Group #16782437 — subgroups

Subgroups — #16782437

Order 3328.

354 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 136 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	#13130777	C₂	1	2	yes	maximal
2	#13130395	C₂	1	4	yes	maximal
3	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#88104	—	2	4	no	—
5	#11719052	C₂²	1	4	yes	—
6	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₄×C₈×D₁₃	C₂²	1	2	yes	—
8	#11718256	—	2	8	no	—
9	C₈²×C₁₃	C₄	1	1	yes	characteristic
10	C₈×#1055	C₄	1	2	yes	—
11	C₈×#1055	C₄	1	1	yes	characteristic
12	C₂×#6118	—	2	4	no	—
13	C₂×C₈×D₁₃	D₄	1	2	yes	—
14	C₂×C₈×D₁₃	Q₈	1	4	yes	—
15	C₄²×D₁₃	C₂³	1	1	yes	characteristic
16	C₄⋊#1057	—	2	8	no	—
17	#88104	—	4	8	no	—
18	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₈×Dic₁₃	D₄	1	4	yes	—
21	C₈×Dic₁₃	Q₈	1	2	yes	—
22	C₄×#1055	C₂×C₄	1	1	yes	characteristic
23	C₄×#1055	C₂×C₄	1	2	yes	—
24	#8823	—	13	1	no	maximal, Sylow
25	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
26	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
27	C₂×#1057	—	4	4	no	—
28	#6118	—	4	8	no	—
29	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
30	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
31	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
33	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂×#1055	C₄⋊C₄	1	2	yes	—
35	C₂×#1055	C₄⋊C₄	1	4	yes	—
36	C₈×D₁₃	—	2	8	no	—
37	C₈×D₁₃	D₈	1	4	yes	—
38	C₈×D₁₃	Q₁₆	1	4	yes	—
39	#1848	—	13	2	no	—
40	#1567	—	13	4	no	—
41	C₂×C₈²	—	13	1	no	—
42	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
45	C₂×Dic₁₃	#127	1	1	yes	characteristic
46	C₂×Dic₁₃	C₄⋊Q₈	1	2	yes	—
47	C₄×D₁₃	—	2	4	no	—
48	C₄×D₁₃	C₂×D₈	1	2	yes	—
49	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
50	#1057	—	8	4	no	—
51	C₈×C₁₃	—	2	4	no	—
52	C₈×C₁₃	#107	1	4	yes	—
53	#1055	#107	1	4	yes	—
54	#1055	#108	1	8	yes	complemented
55	C₂×#108	—	26	4	no	—
56	#423	—	13	4	no	—
57	C₂×C₄×C₈	—	13	2	no	—
58	C₂×C₄×C₈	—	13	1	no	—
59	#335	—	26	8	no	—
60	C₈²	—	13	1	no	—
61	C₈²	—	13	2	no	—
62	C₈²	#261	1	1	yes	characteristic
63	C₂²×C₁₃	#384	1	1	yes	characteristic
64	C₂×D₁₃	—	2	2	no	—
65	C₂×D₁₃	#500	1	2	yes	—
66	C₄×C₁₃	C₂×#107	1	2	yes	—
67	C₄×C₁₃	C₂×#108	1	4	yes	—
68	Dic₁₃	—	2	2	no	—
69	Dic₁₃	#493	1	1	yes	characteristic
70	Dic₁₃	#494	1	1	yes	characteristic
71	C₂×M₁₆	—	26	4	no	—
72	C₂²×C₈	—	13	2	no	—
73	C₂²×C₈	—	13	4	no	—
74	C₂×C₄²	—	13	1	no	—
75	#108	—	52	8	no	—
76	C₄⋊C₈	—	26	8	no	—
77	C₄×C₈	—	13	4	no	—
78	C₄×C₈	—	13	2	no	—
79	C₄×C₈	—	13	2	no	—
80	C₄×C₈	—	13	1	no	—
81	C₄×C₈	C₂×#261	1	2	yes	—
82	C₄×C₈	C₂×#261	1	1	yes	characteristic
83	C₂×C₁₃	#1845	1	1	yes	characteristic
84	C₂×C₁₃	#1848	1	2	yes	—
85	D₁₃	—	2	2	no	—
86	C₂²×C₄	—	13	1	no	—
87	C₂²×C₄	—	13	2	no	—
88	M₁₆	—	52	8	no	—
89	C₂×C₈	—	13	2	no	—
90	C₂×C₈	—	13	4	no	—
91	C₂×C₈	—	13	4	no	—
92	C₂×C₈	—	13	4	no	—
93	C₂×C₈	—	26	8	no	—
94	C₂×C₈	—	52	4	no	—
95	C₂×C₈	C₄⋊#261	1	4	yes	—
96	C₂×C₈	C₄⋊#261	1	2	yes	—
97	C₄²	—	13	2	no	—
98	C₄²	—	13	1	no	—
99	C₄²	C₂²×#261	1	1	yes	characteristic
100	C₁₃	#8823	1	1	yes	characteristic, complemented, Sylow
101	C₂³	—	13	1	no	—
102	C₂×C₄	—	13	1	no	—
103	C₂×C₄	—	13	2	no	—
104	C₂×C₄	—	13	2	no	—
105	C₂×C₄	—	13	2	no	—
106	C₂×C₄	—	26	4	no	—
107	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
108	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
109	C₈	—	2	4	no	—
110	C₈	—	13	4	no	—
111	C₈	—	13	8	no	—
112	C₈	—	104	4	no	—
113	C₈	#88102	1	4	yes	—
114	C₂²	—	13	2	no	—
115	C₂²	—	26	2	no	—
116	C₂²	#11719059	1	1	yes	characteristic
117	C₄	—	13	1	no	—
118	C₄	—	13	1	no	—
119	C₄	—	26	2	no	—
120	C₄	C₂×#88102	1	2	yes	—
121	C₄	D₁₃⋊#108	1	4	yes	—
122	C₂	—	26	2	no	—
123	C₂	#13130772	1	1	yes	characteristic
124	C₂	#13130776	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130777

C₂

yes

maximal

#13130395

C₂

yes

maximal

C₈²×D₁₃

C₂

yes

maximal, characteristic

C₂×#88104

—

#11719052

C₂²

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₄×C₈×D₁₃

C₂²

yes

—

#11718256

—

C₈²×C₁₃

C₄

yes

characteristic

C₈×#1055

C₄

yes

—

C₈×#1055

C₄

yes

characteristic

C₂×#6118

—

C₂×C₈×D₁₃

D₄

yes

—

C₂×C₈×D₁₃

Q₈

yes

—

C₄²×D₁₃

C₂³

yes

characteristic

C₄⋊#1057

—

#88104

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

D₄

yes

—

C₈×Dic₁₃

Q₈

yes

—

C₄×#1055

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

—

#8823

—

maximal, Sylow

C₂×C₄×D₁₃

C₂×D₄

yes

characteristic

C₂×C₄×D₁₃

C₂×Q₈

yes

—

C₂×#1057

—

#6118

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₂×D₄

yes

—

C₄×Dic₁₃

C₂×Q₈

yes

characteristic

C₂×#1055

C₄⋊C₄

yes

—

C₂×#1055

C₄⋊C₄

yes

—

C₈×D₁₃

—

C₈×D₁₃

D₈

yes

—

C₈×D₁₃

Q₁₆

yes

—

#1848

—

#1567

—

C₂×C₈²

—

C₂²×D₁₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₁₃

#127

yes

characteristic

C₂×Dic₁₃

C₄⋊Q₈

yes

—

C₄×D₁₃

—

C₄×D₁₃

C₂×D₈

yes

—

C₄×D₁₃

C₂×Q₁₆

yes

—

#1057

—

C₈×C₁₃

—

C₈×C₁₃

#107

yes

—

#1055

#107

yes

—

yes

—

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#335

—

C₈²

—

C₈²

—

C₈²

yes

C₂²×C₁₃

yes

C₂×D₁₃

—

C₂×D₁₃

#500

yes

—

C₄×C₁₃

C₂×#107

yes

—

C₄×C₁₃

C₂×#108

yes

—

Dic₁₃

—

Dic₁₃

yes

Dic₁₃

yes

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

C₄⋊C₈

—

C₄×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

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊#261

yes

—

C₂×C₈

C₄⋊#261

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×#261

yes

characteristic

100

C₁₃

#8823

yes

characteristic, complemented, Sylow

101

C₂³

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

108

C₂×C₄

C₂×C₄⋊#261

yes

—

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

—

104

—

113

C₈

#88102

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

#11719059

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

C₂×#88102

yes

—

121

C₄

D₁₃⋊#108

yes

—

122

C₂

—

123

C₂

#13130772

yes

characteristic

124

C₂

#13130776

yes

—

	subgroup	G/H
center	C₂²	#11719059
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	#384
prime radical	C₂²×D₁₃	C₄⋊Q₈
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#8823
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

subgroup

G/H

center

C₂²

#11719059

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₄²

C₂²×#261

Fitting

C₈²×C₁₃

C₄

socle

C₂²×C₁₃

#384

prime radical

C₂²×D₁₃

C₄⋊Q₈

cosocle

C₄²×D₁₃

C₂³

C₈²

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈²

N	H ≅ G/N	type
54. #1055	#108	semidirect
100. C₁₃	#8823	semidirect

H ≅ G/N

type

54. #1055

#108

semidirect

100. C₁₃

#8823

semidirect

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

subgroup	index
#13130777	2
#13130395	2
C₈²×D₁₃	2
#8823	13

subgroup

index

#13130777

#13130395

C₈²×D₁₃

#8823

Subgroups — #16782437

Conjugacy classes of subgroups

Complements

Maximal subgroups