Finite Group Databasebeta

← #17043777

Subgroups — #17043777

Order 4352.

1130 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531382C212yesmaximal
2#14529770C218yesmaximal, complemented
3#14528858C214yesmaximal
4C2×C17×#543C211yesmaximal, characteristic
5#11762702—28no—
6#11762669C2214yes—
7#11762665C2214yes—
8C4×C22⋊Dic17C2214yes—
9#11762576C22116yes—
10C17×#543—28no—
11C2×C17×C22⋊Q8C418yescomplemented
12C2×C17×C22⋊Q8C2214yes—
13C22×C22⋊C4×C17C2212yes—
14C22×C22⋊C4×C17C2211yescharacteristic
15C25×C17C2311yescharacteristic
16C22×Q8×C17C2×C414yes—
17C23×C4×C17C2×C414yes—
18C23×C4×C17C2312yes—
19C17×C22⋊Q8—28no—
20C17×C22⋊Q8—28no—
21C17×C22⋊Q8—232no—
22C2×C4⋊C4×C17C2×C4112yes—
23C2×C22⋊C4×C17—28no—
24C2×C22⋊C4×C17C2×C414yes—
25C2×C22⋊C4×C17C2×C414yes—
26C2×C22⋊C4×C17D418yes—
27C2×C22⋊C4×C17C2314yes—
28C2×C22⋊Dic17—24no—
29C2×C22⋊Dic17—24no—
30C2×C22⋊Dic17C2318yes—
31C2×C4⋊Dic17—24no—
32C2×C4×Dic17—24no—
33#10587502—24no—
34#10587502—24no—
35C24×C17—24no—
36C24×C17—82no—
37C24×C17C22×C412yes—
38C24×C17C2×D414yes—
39C24×C17C2411yescharacteristic
40C2×Q8×C17—28no—
41C2×Q8×C17—84no—
42C22×C4×C17—28no—
43C22×C4×C17—82no—
44C22×C4×C17—84no—
45C22×C4×C17C22×C418yes—
46C22×C4×C17C22×C414yes—
47C22×C4×C17C2×D414yes—
48C22×C4×C17C2×D414yes—
49C22×Dic17—28no—
50C4⋊C4×C17—224no—
51C22⋊C4×C17—28no—
52C22⋊C4×C17—28no—
53C22⋊C4×C17C22⋊C4116yes—
54C22⋊Dic17—216no—
55C22⋊Dic17—84no—
56C22⋊Dic17—84no—
57C4⋊Dic17—84no—
58C4×Dic17—84no—
59#21827—171nomaximal, Sylow
60C23×C17—24no—
61C23×C17—28no—
62C23×C17—44no—
63C23×C17—42no—
64C23×C17—44no—
65C23×C17—44no—
66C23×C17—88no—
67C23×C17C2×C22⋊C414yes—
68C23×C17C23×C411yescharacteristic
69C23×C17C22×D412yes—
70C23×C172−1+414yes—
71Q8×C17—88no—
72C2×C4×C17—28no—
73C2×C4×C17—44no—
74C2×C4×C17—44no—
75C2×C4×C17—44no—
76C2×C4×C17—48no—
77C2×C4×C17—88no—
78C2×C4×C17C2×C22⋊C418yes—
79C2×Dic17—48no—
80C2×Dic17—48no—
81C2×Dic17—48no—
82C2×#543D1711yescharacteristic
83#2312—172no—
84#1996—178no—
85#1819—174no—
86C22×C17—22no—
87C22×C17—22no—
88C22×C17—22no—
89C22×C17—24no—
90C22×C17—28no—
91C22×C17—44no—
92C22×C17—48no—
93C22×C17—88no—
94C22×C17C22×C22⋊C411yescharacteristic
95C22×C17#51912yes—
96C22×C17#53614yes—
97C4×C17—28no—
98C4×C17—48no—
99Dic17—88no—
100#543—28no—
101C2×C22⋊Q8Dic1718yescomplemented
102C2×C22⋊Q8C2×D1714yes—
103C22×C22⋊C4C2×D1712yes—
104C22×C22⋊C4C2×D1711yescharacteristic
105#388—348no—
106#380—174no—
107#379—174no—
108C4×C22⋊C4—174no—
109#342—1716no—
110C2×C17—24no—
111C2×C17—22no—
112C2×C17—44no—
113C2×C17#231011yescharacteristic
114C2×C17#288312yes—
115C25C22×D1711yescharacteristic
116C22×Q8C2×Dic1714yes—
117C23×C4C2×Dic1714yes—
118C23×C4C22×D1712yes—
119C22⋊Q8—28no—
120C22⋊Q8—28no—
121C22⋊Q8—232no—
122C2×C4⋊C4—344no—
123C2×C4⋊C4C2×Dic17112yes—
124C2×C22⋊C4—28no—
125C2×C22⋊C4—178no—
126C2×C22⋊C4—344no—
127C2×C22⋊C4—344no—
128C2×C22⋊C4C2×Dic1714yes—
129C2×C22⋊C4C2×Dic1714yes—
130C2×C22⋊C4C22⋊D1718yes—
131C2×C22⋊C4C22×D1714yes—
132C2×C42—344no—
133#95—344no—
134#95—344no—
135C17#2182711yescharacteristic, complemented, Sylow
136C24—24no—
137C24—82no—
138C24C22×Dic1712yes—
139C24C2×C22⋊D1714yes—
140C24C23×D1711yescharacteristic
141C2×Q8—28no—
142C2×Q8—84no—
143C22×C4—28no—
144C22×C4—82no—
145C22×C4—84no—
146C22×C4—348no—
147C22×C4C22×Dic1718yes—
148C22×C4C22×Dic1714yes—
149C22×C4C2×C22⋊D1714yes—
150C22×C4C2×C22⋊D1714yes—
151C4⋊C4—224no—
152C4⋊C4—1364no—
153C22⋊C4—28no—
154C22⋊C4—28no—
155C22⋊C4—3416no—
156C22⋊C4—1364no—
157C22⋊C4—1364no—
158C22⋊C4C22⋊Dic17116yes—
159C42—1364no—
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C22⋊Dic1714yes—
168C23#1058769414yes—
169C23C23×Dic1711yescharacteristic
170C23C22×C22⋊D1712yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—88no—
178C2×C4—688no—
179C2×C4—688no—
180C2×C4—688no—
181C2×C4C2×C22⋊Dic1718yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—28no—
186C22—24no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22C22×C22⋊Dic1711yescharacteristic
191C22#1176328712yes—
192C22#1176338314yes—
193C4—28no—
194C4—48no—
195C4—1368no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2#1453137011yescharacteristic
200C2#1453724512yes—
subgroupG/H
centerC22C22×C22⋊Dic17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#543C2
socleC22×C17C22×C22⋊C4
prime radicalC25×C17C23
cosocleC24×C17C24
hypercenterC2×#543D17
hypocenterC17#21827
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#543

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14529770C2semidirect
11. C2×C17×C22⋊Q8C4semidirect
101. C2×C22⋊Q8Dic17semidirect
135. C17#21827semidirect

Maximal subgroups

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

subgroupindex
#145313822
#145297702
#145288582
C2×C17×#5432
#2182717