Finite Group Databasebeta

← #17951258

Subgroups — #17951258

Order 4352.

604 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 140 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#14545231C212yesmaximal
2#14543664C214yesmaximal
3#14537416C211yesmaximal, characteristic
4#11763754C414yescomplemented
5#11763753C414yescomplemented
6#11763752—22no—
7#11763751—22no—
8C4×C4⋊#595—22no—
9C4×C22⋊#595C2214yes—
10#11763745—22no—
11C2×C42×D17C2211yescharacteristic
12#11762865—22no—
13#11762861—22no—
14#11762833C411yescharacteristic, complemented
15#11762772C2212yes—
16M16×Dic17C412yescomplemented
17C17×#423C411yescharacteristic, complemented
18C22×C4×D17D412yes—
19C22×C4×D17C2311yescharacteristic
20C2×C22⋊#595—24no—
21C2×C4⋊#595—24no—
22C2×C4×#595—24no—
23C2×M16×C17C2×C412yes—
24C2×C42×C17C2×C411yescharacteristic
25C2×C4×Dic17C2×C411yescharacteristic
26C2×C4×Dic17Q812yes—
27C2×#63223C2×C412yes—
28C42×D17C2×C412yes—
29C42×D17C2×C412yes—
30C42×D17D412yes—
31C42×D17D412yes—
32(C2×#595)⋊C4—24no—
33(C2×#595)⋊C4—24no—
34(C2×#595)⋊C4—24no—
35(C2×#595)⋊C4C2×C418yes—
36C17×C4⋊C8—22no—
37#10587491—24no—
38#10587486—22no—
39C8×Dic17—22no—
40C4⋊#3622—22no—
41C23×D17C2×D411yescharacteristic
42C22×#595—28no—
43C22×C4×C17C4⋊C412yes—
44C22×C4×C17C22×C411yescharacteristic
45C22×Dic17C4⋊C412yes—
46C22×Dic17C2×Q811yescharacteristic
47C2×C4×D17—41no—
48C2×C4×D17—41no—
49C2×C4×D17—44no—
50C2×C4×D17C22⋊C412yes—
51C2×C4×D17C22⋊C412yes—
52C2×C4×D17C22⋊C412yes—
53C2×C4×D17C22⋊C412yes—
54C2×C4×D17C22×C412yes—
55C2×C4×D17C2×D412yes—
56C22⋊#595—48no—
57C4⋊#595—48no—
58C4×#595—44no—
59C4×#595—44no—
60M16×C17—42no—
61C2×C8×C17—22no—
62C42×C17C4211yescharacteristic
63C42×C17C4211yescharacteristic
64C42×C17C22⋊C412yes—
65C4×Dic17C4212yes—
66C4×Dic17C22⋊C411yescharacteristic
67C4×Dic17C22⋊C411yescharacteristic
68C4×Dic17C4⋊C412yes—
69C4×Dic17C4⋊C412yes—
70C4×Dic17C4⋊C412yes—
71C4×Dic17C4⋊C412yes—
72#63223—42no—
73C2×#3622—22no—
74#8050—171nomaximal, Sylow
75C23×C17C2×C4⋊C411yescharacteristic
76C22×D17—24no—
77C22×D17—41no—
78C22×D17C2×C22⋊C412yes—
79C2×#595—48no—
80C2×#595—48no—
81C2×#595—48no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—42no—
85C2×C4×C17#9512yes—
86C2×C4×C17#9512yes—
87C2×C4×C17C2×C4211yescharacteristic
88C2×C4×C17C2×C22⋊C411yescharacteristic
89C2×Dic17—42no—
90C2×Dic17—41no—
91C2×Dic17#9512yes—
92C2×Dic17#9512yes—
93C2×Dic17C2×C4⋊C412yes—
94C4×D17—24no—
95C4×D17—24no—
96C4×D17—22no—
97C4×D17—22no—
98C4×D17—42no—
99C4×D17—42no—
100C4×D17—42no—
101C8×C17—42no—
102#3622—42no—
103#2920—171no—
104#2283—172no—
105#1297—174no—
106C22×C17—22no—
107C22×C17—21no—
108C22×C17C2×#9511yescharacteristic
109C2×D17—22no—
110C2×D17—22no—
111C2×D17—44no—
112C2×D17#42114yes—
113#595—88no—
114C4×C17—22no—
115C4×C17—22no—
116C4×C17—21no—
117C4×C17#41011yescharacteristic
118C4×C17#41011yescharacteristic
119Dic17—22no—
120Dic17—22no—
121Dic17—22no—
122C22×C42—171no—
123#432—342no—
124#431—342no—
125#423—171no—
126#423#59511yescharacteristic, complemented
127#407—172no—
128C4×M16—172no—
129#383—174no—
130#382—174no—
131#381—342no—
132#380—342no—
133C4×C4⋊C4—342no—
134C4×C22⋊C4—174no—
135#376—342no—
136C2×C17—41no—
137C2×C17#173312yes—
138C2×C17#174011yescharacteristic
139D17—24no—
140C23×C4—172no—
141C23×C4—171no—
142C2×M16—172no—
143C2×M16C2×#59512yes—
144C2×C4⋊C4—344no—
145C2×C22⋊C4—344no—
146C2×C42—172no—
147C2×C42—171no—
148C2×C42—172no—
149C2×C42—172no—
150C2×C42—172no—
151C2×C42—172no—
152C2×C42—344no—
153C2×C42C2×#59511yescharacteristic
154C4⋊C8—22no—
155C4⋊C8—342no—
156C22⋊C8—344no—
157#97—342no—
158C4×C8—342no—
159#95—178no—
160#95—344no—
161#95—344no—
162#95—344no—
163C17#805011yescharacteristic, complemented, Sylow
164C24—171no—
165C22×C4—172no—
166C22×C4—171no—
167C22×C4—172no—
168C22×C4—172no—
169C22×C4—172no—
170C22×C4—172no—
171C22×C4—172no—
172C22×C4—172no—
173C22×C4—348no—
174C22×C4—681no—
175C22×C4—681no—
176C22×C4—684no—
177C22×C4C4⋊#59512yes—
178C22×C4C22×#59511yescharacteristic
179M16—42no—
180M16—682no—
181C2×C8—22no—
182C2×C8—342no—
183C4⋊C4—688no—
184C22⋊C4—688no—
185C42—172no—
186C42—171no—
187C42—171no—
188C42—172no—
189C42—172no—
190C42—172no—
191C42—172no—
192C42—684no—
193C42—684no—
194C42C4×#59511yescharacteristic
195C42C4×#59511yescharacteristic
196C42C22⋊#59512yes—
197C23—172no—
198C23—344no—
199C23—681no—
200C23C2×C4⋊#59511yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—172no—
205C2×C4—172no—
206C2×C4—172no—
207C2×C4—344no—
208C2×C4—344no—
209C2×C4—342no—
210C2×C4—342no—
211C2×C4—682no—
212C2×C4—682no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4—681no—
216C2×C4—688no—
217C2×C4—688no—
218C2×C4—688no—
219C2×C4(C2×#595)⋊C412yes—
220C2×C4(C2×#595)⋊C412yes—
221C2×C4C2×C4×#59511yescharacteristic
222C2×C4C2×C22⋊#59511yescharacteristic
223C8—42no—
224C8—682no—
225C22—22no—
226C22—21no—
227C22—174no—
228C22—342no—
229C22—342no—
230C22—684no—
231C22C2×(C2×#595)⋊C411yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—342no—
236C4—342no—
237C4—342no—
238C4—1368no—
239C4#1176378911yescharacteristic
240C4#1176379011yescharacteristic
241C2—41no—
242C2—344no—
243C2#1454446612yes—
244C2#1454448411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#423C4
socleC22×C17C2×#95
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenter#423#595
hypocenterC17#8050
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
4. #11763754C4semidirect
5. #11763753C4semidirect
14. #11762833C4semidirect
16. M16×Dic17C4semidirect
17. C17×#423C4semidirect
126. #423#595semidirect
163. C17#8050semidirect

Maximal subgroups

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

subgroupindex
#145452312
#145436642
#145374162
#805017