Group #16820431 — subgroups

Subgroups — #16820431

Order 3712.

280 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 109 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×C₄×Dic₅₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745151	C₂	1	1	yes	maximal, characteristic
3	#14270917	C₂	1	4	yes	maximal
4	C₂×C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₅₈	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₂₉	C₄	1	1	yes	characteristic
9	C₂×#90779	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
11	C₂²×#6597	C₂²	1	2	yes	—
12	C₄×Dic₅₈	—	2	2	no	—
13	C₄×Dic₅₈	—	2	2	no	—
14	C₂₉×C₄⋊C₈	—	2	2	no	—
15	#11745151	—	2	2	no	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
21	C₂×Dic₅₈	—	2	2	no	—
22	C₂×Dic₅₈	—	2	4	no	—
23	C₂×C₈×C₂₉	—	2	2	no	—
24	C₂×C₈×C₂₉	—	2	4	no	—
25	C₄²×C₂₉	D₄	1	2	yes	—
26	C₄²×C₂₉	D₄	1	2	yes	—
27	C₄⋊Dic₂₉	—	2	2	no	—
28	#90779	—	2	4	no	—
29	C₄×Dic₂₉	—	2	2	no	—
30	C₄×Dic₂₉	—	2	2	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂×#6597	—	2	2	no	—
33	C₂×#6597	Q₈	1	4	yes	complemented
34	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	—	2	2	no	—
36	C₂×C₄×C₂₉	—	2	2	no	—
37	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
42	C₂×C₄×C₂₉	#41	1	2	yes	—
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	—	2	2	no	—
45	C₂×Dic₂₉	—	2	2	no	—
46	C₂×Dic₂₉	—	2	4	no	—
47	C₂×Dic₂₉	M₁₆	1	4	yes	—
48	Dic₅₈	—	2	8	no	—
49	C₈×C₂₉	—	4	2	no	—
50	#6597	—	2	4	no	—
51	#1985	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₂₉	C₄×Q₈	1	2	yes	—
54	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
55	C₂²×C₂₉	#131	1	2	yes	—
56	C₄×C₂₉	—	2	2	no	—
57	C₄×C₂₉	—	2	2	no	—
58	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
59	C₄×C₂₉	#124	1	1	yes	characteristic
60	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
61	Dic₂₉	—	2	4	no	—
62	Dic₂₉	—	4	2	no	—
63	C₂×C₄×Q₈	—	29	1	no	—
64	C₂×C₄⋊C₈	D₂₉	1	1	yes	characteristic
65	C₂×#97	—	29	1	no	—
66	#336	—	29	4	no	—
67	C₂×C₂₉	#391	1	1	yes	characteristic
68	C₂×C₂₉	#407	1	1	yes	characteristic
69	C₂×C₂₉	#408	1	1	yes	characteristic
70	C₂×C₂₉	#446	1	4	yes	—
71	C₂²×Q₈	—	29	1	no	—
72	C₂²×C₈	—	29	2	no	—
73	C₂²×C₈	C₂×D₂₉	1	2	yes	—
74	C₄×Q₈	—	58	2	no	—
75	C₄×Q₈	—	58	2	no	—
76	C₂×C₄⋊C₄	—	29	2	no	—
77	C₂×C₄⋊C₄	—	29	1	no	—
78	C₂×C₄²	—	29	2	no	—
79	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
80	C₄⋊C₈	—	2	2	no	—
81	#97	—	58	2	no	—
82	C₂₉	#1985	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	—	58	4	no	—
84	C₂×Q₈	—	58	2	no	—
85	C₂²×C₄	—	29	2	no	—
86	C₂²×C₄	—	29	2	no	—
87	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
88	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
89	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
90	C₂×C₈	—	2	4	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	29	4	no	—
93	C₂×C₈	—	58	2	no	—
94	C₂×C₈	—	58	2	no	—
95	C₄⋊C₄	—	58	4	no	—
96	C₄⋊C₄	—	58	2	no	—
97	C₄²	—	58	2	no	—
98	C₄²	—	58	2	no	—
99	C₄²	D₁₁₆	1	2	yes	—
100	C₄²	C₂²⋊D₂₉	1	2	yes	—
101	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
102	Q₈	—	58	8	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	29	4	no	—
106	C₂×C₄	—	58	2	no	—
107	C₂×C₄	—	58	2	no	—
108	C₂×C₄	—	58	2	no	—
109	C₂×C₄	—	58	4	no	—
110	C₂×C₄	#90781	1	2	yes	—
111	C₂×C₄	#90781	1	2	yes	—
112	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
113	C₂×C₄	#90807	1	2	yes	—
114	C₂×C₄	Q₈×D₂₉	1	2	yes	—
115	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
116	C₈	—	4	2	no	—
117	C₈	—	58	4	no	—
118	C₂²	#11745249	1	2	yes	—
119	C₂²	#11745263	1	2	yes	—
120	C₂²	M₁₆×D₂₉	1	2	yes	—
121	C₂²	C₂×#90781	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	2	no	—
124	C₄	—	58	4	no	—
125	C₄	—	116	2	no	—
126	C₄	#11745259	1	2	yes	—
127	C₄	#11745298	1	1	yes	characteristic
128	C₄	#11745306	1	1	yes	characteristic
129	C₂	#14271068	1	1	yes	characteristic
130	C₂	#14271126	1	1	yes	characteristic
131	C₂	#14271129	1	1	yes	characteristic
132	C₂	#14271292	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₅₈

C₂

yes

maximal, characteristic

C₂×#11745151

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal

C₂×C₂₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₄

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₄

yes

characteristic

C₂×#90779

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

C₄×Dic₅₈

—

C₄×Dic₅₈

—

C₂₉×C₄⋊C₈

—

#11745151

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

Q₈

yes

complemented

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

M₁₆

yes

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1985

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

—

C₂²×C₂₉

#131

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#124

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂×C₄×Q₈

—

C₂×C₄⋊C₈

D₂₉

yes

characteristic

C₂×#97

—

#336

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂²×Q₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

#97

—

C₂₉

#1985

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

characteristic

C₂²×C₄

C₄×D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

D₁₁₆

yes

—

100

C₄²

C₂²⋊D₂₉

yes

—

101

C₂³

C₂×C₄×D₂₉

yes

characteristic

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

#90781

yes

—

111

C₂×C₄

#90781

yes

—

112

C₂×C₄

C₂×D₁₁₆

yes

characteristic

113

C₂×C₄

#90807

yes

—

114

C₂×C₄

Q₈×D₂₉

yes

—

115

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

116

C₈

—

117

C₈

—

118

C₂²

#11745249

yes

—

119

C₂²

#11745263

yes

—

120

C₂²

M₁₆×D₂₉

yes

—

121

C₂²

C₂×#90781

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

116

—

126

C₄

#11745259

yes

—

127

C₄

#11745298

yes

characteristic

128

C₄

#11745306

yes

characteristic

129

C₂

#14271068

yes

characteristic

130

C₂

#14271126

yes

characteristic

131

C₂

#14271129

yes

characteristic

132

C₂

#14271292

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂×C₂₉×C₄⋊C₈	C₂
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₄⋊C₈	D₂₉
hypocenter	C₂₉	#1985
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator, socle, prime radical

C₂³×C₂₉

C₂²×C₄

Fitting

C₂×C₂₉×C₄⋊C₈

C₂

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×C₄⋊C₈

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
33. C₂×#6597	Q₈	semidirect
82. C₂₉	#1985	semidirect

H ≅ G/N

type

33. C₂×#6597

Q₈

semidirect

82. C₂₉

#1985

semidirect

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

subgroup	index
C₂×C₄×Dic₅₈	2
C₂×#11745151	2
#14270917	2
C₂×C₂₉×C₄⋊C₈	2
#1985	29

subgroup

index

C₂×C₄×Dic₅₈

C₂×#11745151

#14270917

C₂×C₂₉×C₄⋊C₈

#1985

Subgroups — #16820431

Conjugacy classes of subgroups

Complements

Maximal subgroups