Group #16786577 — subgroups

Subgroups — #16786577

Order 3328.

366 conjugacy classes of subgroups; only the 196 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 196 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	C₄×D₁₃⋊C₁₆	C₂	1	2	yes	maximal
2	#13129748	C₂	1	4	yes	maximal, complemented
3	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×D₁₃⋊C₁₆	C₄	1	4	yes	—
5	C₄×C₈×D₁₃	C₄	1	2	yes	—
6	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	#11718257	C₄	1	4	yes	—
8	C₄×#6092	C₂²	1	4	yes	—
9	C₈²×C₁₃	C₄	1	1	yes	characteristic
10	C₈×#1055	C₄	1	1	yes	characteristic
11	C₈×#1055	C₂²	1	2	yes	—
12	C₂×C₈×D₁₃	C₈	1	4	yes	—
13	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
14	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×#6092	C₂×C₄	1	8	yes	—
16	D₁₃⋊C₁₆	C₈	1	16	yes	complemented
17	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₈×Dic₁₃	C₈	1	4	yes	—
20	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₄×#1055	C₂×C₄	1	2	yes	—
22	C₄×#1055	C₂³	1	1	yes	characteristic
23	C₂×#1311	—	13	1	no	maximal, Sylow
24	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
25	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
26	C₂×C₈×C₁₃	C₄²	1	2	yes	—
27	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
28	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
30	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
31	C₂×#1055	C₂×C₈	1	4	yes	—
32	C₂×#1055	C₂²×C₄	1	2	yes	—
33	C₈×D₁₃	—	2	8	no	—
34	C₈×D₁₃	C₂×C₈	1	8	yes	—
35	#6092	C₂×C₈	1	16	yes	complemented
36	C₂×C₄×C₁₆	—	13	2	no	—
37	C₂×C₈²	—	13	1	no	—
38	#1311	—	13	4	no	—
39	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
41	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
42	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
43	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
44	C₄×D₁₃	C₄×C₈	1	4	yes	—
45	C₄×D₁₃	M₃₂	1	8	yes	—
46	C₈×C₁₃	—	2	4	no	—
47	C₈×C₁₃	C₄×C₈	1	4	yes	—
48	#1055	—	2	4	no	—
49	#1055	C₂²×C₈	1	4	yes	—
50	C₂²×C₁₆	—	13	4	no	—
51	C₂×C₄×C₈	—	13	2	no	—
52	C₂×C₄×C₈	—	13	1	no	—
53	C₄×C₁₆	—	13	4	no	—
54	C₄×C₁₆	—	13	4	no	—
55	C₈²	—	13	2	no	—
56	C₈²	—	13	1	no	—
57	C₈²	#261	1	1	yes	characteristic
58	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
59	C₂×D₁₃	C₈²	1	2	yes	—
60	C₂×D₁₃	#346	1	4	yes	—
61	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
62	C₄×C₁₃	C₂×M₃₂	1	4	yes	—
63	Dic₁₃	C₈²	1	2	yes	—
64	Dic₁₃	#346	1	4	yes	—
65	C₂²×C₈	—	13	2	no	—
66	C₂²×C₈	—	13	4	no	—
67	C₂×C₄²	—	13	1	no	—
68	C₂×C₁₆	—	13	16	no	—
69	C₂×C₁₆	—	13	8	no	—
70	C₄×C₈	—	13	4	no	—
71	C₄×C₈	—	13	2	no	—
72	C₄×C₈	—	13	1	no	—
73	C₄×C₈	—	13	2	no	—
74	C₄×C₈	C₂×#261	1	2	yes	—
75	C₄×C₈	C₂×#261	1	1	yes	characteristic
76	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
77	C₂×C₁₃	C₂×#346	1	2	yes	—
78	D₁₃	#1311	1	4	yes	complemented
79	C₂²×C₄	—	13	2	no	—
80	C₂²×C₄	—	13	1	no	—
81	C₂×C₈	—	13	2	no	—
82	C₂×C₈	—	13	8	no	—
83	C₂×C₈	—	13	4	no	—
84	C₂×C₈	—	26	8	no	—
85	C₂×C₈	D₁₃⋊C₈	1	4	yes	—
86	C₂×C₈	C₄×#261	1	2	yes	—
87	C₄²	—	13	2	no	—
88	C₄²	—	13	1	no	—
89	C₄²	C₂²×#261	1	1	yes	characteristic
90	C₁₆	—	13	16	no	—
91	C₁₃	C₂×#1311	1	1	yes	characteristic, complemented, Sylow
92	C₂³	—	13	1	no	—
93	C₂×C₄	—	13	2	no	—
94	C₂×C₄	—	13	1	no	—
95	C₂×C₄	—	13	8	no	—
96	C₂×C₄	—	13	4	no	—
97	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
98	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
99	C₈	—	2	4	no	—
100	C₈	—	13	4	no	—
101	C₈	—	26	4	no	—
102	C₈	C₈×#261	1	4	yes	—
103	C₂²	—	13	4	no	—
104	C₂²	—	13	2	no	—
105	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
106	C₄	—	13	4	no	—
107	C₄	—	13	2	no	—
108	C₄	D₁₃⋊M₃₂	1	4	yes	—
109	C₄	C₂×C₈×#261	1	2	yes	—
110	C₂	—	13	4	no	—
111	C₂	C₈×D₁₃⋊C₈	1	1	yes	characteristic
112	C₂	#13131037	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₁₃⋊C₁₆

C₂

yes

maximal

#13129748

C₂

yes

maximal, complemented

C₈²×D₁₃

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₁₆

C₄

yes

—

C₄×C₈×D₁₃

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

#11718257

C₄

yes

—

C₄×#6092

C₂²

yes

—

C₈²×C₁₃

C₄

yes

characteristic

C₈×#1055

C₄

yes

characteristic

C₈×#1055

C₂²

yes

—

C₂×C₈×D₁₃

C₈

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×#6092

C₂×C₄

yes

—

D₁₃⋊C₁₆

C₈

yes

complemented

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

characteristic

C₂×#1311

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₄²

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

C₂×C₈

yes

—

C₂×#1055

C₂²×C₄

yes

—

C₈×D₁₃

—

C₈×D₁₃

C₂×C₈

yes

—

#6092

C₂×C₈

yes

complemented

C₂×C₄×C₁₆

—

C₂×C₈²

—

#1311

—

C₂²×D₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

characteristic

C₂×Dic₁₃

C₄×C₈

yes

—

C₄×D₁₃

C₄×C₈

yes

—

C₄×D₁₃

M₃₂

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄×C₈

yes

—

#1055

—

#1055

C₂²×C₈

yes

—

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₈²

—

C₈²

—

C₈²

#261

yes

characteristic

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×D₁₃

C₈²

yes

—

C₂×D₁₃

#346

yes

—

C₄×C₁₃

C₂×C₄×C₈

yes

—

C₄×C₁₃

C₂×M₃₂

yes

—

Dic₁₃

C₈²

yes

—

Dic₁₃

#346

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#261

yes

—

C₄×C₈

C₂×#261

yes

characteristic

C₂×C₁₃

C₂×C₈²

yes

characteristic

C₂×C₁₃

C₂×#346

yes

—

D₁₃

#1311

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₃⋊C₈

yes

—

C₂×C₈

C₄×#261

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×#261

yes

characteristic

C₁₆

—

C₁₃

C₂×#1311

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₃⋊C₈

yes

—

C₂×C₄

C₂×C₄×#261

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₈

C₈×#261

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₄×D₁₃⋊C₈

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

D₁₃⋊M₃₂

yes

—

109

C₄

C₂×C₈×#261

yes

—

110

C₂

—

111

C₂

C₈×D₁₃⋊C₈

yes

characteristic

112

C₂

#13131037

yes

—

	subgroup	G/H
center	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₂×C₈²
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×#1055	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	C₂×#1311
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₄×C₈

C₂×#261

commutator

C₂×C₁₃

C₂×C₈²

Frattini

C₄²

C₂²×#261

Fitting

C₈²×C₁₃

C₄

socle

C₂²×C₁₃

C₂×C₄×C₈

prime radical

C₂²×D₁₃

C₄×C₈

C₂³

C₈²

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
2. #13129748	C₂	semidirect
16. D₁₃⋊C₁₆	C₈	semidirect
35. #6092	C₂×C₈	semidirect
78. D₁₃	#1311	semidirect
91. C₁₃	C₂×#1311	semidirect

H ≅ G/N

type

2. #13129748

C₂

semidirect

16. D₁₃⋊C₁₆

C₈

semidirect

35. #6092

C₂×C₈

semidirect

78. D₁₃

#1311

semidirect

91. C₁₃

C₂×#1311

semidirect

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

subgroup	index
C₄×D₁₃⋊C₁₆	2
#13129748	2
C₈²×D₁₃	2
C₂×#1311	13

subgroup

index

C₄×D₁₃⋊C₁₆

#13129748

C₈²×D₁₃

C₂×#1311

Subgroups — #16786577

Conjugacy classes of subgroups

Complements

Maximal subgroups