Group #16835032 — subgroups

Subgroups — #16835032

Order 3712.

210 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 60 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	#14272168	C₂	1	2	yes	maximal
2	#14272022	C₂	1	4	yes	maximal, complemented
3	#14271719	C₂	1	1	yes	maximal, characteristic
4	C₂×#90796	—	2	2	no	—
5	C₂₉×#125	C₄	1	1	yes	characteristic
6	#11745258	—	2	2	no	—
7	#11745254	C₄	1	2	yes	—
8	#11745250	C₂²	1	2	yes	—
9	#11745249	—	2	2	no	—
10	C₄²×D₂₉	C₂²	1	1	yes	characteristic
11	#11745232	C₄	1	1	yes	characteristic
12	#11745220	—	2	2	no	—
13	#11745220	C₂²	1	4	yes	—
14	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×D₂₉	D₄	1	2	yes	—
16	C₂×Dic₅₈	—	2	2	no	—
17	C₂×#6599	—	2	4	no	—
18	#90796	—	4	4	no	—
19	C₄⋊C₄×C₂₉	—	2	2	no	—
20	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
21	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
22	#90781	—	2	2	no	—
23	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
24	#90779	—	2	2	no	—
25	#90779	—	2	2	no	—
26	C₄×Dic₂₉	—	2	2	no	—
27	C₄×Dic₂₉	D₄	1	2	yes	—
28	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
29	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₂₉	—	2	2	no	—
34	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₂₉	C₂×D₄	1	2	yes	—
36	C₄×D₂₉	—	2	2	no	—
37	C₄×D₂₉	—	2	2	no	—
38	C₄×D₂₉	—	2	2	no	—
39	Dic₅₈	—	4	2	no	—
40	Dic₅₈	—	4	2	no	—
41	#6599	—	4	4	no	—
42	#1561	—	29	1	no	maximal, Sylow
43	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
44	C₂×D₂₉	—	2	1	no	—
45	C₂×D₂₉	—	2	2	no	—
46	C₄×C₂₉	—	2	1	no	—
47	C₄×C₂₉	—	2	2	no	—
48	C₄×C₂₉	—	4	2	no	—
49	Dic₂₉	—	4	2	no	—
50	Dic₂₉	#101	1	2	yes	—
51	Dic₂₉	AGL(1,ℤ/8)	1	2	yes	—
52	Dic₂₉	#137	1	2	yes	—
53	#533	—	29	1	no	—
54	#423	—	29	2	no	—
55	#332	—	29	4	no	—
56	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
57	C₂×C₂₉	#417	1	2	yes	—
58	D₂₉	—	4	1	no	—
59	C₂×M₁₆	—	58	2	no	—
60	C₄⋊Q₈	—	29	2	no	—
61	#125	—	29	1	no	—
62	#125	#1181	1	1	yes	characteristic
63	C₂²⋊Q₈	—	58	2	no	—
64	C₄×Q₈	—	58	2	no	—
65	#117	—	29	2	no	—
66	C₂×C₄²	—	29	1	no	—
67	C₄⋊C₈	—	29	4	no	—
68	C₄⋊C₈	—	58	2	no	—
69	C₂₉	#1561	1	1	yes	characteristic, complemented, Sylow
70	C₂×Q₈	—	58	2	no	—
71	C₂²×C₄	—	29	2	no	—
72	C₂²×C₄	—	29	1	no	—
73	M₁₆	—	116	4	no	—
74	C₂×C₈	—	58	4	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	29	2	no	—
77	C₄⋊C₄	—	58	2	no	—
78	C₄⋊C₄	—	58	2	no	—
79	C₄⋊C₄	C₂×#1181	1	2	yes	—
80	C₂²⋊C₄	—	58	2	no	—
81	C₄²	—	29	2	no	—
82	C₄²	—	29	1	no	—
83	C₄²	—	58	2	no	—
84	C₄²	C₂×#1181	1	1	yes	characteristic
85	C₂³	—	29	1	no	—
86	Q₈	—	116	2	no	—
87	Q₈	—	116	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	29	1	no	—
90	C₂×C₄	—	29	2	no	—
91	C₂×C₄	—	58	2	no	—
92	C₂×C₄	—	58	2	no	—
93	C₂×C₄	—	58	2	no	—
94	C₂×C₄	—	58	2	no	—
95	C₂×C₄	C₂²⋊#1181	1	2	yes	—
96	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
97	C₈	—	116	4	no	—
98	C₂²	—	58	1	no	—
99	C₂²	—	58	2	no	—
100	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	2	2	no	—
103	C₄	—	4	2	no	—
104	C₄	—	29	2	no	—
105	C₄	—	29	2	no	—
106	C₄	—	29	2	no	—
107	C₄	—	116	2	no	—
108	C₂	—	116	1	no	—
109	C₂	D₂₉⋊#101	1	1	yes	characteristic
110	C₂	#14272154	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272168

C₂

yes

maximal

#14272022

C₂

yes

maximal, complemented

#14271719

C₂

yes

maximal, characteristic

C₂×#90796

—

C₂₉×#125

C₄

yes

characteristic

#11745258

—

#11745254

C₄

yes

—

#11745250

C₂²

yes

—

#11745249

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745232

C₄

yes

characteristic

#11745220

—

#11745220

C₂²

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

—

C₂×Dic₅₈

—

C₂×#6599

—

#90796

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

#90781

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

Dic₅₈

—

#6599

—

#1561

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

#101

yes

—

Dic₂₉

AGL(1,ℤ/8)

yes

—

Dic₂₉

#137

yes

—

#533

—

#423

—

#332

—

C₂×C₂₉

C₂×#101

yes

characteristic

C₂×C₂₉

#417

yes

—

D₂₉

—

C₂×M₁₆

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂₉

#1561

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

116

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#1181

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#1181

yes

—

C₂×C₄

C₂²×#1181

yes

characteristic

C₈

—

116

—

C₂²

—

C₂²

—

100

C₂²

C₂×C₂²⋊#1181

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

116

—

108

C₂

—

116

—

109

C₂

D₂₉⋊#101

yes

characteristic

110

C₂

#14272154

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#125	C₄
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	#125	#1181
hypocenter	C₂₉	#1561
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#125

C₄

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄×Dic₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
2. #14272022	C₂	semidirect
69. C₂₉	#1561	semidirect

H ≅ G/N

type

2. #14272022

C₂

semidirect

69. C₂₉

#1561

semidirect

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

subgroup	index
#14272168	2
#14272022	2
#14271719	2
#1561	29

subgroup

index

Subgroups — #16835032

Conjugacy classes of subgroups

Complements

Maximal subgroups