Group #16818281 — subgroups

Subgroups — #16818281

Order 3712.

158 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14271216	C₂	1	1	yes	maximal, characteristic
2	#14271187	C₂	1	1	yes	maximal, characteristic
3	#14270916	C₂	1	2	yes	maximal, complemented
4	#14270914	C₂	1	2	yes	maximal, complemented
5	C₂₉×#431	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×#90777	—	2	1	no	—
8	C₂₉×C₄⋊C₈	C₄	1	2	yes	—
9	C₂₉×C₂²⋊C₈	C₄	1	2	yes	—
10	C₄×C₈×C₂₉	C₂²	1	2	yes	—
11	C₂²⋊#6597	—	2	1	no	—
12	C₄⋊#6597	—	2	1	no	—
13	C₄⋊#6597	C₂²	1	1	yes	characteristic
14	C₄⋊#6597	C₂²	1	2	yes	—
15	C₄⋊#6597	C₂²	1	1	yes	characteristic
16	C₄×#6597	—	2	1	no	—
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₉	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
21	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₉	D₄	1	1	yes	characteristic
23	C₄²×C₂₉	Q₈	1	1	yes	characteristic
24	C₄²×C₂₉	C₂³	1	1	yes	characteristic
25	#90777	—	4	2	no	—
26	C₂×#6597	—	2	2	no	—
27	C₂×#6597	—	2	1	no	—
28	C₂×#6597	—	2	1	no	—
29	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	2	2	no	—
32	C₂×C₄×C₂₉	—	2	1	no	—
33	C₂×C₄×C₂₉	—	2	1	no	—
34	C₂×C₄×C₂₉	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₂₉	—	2	4	no	—
41	#6597	—	4	1	no	—
42	#6597	—	4	2	no	—
43	#6597	—	4	1	no	—
44	#1574	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	—	2	1	no	—
46	C₂²×C₂₉	—	2	1	no	—
47	C₂²×C₂₉	—	2	1	no	—
48	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₂₉	—	2	1	no	—
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	—	2	1	no	—
52	C₄×C₂₉	#108	1	2	yes	—
53	C₄×C₂₉	#131	1	2	yes	—
54	C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₄×C₂₉	#137	1	1	yes	characteristic
56	#431	—	29	1	no	—
57	#431	D₂₉	1	1	yes	characteristic
58	#423	—	29	1	no	—
59	#335	—	29	2	no	—
60	#334	—	29	2	no	—
61	C₂×C₂₉	—	4	1	no	—
62	C₂×C₂₉	#424	1	1	yes	characteristic
63	C₂×C₂₉	#428	1	1	yes	characteristic
64	C₂×C₂₉	C₂×#108	1	1	yes	characteristic
65	C₂×M₁₆	—	58	1	no	—
66	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
67	C₄⋊C₈	—	29	1	no	—
68	C₄⋊C₈	—	29	2	no	—
69	C₄⋊C₈	—	29	1	no	—
70	C₄⋊C₈	—	58	1	no	—
71	C₄⋊C₈	Dic₂₉	1	2	yes	—
72	C₂²⋊C₈	—	58	1	no	—
73	C₂²⋊C₈	Dic₂₉	1	2	yes	—
74	C₄×C₈	—	58	1	no	—
75	C₄×C₈	C₂×D₂₉	1	2	yes	—
76	C₂₉	#1574	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	2	no	—
81	C₂×C₈	—	58	1	no	—
82	C₂×C₈	—	58	1	no	—
83	C₂×C₈	—	58	2	no	—
84	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
85	C₄²	Dic₅₈	1	1	yes	characteristic
86	C₄²	D₁₁₆	1	1	yes	characteristic
87	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
88	C₄²	C₂²×D₂₉	1	1	yes	characteristic
89	C₂³	C₄⋊Dic₂₉	1	1	yes	characteristic
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
95	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
96	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
97	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
98	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
100	C₈	—	2	4	no	—
101	C₈	—	116	2	no	—
102	C₈	—	116	1	no	—
103	C₈	—	116	1	no	—
104	C₂²	—	2	1	no	—
105	C₂²	—	2	1	no	—
106	C₂²	—	2	1	no	—
107	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	#11745167	1	2	yes	—
112	C₄	#11745270	1	1	yes	characteristic
113	C₄	#11745271	1	1	yes	characteristic
114	C₄	#11745310	1	2	yes	—
115	C₂	—	4	1	no	—
116	C₂	#14271190	1	1	yes	characteristic
117	C₂	#14271205	1	1	yes	characteristic
118	C₂	C₂×#11745167	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271216

C₂

yes

maximal, characteristic

#14271187

C₂

yes

maximal, characteristic

#14270916

C₂

yes

maximal, complemented

#14270914

C₂

yes

maximal, complemented

C₂₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

—

C₂₉×C₄⋊C₈

C₄

yes

—

C₂₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

C₂²⋊#6597

—

C₄⋊#6597

—

C₄⋊#6597

C₂²

yes

characteristic

C₄⋊#6597

C₂²

yes

—

C₄⋊#6597

C₂²

yes

characteristic

C₄×#6597

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

Q₈

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

Q₈

yes

characteristic

C₄²×C₂₉

C₂³

yes

—

—

—

—

C₂³×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₈×C₂₉

—

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#108

yes

—

C₄×C₂₉

#131

yes

—

C₄×C₂₉

yes

C₄×C₂₉

yes

—

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×M₁₆

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

Dic₂₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₂₉

yes

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

—

C₂₉

#1574

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₅₈

yes

characteristic

C₂²×C₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₂₉

yes

characteristic

M₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₄²

Dic₅₈

yes

characteristic

C₄²

D₁₁₆

yes

characteristic

C₄²

C₂×Dic₂₉

yes

characteristic

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

100

C₈

—

101

C₈

—

116

—

102

C₈

—

116

—

103

C₈

—

116

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₂×C₄⋊Dic₂₉

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#11745167

yes

—

112

C₄

#11745270

yes

characteristic

113

C₄

#11745271

yes

characteristic

114

C₄

#11745310

yes

—

115

C₂

—

116

C₂

#14271190

yes

characteristic

117

C₂

#14271205

yes

characteristic

118

C₂

C₂×#11745167

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₆
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#431	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₉	C₄⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#431	D₂₉
hypocenter	C₂₉	#1574
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

C₂×D₁₁₆

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#431

C₂

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂³×C₂₉

C₄⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
3. #14270916	C₂	semidirect
4. #14270914	C₂	semidirect
76. C₂₉	#1574	semidirect

H ≅ G/N

type

3. #14270916

C₂

semidirect

4. #14270914

C₂

semidirect

76. C₂₉

#1574

semidirect

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

subgroup	index
#14271216	2
#14271187	2
#14270916	2
#14270914	2
C₂₉×#431	2
#1574	29

subgroup

index

C₂₉×#431

Subgroups — #16818281

Conjugacy classes of subgroups

Complements

Maximal subgroups