Group #16818613 — subgroups

Subgroups — #16818613

Order 3712.

218 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271535	C₂	1	1	yes	maximal, characteristic
2	#14271458	C₂	1	2	yes	maximal, complemented
3	#14270907	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊#6597	C₂	1	2	yes	maximal, complemented
5	C₂₉×#559	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#127	C₂²	1	1	yes	characteristic
7	C₂₉×#124	—	2	2	no	—
8	C₂₉×#123	—	2	2	no	—
9	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
10	C₄×D₄×C₂₉	—	2	2	no	—
11	C₂×#90783	—	2	2	no	—
12	#11745231	C₂²	1	1	yes	characteristic
13	#11745183	—	2	2	no	—
14	#11745155	—	2	2	no	—
15	C₄⋊#6597	C₂²	1	2	yes	—
16	C₄×#6597	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₂₉	D₄	1	2	yes	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	D₄	1	2	yes	—
20	C₂²×C₄×C₂₉	—	2	2	no	—
21	C₂×Dic₅₈	—	2	1	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
24	C₂²⋊C₄×C₂₉	—	2	4	no	—
25	C₂²⋊C₄×C₂₉	—	2	2	no	—
26	C₄²×C₂₉	—	2	2	no	—
27	C₄²×C₂₉	C₂³	1	1	yes	characteristic
28	#90783	—	4	4	no	—
29	C₄⋊Dic₂₉	—	2	2	no	—
30	C₂×#6597	—	2	1	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂³×C₂₉	—	2	2	no	—
33	Q₈×C₂₉	—	2	2	no	—
34	Q₈×C₂₉	—	2	2	no	—
35	D₄×C₂₉	—	4	2	no	—
36	D₄×C₂₉	—	4	2	no	—
37	D₄×C₂₉	—	4	2	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	—	8	2	no	—
41	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
43	C₂×Dic₂₉	—	4	1	no	—
44	Dic₅₈	—	4	2	no	—
45	#6597	—	2	2	no	—
46	#6597	—	4	2	no	—
47	#1630	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	—	4	4	no	—
49	C₂²×C₂₉	—	4	2	no	—
50	C₂²×C₂₉	#120	1	1	yes	characteristic
51	C₄×C₂₉	—	2	1	no	—
52	C₄×C₂₉	—	4	2	no	—
53	C₄×C₂₉	—	4	2	no	—
54	C₄×C₂₉	#135	1	2	yes	—
55	C₄×C₂₉	#137	1	2	yes	—
56	Dic₂₉	—	8	1	no	—
57	#559	D₂₉	1	1	yes	characteristic
58	#492	—	29	1	no	—
59	#477	—	29	2	no	—
60	#331	—	29	1	no	—
61	Q₈⋊C₈	—	29	2	no	—
62	C₂×C₂₉	—	8	2	no	—
63	C₂×C₂₉	#452	1	2	yes	—
64	C₂×C₂₉	#453	1	1	yes	characteristic
65	C₂×SD₁₆	—	58	2	no	—
66	C₄⋊Q₈	—	29	1	no	—
67	#127	C₂×D₂₉	1	1	yes	characteristic
68	#124	—	2	2	no	—
69	#123	—	2	2	no	—
70	C₄×Q₈	C₂×D₂₉	1	2	yes	—
71	C₄×D₄	—	2	2	no	—
72	#107	—	58	2	no	—
73	C₄⋊C₈	—	29	2	no	—
74	#103	—	58	2	no	—
75	C₄×C₈	—	29	1	no	—
76	C₂₉	#1630	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	58	1	no	—
78	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
79	C₂×D₄	—	2	2	no	—
80	C₂×D₄	C₂²⋊D₂₉	1	2	yes	—
81	C₂²×C₄	—	2	2	no	—
82	SD₁₆	—	116	4	no	—
83	C₂×C₈	—	58	1	no	—
84	C₂×C₈	—	58	2	no	—
85	C₄⋊C₄	—	2	2	no	—
86	C₄⋊C₄	—	58	2	no	—
87	C₄⋊C₄	C₂²⋊D₂₉	1	2	yes	—
88	C₂²⋊C₄	—	2	4	no	—
89	C₂²⋊C₄	—	2	2	no	—
90	C₄²	—	2	2	no	—
91	C₄²	C₂²×D₂₉	1	1	yes	characteristic
92	C₂³	—	2	2	no	—
93	Q₈	—	2	2	no	—
94	Q₈	—	2	2	no	—
95	Q₈	—	116	2	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	2	no	—
98	D₄	—	4	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	8	2	no	—
102	C₂×C₄	—	116	1	no	—
103	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
104	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
105	C₈	—	58	2	no	—
106	C₈	—	116	2	no	—
107	C₂²	—	4	4	no	—
108	C₂²	—	4	2	no	—
109	C₂²	#11745315	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	4	2	no	—
112	C₄	—	4	2	no	—
113	C₄	—	232	1	no	—
114	C₄	#11745312	1	2	yes	—
115	C₄	#11745313	1	2	yes	—
116	C₂	—	8	2	no	—
117	C₂	#14271325	1	2	yes	—
118	C₂	#14271331	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271535

C₂

yes

maximal, characteristic

#14271458

C₂

yes

maximal, complemented

#14270907

C₂

yes

maximal, characteristic

Q₈⋊#6597

C₂

yes

maximal, complemented

C₂₉×#559

C₂

yes

maximal, characteristic

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#124

—

C₂₉×#123

—

C₄×Q₈×C₂₉

C₂²

yes

—

C₄×D₄×C₂₉

—

C₂×#90783

—

#11745231

C₂²

yes

—

—

C₂²

yes

—

C₄×#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

D₄

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

—

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₂²⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90783

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#135

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

#559

D₂₉

yes

—

—

—

Q₈⋊C₈

—

C₂×C₂₉

—

C₂×C₂₉

#452

yes

—

C₂×C₂₉

#453

yes

characteristic

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₂₉

yes

characteristic

#124

—

#123

—

C₄×Q₈

C₂×D₂₉

yes

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₂₉

#1630

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₂₉

yes

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

—

SD₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₂₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

116

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

116

—

103

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

104

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

105

C₈

—

106

C₈

—

116

—

107

C₂²

—

108

C₂²

—

109

C₂²

#11745315

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

232

—

114

C₄

#11745312

yes

—

115

C₄

#11745313

yes

—

116

C₂

—

117

C₂

#14271325

yes

—

118

C₂

#14271331

yes

characteristic

	subgroup	G/H
center	C₂²	#11745315
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#559	C₂
socle	C₂²×C₂₉	#120
prime radical	C₂₉×#127	C₂²
hypercenter	#559	D₂₉
hypocenter	C₂₉	#1630
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #559

subgroup

G/H

center

C₂²

#11745315

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#559

C₂

socle

C₂²×C₂₉

#120

prime radical

C₂₉×#127

C₂²

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #559

N	H ≅ G/N	type
2. #14271458	C₂	semidirect
4. Q₈⋊#6597	C₂	semidirect
76. C₂₉	#1630	semidirect

H ≅ G/N

type

2. #14271458

C₂

semidirect

4. Q₈⋊#6597

C₂

semidirect

76. C₂₉

#1630

semidirect

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

subgroup	index
#14271535	2
#14271458	2
#14270907	2
Q₈⋊#6597	2
C₂₉×#559	2
#1630	29

subgroup

index

C₂₉×#559

Subgroups — #16818613

Conjugacy classes of subgroups

Complements

Maximal subgroups