Group #16786600 — subgroups

Subgroups — #16786600

Order 3328.

322 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 160 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×#88098	C₂	1	2	yes	maximal
2	#13129749	C₂	1	4	yes	maximal, complemented
3	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#88098	C₄	1	4	yes	—
5	C₄×C₈×D₁₃	C₄	1	2	yes	—
6	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	#11718258	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	#88098	—	2	8	no	—
17	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
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	#11402	—	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	M₁₆	1	8	yes	—
35	#6092	—	2	8	no	—
36	C₄×M₃₂	—	13	2	no	—
37	C₂×C₈²	—	13	1	no	—
38	#1312	—	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	2	yes	—
43	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
44	C₄×D₁₃	—	2	4	no	—
45	C₄×D₁₃	#97	1	4	yes	—
46	C₈×C₁₃	#97	1	4	yes	—
47	C₈×C₁₃	M₃₂	1	8	yes	complemented
48	#1055	—	2	4	no	—
49	#1055	C₂×M₁₆	1	4	yes	—
50	C₂×M₃₂	—	13	4	no	—
51	C₂×C₄×C₈	—	13	1	no	—
52	C₂×C₄×C₈	—	13	2	no	—
53	#346	—	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	—	2	2	no	—
60	C₂×D₁₃	#322	1	2	yes	—
61	C₄×C₁₃	C₂×#97	1	2	yes	—
62	C₄×C₁₃	C₂×M₃₂	1	4	yes	—
63	Dic₁₃	—	2	2	no	—
64	Dic₁₃	#322	1	2	yes	—
65	C₂²×C₈	—	13	2	no	—
66	C₂²×C₈	—	13	4	no	—
67	C₂×C₄²	—	13	1	no	—
68	M₃₂	—	26	8	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×#322	1	1	yes	characteristic
77	C₂×C₁₃	C₄×M₃₂	1	2	yes	—
78	D₁₃	—	2	2	no	—
79	C₂²×C₄	—	13	1	no	—
80	C₂²×C₄	—	13	2	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	—	26	8	no	—
91	C₁₃	#11402	1	1	yes	characteristic, complemented, Sylow
92	C₂³	—	13	1	no	—
93	C₂×C₄	—	13	1	no	—
94	C₂×C₄	—	13	4	no	—
95	C₂×C₄	—	13	2	no	—
96	C₂×C₄	—	26	4	no	—
97	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
98	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
99	C₈	—	13	4	no	—
100	C₈	—	26	4	no	—
101	C₈	#88098	1	8	yes	complemented
102	C₈	#88100	1	4	yes	—
103	C₂²	—	13	2	no	—
104	C₂²	—	26	2	no	—
105	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
106	C₄	—	13	2	no	—
107	C₄	—	26	2	no	—
108	C₄	C₂×#88098	1	4	yes	—
109	C₄	C₂×#88100	1	2	yes	—
110	C₂	—	26	2	no	—
111	C₂	#13130030	1	1	yes	characteristic
112	C₂	C₄×#88098	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#88098

C₂

yes

maximal

#13129749

C₂

yes

maximal, complemented

C₈²×D₁₃

C₂

yes

maximal, characteristic

C₂×#88098

C₄

yes

—

C₄×C₈×D₁₃

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

#11718258

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

—

#88098

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₈×Dic₁₃

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

characteristic

#11402

—

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

M₁₆

yes

—

#6092

—

C₄×M₃₂

—

C₂×C₈²

—

#1312

—

C₂²×D₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

#97

yes

—

C₈×C₁₃

#97

yes

—

C₈×C₁₃

M₃₂

yes

complemented

#1055

—

#1055

C₂×M₁₆

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₈²

—

C₈²

—

C₈²

#261

yes

characteristic

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

#322

yes

—

C₄×C₁₃

C₂×#97

yes

—

C₄×C₁₃

C₂×M₃₂

yes

—

Dic₁₃

—

Dic₁₃

#322

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#261

yes

—

C₄×C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

C₄×M₃₂

yes

—

D₁₃

—

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

#11402

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

#88098

yes

complemented

102

C₈

#88100

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₄×D₁₃⋊C₈

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

C₂×#88098

yes

—

109

C₄

C₂×#88100

yes

—

110

C₂

—

111

C₂

#13130030

yes

characteristic

112

C₂

C₄×#88098

yes

—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₈²×C₁₃	C₄
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×#1055	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#11402
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₈²

subgroup

G/H

center, Frattini

C₄²

C₂²×#261

commutator, socle

C₂²×C₁₃

C₂×C₄×C₈

Fitting

C₈²×C₁₃

C₄

prime radical

C₂²×D₁₃

C₄×C₈

C₂³

C₈²

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₄² ◁ C₈²

N	H ≅ G/N	type
2. #13129749	C₂	semidirect
47. C₈×C₁₃	M₃₂	semidirect
91. C₁₃	#11402	semidirect
101. C₈	#88098	semidirect

H ≅ G/N

type

2. #13129749

C₂

semidirect

47. C₈×C₁₃

M₃₂

semidirect

91. C₁₃

#11402

semidirect

101. C₈

#88098

semidirect

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

subgroup	index
C₄×#88098	2
#13129749	2
C₈²×D₁₃	2
#11402	13

subgroup

index

C₄×#88098

#13129749

C₈²×D₁₃

#11402

Subgroups — #16786600

Conjugacy classes of subgroups

Complements

Maximal subgroups