Group #16818208 — subgroups

Subgroups — #16818208

Order 3712.

228 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 77 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	C₂×#11745231	C₂	1	1	yes	maximal, characteristic
2	#14271220	C₂	1	1	yes	maximal, characteristic
3	#14270908	C₂	1	4	yes	maximal, complemented
4	C₂₉×#432	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₅₈	—	2	1	no	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₂₉	—	2	1	no	—
8	C₂×C₄⋊Dic₂₉	C₄	1	2	yes	—
9	#11745231	—	2	1	no	—
10	#11745231	—	2	1	no	—
11	#11745231	C₄	1	2	yes	—
12	#11745231	C₂²	1	2	yes	—
13	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂₉×C₂²⋊C₈	—	2	1	no	—
15	C₂₉×#97	—	2	1	no	—
16	C₂²⋊#6597	—	2	1	no	—
17	C₄⋊#6597	C₂²	1	2	yes	—
18	#11745151	—	2	1	no	—
19	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
22	C₂²×Dic₂₉	—	2	2	no	—
23	C₂×Dic₅₈	—	2	2	no	—
24	C₂×Dic₅₈	—	2	2	no	—
25	C₂×Dic₅₈	—	4	4	no	—
26	C₂×C₈×C₂₉	—	2	2	no	—
27	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₂₉	D₄	1	1	yes	characteristic
29	C₄²×C₂₉	D₄	1	1	yes	characteristic
30	C₄²×C₂₉	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₂₉	—	2	2	no	—
32	C₄⋊Dic₂₉	—	2	2	no	—
33	C₄⋊Dic₂₉	—	2	2	no	—
34	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
35	C₂×#6597	—	2	2	no	—
36	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	—	2	2	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₂₉	—	2	4	no	—
47	C₂×Dic₂₉	—	4	4	no	—
48	Dic₅₈	—	4	4	no	—
49	Dic₅₈	—	4	4	no	—
50	C₈×C₂₉	—	4	2	no	—
51	#6597	—	4	2	no	—
52	#1556	—	29	1	no	maximal, Sylow
53	C₂²×C₂₉	—	2	1	no	—
54	C₂²×C₂₉	—	2	1	no	—
55	C₂²×C₂₉	#101	1	2	yes	—
56	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₂₉	—	2	1	no	—
58	C₄×C₂₉	—	2	1	no	—
59	C₄×C₂₉	—	2	1	no	—
60	C₄×C₂₉	—	2	1	no	—
61	C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
62	C₄×C₂₉	#137	1	2	yes	—
63	Dic₂₉	—	4	4	no	—
64	C₂×C₄⋊Q₈	—	29	1	no	—
65	#432	—	29	1	no	—
66	#432	D₂₉	1	1	yes	characteristic
67	#332	—	29	4	no	—
68	C₂×C₂₉	—	2	2	no	—
69	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
70	C₂×C₂₉	#418	1	1	yes	characteristic
71	C₂×C₂₉	#419	1	1	yes	characteristic
72	C₂²×Q₈	—	58	1	no	—
73	C₄⋊Q₈	—	29	2	no	—
74	C₄⋊Q₈	—	29	2	no	—
75	C₄⋊Q₈	—	58	1	no	—
76	C₄⋊Q₈	—	58	1	no	—
77	C₂×C₄⋊C₄	—	29	2	no	—
78	C₂×C₄⋊C₄	—	58	1	no	—
79	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
80	C₄⋊C₈	—	29	2	no	—
81	C₄⋊C₈	C₂×D₂₉	1	2	yes	—
82	C₂²⋊C₈	—	2	1	no	—
83	C₂²⋊C₈	—	58	1	no	—
84	#97	—	2	1	no	—
85	#97	—	58	1	no	—
86	C₂₉	#1556	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	58	2	no	—
88	C₂×Q₈	—	58	2	no	—
89	C₂×Q₈	—	116	4	no	—
90	C₂²×C₄	—	58	2	no	—
91	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
92	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
93	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	58	2	no	—
96	C₄⋊C₄	—	29	4	no	—
97	C₄⋊C₄	—	58	2	no	—
98	C₄⋊C₄	—	58	2	no	—
99	C₄⋊C₄	—	58	2	no	—
100	C₄²	C₄×D₂₉	1	1	yes	characteristic
101	C₄²	D₁₁₆	1	1	yes	characteristic
102	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
103	C₄²	C₂²×D₂₉	1	1	yes	characteristic
104	C₂³	#90781	1	1	yes	characteristic
105	Q₈	—	116	4	no	—
106	Q₈	—	116	4	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	58	4	no	—
111	C₂×C₄	—	116	4	no	—
112	C₂×C₄	#90781	1	1	yes	characteristic
113	C₂×C₄	#90781	1	1	yes	characteristic
114	C₂×C₄	#90781	1	1	yes	characteristic
115	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
116	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
118	C₈	—	4	2	no	—
119	C₈	—	116	2	no	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	#11745172	1	2	yes	—
123	C₂²	C₂×#90781	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	2	1	no	—
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	116	4	no	—
129	C₄	#11745270	1	2	yes	—
130	C₄	#11745313	1	2	yes	—
131	C₂	—	2	2	no	—
132	C₂	C₂×#11745172	1	1	yes	characteristic
133	C₂	#14271169	1	1	yes	characteristic
134	C₂	#14271171	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745231

C₂

yes

maximal, characteristic

#14271220

C₂

yes

maximal, characteristic

#14270908

C₂

yes

maximal, complemented

C₂₉×#432

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

—

C₂×C₄⋊Dic₂₉

C₄

yes

—

#11745231

—

#11745231

—

#11745231

C₄

yes

—

#11745231

C₂²

yes

—

C₂₉×C₄⋊C₈

C₂²

yes

—

C₂₉×C₂²⋊C₈

—

C₂₉×#97

—

C₂²⋊#6597

—

C₄⋊#6597

C₂²

yes

—

#11745151

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×Dic₂₉

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₂×#6597

—

C₂³×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1556

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#101

yes

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

C₂×C₄⋊Q₈

—

#432

—

#432

D₂₉

yes

characteristic

#332

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂×D₂₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₂₉

#1556

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

116

—

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

characteristic

C₂²×C₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄²

C₄×D₂₉

yes

characteristic

101

C₄²

D₁₁₆

yes

characteristic

102

C₄²

C₂²⋊D₂₉

yes

characteristic

103

C₄²

C₂²×D₂₉

yes

characteristic

104

C₂³

#90781

yes

characteristic

105

Q₈

—

116

—

106

Q₈

—

116

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

116

—

112

C₂×C₄

#90781

yes

characteristic

113

C₂×C₄

#90781

yes

characteristic

114

C₂×C₄

#90781

yes

characteristic

115

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

116

C₂×C₄

C₂×D₁₁₆

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

118

C₈

—

119

C₈

—

116

—

120

C₂²

—

121

C₂²

—

122

C₂²

#11745172

yes

—

123

C₂²

C₂×#90781

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

116

—

129

C₄

#11745270

yes

—

130

C₄

#11745313

yes

—

131

C₂

—

132

C₂

C₂×#11745172

yes

characteristic

133

C₂

#14271169

yes

characteristic

134

C₂

#14271171

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#90781
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#432	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#432	D₂₉
hypocenter	C₂₉	#1556
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₂×#90781

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#432

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₂₉

C₂²⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
3. #14270908	C₂	semidirect
86. C₂₉	#1556	semidirect

H ≅ G/N

type

3. #14270908

C₂

semidirect

86. C₂₉

#1556

semidirect

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

subgroup	index
C₂×#11745231	2
#14271220	2
#14270908	2
C₂₉×#432	2
#1556	29

subgroup

index

C₂₉×#432

Subgroups — #16818208

Conjugacy classes of subgroups

Complements

Maximal subgroups