Group #16818611 — subgroups

Subgroups — #16818611

Order 3712.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14271899	C₂	1	1	yes	maximal, characteristic
2	#14271455	C₂	1	2	yes	maximal, complemented
3	#14270907	C₂	1	1	yes	maximal, characteristic
4	#14270895	C₂	1	2	yes	maximal, complemented
5	C₂₉×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×SD₁₆×C₂₉	—	2	2	no	—
7	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	#11745298	—	2	2	no	—
10	#11745297	—	2	2	no	—
11	D₄×Dic₂₉	—	2	2	no	—
12	C₄×Dic₅₈	C₂²	1	2	yes	—
13	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
14	#11745158	—	2	2	no	—
15	#11745155	—	2	2	no	—
16	C₄⋊#6597	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₉	—	2	1	no	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	D₄	1	2	yes	—
20	C₂²×Dic₂₉	—	2	2	no	—
21	C₂×Dic₅₈	D₄	1	2	yes	—
22	SD₁₆×C₂₉	—	4	4	no	—
23	C₂×C₈×C₂₉	—	2	1	no	—
24	C₄⋊C₄×C₂₉	—	2	2	no	—
25	C₄²×C₂₉	C₂³	1	1	yes	characteristic
26	C₂²⋊Dic₂₉	—	2	4	no	—
27	C₂²⋊Dic₂₉	—	2	2	no	—
28	C₄⋊Dic₂₉	D₄	1	2	yes	—
29	#90779	—	2	2	no	—
30	C₄×Dic₂₉	—	2	2	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂³×C₂₉	—	2	2	no	—
33	Q₈×C₂₉	—	4	2	no	—
34	D₄×C₂₉	—	4	2	no	—
35	D₄×C₂₉	—	4	2	no	—
36	D₄×C₂₉	—	4	2	no	—
37	C₂×C₄×C₂₉	—	4	1	no	—
38	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₂₉	—	2	2	no	—
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	—	8	2	no	—
43	Dic₅₈	—	2	2	no	—
44	Dic₅₈	—	2	2	no	—
45	C₈×C₂₉	—	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	—	8	1	no	—
53	C₄×C₂₉	#135	1	2	yes	—
54	C₄×C₂₉	#137	1	2	yes	—
55	Dic₂₉	—	4	2	no	—
56	Dic₂₉	—	4	2	no	—
57	#559	—	29	1	no	—
58	#492	D₂₉	1	1	yes	characteristic
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	—	2	2	no	—
66	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
67	#127	C₂×D₂₉	1	1	yes	characteristic
68	#124	—	58	2	no	—
69	#123	—	58	2	no	—
70	C₄×Q₈	—	29	2	no	—
71	C₄×D₄	—	58	2	no	—
72	#107	—	58	2	no	—
73	C₄⋊C₈	—	29	2	no	—
74	#103	—	58	2	no	—
75	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
76	C₂₉	#1630	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	2	1	no	—
78	C₂×Q₈	—	29	2	no	—
79	C₂×D₄	—	2	2	no	—
80	C₂×D₄	C₂²⋊D₂₉	1	2	yes	—
81	C₂²×C₄	—	58	2	no	—
82	SD₁₆	—	4	4	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	58	2	no	—
85	C₄⋊C₄	—	2	2	no	—
86	C₄⋊C₄	—	29	2	no	—
87	C₄⋊C₄	—	58	2	no	—
88	C₂²⋊C₄	—	58	4	no	—
89	C₂²⋊C₄	—	58	2	no	—
90	C₄²	—	58	2	no	—
91	C₄²	C₂²×D₂₉	1	1	yes	characteristic
92	C₂³	—	2	2	no	—
93	Q₈	—	4	2	no	—
94	Q₈	—	58	2	no	—
95	Q₈	—	58	2	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	2	no	—
98	D₄	—	4	2	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	58	2	no	—
101	C₂×C₄	—	58	2	no	—
102	C₂×C₄	—	232	2	no	—
103	C₂×C₄	D₄×D₂₉	1	2	yes	—
104	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	116	2	no	—
107	C₂²	—	4	4	no	—
108	C₂²	—	4	2	no	—
109	C₂²	#11745299	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	8	1	no	—
112	C₄	—	116	2	no	—
113	C₄	—	116	2	no	—
114	C₄	#11745277	1	2	yes	—
115	C₄	#11745278	1	2	yes	—
116	C₂	—	8	2	no	—
117	C₂	#14271322	1	2	yes	—
118	C₂	#14271330	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271899

C₂

yes

maximal, characteristic

#14271455

C₂

yes

maximal, complemented

#14270907

C₂

yes

maximal, characteristic

#14270895

C₂

yes

maximal, complemented

C₂₉×#492

C₂

yes

maximal, characteristic

C₂×SD₁₆×C₂₉

—

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

characteristic

#11745298

—

#11745297

—

D₄×Dic₂₉

—

C₄×Dic₅₈

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

D₄

yes

—

C₂²×Dic₂₉

—

C₂×Dic₅₈

D₄

yes

—

SD₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

#90779

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂³×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1630

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#135

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

Dic₂₉

—

#559

—

#492

D₂₉

yes

characteristic

#477

—

#331

—

Q₈⋊C₈

—

C₂×C₂₉

—

C₂×C₂₉

#452

yes

—

C₂×C₂₉

#453

yes

characteristic

C₂×SD₁₆

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#127

C₂×D₂₉

yes

characteristic

#124

—

#123

—

C₄×Q₈

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1630

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

—

SD₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

232

—

103

C₂×C₄

D₄×D₂₉

yes

—

104

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

105

C₈

—

106

C₈

—

116

—

107

C₂²

—

108

C₂²

—

109

C₂²

#11745299

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

116

—

113

C₄

—

116

—

114

C₄

#11745277

yes

—

115

C₄

#11745278

yes

—

116

C₂

—

117

C₂

#14271322

yes

—

118

C₂

#14271330

yes

characteristic

	subgroup	G/H
center	C₂²	#11745299
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#492	C₂
socle	C₂²×C₂₉	#120
prime radical	C₂₉×#127	C₂²
hypercenter	#492	D₂₉
hypocenter	C₂₉	#1630
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#11745299

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#492

C₂

socle

C₂²×C₂₉

#120

prime radical

C₂₉×#127

C₂²

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
2. #14271455	C₂	semidirect
4. #14270895	C₂	semidirect
76. C₂₉	#1630	semidirect

H ≅ G/N

type

2. #14271455

C₂

semidirect

4. #14270895

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
#14271899	2
#14271455	2
#14270907	2
#14270895	2
C₂₉×#492	2
#1630	29

subgroup

index

C₂₉×#492

Subgroups — #16818611

Conjugacy classes of subgroups

Complements

Maximal subgroups