Group #16819608 — subgroups

Subgroups — #16819608

Order 3712.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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⋊#6597	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₂₉	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×C₈×C₂₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
11	C₂²×#6597	C₂²	1	2	yes	—
12	C₂₉×C₄⋊C₈	—	2	2	no	—
13	C₄⋊#6597	—	2	2	no	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
18	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	4	no	—
21	C₄²×C₂₉	D₄	1	2	yes	—
22	C₄²×C₂₉	Q₈	1	2	yes	—
23	C₄×Dic₂₉	—	2	2	no	—
24	C₄×Dic₂₉	—	2	2	no	—
25	C₄×Dic₂₉	—	2	2	no	—
26	C₄×Dic₂₉	—	2	4	no	—
27	C₄×Dic₂₉	C₈	1	4	yes	complemented
28	C₂×#6597	—	2	2	no	—
29	C₂×#6597	—	2	4	no	—
30	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₉	—	2	2	no	—
32	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₂₉	#41	1	2	yes	—
39	C₂×C₄×C₂₉	#41	1	2	yes	—
40	C₂×Dic₂₉	—	2	2	no	—
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	—	2	2	no	—
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
45	C₂×Dic₂₉	M₁₆	1	4	yes	—
46	C₈×C₂₉	—	4	2	no	—
47	#6597	—	4	2	no	—
48	#1831	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₂₉	#117	1	2	yes	—
51	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
52	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
53	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
54	C₄×C₂₉	—	2	2	no	—
55	C₄×C₂₉	C₄⋊C₈	1	4	yes	—
56	C₄×C₂₉	#124	1	1	yes	characteristic
57	C₄×C₂₉	#124	1	1	yes	characteristic
58	C₄×C₂₉	#125	1	2	yes	—
59	Dic₂₉	—	2	4	no	—
60	Dic₂₉	—	2	4	no	—
61	C₂×C₄⋊C₈	—	29	1	no	—
62	C₂×C₄⋊C₈	D₂₉	1	1	yes	characteristic
63	C₄³	—	29	1	no	—
64	#336	—	29	4	no	—
65	C₂×C₂₉	#382	1	1	yes	characteristic
66	C₂×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
67	C₂×C₂₉	#423	1	1	yes	characteristic
68	C₂×C₂₉	#431	1	2	yes	—
69	C₂×C₂₉	#432	1	2	yes	—
70	C₂²×C₈	—	29	2	no	—
71	C₂²×C₈	C₂×D₂₉	1	2	yes	—
72	C₂×C₄²	—	29	1	no	—
73	C₂×C₄²	—	29	2	no	—
74	C₂×C₄²	—	29	1	no	—
75	C₂×C₄²	—	29	2	no	—
76	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
77	C₄⋊C₈	—	2	2	no	—
78	C₄⋊C₈	—	58	2	no	—
79	C₂₉	#1831	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₄	—	29	2	no	—
81	C₂²×C₄	—	29	2	no	—
82	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
83	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
84	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
85	C₂×C₈	—	2	4	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	58	4	no	—
88	C₂×C₈	—	58	2	no	—
89	C₄²	—	29	4	no	—
90	C₄²	—	58	4	no	—
91	C₄²	—	58	2	no	—
92	C₄²	—	58	2	no	—
93	C₄²	—	58	2	no	—
94	C₄²	Dic₅₈	1	2	yes	—
95	C₄²	C₂²⋊D₂₉	1	2	yes	—
96	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	29	4	no	—
99	C₂×C₄	—	29	4	no	—
100	C₂×C₄	—	58	2	no	—
101	C₂×C₄	—	58	2	no	—
102	C₂×C₄	—	58	2	no	—
103	C₂×C₄	—	58	2	no	—
104	C₂×C₄	C₈×D₂₉	1	2	yes	—
105	C₂×C₄	#90772	1	2	yes	—
106	C₂×C₄	#90779	1	2	yes	—
107	C₂×C₄	#90779	1	2	yes	—
108	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
109	C₂×C₄	#90807	1	2	yes	—
110	C₂×C₄	#90809	1	2	yes	—
111	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
112	C₈	—	4	2	no	—
113	C₈	—	116	2	no	—
114	C₂²	#11745254	1	2	yes	—
115	C₂²	C₂×C₈×D₂₉	1	1	yes	characteristic
116	C₂²	C₂×#90772	1	1	yes	characteristic
117	C₂²	M₁₆×D₂₉	1	2	yes	—
118	C₂²	C₂×#90779	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	—	58	4	no	—
121	C₄	—	58	4	no	—
122	C₄	#11745162	1	4	yes	—
123	C₄	#11745252	1	2	yes	—
124	C₄	#11745298	1	1	yes	characteristic
125	C₄	#11745309	1	1	yes	characteristic
126	C₂	#14271028	1	1	yes	characteristic
127	C₂	C₂×#11745162	1	1	yes	characteristic
128	C₂	#14271186	1	1	yes	characteristic
129	C₂	#14271215	1	2	yes	—
130	C₂	#14271219	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6597

C₂

yes

maximal, characteristic

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal

C₂×C₂₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

C₂₉×C₄⋊C₈

—

C₄⋊#6597

—

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×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₈

yes

complemented

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₈×C₂₉

—

#6597

—

#1831

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

characteristic

C₂²×C₂₉

C₂×M₁₆

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₄⋊C₈

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

Dic₂₉

—

Dic₂₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₂₉

yes

characteristic

C₄³

—

#336

—

C₂×C₂₉

#382

yes

characteristic

C₂×C₂₉

C₂×C₄⋊C₈

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#432

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂₉

#1831

yes

characteristic, complemented, Sylow

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

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₅₈

yes

—

C₄²

C₂²⋊D₂₉

yes

—

C₂³

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₈×D₂₉

yes

—

105

C₂×C₄

#90772

yes

—

106

C₂×C₄

#90779

yes

—

107

C₂×C₄

#90779

yes

—

108

C₂×C₄

C₂×Dic₅₈

yes

characteristic

109

C₂×C₄

#90807

yes

—

110

C₂×C₄

#90809

yes

—

111

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

112

C₈

—

113

C₈

—

116

—

114

C₂²

#11745254

yes

—

115

C₂²

C₂×C₈×D₂₉

yes

characteristic

116

C₂²

C₂×#90772

yes

characteristic

117

C₂²

M₁₆×D₂₉

yes

—

118

C₂²

C₂×#90779

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11745162

yes

—

123

C₄

#11745252

yes

—

124

C₄

#11745298

yes

characteristic

125

C₄

#11745309

yes

characteristic

126

C₂

#14271028

yes

characteristic

127

C₂

C₂×#11745162

yes

characteristic

128

C₂

#14271186

yes

characteristic

129

C₂

#14271215

yes

—

130

C₂

#14271219

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₂₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₄⋊C₈	D₂₉
hypocenter	C₂₉	#1831
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator

C₂²×C₂₉

C₂²×C₈

Fitting

C₂×C₂₉×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×C₄⋊C₈

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
27. C₄×Dic₂₉	C₈	semidirect
79. C₂₉	#1831	semidirect

H ≅ G/N

type

27. C₄×Dic₂₉

C₈

semidirect

79. C₂₉

#1831

semidirect

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

subgroup	index
C₂×C₄⋊#6597	2
C₄²×Dic₂₉	2
#14270917	2
C₂×C₂₉×C₄⋊C₈	2
#1831	29

subgroup

index

C₂×C₄⋊#6597

C₄²×Dic₂₉

#14270917

C₂×C₂₉×C₄⋊C₈

#1831

Subgroups — #16819608

Conjugacy classes of subgroups

Complements

Maximal subgroups