Group #16834698 — subgroups

Subgroups — #16834698

Order 3712.

212 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 104 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	#14272182	C₂	1	1	yes	maximal, characteristic
2	C₄×D₂₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#6599⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₈×#6599	C₂	1	2	yes	maximal, complemented
5	#14271215	C₂	1	1	yes	maximal, characteristic
6	C₂×D₂₉⋊C₈	C₄	1	2	yes	—
7	C₄²×D₂₉	C₂²	1	1	yes	characteristic
8	#11745219	C₄	1	2	yes	—
9	C₄⋊#6599	C₄	1	2	yes	—
10	C₄×#6599	C₄	1	2	yes	—
11	C₄×#6599	C₂²	1	1	yes	characteristic
12	C₄×#6599	C₂²	1	2	yes	—
13	C₄×#6599	C₂²	1	1	yes	characteristic
14	C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic
15	#11745168	C₄	1	2	yes	—
16	C₈×Dic₂₉	C₂²	1	2	yes	—
17	C₄⋊#6597	C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×#6599	C₂×C₄	1	4	yes	—
22	C₂×#6599	C₂×C₄	1	2	yes	—
23	C₂×#6599	C₂×C₄	1	2	yes	—
24	D₂₉⋊C₈	C₈	1	8	yes	complemented
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
30	C₂×#6597	C₂×C₄	1	2	yes	—
31	C₂²×D₂₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₂₉	C₄²	1	1	yes	characteristic
36	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₄×D₂₉	—	2	1	no	—
39	C₄×D₂₉	—	2	1	no	—
40	C₄×D₂₉	—	2	2	no	—
41	C₄×D₂₉	C₂×C₈	1	4	yes	—
42	#6599	—	2	4	no	—
43	#6599	C₂×C₈	1	4	yes	—
44	#6599	C₂×C₈	1	4	yes	—
45	C₈×C₂₉	—	2	2	no	—
46	#6597	—	2	2	no	—
47	#1450	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
49	C₂×D₂₉	—	2	1	no	—
50	C₂×D₂₉	—	2	1	no	—
51	C₂×D₂₉	C₄×C₈	1	2	yes	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	C₄×C₈	1	2	yes	—
54	C₄×C₂₉	#131	1	1	yes	characteristic
55	C₄×C₂₉	#131	1	1	yes	characteristic
56	Dic₂₉	—	2	1	no	—
57	Dic₂₉	C₂²×C₈	1	2	yes	—
58	Dic₂₉	#131	1	2	yes	—
59	#431	—	29	1	no	—
60	#431	—	29	1	no	—
61	C₂×C₄×C₈	—	29	1	no	—
62	#322	—	29	2	no	—
63	C₈²	—	29	2	no	—
64	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
65	C₂×C₂₉	#405	1	1	yes	characteristic
66	C₂×C₂₉	#405	1	1	yes	characteristic
67	D₂₉	—	2	2	no	—
68	C₂²×C₈	—	29	2	no	—
69	C₂×C₄²	—	29	1	no	—
70	C₄⋊C₈	—	29	2	no	—
71	C₄⋊C₈	—	29	1	no	—
72	C₄⋊C₈	#1181	1	1	yes	characteristic
73	C₂²⋊C₈	—	29	2	no	—
74	C₂²⋊C₈	—	29	2	no	—
75	C₄×C₈	—	29	1	no	—
76	C₄×C₈	—	29	2	no	—
77	C₄×C₈	—	29	1	no	—
78	C₄×C₈	—	29	2	no	—
79	C₄×C₈	—	29	2	no	—
80	C₂₉	#1450	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	29	1	no	—
82	C₂²×C₄	—	29	1	no	—
83	C₂²×C₄	—	29	1	no	—
84	C₂×C₈	—	29	2	no	—
85	C₂×C₈	—	29	2	no	—
86	C₂×C₈	—	29	8	no	—
87	C₂×C₈	—	29	4	no	—
88	C₂×C₈	—	29	2	no	—
89	C₂×C₈	C₂×#1181	1	2	yes	—
90	C₄²	—	29	1	no	—
91	C₄²	—	29	1	no	—
92	C₄²	—	29	1	no	—
93	C₄²	C₂×#1181	1	1	yes	characteristic
94	C₂³	—	29	1	no	—
95	C₂×C₄	—	29	1	no	—
96	C₂×C₄	—	29	1	no	—
97	C₂×C₄	—	29	4	no	—
98	C₂×C₄	—	29	1	no	—
99	C₂×C₄	—	58	2	no	—
100	C₂×C₄	—	58	1	no	—
101	C₂×C₄	—	58	1	no	—
102	C₂×C₄	C₄×#1181	1	1	yes	characteristic
103	C₂×C₄	C₄×#1181	1	1	yes	characteristic
104	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	29	4	no	—
107	C₈	—	29	4	no	—
108	C₈	—	58	4	no	—
109	C₈	—	58	2	no	—
110	C₂²	—	29	2	no	—
111	C₂²	—	58	1	no	—
112	C₂²	—	58	1	no	—
113	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	29	2	no	—
116	C₄	—	29	2	no	—
117	C₄	—	58	1	no	—
118	C₄	C₈×#1181	1	2	yes	—
119	C₄	#11745346	1	1	yes	characteristic
120	C₄	#11745348	1	1	yes	characteristic
121	C₂	—	58	2	no	—
122	C₂	C₂×C₈×#1181	1	1	yes	characteristic
123	C₂	#14272128	1	1	yes	characteristic
124	C₂	#14272129	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272182

C₂

yes

maximal, characteristic

C₄×D₂₉⋊C₈

C₂

yes

maximal, characteristic

#6599⋊C₈

C₂

yes

maximal, complemented

C₈×#6599

C₂

yes

maximal, complemented

#14271215

C₂

yes

maximal, characteristic

C₂×D₂₉⋊C₈

C₄

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745219

C₄

yes

—

C₄⋊#6599

C₄

yes

—

C₄×#6599

C₄

yes

—

C₄×#6599

C₂²

yes

characteristic

C₄×#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₄

yes

characteristic

#11745168

C₄

yes

—

C₈×Dic₂₉

C₂²

yes

—

C₄⋊#6597

C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×#6599

C₂×C₄

yes

—

C₂×#6599

C₂×C₄

yes

—

C₂×#6599

C₂×C₄

yes

—

D₂₉⋊C₈

C₈

yes

complemented

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂³

yes

characteristic

C₂×#6597

C₂×C₄

yes

—

C₂²×D₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄²

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

C₂×C₈

yes

—

#6599

—

#6599

C₂×C₈

yes

—

#6599

C₂×C₈

yes

—

C₈×C₂₉

—

#6597

—

#1450

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

C₄×C₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄×C₈

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

C₂²×C₈

yes

—

Dic₂₉

#131

yes

—

#431

—

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂×C₂₉

C₂×C₄×C₈

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#1181

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#1450

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄×#1181

yes

characteristic

103

C₂×C₄

C₄×#1181

yes

characteristic

104

C₂×C₄

C₂²×#1181

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

—

109

C₈

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×C₄×#1181

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

C₈×#1181

yes

—

119

C₄

#11745346

yes

characteristic

120

C₄

#11745348

yes

characteristic

121

C₂

—

122

C₂

C₂×C₈×#1181

yes

characteristic

123

C₂

#14272128

yes

characteristic

124

C₂

#14272129

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator	C₂×C₂₉	C₂×C₄×C₈
Fitting	C₂₉×C₄⋊C₈	C₄
socle	C₂²×C₂₉	C₂×C₄²
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₄⋊C₈	#1181
hypocenter	C₂₉	#1450
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#1181

commutator

C₂×C₂₉

C₂×C₄×C₈

Fitting

C₂₉×C₄⋊C₈

C₄

socle

C₂²×C₂₉

C₂×C₄²

prime radical

C₂²×D₂₉

C₄²

cosocle

C₄×Dic₂₉

C₂³

C₄⋊C₈

C₂₉

G ▷ C₂×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
3. #6599⋊C₈	C₂	semidirect
4. C₈×#6599	C₂	semidirect
24. D₂₉⋊C₈	C₈	semidirect
80. C₂₉	#1450	semidirect

H ≅ G/N

type

3. #6599⋊C₈

C₂

semidirect

4. C₈×#6599

C₂

semidirect

24. D₂₉⋊C₈

C₈

semidirect

80. C₂₉

#1450

semidirect

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

subgroup	index
#14272182	2
C₄×D₂₉⋊C₈	2
#6599⋊C₈	2
C₈×#6599	2
#14271215	2
#1450	29

subgroup

index

C₄×D₂₉⋊C₈

Subgroups — #16834698

Conjugacy classes of subgroups

Complements

Maximal subgroups