Group #16015510 — subgroups

Subgroups — #16015510

Order 3328.

806 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 331 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	C₂×#11718344	C₂	1	4	yes	maximal
2	#13123199	C₂	1	2	yes	maximal
3	#13115004	C₂	1	8	yes	maximal
4	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×#88124	C₂²	1	4	yes	—
6	C₂×C₁₃×#97	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₄³×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88058	C₂²	1	8	yes	—
10	C₂×#88057	C₂²	1	8	yes	—
11	#11718597	C₂²	1	4	yes	—
12	#11718596	C₂²	1	4	yes	—
13	#11718589	—	2	8	no	—
14	#11718344	—	2	16	no	—
15	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
16	C₂×C₄²×C₁₃	D₄	1	4	yes	—
17	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
19	C₂×C₄⋊Dic₁₃	—	2	8	no	—
20	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
21	C₂×#6101	—	2	8	no	—
22	#88124	—	2	16	no	—
23	C₁₃×#97	Q₈	1	16	yes	—
24	C₄×C₈×C₁₃	D₄	1	8	yes	—
25	#88071	—	2	8	no	—
26	#88058	—	2	16	no	—
27	#88057	—	2	16	no	—
28	#33315	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
31	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
32	C₂²×Dic₁₃	—	2	8	no	—
33	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
34	C₂×C₈×C₁₃	C₂×Q₈	1	16	yes	—
35	C₄²×C₁₃	—	4	4	no	—
36	C₄²×C₁₃	C₂×D₄	1	4	yes	—
37	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
38	C₄⋊Dic₁₃	—	2	16	no	—
39	C₄⋊Dic₁₃	—	4	16	no	—
40	#6101	—	4	16	no	—
41	C₂×#499	—	13	4	no	—
42	#2859	—	13	2	no	—
43	#1847	—	13	8	no	—
44	C₄×#97	D₁₃	1	1	yes	characteristic
45	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₃	—	2	8	no	—
47	C₂×C₄×C₁₃	—	2	4	no	—
48	C₂×C₄×C₁₃	#127	1	4	yes	—
49	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
50	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
51	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
52	C₂×Dic₁₃	—	4	8	no	—
53	C₂×Dic₁₃	—	4	16	no	—
54	C₈×C₁₃	C₄⋊Q₈	1	16	yes	—
55	C₂×#125	—	13	4	no	—
56	#499	—	26	16	no	—
57	C₂×#107	—	13	8	no	—
58	C₂×#106	—	13	8	no	—
59	C₂×#97	C₂×D₁₃	1	4	yes	—
60	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
61	#389	—	26	8	no	—
62	#384	—	13	4	no	—
63	#382	—	13	4	no	—
64	C₄³	C₂×D₁₃	1	1	yes	characteristic
65	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
66	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
67	C₂²×C₁₃	#575	1	4	yes	—
68	C₄×C₁₃	—	2	4	no	—
69	C₄×C₁₃	—	2	8	no	—
70	C₄×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
71	Dic₁₃	—	8	8	no	—
72	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
73	#125	—	26	16	no	—
74	C₂×C₄⋊C₄	—	13	8	no	—
75	C₂×C₄⋊C₄	—	26	8	no	—
76	C₂×C₄⋊C₄	—	26	8	no	—
77	C₂×C₄²	D₅₂	1	4	yes	—
78	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
79	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
80	#107	—	26	16	no	—
81	#106	—	26	16	no	—
82	#97	Dic₂₆	1	16	yes	—
83	C₄×C₈	D₅₂	1	8	yes	—
84	#95	—	26	8	no	—
85	C₂×C₁₃	#2868	1	1	yes	characteristic
86	C₂×C₁₃	#3150	1	2	yes	—
87	C₂×C₁₃	#3166	1	4	yes	—
88	C₂²×C₄	—	26	8	no	—
89	C₂²×C₄	C₂×D₅₂	1	4	yes	—
90	C₂²×C₄	C₂×D₅₂	1	2	yes	—
91	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
92	C₂×C₈	C₂×Dic₂₆	1	16	yes	—
93	C₂×C₈	C₂×D₅₂	1	8	yes	—
94	C₄⋊C₄	—	26	16	no	—
95	C₄⋊C₄	—	52	16	no	—
96	C₄⋊C₄	—	52	16	no	—
97	C₄²	—	4	4	no	—
98	C₄²	C₂×Dic₂₆	1	8	yes	—
99	C₄²	C₂×D₅₂	1	4	yes	—
100	C₁₃	#33315	1	1	yes	characteristic, complemented, Sylow
101	C₂³	C₂²×D₅₂	1	1	yes	characteristic
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	52	8	no	—
105	C₂×C₄	—	52	16	no	—
106	C₂×C₄	#88123	1	8	yes	—
107	C₂×C₄	#88128	1	4	yes	—
108	C₂×C₄	C₂²×Dic₂₆	1	4	yes	—
109	C₂×C₄	C₂²×D₅₂	1	2	yes	—
110	C₈	#88123	1	16	yes	—
111	C₂²	C₂×#88123	1	2	yes	—
112	C₂²	C₂×#88128	1	1	yes	characteristic
113	C₂²	#11719453	1	4	yes	—
114	C₄	—	2	8	no	—
115	C₄	—	2	4	no	—
116	C₄	—	104	8	no	—
117	C₄	C₂×#88123	1	4	yes	—
118	C₂	#13123234	1	1	yes	characteristic
119	C₂	#13125282	1	2	yes	—
120	C₂	#13125388	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718344

C₂

yes

maximal

#13123199

C₂

yes

maximal

#13115004

C₂

yes

maximal

C₄×C₁₃×#97

C₂

yes

maximal, characteristic

C₂×#88124

C₂²

yes

—

C₂×C₁₃×#97

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×#88058

C₂²

yes

—

C₂×#88057

C₂²

yes

—

#11718597

C₂²

yes

—

#11718596

C₂²

yes

—

#11718589

—

#11718344

—

C₂²×C₈×C₁₃

C₂³

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂³

yes

—

C₂×#6101

—

#88124

—

C₁₃×#97

Q₈

yes

—

C₄×C₈×C₁₃

D₄

yes

—

—

—

—

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂⁴

yes

characteristic

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

C₄×#97

D₁₃

yes

characteristic

C₂³×C₁₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#127

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃

C₂²×D₄

yes

—

C₂×C₄×C₁₃

C₂²×Q₈

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

C₄⋊Q₈

yes

—

—

—

—

—

C₂×#97

C₂×D₁₃

yes

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

#389

—

#384

—

#382

—

C₄³

C₂×D₁₃

yes

characteristic

C₂²×C₁₃

C₂×#127

yes

characteristic

C₂²×C₁₃

C₂×C₄⋊Q₈

yes

—

C₂²×C₁₃

#575

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊Q₈

yes

—

Dic₁₃

—

C₂²×C₈

C₂²×D₁₃

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

D₅₂

yes

—

C₂×C₄²

C₂²×D₁₃

yes

—

C₂×C₄²

C₂²×D₁₃

yes

—

—

Dic₂₆

yes

—

C₄×C₈

D₅₂

yes

—

#95

—

C₂×C₁₃

#2868

yes

characteristic

C₂×C₁₃

#3150

yes

—

C₂×C₁₃

#3166

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×D₅₂

yes

—

C₂²×C₄

C₂×D₅₂

yes

—

C₂²×C₄

C₂³×D₁₃

yes

characteristic

C₂×C₈

C₂×Dic₂₆

yes

—

C₂×C₈

C₂×D₅₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×Dic₂₆

yes

—

C₄²

C₂×D₅₂

yes

—

100

C₁₃

#33315

yes

characteristic, complemented, Sylow

101

C₂³

C₂²×D₅₂

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#88123

yes

—

107

C₂×C₄

#88128

yes

—

108

C₂×C₄

C₂²×Dic₂₆

yes

—

109

C₂×C₄

C₂²×D₅₂

yes

—

110

C₈

#88123

yes

—

111

C₂²

C₂×#88123

yes

—

112

C₂²

C₂×#88128

yes

characteristic

113

C₂²

#11719453

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

104

—

117

C₄

C₂×#88123

yes

—

118

C₂

#13123234

yes

characteristic

119

C₂

#13125282

yes

—

120

C₂

#13125388

yes

—

	subgroup	G/H
center	C₂³	C₂²×D₅₂
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#97	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	C₄×#97	D₁₃
hypocenter	C₁₃	#33315
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

subgroup

G/H

center

C₂³

C₂²×D₅₂

commutator, cosocle

C₂²×C₄×C₁₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₁₃

Fitting

C₄×C₁₃×#97

C₂

socle, prime radical

C₂³×C₁₃

C₂²×D₄

hypercenter

C₄×#97

D₁₃

hypocenter

C₁₃

#33315

LCS

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
100. C₁₃	#33315	semidirect

H ≅ G/N

type

100. C₁₃

#33315

semidirect

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

subgroup	index
C₂×#11718344	2
#13123199	2
#13115004	2
C₄×C₁₃×#97	2
#33315	13

subgroup

index

C₄×C₁₃×#97

Subgroups — #16015510

Conjugacy classes of subgroups

Complements

Maximal subgroups