Group #16777437 — subgroups

Subgroups — #16777437

Order 3328.

200 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 66 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	#13130393	C₂	1	2	yes	maximal
2	#13116591	C₂	1	1	yes	maximal, characteristic
3	#11719129	—	2	2	no	—
4	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
5	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88052	C₄	1	1	yes	characteristic
7	#11718256	C₄	1	4	yes	—
8	#11718254	—	2	2	no	—
9	#11718093	—	2	2	no	—
10	C₂×#6122	—	4	2	no	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
13	C₂²×#1055	Q₈	1	1	yes	characteristic
14	#88112	—	4	2	no	—
15	C₄⋊#1057	—	2	4	no	—
16	C₁₃×M₃₂	—	4	1	no	—
17	C₂×C₁₃×C₁₆	—	2	1	no	—
18	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
19	C₈×Dic₁₃	D₄	1	2	yes	—
20	#88052	—	4	1	no	—
21	C₂×#6090	—	2	1	no	—
22	#7245	—	13	1	no	maximal, Sylow
23	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂²×Dic₁₃	SD₁₆	1	2	yes	—
25	#6122	—	8	4	no	—
26	C₂×#1057	—	4	4	no	—
27	C₂×C₈×C₁₃	—	2	1	no	—
28	C₂×C₈×C₁₃	—	2	1	no	—
29	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
30	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×Dic₁₃	C₂²⋊C₄	1	2	yes	—
32	C₄×Dic₁₃	D₈	1	1	yes	characteristic
33	C₄×Dic₁₃	Q₁₆	1	1	yes	characteristic
34	C₂×#1055	—	4	1	no	—
35	C₂×#1055	C₄⋊C₄	1	2	yes	—
36	C₁₃×C₁₆	—	4	1	no	—
37	#6090	—	4	1	no	—
38	#2150	—	13	1	no	—
39	#1567	—	13	2	no	—
40	C₂³×C₁₃	#106	1	1	yes	characteristic
41	C₂×C₄×C₁₃	—	2	1	no	—
42	C₂×C₄×C₁₃	—	2	1	no	—
43	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
44	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
45	C₂×Dic₁₃	—	2	2	no	—
46	C₂×Dic₁₃	—	2	2	no	—
47	C₂×Dic₁₃	#102	1	2	yes	—
48	C₂×Dic₁₃	#103	1	2	yes	—
49	#1057	—	8	4	no	—
50	C₈×C₁₃	—	2	1	no	—
51	C₈×C₁₃	#100	1	1	yes	characteristic
52	C₈×C₁₃	#101	1	1	yes	characteristic
53	#1055	—	2	2	no	—
54	C₂×M₃₂	—	13	1	no	—
55	C₂×M₃₂	#261	1	1	yes	characteristic
56	#423	—	26	2	no	—
57	C₂×C₄×C₈	—	13	1	no	—
58	C₄⋊C₁₆	—	26	2	no	—
59	#335	—	13	4	no	—
60	#335	—	26	2	no	—
61	C₂²×C₁₃	—	2	1	no	—
62	C₂²×C₁₃	—	2	2	no	—
63	C₂²×C₁₃	#340	1	1	yes	characteristic
64	C₄×C₁₃	—	2	1	no	—
65	C₄×C₁₃	#338	1	1	yes	characteristic
66	C₄×C₁₃	#343	1	1	yes	characteristic
67	Dic₁₃	—	2	2	no	—
68	Dic₁₃	#361	1	2	yes	—
69	Dic₁₃	#362	1	2	yes	—
70	C₂×M₁₆	—	52	2	no	—
71	C₂²×C₈	—	13	1	no	—
72	C₂²×C₈	C₂×#261	1	1	yes	characteristic
73	C₂×C₄²	—	13	1	no	—
74	M₃₂	—	4	1	no	—
75	M₃₂	—	52	1	no	—
76	C₂×C₁₆	—	2	1	no	—
77	C₂×C₁₆	—	26	1	no	—
78	C₄⋊C₈	—	26	4	no	—
79	C₄⋊C₈	—	52	2	no	—
80	C₄×C₈	—	13	2	no	—
81	C₄×C₈	—	13	2	no	—
82	C₂×C₁₃	—	4	1	no	—
83	C₂×C₁₃	#1292	1	1	yes	characteristic
84	C₂×C₁₃	#1387	1	2	yes	—
85	C₂²×C₄	—	13	2	no	—
86	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
87	M₁₆	—	104	4	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	13	2	no	—
91	C₂×C₈	—	52	1	no	—
92	C₂×C₈	—	52	4	no	—
93	C₂×C₈	C₄×#261	1	1	yes	characteristic
94	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
95	C₄²	—	13	1	no	—
96	C₄²	—	13	1	no	—
97	C₄²	—	13	2	no	—
98	C₁₆	—	4	1	no	—
99	C₁₆	—	52	1	no	—
100	C₁₃	#7245	1	1	yes	characteristic, complemented, Sylow
101	C₂³	#88101	1	1	yes	characteristic
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	13	2	no	—
105	C₂×C₄	—	13	2	no	—
106	C₂×C₄	—	26	2	no	—
107	C₂×C₄	—	26	2	no	—
108	C₂×C₄	#88102	1	1	yes	characteristic
109	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	26	2	no	—
112	C₈	—	104	4	no	—
113	C₈	#88113	1	1	yes	characteristic
114	C₈	#88121	1	1	yes	characteristic
115	C₂²	—	2	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	#11718265	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	13	2	no	—
120	C₄	—	13	2	no	—
121	C₄	—	26	2	no	—
122	C₄	#11718269	1	1	yes	characteristic
123	C₄	#11718291	1	1	yes	characteristic
124	C₂	—	4	1	no	—
125	C₂	#13129706	1	1	yes	characteristic
126	C₂	#13129911	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130393

C₂

yes

maximal

#13116591

C₂

yes

maximal, characteristic

#11719129

—

C₂×C₁₃×M₃₂

C₄

yes

characteristic

C₂×C₈×Dic₁₃

C₂²

yes

characteristic

C₂×#88052

C₄

yes

characteristic

#11718256

C₄

yes

—

#11718254

—

#11718093

—

C₂×#6122

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

D₄

yes

characteristic

C₂²×#1055

Q₈

yes

characteristic

#88112

—

C₄⋊#1057

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₈×Dic₁₃

D₄

yes

—

—

—

—

C₂²×C₄×C₁₃

C₄⋊C₄

yes

characteristic

C₂²×Dic₁₃

SD₁₆

yes

—

#6122

—

C₂×#1057

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₄×Dic₁₃

C₂²⋊C₄

yes

—

C₄×Dic₁₃

D₈

yes

characteristic

C₄×Dic₁₃

Q₁₆

yes

characteristic

C₂×#1055

—

C₂×#1055

C₄⋊C₄

yes

—

C₁₃×C₁₆

—

#6090

—

#2150

—

#1567

—

C₂³×C₁₃

#106

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#102

yes

—

C₂×Dic₁₃

#103

yes

—

#1057

—

C₈×C₁₃

—

C₈×C₁₃

yes

C₈×C₁₃

yes

—

C₂×M₃₂

—

C₂×M₃₂

#261

yes

characteristic

#423

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

#335

—

#335

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#340

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

#361

yes

—

Dic₁₃

#362

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#1292

yes

characteristic

C₂×C₁₃

#1387

yes

—

C₂²×C₄

—

C₂²×C₄

C₄⋊#261

yes

characteristic

M₁₆

—

104

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×#261

yes

characteristic

C₂×C₈

C₂²⋊#261

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

100

C₁₃

#7245

yes

characteristic, complemented, Sylow

101

C₂³

#88101

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

#88102

yes

characteristic

109

C₂×C₄

(C₂×#261)⋊C₄

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

104

—

113

C₈

#88113

yes

characteristic

114

C₈

#88121

yes

characteristic

115

C₂²

—

116

C₂²

—

117

C₂²

#11718265

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11718269

yes

characteristic

123

C₄

#11718291

yes

characteristic

124

C₂

—

125

C₂

#13129706

yes

characteristic

126

C₂

#13129911

yes

—

	subgroup	G/H
center	C₂²	#11718265
commutator	C₂×C₈×C₁₃	C₄²
Frattini	C₂²×C₈	C₂×#261
Fitting	C₂×C₁₃×M₃₂	C₄
socle	C₂²×C₁₃	#340
prime radical	C₂³×C₁₃	#106
cosocle	C₂×C₈×Dic₁₃	C₂²
hypercenter	C₂×M₃₂	#261
hypocenter	C₁₃	#7245
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

#11718265

commutator

C₂×C₈×C₁₃

C₄²

Frattini

C₂²×C₈

C₂×#261

Fitting

C₂×C₁₃×M₃₂

C₄

C₂²×C₁₃

C₂³×C₁₃

C₂×C₈×Dic₁₃

C₂²

C₂×M₃₂

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
100. C₁₃	#7245	semidirect

H ≅ G/N

type

100. C₁₃

#7245

semidirect

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

subgroup	index
#13130393	2
#13116591	2
#7245	13

subgroup

index

#13130393

#13116591

#7245

Subgroups — #16777437

Conjugacy classes of subgroups

Complements

Maximal subgroups