Group #16818085 — subgroups

Subgroups — #16818085

Order 3712.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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	#14271719	C₂	1	1	yes	maximal, characteristic
2	#14271115	C₂	1	2	yes	maximal
3	#14270905	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270904	C₂	1	2	yes	maximal, complemented
5	C₂₉×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#125	C₂²	1	1	yes	characteristic
7	C₂×#90772	—	2	2	no	—
8	#11745258	—	2	2	no	—
9	#11745254	C₄	1	2	yes	—
10	#11745250	C₄	1	2	yes	—
11	#11745249	—	2	2	no	—
12	C₄²×D₂₉	C₂²	1	1	yes	characteristic
13	#11745232	C₂²	1	1	yes	characteristic
14	C₂₉×#97	C₂²	1	2	yes	—
15	C₈×Dic₂₉	—	2	2	no	—
16	#11745151	C₂²	1	2	yes	—
17	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	D₄	1	2	yes	—
19	C₂×Dic₅₈	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
23	C₄²×C₂₉	C₂³	1	1	yes	characteristic
24	#90781	—	2	2	no	—
25	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
26	#90779	—	2	2	no	—
27	#90779	—	2	2	no	—
28	C₄×Dic₂₉	—	2	2	no	—
29	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₉	D₄	1	2	yes	—
31	C₂×#6597	—	2	2	no	—
32	#90772	—	2	8	no	—
33	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
37	C₂×Dic₂₉	—	2	2	no	—
38	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
40	C₄×D₂₉	—	2	2	no	—
41	C₄×D₂₉	—	2	4	no	—
42	Dic₅₈	—	4	4	no	—
43	C₈×C₂₉	—	2	4	no	—
44	#6597	—	2	4	no	—
45	#1526	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₂×D₂₉	—	2	1	no	—
48	C₂×D₂₉	—	2	2	no	—
49	C₄×C₂₉	—	2	1	no	—
50	C₄×C₂₉	—	2	2	no	—
51	C₄×C₂₉	—	4	2	no	—
52	Dic₂₉	—	4	2	no	—
53	Dic₂₉	#101	1	2	yes	—
54	Dic₂₉	#104	1	4	yes	—
55	#533	—	29	1	no	—
56	C₄×M₁₆	—	29	2	no	—
57	#330	—	29	1	no	—
58	#330	—	29	2	no	—
59	#330	D₂₉	1	1	yes	characteristic, complemented
60	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
61	C₂×C₂₉	C₂×#104	1	2	yes	—
62	D₂₉	—	4	1	no	—
63	C₂×M₁₆	—	58	2	no	—
64	C₄⋊Q₈	—	29	2	no	—
65	#125	—	29	1	no	—
66	#125	C₂×D₂₉	1	1	yes	characteristic
67	C₂²⋊Q₈	—	58	2	no	—
68	C₄×Q₈	—	58	2	no	—
69	#117	—	29	2	no	—
70	C₂×C₄²	—	29	1	no	—
71	#97	—	29	2	no	—
72	#97	C₂×D₂₉	1	2	yes	—
73	C₄×C₈	—	58	2	no	—
74	C₂₉	#1526	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₈	—	58	2	no	—
76	C₂²×C₄	—	29	1	no	—
77	C₂²×C₄	—	29	2	no	—
78	M₁₆	—	58	8	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	58	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	29	2	no	—
83	C₄⋊C₄	—	58	2	no	—
84	C₄⋊C₄	—	58	2	no	—
85	C₄⋊C₄	C₄×D₂₉	1	2	yes	—
86	C₂²⋊C₄	—	58	2	no	—
87	C₄²	—	29	1	no	—
88	C₄²	—	29	2	no	—
89	C₄²	—	58	2	no	—
90	C₄²	C₂²×D₂₉	1	1	yes	characteristic
91	C₂³	—	29	1	no	—
92	Q₈	—	116	4	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	29	1	no	—
95	C₂×C₄	—	29	2	no	—
96	C₂×C₄	—	58	4	no	—
97	C₂×C₄	—	58	2	no	—
98	C₂×C₄	—	58	2	no	—
99	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
100	C₂×C₄	D₄×D₂₉	1	2	yes	—
101	C₈	—	2	4	no	—
102	C₈	—	58	4	no	—
103	C₂²	—	58	1	no	—
104	C₂²	—	58	2	no	—
105	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	2	no	—
108	C₄	—	4	2	no	—
109	C₄	—	29	2	no	—
110	C₄	—	29	4	no	—
111	C₄	—	116	2	no	—
112	C₂	—	116	1	no	—
113	C₂	#101×D₂₉	1	1	yes	characteristic
114	C₂	#104×D₂₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271719

C₂

yes

maximal, characteristic

#14271115

C₂

yes

maximal

#14270905

C₂

yes

maximal, characteristic, complemented

#14270904

C₂

yes

maximal, complemented

C₂₉×#330

C₂

yes

maximal, characteristic, complemented

C₂₉×#125

C₂²

yes

—

—

C₄

yes

—

#11745250

C₄

yes

—

#11745249

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745232

C₂²

yes

characteristic

C₂₉×#97

C₂²

yes

—

C₈×Dic₂₉

—

#11745151

C₂²

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

—

C₂×Dic₅₈

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

#90781

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂×#6597

—

#90772

—

C₂²×D₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1526

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

#101

yes

—

Dic₂₉

#104

yes

—

#533

—

C₄×M₁₆

—

#330

—

#330

—

#330

D₂₉

yes

characteristic, complemented

C₂×C₂₉

C₂×#101

yes

characteristic

C₂×C₂₉

C₂×#104

yes

—

D₂₉

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₂₉

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#97

—

#97

C₂×D₂₉

yes

—

C₄×C₈

—

C₂₉

#1526

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₂₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

100

C₂×C₄

D₄×D₂₉

yes

—

101

C₈

—

102

C₈

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₂²⋊C₄×D₂₉

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

116

—

112

C₂

—

116

—

113

C₂

#101×D₂₉

yes

characteristic

114

C₂

#104×D₂₉

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#330	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#330	D₂₉
hypocenter	C₂₉	#1526
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#330

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #14270905	C₂	semidirect
4. #14270904	C₂	semidirect
5. C₂₉×#330	C₂	semidirect
59. #330	D₂₉	semidirect
74. C₂₉	#1526	semidirect

H ≅ G/N

type

3. #14270905

C₂

semidirect

4. #14270904

C₂

semidirect

5. C₂₉×#330

C₂

semidirect

59. #330

D₂₉

semidirect

74. C₂₉

#1526

semidirect

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

subgroup	index
#14271719	2
#14271115	2
#14270905	2
#14270904	2
C₂₉×#330	2
#1526	29

subgroup

index

C₂₉×#330

Subgroups — #16818085

Conjugacy classes of subgroups

Complements

Maximal subgroups