Group #16955174 — subgroups

Subgroups — #16955174

Order 4352.

190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11762642	C₂	1	1	yes	maximal, characteristic
2	#14530872	C₂	1	2	yes	maximal
3	#14526986	C₂	1	1	yes	maximal, characteristic, complemented
4	#14526965	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
7	#11763047	—	2	2	no	—
8	#11762642	—	2	2	no	—
9	C₂×#10587465	C₂²	1	1	yes	characteristic
10	#11762635	C₂²	1	2	yes	—
11	#11762613	—	2	2	no	—
12	C₂×C₁₇×Q₃₂	C₂²	1	2	yes	—
13	C₁₇×Q₆₄	—	2	2	no	—
14	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₁₇	—	2	2	no	—
16	#10587632	—	4	2	no	—
17	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
18	C₁₇×Q₃₂	—	2	2	no	—
19	C₁₇×Q₃₂	—	2	2	no	—
20	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
21	#10587506	—	4	2	no	—
22	#10587489	—	2	2	no	—
23	C₂×#63214	D₄	1	1	yes	characteristic
24	C₁₆×D₁₇	—	2	1	no	—
25	C₁₆×D₁₇	—	2	1	no	—
26	C₁₇×C₃₂	D₄	1	2	yes	—
27	#10587465	—	2	1	no	—
28	C₂×Q₈×C₁₇	—	4	2	no	—
29	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
30	Q₁₆×C₁₇	—	4	2	no	—
31	Q₁₆×C₁₇	—	4	2	no	—
32	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
33	#63227	—	8	2	no	—
34	C₄⋊Dic₁₇	—	4	2	no	—
35	#63225	—	8	2	no	—
36	C₂×#3622	D₈	1	1	yes	characteristic
37	C₈×D₁₇	—	2	1	no	—
38	C₈×D₁₇	—	2	1	no	—
39	C₁₆×C₁₇	C₂×D₄	1	1	yes	characteristic
40	C₁₆×C₁₇	#41	1	1	yes	characteristic
41	#63214	—	2	1	no	—
42	#13698	—	17	1	no	maximal, Sylow
43	C₂²×D₁₇	D₁₆	1	1	yes	characteristic
44	Q₈×C₁₇	—	8	2	no	—
45	Q₈×C₁₇	—	8	2	no	—
46	C₂×C₄×C₁₇	—	8	2	no	—
47	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
48	C₂×Dic₁₇	—	8	2	no	—
49	C₂×Dic₁₇	D₁₆	1	1	yes	characteristic
50	C₄×D₁₇	—	2	1	no	—
51	C₄×D₁₇	—	2	1	no	—
52	C₈×C₁₇	#121	1	1	yes	characteristic
53	C₈×C₁₇	#135	1	1	yes	characteristic
54	#3622	—	2	1	no	—
55	C₂×Q₆₄	D₁₇	1	1	yes	characteristic, complemented
56	C₂×M₆₄	—	17	1	no	—
57	#2216	—	17	2	no	—
58	#1424	—	17	1	no	—
59	#1416	—	17	2	no	—
60	C₂²×C₁₇	C₂×D₁₆	1	1	yes	characteristic
61	C₂×D₁₇	—	2	1	no	—
62	C₂×D₁₇	—	2	2	no	—
63	C₄×C₁₇	—	16	2	no	—
64	C₄×C₁₇	#466	1	1	yes	characteristic
65	C₄×C₁₇	#508	1	1	yes	characteristic
66	Dic₁₇	—	2	1	no	—
67	Dic₁₇	—	16	2	no	—
68	C₂×Q₃₂	C₂×D₁₇	1	2	yes	—
69	C₂²×C₁₆	—	17	1	no	—
70	#467	—	34	2	no	—
71	Q₆₄	—	2	2	no	—
72	M₆₄	—	34	2	no	—
73	C₂×C₃₂	—	17	1	no	—
74	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
75	#366	—	17	2	no	—
76	#358	—	34	2	no	—
77	C₂×C₁₇	#2215	1	1	yes	characteristic
78	C₂×C₁₇	#2264	1	2	yes	—
79	D₁₇	—	4	1	no	—
80	C₂×Q₁₆	—	2	2	no	—
81	C₂²×C₈	—	17	1	no	—
82	C₂²⋊Q₈	—	68	2	no	—
83	Q₃₂	—	2	2	no	—
84	Q₃₂	—	2	2	no	—
85	C₂×C₁₆	—	17	1	no	—
86	C₂×C₁₆	—	34	1	no	—
87	C₂×C₁₆	—	34	1	no	—
88	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
89	#107	—	34	2	no	—
90	#103	—	68	2	no	—
91	C₃₂	—	34	1	no	—
92	C₃₂	C₂²⋊D₁₇	1	2	yes	—
93	C₁₇	#13698	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	4	2	no	—
95	C₂²×C₄	—	17	1	no	—
96	Q₁₆	—	4	2	no	—
97	Q₁₆	—	4	2	no	—
98	C₂×C₈	—	17	1	no	—
99	C₂×C₈	—	34	1	no	—
100	C₂×C₈	—	34	1	no	—
101	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
102	C₄⋊C₄	—	68	2	no	—
103	C₄⋊C₄	—	136	2	no	—
104	C₂²⋊C₄	—	136	2	no	—
105	C₁₆	—	34	1	no	—
106	C₁₆	#63254	1	1	yes	characteristic
107	C₁₆	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
108	C₂³	—	17	1	no	—
109	Q₈	—	8	2	no	—
110	Q₈	—	8	2	no	—
111	C₂×C₄	—	8	2	no	—
112	C₂×C₄	—	17	1	no	—
113	C₂×C₄	—	34	1	no	—
114	C₂×C₄	—	34	1	no	—
115	C₂×C₄	—	136	2	no	—
116	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
117	C₈	—	34	1	no	—
118	C₈	#10587598	1	1	yes	characteristic
119	C₈	#10587624	1	1	yes	characteristic
120	C₂²	—	34	2	no	—
121	C₂²	—	34	1	no	—
122	C₂²	D₁₆×D₁₇	1	1	yes	characteristic
123	C₄	—	16	2	no	—
124	C₄	—	272	2	no	—
125	C₄	—	34	1	no	—
126	C₄	#11763042	1	1	yes	characteristic
127	C₄	#11763238	1	1	yes	characteristic
128	C₂	—	68	1	no	—
129	C₂	#14530867	1	1	yes	characteristic
130	C₂	#14531103	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762642

C₂

yes

maximal, characteristic

#14530872

C₂

yes

maximal

#14526986

C₂

yes

maximal, characteristic, complemented

#14526965

C₂

yes

maximal, complemented

C₂×C₁₇×Q₆₄

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₁₇

C₂²

yes

—

—

C₂²

yes

characteristic

#11762635

C₂²

yes

—

#11762613

—

C₂×C₁₇×Q₃₂

C₂²

yes

—

C₁₇×Q₆₄

—

C₂×C₁₇×C₃₂

C₂²

yes

characteristic

C₂×Q₁₆×C₁₇

—

#10587632

—

C₂×C₈×D₁₇

D₄

yes

characteristic

C₁₇×Q₃₂

—

C₁₇×Q₃₂

—

C₂×C₁₆×C₁₇

C₂³

yes

—

—

D₄

yes

characteristic

C₁₆×D₁₇

—

C₁₆×D₁₇

—

C₁₇×C₃₂

D₄

yes

—

#10587465

—

C₂×Q₈×C₁₇

—

C₂×C₄×D₁₇

D₈

yes

characteristic

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

#63227

—

C₄⋊Dic₁₇

—

#63225

—

C₂×#3622

D₈

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₁₆×C₁₇

C₂×D₄

yes

C₁₆×C₁₇

yes

—

—

C₂²×D₁₇

D₁₆

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

D₁₆

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

—

C₂×Q₆₄

D₁₇

yes

characteristic, complemented

C₂×M₆₄

—

#2216

—

#1424

—

#1416

—

C₂²×C₁₇

C₂×D₁₆

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

—

C₂×Q₃₂

C₂×D₁₇

yes

—

C₂²×C₁₆

—

#467

—

Q₆₄

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₁₇

yes

characteristic

#366

—

#358

—

C₂×C₁₇

#2215

yes

characteristic

C₂×C₁₇

#2264

yes

—

D₁₇

—

C₂×Q₁₆

—

C₂²×C₈

—

C₂²⋊Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂²×D₁₇

yes

characteristic

#107

—

#103

—

C₃₂

—

C₃₂

C₂²⋊D₁₇

yes

—

C₁₇

#13698

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

D₄×D₁₇

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

136

—

104

C₂²⋊C₄

—

136

—

105

C₁₆

—

106

C₁₆

#63254

yes

characteristic

107

C₁₆

C₂×C₂²⋊D₁₇

yes

characteristic

108

C₂³

—

109

Q₈

—

110

Q₈

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

136

—

116

C₂×C₄

D₈×D₁₇

yes

characteristic

117

C₈

—

118

C₈

#10587598

yes

characteristic

119

C₈

#10587624

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

D₁₆×D₁₇

yes

characteristic

123

C₄

—

124

C₄

—

272

—

125

C₄

—

126

C₄

#11763042

yes

characteristic

127

C₄

#11763238

yes

characteristic

128

C₂

—

129

C₂

#14530867

yes

characteristic

130

C₂

#14531103

yes

—

	subgroup	G/H
center	C₂²	D₁₆×D₁₇
commutator, cosocle	C₂×C₁₆×C₁₇	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₇
Fitting	C₂×C₁₇×Q₆₄	C₂
socle	C₂²×C₁₇	C₂×D₁₆
prime radical	C₂²×D₁₇	D₁₆
hypercenter	C₂×Q₆₄	D₁₇
hypocenter	C₁₇	#13698
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₆₄

subgroup

G/H

center

C₂²

D₁₆×D₁₇

commutator, cosocle

C₂×C₁₆×C₁₇

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₇

Fitting

C₂×C₁₇×Q₆₄

C₂

socle

C₂²×C₁₇

C₂×D₁₆

prime radical

C₂²×D₁₇

D₁₆

hypercenter

C₂×Q₆₄

D₁₇

hypocenter

C₁₇

#13698

LCS

G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₆₄

N	H ≅ G/N	type
3. #14526986	C₂	semidirect
4. #14526965	C₂	semidirect
5. C₂×C₁₇×Q₆₄	C₂	semidirect
55. C₂×Q₆₄	D₁₇	semidirect
93. C₁₇	#13698	semidirect

H ≅ G/N

type

3. #14526986

C₂

semidirect

4. #14526965

C₂

semidirect

5. C₂×C₁₇×Q₆₄

C₂

semidirect

55. C₂×Q₆₄

D₁₇

semidirect

93. C₁₇

#13698

semidirect

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

subgroup	index
C₂×#11762642	2
#14530872	2
#14526986	2
#14526965	2
C₂×C₁₇×Q₆₄	2
#13698	17

subgroup

index

C₂×C₁₇×Q₆₄

Subgroups — #16955174

Conjugacy classes of subgroups

Complements

Maximal subgroups