₄×D₂₉	—	2	2	no	—
42	C₄×D₂₉	—	2	2	no	—
43	C₄×D₂₉	—	2	2	no	—
44	C₈×C₂₉	—	2	2	no	—
45	C₈×C₂₉	—	2	2	no	—
46	C₈×C₂₉	—	2	2	no	—
47	#6597	—	2	2	no	—
48	#6597	—	2	2	no	—
49	#6597	—	2	2	no	—
50	#1454	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
52	C₂×D₂₉	—	2	1	no	—
53	C₂×D₂₉	—	2	1	no	—
54	C₂×D₂₉	—	2	1	no	—
55	C₄×C₂₉	#131	1	2	yes	—
56	C₄×C₂₉	#131	1	2	yes	—
57	C₄×C₂₉	#131	1	2	yes	—
58	Dic₂₉	—	2	1	no	—
59	Dic₂₉	—	2	1	no	—
60	Dic₂₉	—	2	1	no	—
61	#431	—	29	1	no	—
62	#431	—	29	1	no	—
63	#431	—	29	1	no	—
64	#322	—	29	1	no	—
65	#322	—	29	1	no	—
66	#322	D₂₉	1	1	yes	characteristic, complemented
67	C₈²	—	29	1	no	—
68	C₂×C₂₉	#405	1	1	yes	characteristic
69	C₂×C₂₉	#405	1	1	yes	characteristic
70	C₂×C₂₉	#405	1	1	yes	characteristic
71	D₂₉	—	4	1	no	—
72	C₂×C₄²	—	29	1	no	—
73	C₄⋊C₈	—	29	2	no	—
74	C₄⋊C₈	—	29	2	no	—
75	C₄⋊C₈	—	29	2	no	—
76	C₂²⋊C₈	—	29	2	no	—
77	C₂²⋊C₈	—	29	2	no	—
78	C₂²⋊C₈	—	29	2	no	—
79	C₄×C₈	—	29	1	no	—
80	C₄×C₈	—	29	1	no	—
81	C₄×C₈	—	29	1	no	—
82	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
83	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
84	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
85	C₂₉	#1454	1	1	yes	characteristic, complemented, Sylow
86	C₂²×C₄	—	29	1	no	—
87	C₂²×C₄	—	29	1	no	—
88	C₂²×C₄	—	29	1	no	—
89	C₂×C₈	—	29	2	no	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	29	2	no	—
92	C₂×C₈	C₄×D₂₉	1	2	yes	—
93	C₂×C₈	C₄×D₂₉	1	2	yes	—
94	C₂×C₈	C₄×D₂₉	1	2	yes	—
95	C₄²	—	29	1	no	—
96	C₄²	—	29	1	no	—
97	C₄²	—	29	1	no	—
98	C₄²	C₂²×D₂₉	1	1	yes	characteristic
99	C₂³	—	29	1	no	—
100	C₂×C₄	—	29	1	no	—
101	C₂×C₄	—	29	1	no	—
102	C₂×C₄	—	29	1	no	—
103	C₂×C₄	—	58	2	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	—	58	2	no	—
106	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
107	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
108	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
109	C₈	—	2	2	no	—
110	C₈	—	2	2	no	—
111	C₈	—	2	2	no	—
112	C₈	—	58	2	no	—
113	C₈	—	58	2	no	—
114	C₈	—	58	2	no	—
115	C₂²	—	58	1	no	—
116	C₂²	—	58	1	no	—
117	C₂²	—	58	1	no	—
118	C₂²	C₄²×D₂₉	1	1	yes	characteristic
119	C₄	—	58	1	no	—
120	C₄	—	58	1	no	—
121	C₄	—	58	1	no	—
122	C₄	#11745263	1	2	yes	—
123	C₄	#11745269	1	2	yes	—
124	C₄	#11745269	1	2	yes	—
125	C₂	—	116	1	no	—
126	C₂	#14271117	1	1	yes	characteristic
127	C₂	#14271120	1	1	yes	characteristic
128	C₂	#14271120	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271214

C₂

yes

maximal, characteristic

#14271214

C₂

yes

maximal, characteristic

#14271214

C₂

yes

maximal, characteristic

#14270885

C₂

yes

maximal, characteristic, complemented

#14270884

C₂

yes

maximal, characteristic, complemented

C₈×#6597

C₂

yes

maximal, characteristic, complemented

C₂₉×#322

C₂

yes

maximal, characteristic, complemented

C₄²×D₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745168

C₄

yes

—

#11745168

C₄

yes

—

#11745168

C₄

yes

—

#11745162

C₄

yes

—

#11745162

C₄

yes

—

#11745162

C₄

yes

—

C₄×#6597

C₂²

yes

characteristic

C₄×#6597

C₂²

yes

characteristic

C₄×#6597

C₂²

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂²×D₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄²

yes

characteristic

C₂×Dic₂₉

C₄²

yes

characteristic

C₂×Dic₂₉

C₄²

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

—

—

—

—

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

#131

yes

—

C₄×C₂₉

#131

yes

—

C₄×C₂₉

#131

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

—

D₂₉

yes

characteristic, complemented

C₈²

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₄×C₈

C₂×D₂₉

yes

characteristic

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1454

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

—

C₂×C₈

C₄×D₂₉

yes

—

C₂×C₈

C₄×D₂₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

107

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

108

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

C₄²×D₂₉

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11745263

yes

—

123

C₄

#11745269

yes

—

124

C₄

#11745269

yes

—

125

C₂

—

116

—

126

C₂

#14271117

yes

characteristic

127

C₂

#14271120

yes

characteristic

128

C₂

#14271120

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₂₉×#322	C₂
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1454
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×D₂₉

commutator, socle

C₂²×C₂₉

C₂×C₄²

Fitting

C₂₉×#322

C₂

prime radical

C₂²×D₂₉

C₄²

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
4. #14270885	C₂	semidirect
5. #14270884	C₂	semidirect
6. C₈×#6597	C₂	semidirect
7. C₂₉×#322	C₂	semidirect
66. #322	D₂₉	semidirect
85. C₂₉	#1454	semidirect

H ≅ G/N

type

4. #14270885

C₂

semidirect

5. #14270884

C₂

semidirect

6. C₈×#6597

C₂

semidirect

7. C₂₉×#322

C₂

semidirect

66. #322

D₂₉

semidirect

85. C₂₉

#1454

semidirect

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

subgroup	index
#14271214	2
#14270885	2
#14270884	2
C₈×#6597	2
C₂₉×#322	2
#1454	29

subgroup

index

C₂₉×#322

Subgroups — #16817793

Conjugacy classes of subgroups

Complements

Maximal subgroups