Group #16817388 — subgroups

Subgroups — #16817388

Order 3712.

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

normal subgroups only

This group has 148 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	#14271187	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#6597	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#431	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×#90777	—	2	1	no	—
6	C₂²×#6597	—	2	1	no	—
7	C₂₉×C₄⋊C₈	—	2	1	no	—
8	C₂₉×C₂²⋊C₈	C₄	1	2	yes	—
9	C₄×C₈×C₂₉	—	2	1	no	—
10	C₄⋊#6597	—	2	1	no	—
11	C₄⋊#6597	—	2	1	no	—
12	C₄⋊#6597	C₄	1	2	yes	—
13	C₄⋊#6597	C₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₂₉	—	2	2	no	—
18	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₉	D₄	1	1	yes	characteristic
21	C₄²×C₂₉	D₄	1	1	yes	characteristic
22	#90777	—	4	1	no	—
23	#90777	—	4	1	no	—
24	C₂×#6597	—	2	2	no	—
25	C₂×#6597	—	2	2	no	—
26	C₂×#6597	—	4	1	no	—
27	C₂×#6597	—	4	1	no	—
28	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	—	2	2	no	—
30	C₂×C₄×C₂₉	—	4	1	no	—
31	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
39	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
40	C₂×C₄×C₂₉	Q₁₆	1	1	yes	characteristic
41	C₈×C₂₉	—	4	2	no	—
42	#6597	—	4	2	no	—
43	#6597	—	4	2	no	—
44	#1301	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	—	2	1	no	—
46	C₂²×C₂₉	—	2	1	no	—
47	C₂²×C₂₉	#95	1	1	yes	characteristic
48	C₂²×C₂₉	#106	1	1	yes	characteristic
49	C₂²×C₂₉	#107	1	1	yes	characteristic
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	—	2	1	no	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	#102	1	1	yes	characteristic
54	C₄×C₂₉	#102	1	1	yes	characteristic
55	C₄×C₂₉	#103	1	1	yes	characteristic
56	C₄×C₂₉	#103	1	1	yes	characteristic
57	C₄×C₂₉	#108	1	2	yes	—
58	#431	D₂₉	1	1	yes	characteristic
59	#423	—	29	1	no	—
60	C₂×C₄⋊C₈	—	29	1	no	—
61	C₂×C₂₉	—	2	1	no	—
62	C₂×C₂₉	—	2	1	no	—
63	C₂×C₂₉	#340	1	1	yes	characteristic
64	C₂×C₂₉	#341	1	1	yes	characteristic
65	C₂×C₂₉	#344	1	1	yes	characteristic
66	C₂×M₁₆	—	58	1	no	—
67	C₂²×C₈	—	58	1	no	—
68	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
69	C₄⋊C₈	—	2	1	no	—
70	C₄⋊C₈	—	29	2	no	—
71	C₄⋊C₈	—	29	2	no	—
72	C₄⋊C₈	—	58	1	no	—
73	C₄⋊C₈	—	58	1	no	—
74	C₂²⋊C₈	Dic₂₉	1	2	yes	—
75	C₄×C₈	—	2	1	no	—
76	C₂₉	#1301	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	Dic₅₈	1	1	yes	characteristic
78	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
79	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
80	M₁₆	—	116	1	no	—
81	M₁₆	—	116	1	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	58	2	no	—
84	C₂×C₈	—	58	2	no	—
85	C₂×C₈	—	116	1	no	—
86	C₂×C₈	—	116	1	no	—
87	C₄²	C₄×D₂₉	1	1	yes	characteristic
88	C₄²	C₄×D₂₉	1	1	yes	characteristic
89	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
90	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
91	C₂³	C₄⋊Dic₂₉	1	1	yes	characteristic
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	#90773	1	1	yes	characteristic
95	C₂×C₄	#90773	1	1	yes	characteristic
96	C₂×C₄	D₂₃₂	1	1	yes	characteristic
97	C₂×C₄	Dic₁₁₆	1	1	yes	characteristic
98	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
99	C₂×C₄	#90779	1	1	yes	characteristic
100	C₂×C₄	#90779	1	1	yes	characteristic
101	C₂×C₄	#90781	1	1	yes	characteristic
102	C₂×C₄	#90781	1	1	yes	characteristic
103	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
104	C₈	—	4	2	no	—
105	C₈	—	116	2	no	—
106	C₈	—	116	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	#11745165	1	1	yes	characteristic
110	C₂²	#11745166	1	1	yes	characteristic
111	C₂²	#11745179	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	#11745164	1	1	yes	characteristic
116	C₄	#11745164	1	1	yes	characteristic
117	C₄	#11745169	1	1	yes	characteristic
118	C₄	#11745169	1	1	yes	characteristic
119	C₄	#11745170	1	2	yes	—
120	C₂	—	2	1	no	—
121	C₂	—	2	1	no	—
122	C₂	#14270926	1	1	yes	characteristic
123	C₂	#14270927	1	1	yes	characteristic
124	C₂	#14270933	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271187

C₂

yes

maximal, characteristic

C₂×C₄⋊#6597

C₂

yes

maximal, characteristic

C₂₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

—

C₂²×#6597

—

C₂₉×C₄⋊C₈

—

C₂₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₂₉

—

C₄⋊#6597

—

C₄⋊#6597

—

C₄⋊#6597

C₄

yes

—

C₄⋊#6597

C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

Q₈

yes

characteristic

C₂×C₈×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

D₄

yes

—

—

—

—

—

—

C₂³×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄²

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

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

D₈

yes

characteristic

C₂×C₄×C₂₉

SD₁₆

yes

characteristic

C₂×C₄×C₂₉

SD₁₆

yes

characteristic

C₂×C₄×C₂₉

Q₁₆

yes

characteristic

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

#431

D₂₉

yes

characteristic

#423

—

C₂×C₄⋊C₈

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

Dic₂₉

yes

—

C₄×C₈

—

C₂₉

#1301

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₅₈

yes

characteristic

C₂²×C₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₂₉

yes

characteristic

M₁₆

—

116

—

M₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

116

—

C₂×C₈

—

116

—

C₄²

C₄×D₂₉

yes

characteristic

C₄²

C₄×D₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

characteristic

C₂³

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

D₂₃₂

yes

characteristic

C₂×C₄

Dic₁₁₆

yes

characteristic

C₂×C₄

C₄×Dic₂₉

yes

characteristic

C₂×C₄

#90779

yes

characteristic

100

C₂×C₄

#90779

yes

characteristic

101

C₂×C₄

#90781

yes

characteristic

102

C₂×C₄

#90781

yes

characteristic

103

C₂×C₄

C₂²⋊Dic₂₉

yes

characteristic

104

C₈

—

105

C₈

—

116

—

106

C₈

—

116

—

107

C₂²

—

108

C₂²

—

109

C₂²

#11745165

yes

characteristic

110

C₂²

#11745166

yes

characteristic

111

C₂²

#11745179

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#11745164

yes

characteristic

116

C₄

#11745164

yes

characteristic

117

C₄

#11745169

yes

characteristic

118

C₄

#11745169

yes

characteristic

119

C₄

#11745170

yes

—

120

C₂

—

121

C₂

—

122

C₂

#14270926

yes

characteristic

123

C₂

#14270927

yes

characteristic

124

C₂

#14270933

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#90781
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₂×C₄²	C₂×D₂₉
Fitting	C₂₉×#431	C₂
socle	C₂²×C₂₉	#95
prime radical	C₂³×C₂₉	C₄⋊C₄
cosocle	C₂×C₄²×C₂₉	C₂²
hypercenter	#431	D₂₉
hypocenter	C₂₉	#1301
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

#90781

commutator

C₂×C₄×C₂₉

C₄²

Frattini

C₂×C₄²

C₂×D₂₉

Fitting

C₂₉×#431

C₂

socle

C₂²×C₂₉

#95

prime radical

C₂³×C₂₉

C₄⋊C₄

cosocle

C₂×C₄²×C₂₉

C₂²

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
76. C₂₉	#1301	semidirect

H ≅ G/N

type

76. C₂₉

#1301

semidirect

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

subgroup	index
#14271187	2
C₂×C₄⋊#6597	2
C₂₉×#431	2
#1301	29

subgroup

index

#14271187

C₂×C₄⋊#6597

C₂₉×#431

#1301

Subgroups — #16817388

Conjugacy classes of subgroups

Complements

Maximal subgroups