Group #16786697 — subgroups

Subgroups — #16786697

Order 3328.

228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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	#13131199	C₂	1	2	yes	maximal
2	#13129754	C₂	1	4	yes	maximal, complemented
3	#13113118	C₂	1	1	yes	maximal, characteristic
4	#11718346	C₄	1	2	yes	—
5	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
6	#11718260	C₄	1	4	yes	—
7	#11718259	C₄	1	4	yes	—
8	#11718231	C₂²	1	4	yes	—
9	C₈²×C₁₃	C₄	1	1	yes	characteristic
10	#11718046	C₂²	1	2	yes	—
11	C₈×#1055	C₄	1	1	yes	characteristic
12	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
13	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#6092	C₂×C₄	1	8	yes	—
15	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	#88060	—	2	2	no	—
18	#88054	—	2	2	no	—
19	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
20	C₄×#1055	C₂×C₄	1	2	yes	—
21	C₄×#1055	C₂³	1	1	yes	characteristic
22	#11416	—	13	1	no	maximal, Sylow
23	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
24	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	C₄²	1	2	yes	—
27	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
29	C₄×Dic₁₃	M₁₆	1	2	yes	—
30	C₂×#1055	—	2	2	no	—
31	C₂×#1055	C₂²×C₄	1	2	yes	—
32	C₈×D₁₃	—	2	4	no	—
33	#6092	—	2	8	no	—
34	#2163	—	13	2	no	—
35	#1450	—	13	1	no	—
36	#1313	—	13	4	no	—
37	C₂²×D₁₃	#97	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
40	C₂×Dic₁₃	#97	1	2	yes	—
41	C₂×Dic₁₃	#97	1	1	yes	characteristic
42	C₄×D₁₃	—	2	2	no	—
43	C₄×D₁₃	—	4	2	no	—
44	C₈×C₁₃	—	2	2	no	—
45	C₈×C₁₃	—	4	2	no	—
46	#1055	—	4	2	no	—
47	#1055	#131	1	4	yes	—
48	#431	—	13	2	no	—
49	C₂×C₄×C₈	—	13	1	no	—
50	C₄⋊C₁₆	—	13	4	no	—
51	C₂²⋊C₁₆	—	13	4	no	—
52	#346	—	13	4	no	—
53	#322	—	13	2	no	—
54	C₈²	—	13	1	no	—
55	C₈²	#261	1	1	yes	characteristic
56	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
57	C₂×D₁₃	—	2	2	no	—
58	C₂×D₁₃	—	2	1	no	—
59	C₄×C₁₃	—	2	2	no	—
60	C₄×C₁₃	#405	1	2	yes	—
61	Dic₁₃	—	2	2	no	—
62	Dic₁₃	—	2	1	no	—
63	C₂²×C₈	—	13	2	no	—
64	C₂×C₄²	—	13	1	no	—
65	C₂×C₁₆	—	13	8	no	—
66	C₄⋊C₈	—	26	2	no	—
67	C₂²⋊C₈	—	26	2	no	—
68	C₄×C₈	—	13	2	no	—
69	C₄×C₈	—	13	1	no	—
70	C₄×C₈	—	13	2	no	—
71	C₄×C₈	C₂×#261	1	2	yes	—
72	C₄×C₈	C₂×#261	1	1	yes	characteristic
73	C₂×C₁₃	#1452	1	1	yes	characteristic
74	C₂×C₁₃	#2110	1	2	yes	—
75	D₁₃	—	4	1	no	—
76	C₂²×C₄	—	13	1	no	—
77	C₂²×C₄	—	13	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	13	2	no	—
80	C₂×C₈	—	26	4	no	—
81	C₂×C₈	—	26	2	no	—
82	C₂×C₈	C₄×#261	1	2	yes	—
83	C₄²	—	13	2	no	—
84	C₄²	—	13	1	no	—
85	C₄²	C₂²×#261	1	1	yes	characteristic
86	C₁₆	—	26	8	no	—
87	C₁₃	#11416	1	1	yes	characteristic, complemented, Sylow
88	C₂³	—	13	1	no	—
89	C₂×C₄	—	13	2	no	—
90	C₂×C₄	—	13	1	no	—
91	C₂×C₄	—	26	2	no	—
92	C₂×C₄	—	52	2	no	—
93	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
94	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
95	C₈	—	2	2	no	—
96	C₈	—	4	2	no	—
97	C₈	—	13	4	no	—
98	C₈	—	52	2	no	—
99	C₂²	—	26	2	no	—
100	C₂²	—	26	1	no	—
101	C₂²	#11719047	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	26	2	no	—
104	C₄	—	26	1	no	—
105	C₄	#11719089	1	2	yes	—
106	C₂	—	52	1	no	—
107	C₂	#13130050	1	1	yes	characteristic
108	C₂	#13131058	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13131199

C₂

yes

maximal

#13129754

C₂

yes

maximal, complemented

#13113118

C₂

yes

maximal, characteristic

#11718346

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

#11718260

C₄

yes

—

#11718259

C₄

yes

—

#11718231

C₂²

yes

—

C₈²×C₁₃

C₄

yes

characteristic

#11718046

C₂²

yes

—

C₈×#1055

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×#6092

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

#88060

—

#88054

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

characteristic

#11416

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

M₁₆

yes

—

C₂×#1055

—

C₂×#1055

C₂²×C₄

yes

—

C₈×D₁₃

—

—

—

—

—

C₂²×D₁₃

#97

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×Dic₁₃

#97

yes

—

C₂×Dic₁₃

#97

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#1055

#131

yes

—

#431

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#322

—

C₈²

—

C₈²

#261

yes

characteristic

C₂²×C₁₃

C₂×#97

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#405

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#261

yes

—

C₄×C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×#261

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×#261

yes

characteristic

C₁₆

—

C₁₃

#11416

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₃⋊M₁₆

yes

—

C₂×C₄

C₂×C₄×#261

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

100

C₂²

—

101

C₂²

#11719047

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#11719089

yes

—

106

C₂

—

107

C₂

#13130050

yes

characteristic

108

C₂

#13131058

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×#261
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂²×D₁₃	#97
cosocle	C₄×#1055	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#11416
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈²

subgroup

G/H

center

C₂×C₄

C₂×C₄×#261

commutator

C₂×C₄×C₁₃

C₂×C₄²

Frattini

C₄²

C₂²×#261

Fitting

C₈²×C₁₃

C₄

socle

C₂²×C₁₃

C₂×#97

C₂²×D₁₃

C₂³

C₈²

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ C₈²

N	H ≅ G/N	type
2. #13129754	C₂	semidirect
87. C₁₃	#11416	semidirect

H ≅ G/N

type

2. #13129754

C₂

semidirect

87. C₁₃

#11416

semidirect

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

subgroup	index
#13131199	2
#13129754	2
#13113118	2
#11416	13

subgroup

index

Subgroups — #16786697

Conjugacy classes of subgroups

Complements

Maximal subgroups