Group #16830041 — subgroups

Subgroups — #16830041

Order 3712.

348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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	#14271720	C₂	1	1	yes	maximal, characteristic
2	#14271573	C₂	1	4	yes	maximal, complemented
3	#14271562	C₂	1	4	yes	maximal, complemented
4	#14271203	C₂	1	4	yes	maximal
5	C₄×#90777	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×#125	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#125	—	2	2	no	—
8	C₂₉×#125	C₂²	1	2	yes	—
9	C₂₉×#125	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	#11745288	C₂²	1	2	yes	—
14	#11745286	—	2	2	no	—
15	C₂×#90777	C₂²	1	2	yes	—
16	#11745232	C₂²	1	2	yes	—
17	#11745231	C₂²	1	2	yes	—
18	C₄×Dic₅₈	—	2	2	no	—
19	#11745156	C₂²	1	8	yes	—
20	#11745155	C₂²	1	8	yes	—
21	#11745151	C₂²	1	2	yes	—
22	C₄×#6597	C₂²	1	2	yes	—
23	C₂²×C₄×C₂₉	—	2	2	no	—
24	C₂²×C₄×C₂₉	D₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂×Dic₅₈	—	2	2	no	—
27	C₄⋊C₄×C₂₉	—	2	4	no	—
28	C₄⋊C₄×C₂₉	—	2	4	no	—
29	C₄⋊C₄×C₂₉	—	2	2	no	—
30	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
31	C₄²×C₂₉	D₄	1	2	yes	—
32	C₄²×C₂₉	C₂³	1	1	yes	characteristic
33	C₄²×C₂₉	C₂³	1	1	yes	characteristic
34	C₂²⋊Dic₂₉	—	2	2	no	—
35	C₄⋊Dic₂₉	—	2	2	no	—
36	C₄⋊Dic₂₉	C₂³	1	4	yes	—
37	#90779	—	2	4	no	—
38	C₄×Dic₂₉	—	2	2	no	—
39	#90777	Q₈	1	8	yes	complemented
40	C₂×#6597	C₂³	1	4	yes	—
41	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	—	2	4	no	—
43	C₂×C₄×C₂₉	—	4	2	no	—
44	C₂×C₄×C₂₉	—	4	4	no	—
45	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
49	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₂₉	—	2	4	no	—
51	Dic₅₈	—	4	4	no	—
52	#6597	C₂×Q₈	1	8	yes	—
53	#3166	—	29	1	no	maximal, Sylow
54	C₂²×C₂₉	—	2	2	no	—
55	C₂²×C₂₉	C₄⋊Q₈	1	2	yes	—
56	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
57	C₄×C₂₉	—	2	2	no	—
58	C₄×C₂₉	—	2	2	no	—
59	C₄×C₂₉	—	4	4	no	—
60	C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
61	C₄×C₂₉	C₂²×Q₈	1	2	yes	—
62	Dic₂₉	—	4	4	no	—
63	#533	—	29	1	no	—
64	C₂×#125	D₂₉	1	1	yes	characteristic
65	#501	—	29	4	no	—
66	#499	—	29	4	no	—
67	#428	—	29	4	no	—
68	C₄×M₁₆	—	29	1	no	—
69	C₂×C₂₉	—	2	2	no	—
70	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₂₉	#575	1	2	yes	—
72	C₂×M₁₆	—	29	2	no	—
73	C₄⋊Q₈	—	29	2	no	—
74	#125	—	2	2	no	—
75	#125	—	29	2	no	—
76	#125	C₂×D₂₉	1	2	yes	—
77	#125	C₂×D₂₉	1	2	yes	—
78	C₂²⋊Q₈	—	58	2	no	—
79	C₄×Q₈	—	58	2	no	—
80	#117	—	29	2	no	—
81	C₂×C₄⋊C₄	—	2	2	no	—
82	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
83	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
84	#107	—	29	8	no	—
85	#106	—	29	8	no	—
86	#97	—	29	2	no	—
87	C₄×C₈	—	29	2	no	—
88	C₂₉	#3166	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	58	2	no	—
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
92	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
93	M₁₆	—	29	8	no	—
94	C₂×C₈	—	29	4	no	—
95	C₄⋊C₄	—	2	4	no	—
96	C₄⋊C₄	—	2	4	no	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	29	4	no	—
99	C₄⋊C₄	—	58	4	no	—
100	C₄⋊C₄	—	58	2	no	—
101	C₄⋊C₄	C₂²×D₂₉	1	4	yes	—
102	C₂²⋊C₄	—	58	2	no	—
103	C₄²	—	58	2	no	—
104	C₄²	C₂²⋊D₂₉	1	2	yes	—
105	C₄²	C₂²×D₂₉	1	1	yes	characteristic
106	C₄²	C₂²×D₂₉	1	1	yes	characteristic
107	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
108	Q₈	—	116	4	no	—
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	4	4	no	—
112	C₂×C₄	—	58	4	no	—
113	C₂×C₄	Q₈×D₂₉	1	4	yes	—
114	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
115	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
116	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
117	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
118	C₈	—	29	8	no	—
119	C₂²	—	2	2	no	—
120	C₂²	#11745306	1	2	yes	—
121	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	2	no	—
124	C₄	—	4	4	no	—
125	C₄	—	116	4	no	—
126	C₄	#11745306	1	2	yes	—
127	C₄	C₂×Q₈×D₂₉	1	2	yes	—
128	C₂	—	2	2	no	—
129	C₂	C₂×#11745306	1	1	yes	characteristic
130	C₂	#14271961	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271720

C₂

yes

maximal, characteristic

#14271573

C₂

yes

maximal, complemented

#14271562

C₂

yes

maximal, complemented

#14271203

C₂

yes

maximal

C₄×#90777

C₂

yes

maximal, characteristic

C₂×C₂₉×#125

C₂

yes

maximal, characteristic

C₂₉×#125

—

C₂₉×#125

C₂²

yes

—

C₂₉×#125

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

—

#11745286

—

C₂×#90777

C₂²

yes

—

#11745232

C₂²

yes

—

#11745231

C₂²

yes

—

C₄×Dic₅₈

—

#11745156

C₂²

yes

—

#11745155

C₂²

yes

—

#11745151

C₂²

yes

—

C₄×#6597

C₂²

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

#90779

—

C₄×Dic₂₉

—

#90777

Q₈

yes

complemented

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

#6597

C₂×Q₈

yes

—

#3166

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₄⋊Q₈

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄⋊Q₈

yes

—

C₄×C₂₉

C₂²×Q₈

yes

—

Dic₂₉

—

#533

—

C₂×#125

D₂₉

yes

—

—

—

C₄×M₁₆

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₉

#575

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

—

#125

C₂×D₂₉

yes

—

#125

C₂×D₂₉

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

C₄×C₈

—

C₂₉

#3166

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂²×D₂₉

yes

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

C₂²⋊D₂₉

yes

—

105

C₄²

C₂²×D₂₉

yes

characteristic

106

C₄²

C₂²×D₂₉

yes

characteristic

107

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

108

Q₈

—

116

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

Q₈×D₂₉

yes

—

114

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

115

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

116

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

117

C₂×C₄

C₂³×D₂₉

yes

characteristic

118

C₈

—

119

C₂²

—

120

C₂²

#11745306

yes

—

121

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

116

—

126

C₄

#11745306

yes

—

127

C₄

C₂×Q₈×D₂₉

yes

—

128

C₂

—

129

C₂

C₂×#11745306

yes

characteristic

130

C₂

#14271961

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂×C₂₉×#125	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂³×C₂₉	C₂×D₄
hypercenter	C₂×#125	D₂₉
hypocenter	C₂₉	#3166
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₂₉

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂×C₂₉×#125

C₂

socle

C₂²×C₂₉

C₂²×D₄

prime radical

C₂³×C₂₉

C₂×D₄

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #14271573	C₂	semidirect
3. #14271562	C₂	semidirect
39. #90777	Q₈	semidirect
88. C₂₉	#3166	semidirect

H ≅ G/N

type

2. #14271573

C₂

semidirect

3. #14271562

C₂

semidirect

39. #90777

Q₈

semidirect

88. C₂₉

#3166

semidirect

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

subgroup	index
#14271720	2
#14271573	2
#14271562	2
#14271203	2
C₄×#90777	2
C₂×C₂₉×#125	2
#3166	29

subgroup

index

C₂×C₂₉×#125

Subgroups — #16830041

Conjugacy classes of subgroups

Complements

Maximal subgroups