Finite Group Databasebeta

← #16927811

Subgroups — #16927811

Order 4352.

450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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#14527118C212yesmaximal
2#14526640C214yesmaximal, complemented
3C17×#2296C211yesmaximal, characteristic
4#11762866C2214yes—
5#11762535—22no—
6#11762533—22no—
7C2×C17×#117C411yescharacteristic
8C2×C17×#117C2211yescharacteristic
9C22×C42×C17C411yescharacteristic
10C17×#389—22no—
11C17×#385—22no—
12C4×C4⋊C4×C17C412yes—
13C4×C4⋊C4×C17C2212yes—
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C17×#117—24no—
17C17×#117—42no—
18C2×C4⋊C4×C17—21no—
19C2×C4⋊C4×C17—22no—
20C2×C4⋊C4×C17—22no—
21C2×C4⋊C4×C17D412yes—
22C2×C22⋊C4×C17—21no—
23C2×C22⋊C4×C17D412yes—
24C2×C42×C17—21no—
25C2×C42×C17—42no—
26C2×C42×C17C2×C411yescharacteristic
27C2×C42×C17C2×C412yes—
28C2×C42×C17C2×C412yes—
29C2×C42×C17C2311yescharacteristic
30C17×#95—22no—
31C17×#95—22no—
32C22⋊#3622—24no—
33C4⋊#3622—24no—
34#10587474—24no—
35C24×C17C22⋊C411yescharacteristic
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—44no—
42C22×C4×C17—42no—
43C22×C4×C17C22⋊C411yescharacteristic
44C22×C4×C17C22⋊C412yes—
45C22×C4×C17C22×C411yescharacteristic
46C22×C4×C17C2×D412yes—
47C4⋊C4×C17—24no—
48C4⋊C4×C17—44no—
49C4⋊C4×C17—44no—
50C4⋊C4×C17—42no—
51C22⋊C4×C17—24no—
52C22⋊C4×C17—42no—
53C42×C17—22no—
54C42×C17—42no—
55C42×C17—42no—
56C42×C17—42no—
57C42×C17#4114yes—
58C2×#3622—44no—
59#8742—171nomaximal, Sylow
60C23×C17—21no—
61C23×C17—21no—
62C23×C17—42no—
63C23×C17#10012yes—
64C23×C17C2×C22⋊C411yescharacteristic
65C2×C4×C17—28no—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—24no—
71C2×C4×C17—22no—
72C2×C4×C17—42no—
73C2×C4×C17—42no—
74C2×C4×C17—48no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—42no—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17#10112yes—
81C2×C4×C17#11712yes—
82C2×C4×C17#12314yes—
83#3622—84no—
84#2296D1711yescharacteristic
85#1464—172no—
86#1285—174no—
87C22×C17—22no—
88C22×C17—22no—
89C22×C17—42no—
90C22×C17—42no—
91C22×C17—42no—
92C22×C17#38111yescharacteristic
93C22×C17C2×#10011yescharacteristic
94C22×C17C2×#10111yescharacteristic
95C4×C17—22no—
96C4×C17—22no—
97C4×C17—24no—
98C4×C17—44no—
99C4×C17—42no—
100C4×C17—82no—
101C2×#117Dic1711yescharacteristic
102C2×#117C2×D1711yescharacteristic
103C22×C42Dic1711yescharacteristic
104#432—174no—
105#389—22no—
106#385—22no—
107C4×C4⋊C4Dic1712yes—
108C4×C4⋊C4C2×D1712yes—
109#324—342no—
110#323—342no—
111C2×C17—21no—
112C2×C17—21no—
113C2×C17—42no—
114C2×C17#182111yescharacteristic
115C2×C17#182712yes—
116C23×C4—21no—
117C23×C4C2×Dic1711yescharacteristic
118#117—24no—
119#117—42no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4C22⋊D1712yes—
124C2×C22⋊C4—21no—
125C2×C22⋊C4C22⋊D1712yes—
126C2×C42—21no—
127C2×C42—42no—
128C2×C42C2×Dic1711yescharacteristic
129C2×C42C2×Dic1712yes—
130C2×C42C2×Dic1712yes—
131C2×C42C22×D1711yescharacteristic
132C4⋊C8—344no—
133C22⋊C8—344no—
134#97—344no—
135#95—22no—
136#95—22no—
137C17#874211yescharacteristic, complemented, Sylow
138C24C22⋊Dic1711yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—44no—
145C22×C4—42no—
146C22×C4C22⋊Dic1711yescharacteristic
147C22×C4C22⋊Dic1712yes—
148C22×C4C22×Dic1711yescharacteristic
149C22×C4C2×C22⋊D1712yes—
150C2×C8—684no—
151C4⋊C4—24no—
152C4⋊C4—44no—
153C4⋊C4—44no—
154C4⋊C4—42no—
155C22⋊C4—24no—
156C22⋊C4—42no—
157C42—22no—
158C42—42no—
159C42—42no—
160C42—42no—
161C42#6325214yes—
162C23—21no—
163C23—21no—
164C23—42no—
165C23#1058750412yes—
166C23C2×C22⋊Dic1711yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4#1058750712yes—
183C2×C4#1058761212yes—
184C2×C4#1058761514yes—
185C8—1364no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#1176267211yescharacteristic
192C22C2×#1058750411yescharacteristic
193C22C2×#1058750711yescharacteristic
194C4—22no—
195C4—22no—
196C4—24no—
197C4—44no—
198C4—42no—
199C4—82no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#1452886411yescharacteristic
204C2#1452888812yes—
subgroupG/H
centerC22#11762672
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2296C2
socleC22×C17#381
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2296D17
hypocenterC17#8742
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #14526640C2semidirect
137. C17#8742semidirect

Maximal subgroups

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

subgroupindex
#145271182
#145266402
C17×#22962
#874217