Group #14545022 — subgroups

Subgroups — #14545022

Order 2176.

220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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	C₂×#10587538	C₂	1	2	yes	maximal, complemented
2	#11763706	C₂	1	4	yes	maximal, complemented
3	C₂×#10587593	C₂	1	1	yes	maximal, characteristic
4	C₂×#63252	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₁₇	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	#10587593	—	2	2	no	—
8	#10587593	—	2	2	no	—
9	C₂×#63218	C₂²	1	2	yes	—
10	C₂×C₈×D₁₇	C₄	1	2	yes	—
11	#10587538	—	2	2	no	—
12	#10587538	C₂²	1	4	yes	—
13	C₂×#63216	—	2	2	no	—
14	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₂²⋊D₁₇	C₈	1	2	yes	—
16	#63252	—	2	2	no	—
17	#63252	—	2	2	no	—
18	C₂×D₆₈	C₈	1	1	yes	characteristic
19	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
20	C₂×Dic₃₄	C₈	1	1	yes	characteristic
21	M₁₆×C₁₇	—	2	2	no	—
22	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
23	C₂×#3622	C₂×C₄	1	1	yes	characteristic
24	C₂×#3622	D₄	1	2	yes	—
25	C₂×#3622	D₄	1	2	yes	—
26	C₂×#3622	C₂³	1	1	yes	characteristic
27	#63218	—	2	4	no	—
28	C₈×D₁₇	—	2	2	no	—
29	C₈×D₁₇	—	2	2	no	—
30	#63216	—	2	4	no	—
31	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂²×D₁₇	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
36	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂²⋊D₁₇	—	2	4	no	—
38	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
39	D₆₈	—	2	2	no	—
40	C₄×D₁₇	—	2	2	no	—
41	C₄×D₁₇	—	2	2	no	—
42	Dic₃₄	—	2	2	no	—
43	C₈×C₁₇	—	2	2	no	—
44	#3622	C₂²⋊C₄	1	1	yes	characteristic
45	#3622	C₂²⋊C₄	1	1	yes	characteristic
46	#3622	C₂×D₄	1	2	yes	—
47	#2115	—	17	1	no	maximal, Sylow
48	C₂²×C₁₇	—	4	1	no	—
49	C₂²×C₁₇	C₂²⋊C₈	1	2	yes	—
50	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
51	C₂×D₁₇	—	2	2	no	—
52	C₂×D₁₇	—	4	2	no	—
53	C₄×C₁₇	C₂²⋊C₈	1	2	yes	—
54	C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
56	Dic₁₇	—	2	2	no	—
57	C₂×#131	—	17	1	no	—
58	C₂×M₃₂	—	17	2	no	—
59	#349	—	17	4	no	—
60	C₂×C₁₇	—	2	1	no	—
61	C₂×C₁₇	—	2	2	no	—
62	C₂×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
63	D₁₇	—	4	2	no	—
64	C₂×#41	—	17	1	no	—
65	#131	—	34	2	no	—
66	#131	—	34	2	no	—
67	C₂×M₁₆	—	17	2	no	—
68	C₂×M₁₆	#595	1	1	yes	characteristic
69	C₂²×C₈	—	17	1	no	—
70	C₂²×C₈	—	17	2	no	—
71	M₃₂	—	17	4	no	—
72	M₃₂	—	34	2	no	—
73	C₂×C₁₆	—	34	2	no	—
74	C₁₇	#2115	1	1	yes	characteristic, complemented, Sylow
75	#41	—	34	2	no	—
76	#41	—	34	2	no	—
77	C₂×Q₈	—	17	1	no	—
78	C₂×D₄	—	17	2	no	—
79	C₂×D₄	—	17	1	no	—
80	C₂²×C₄	—	17	2	no	—
81	C₂²×C₄	C₂×#595	1	1	yes	characteristic
82	M₁₆	—	2	2	no	—
83	M₁₆	—	34	4	no	—
84	C₂×C₈	—	17	2	no	—
85	C₂×C₈	—	17	2	no	—
86	C₂×C₈	—	17	1	no	—
87	C₂×C₈	—	17	1	no	—
88	C₂×C₈	—	34	2	no	—
89	C₂×C₈	—	34	2	no	—
90	C₂×C₈	C₂×#595	1	2	yes	—
91	C₁₆	—	34	4	no	—
92	C₂³	—	17	2	no	—
93	C₂³	#63242	1	1	yes	characteristic
94	Q₈	—	34	2	no	—
95	D₄	—	34	4	no	—
96	D₄	—	34	2	no	—
97	C₂×C₄	—	17	2	no	—
98	C₂×C₄	—	34	2	no	—
99	C₂×C₄	—	34	2	no	—
100	C₂×C₄	#63242	1	1	yes	characteristic
101	C₂×C₄	#63243	1	2	yes	—
102	C₂×C₄	C₂²⋊#595	1	2	yes	—
103	C₂×C₄	C₂²×#595	1	1	yes	characteristic
104	C₈	—	2	2	no	—
105	C₈	—	17	2	no	—
106	C₈	—	17	1	no	—
107	C₈	—	17	1	no	—
108	C₂²	—	4	1	no	—
109	C₂²	—	34	2	no	—
110	C₂²	—	68	2	no	—
111	C₂²	#10587543	1	2	yes	—
112	C₂²	C₂×#63242	1	1	yes	characteristic
113	C₄	—	34	2	no	—
114	C₄	#10587543	1	2	yes	—
115	C₄	C₂×#63243	1	1	yes	characteristic
116	C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	2	no	—
119	C₂	—	68	2	no	—
120	C₂	C₂×#10587543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587538

C₂

yes

maximal, complemented

#11763706

C₂

yes

maximal, complemented

C₂×#10587593

C₂

yes

maximal, characteristic

C₂×#63252

C₄

yes

characteristic

C₂×M₁₆×C₁₇

C₄

yes

characteristic

C₂²×#3622

C₂²

yes

—

—

C₂²

yes

—

C₂×C₈×D₁₇

C₄

yes

—

#10587538

—

#10587538

C₂²

yes

—

C₂×#63216

—

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₁₇

C₈

yes

—

#63252

—

#63252

—

C₂×D₆₈

C₈

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

—

C₂×Dic₃₄

C₈

yes

characteristic

M₁₆×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

D₄

yes

—

C₂×#3622

D₄

yes

—

C₂×#3622

C₂³

yes

characteristic

#63218

—

C₈×D₁₇

—

C₈×D₁₇

—

#63216

—

C₂³×C₁₇

C₂×C₈

yes

characteristic

C₂²×D₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂²⋊D₁₇

—

C₂×Dic₁₇

C₂×C₈

yes

—

D₆₈

—

C₄×D₁₇

—

C₄×D₁₇

—

Dic₃₄

—

C₈×C₁₇

—

#3622

C₂²⋊C₄

yes

characteristic

#3622

C₂²⋊C₄

yes

characteristic

#3622

C₂×D₄

yes

—

#2115

—

maximal, Sylow

C₂²×C₁₇

—

C₂²×C₁₇

C₂²⋊C₈

yes

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

C₂²⋊C₈

yes

—

C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

C₂×#131

—

C₂×M₃₂

—

#349

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

D₁₇

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

#595

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₁₇

#2115

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#595

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

—

C₁₆

—

C₂³

—

C₂³

#63242

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

#63242

yes

characteristic

101

C₂×C₄

#63243

yes

—

102

C₂×C₄

C₂²⋊#595

yes

—

103

C₂×C₄

C₂²×#595

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

#10587543

yes

—

112

C₂²

C₂×#63242

yes

characteristic

113

C₄

—

114

C₄

#10587543

yes

—

115

C₄

C₂×#63243

yes

characteristic

116

C₄

C₂×C₂²⋊#595

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

C₂×#10587543

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊#595
commutator	C₂²×C₁₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×#595
Fitting	C₂×M₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂×C₂²⋊C₈
prime radical	C₂×#63252	C₄
cosocle	C₂×#3622	C₂³
hypercenter	C₂×M₁₆	#595
hypocenter	C₁₇	#2115
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

C₂×C₂²⋊#595

commutator

C₂²×C₁₇

C₂²×C₈

Frattini

C₂×C₄

C₂²×#595

Fitting

C₂×M₁₆×C₁₇

C₄

socle

C₂×C₁₇

C₂×C₂²⋊C₈

C₄

C₂³

C₂×M₁₆

C₁₇

G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#10587538	C₂	semidirect
2. #11763706	C₂	semidirect
74. C₁₇	#2115	semidirect

H ≅ G/N

type

1. C₂×#10587538

C₂

semidirect

2. #11763706

C₂

semidirect

74. C₁₇

#2115

semidirect

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

subgroup	index
C₂×#10587538	2
#11763706	2
C₂×#10587593	2
#2115	17

subgroup

index

Subgroups — #14545022

Conjugacy classes of subgroups

Complements

Maximal subgroups