Group #16835031 — subgroups

Subgroups — #16835031

Order 3712.

210 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 62 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	#14272166	C₂	1	2	yes	maximal
2	#14272022	C₂	1	4	yes	maximal, complemented
3	#14271716	C₂	1	1	yes	maximal, characteristic
4	C₂×#90800	—	2	2	no	—
5	C₂₉×#117	C₄	1	1	yes	characteristic
6	#11745288	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
8	#11745252	C₄	1	2	yes	—
9	#11745250	C₂²	1	2	yes	—
10	#11745240	—	2	2	no	—
11	C₄×Dic₅₈	—	2	2	no	—
12	#11745220	C₂²	1	4	yes	—
13	C₄⋊#6599	—	2	2	no	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₂₉	D₄	1	2	yes	—
16	C₂×Dic₅₈	—	2	2	no	—
17	#90800	—	4	4	no	—
18	C₂×#6599	—	2	4	no	—
19	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
20	C₂²⋊C₄×C₂₉	—	2	1	no	—
21	C₄²×C₂₉	—	2	1	no	—
22	C₂²⋊Dic₂₉	—	2	1	no	—
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
25	#90779	—	2	2	no	—
26	#90779	—	2	2	no	—
27	C₄×Dic₂₉	—	2	1	no	—
28	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₂₉	D₄	1	2	yes	—
30	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
31	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	—	2	2	no	—
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₂₉	—	2	2	no	—
37	C₂×Dic₂₉	—	2	2	no	—
38	C₂×Dic₂₉	—	2	2	no	—
39	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
40	C₂×Dic₂₉	C₂×D₄	1	2	yes	—
41	Dic₅₈	—	4	2	no	—
42	Dic₅₈	—	4	2	no	—
43	#6599	—	4	4	no	—
44	#1561	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	—	2	1	no	—
46	C₂²×C₂₉	—	2	2	no	—
47	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	4	2	no	—
50	C₄×C₂₉	#101	1	2	yes	—
51	Dic₂₉	—	2	2	no	—
52	Dic₂₉	—	4	2	no	—
53	Dic₂₉	AGL(1,ℤ/8)	1	2	yes	—
54	Dic₂₉	#137	1	2	yes	—
55	#533	—	29	1	no	—
56	#423	—	29	2	no	—
57	#332	—	29	4	no	—
58	C₂×C₂₉	—	4	1	no	—
59	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
60	C₂×C₂₉	#417	1	2	yes	—
61	C₂×M₁₆	—	58	2	no	—
62	C₄⋊Q₈	—	29	2	no	—
63	#125	—	29	2	no	—
64	C₂²⋊Q₈	—	58	2	no	—
65	C₄×Q₈	—	58	2	no	—
66	#117	—	29	1	no	—
67	#117	#1181	1	1	yes	characteristic
68	C₂×C₄²	—	29	1	no	—
69	C₄⋊C₈	—	29	4	no	—
70	C₄⋊C₈	—	58	2	no	—
71	C₂₉	#1561	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	58	2	no	—
73	C₂²×C₄	—	29	2	no	—
74	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
75	M₁₆	—	116	4	no	—
76	C₂×C₈	—	58	4	no	—
77	C₄⋊C₄	—	29	2	no	—
78	C₄⋊C₄	—	58	2	no	—
79	C₄⋊C₄	—	58	2	no	—
80	C₄⋊C₄	—	58	2	no	—
81	C₄⋊C₄	C₂×#1181	1	2	yes	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	—	58	1	no	—
84	C₄²	—	2	1	no	—
85	C₄²	—	29	2	no	—
86	C₄²	—	29	1	no	—
87	C₄²	—	29	1	no	—
88	C₄²	—	58	1	no	—
89	C₂³	C₂²⋊#1181	1	1	yes	characteristic
90	Q₈	—	116	2	no	—
91	Q₈	—	116	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	29	2	no	—
95	C₂×C₄	—	29	2	no	—
96	C₂×C₄	—	58	2	no	—
97	C₂×C₄	—	58	2	no	—
98	C₂×C₄	—	58	2	no	—
99	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
100	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
101	C₈	—	116	4	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	2	no	—
104	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	2	no	—
107	C₄	—	29	2	no	—
108	C₄	—	29	2	no	—
109	C₄	—	58	2	no	—
110	C₄	—	116	2	no	—
111	C₄	#11745221	1	2	yes	—
112	C₂	—	4	1	no	—
113	C₂	C₂×#11745221	1	1	yes	characteristic
114	C₂	#14272154	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272166

C₂

yes

maximal

#14272022

C₂

yes

maximal, complemented

#14271716

C₂

yes

maximal, characteristic

C₂×#90800

—

C₂₉×#117

C₄

yes

characteristic

#11745288

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

#11745252

C₄

yes

—

#11745250

C₂²

yes

—

#11745240

—

C₄×Dic₅₈

—

#11745220

C₂²

yes

—

C₄⋊#6599

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

D₄

yes

—

C₂×Dic₅₈

—

#90800

—

C₂×#6599

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂³×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

—

Dic₅₈

—

Dic₅₈

—

#6599

—

#1561

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#101

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

AGL(1,ℤ/8)

yes

—

Dic₂₉

#137

yes

—

#533

—

#423

—

#332

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#101

yes

characteristic

C₂×C₂₉

#417

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

—

yes

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂₉

#1561

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

characteristic

M₁₆

—

116

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#1181

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#1181

yes

characteristic

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#1181

yes

characteristic

100

C₂×C₄

C₂²×#1181

yes

characteristic

101

C₈

—

116

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊#1181

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

116

—

111

C₄

#11745221

yes

—

112

C₂

—

113

C₂

C₂×#11745221

yes

characteristic

114

C₂

#14272154

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×#117	C₄
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	#117	#1181
hypocenter	C₂₉	#1561
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

subgroup

G/H

center

C₂²

C₂×C₂²⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×#117

C₄

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₂₉

C₂²⋊C₄

cosocle

C₄×Dic₂₉

C₂³

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

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

H ≅ G/N

type

2. #14272022

C₂

semidirect

71. C₂₉

#1561

semidirect

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

subgroup	index
#14272166	2
#14272022	2
#14271716	2
#1561	29

subgroup

index

Subgroups — #16835031

Conjugacy classes of subgroups

Complements

Maximal subgroups