Group #16782432 — subgroups

Subgroups — #16782432

Order 3328.

354 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 144 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	#13130775	C₂	1	2	yes	maximal
2	#13130391	C₂	1	4	yes	maximal
3	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#88103	—	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	#11718253	—	2	8	no	—
9	C₈²×C₁₃	C₄	1	1	yes	characteristic
10	C₈×#1055	C₄	1	1	yes	characteristic
11	C₈×#1055	C₄	1	2	yes	—
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	#88103	—	4	8	no	—
18	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₈×Dic₁₃	D₄	1	4	yes	—
21	C₈×Dic₁₃	Q₈	1	2	yes	—
22	C₄×#1055	C₂×C₄	1	2	yes	—
23	C₄×#1055	C₂×C₄	1	1	yes	characteristic
24	#8822	—	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	2	yes	—
30	C₂×C₈×C₁₃	C₄⋊C₄	1	4	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	4	yes	—
35	C₂×#1055	C₄⋊C₄	1	2	yes	—
36	C₈×D₁₃	—	2	8	no	—
37	C₈×D₁₃	SD₁₆	1	8	yes	—
38	#1848	—	13	2	no	—
39	#1566	—	13	4	no	—
40	C₂×C₈²	—	13	1	no	—
41	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
44	C₂×Dic₁₃	#127	1	1	yes	characteristic
45	C₂×Dic₁₃	C₄⋊Q₈	1	2	yes	—
46	C₄×D₁₃	—	2	4	no	—
47	C₄×D₁₃	C₂×SD₁₆	1	4	yes	—
48	#1057	—	8	4	no	—
49	C₈×C₁₃	#106	1	4	yes	—
50	C₈×C₁₃	#108	1	8	yes	complemented
51	#1055	—	2	4	no	—
52	#1055	#106	1	4	yes	—
53	C₂×#108	—	26	4	no	—
54	#423	—	13	4	no	—
55	C₂×C₄×C₈	—	13	2	no	—
56	C₂×C₄×C₈	—	13	1	no	—
57	#334	—	26	8	no	—
58	C₈²	—	13	2	no	—
59	C₈²	—	13	1	no	—
60	C₈²	#261	1	1	yes	characteristic
61	C₂²×C₁₃	#384	1	1	yes	characteristic
62	C₂×D₁₃	—	2	2	no	—
63	C₂×D₁₃	#498	1	2	yes	—
64	C₄×C₁₃	C₂×#106	1	2	yes	—
65	C₄×C₁₃	C₂×#108	1	4	yes	—
66	Dic₁₃	—	2	2	no	—
67	Dic₁₃	#492	1	2	yes	—
68	C₂×M₁₆	—	26	4	no	—
69	C₂²×C₈	—	13	2	no	—
70	C₂²×C₈	—	13	4	no	—
71	C₂×C₄²	—	13	1	no	—
72	#108	—	52	8	no	—
73	C₄⋊C₈	—	26	8	no	—
74	C₄×C₈	—	13	4	no	—
75	C₄×C₈	—	13	2	no	—
76	C₄×C₈	—	13	1	no	—
77	C₄×C₈	—	13	2	no	—
78	C₄×C₈	C₂×#261	1	1	yes	characteristic
79	C₄×C₈	C₂×#261	1	2	yes	—
80	C₂×C₁₃	#1844	1	1	yes	characteristic
81	C₂×C₁₃	#1848	1	2	yes	—
82	D₁₃	—	2	2	no	—
83	C₂²×C₄	—	13	1	no	—
84	C₂²×C₄	—	13	2	no	—
85	M₁₆	—	52	8	no	—
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	—	13	8	no	—
88	C₂×C₈	—	13	4	no	—
89	C₂×C₈	—	26	8	no	—
90	C₂×C₈	—	52	4	no	—
91	C₂×C₈	C₄⋊#261	1	2	yes	—
92	C₂×C₈	C₄⋊#261	1	4	yes	—
93	C₄²	—	13	2	no	—
94	C₄²	—	13	1	no	—
95	C₄²	C₂²×#261	1	1	yes	characteristic
96	C₁₃	#8822	1	1	yes	characteristic, complemented, Sylow
97	C₂³	—	13	1	no	—
98	C₂×C₄	—	13	1	no	—
99	C₂×C₄	—	13	4	no	—
100	C₂×C₄	—	13	2	no	—
101	C₂×C₄	—	26	4	no	—
102	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
103	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
104	C₈	—	13	4	no	—
105	C₈	—	26	4	no	—
106	C₈	—	104	4	no	—
107	C₈	#88101	1	4	yes	—
108	C₈	#88103	1	8	yes	complemented
109	C₂²	—	13	2	no	—
110	C₂²	—	26	2	no	—
111	C₂²	#11719059	1	1	yes	characteristic
112	C₄	—	13	2	no	—
113	C₄	—	26	2	no	—
114	C₄	C₂×#88101	1	2	yes	—
115	C₄	C₂×#88103	1	4	yes	—
116	C₂	—	26	2	no	—
117	C₂	#13130771	1	1	yes	characteristic
118	C₂	#13130775	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130775

C₂

yes

maximal

#13130391

C₂

yes

maximal

C₈²×D₁₃

C₂

yes

maximal, characteristic

C₂×#88103

—

#11719052

C₂²

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₄×C₈×D₁₃

C₂²

yes

—

#11718253

—

C₈²×C₁₃

C₄

yes

characteristic

C₈×#1055

C₄

yes

characteristic

C₈×#1055

C₄

yes

—

C₂×#6118

—

C₂×C₈×D₁₃

D₄

yes

—

C₂×C₈×D₁₃

Q₈

yes

—

C₄²×D₁₃

C₂³

yes

characteristic

C₄⋊#1057

—

#88103

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₈×Dic₁₃

D₄

yes

—

C₈×Dic₁₃

Q₈

yes

—

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

characteristic

#8822

—

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

SD₁₆

yes

—

#1848

—

#1566

—

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×SD₁₆

yes

—

#1057

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

yes

—

yes

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#334

—

C₈²

—

C₈²

—

C₈²

yes

C₂²×C₁₃

yes

C₂×D₁₃

—

C₂×D₁₃

#498

yes

—

C₄×C₁₃

C₂×#106

yes

—

C₄×C₁₃

C₂×#108

yes

—

Dic₁₃

—

Dic₁₃

#492

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

characteristic

C₄×C₈

C₂×#261

yes

—

C₂×C₁₃

#1844

yes

characteristic

C₂×C₁₃

#1848

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

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

C₁₃

#8822

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

103

C₂×C₄

C₂×C₄⋊#261

yes

—

104

C₈

—

105

C₈

—

106

C₈

—

104

—

107

C₈

#88101

yes

—

108

C₈

#88103

yes

complemented

109

C₂²

—

110

C₂²

—

111

C₂²

#11719059

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

C₂×#88101

yes

—

115

C₄

C₂×#88103

yes

—

116

C₂

—

117

C₂

#13130771

yes

characteristic

118

C₂

#13130775

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	#8822
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
50. C₈×C₁₃	#108	semidirect
96. C₁₃	#8822	semidirect
108. C₈	#88103	semidirect

H ≅ G/N

type

50. C₈×C₁₃

#108

semidirect

96. C₁₃

#8822

semidirect

108. C₈

#88103

semidirect

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

subgroup	index
#13130775	2
#13130391	2
C₈²×D₁₃	2
#8822	13

subgroup

index

#13130775

#13130391

C₈²×D₁₃

#8822

Subgroups — #16782432

Conjugacy classes of subgroups

Complements

Maximal subgroups