Finite Group Databasebeta

← #17043799

Subgroups — #17043799

Order 4352.

914 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 235 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
1C2×#11763440C211yesmaximal, characteristic
2#14537419C212yesmaximal
3#14529775C214yesmaximal, complemented
4#14529771C214yesmaximal, complemented
5#14528865C212yesmaximal
6#14528864C211yesmaximal, characteristic
7C17×#1821C211yesmaximal, characteristic
8#11763440—28no—
9C2×#10587574C412yes—
10C2×#10587574C2212yes—
11C2×#10587576C412yes—
12C2×#10587576C2212yes—
13C2×#10587610C414yes—
14C2×#10587612C2211yescharacteristic
15C2×#10587612C2211yescharacteristic
16#11762867—28no—
17#11762832C2214yes—
18#11762773C2212yes—
19M16×Dic17C2214yes—
20#11762578C2214yes—
21#11762577C2214yes—
22#11762577C2214yes—
23C22×C4⋊C4×C17C2211yescharacteristic
24C17×#407C2212yes—
25C17×#343C2214yes—
26C23×C4×C17C2×C412yes—
27C23×C4×C17C2311yescharacteristic
28C22×Dic34C2×C414yes—
29C2×M16×C17C2314yes—
30C2×C4⋊C4×C17—24no—
31C2×C4⋊C4×C17C2×C412yes—
32C2×C4⋊C4×C17C2312yes—
33C2×C22⋊Dic17C2×C412yes—
34C2×C22⋊Dic17C2×C412yes—
35#10587612—24no—
36#10587612D418yes—
37C2×C4⋊Dic17C2×C414yes—
38C2×C4⋊Dic17C2×C411yescharacteristic
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×C4⋊Dic17C2311yescharacteristic
41C2×C4⋊Dic17C2311yescharacteristic
42#10587610—216no—
43C2×#63225C2×C414yes—
44C2×#63225C2×C414yes—
45C2×C4×Dic17C2×C412yes—
46C2×C4×Dic17C2312yes—
47C2×#63223C2314yes—
48#10587576—28no—
49#10587576—24no—
50#10587576—24no—
51#10587574—28no—
52#10587574—24no—
53#10587574—24no—
54C17×C22⋊C8—24no—
55C22⋊#3622—24no—
56#10587486—24no—
57#10587485—28no—
58C8×Dic17—24no—
59C24×C17C22×C411yescharacteristic
60C22×C4×C17—24no—
61C22×C4×C17—24no—
62C22×C4×C17—82no—
63C22×C4×C17C22×C411yescharacteristic
64C22×C4×C17C22×C414yes—
65C22×C4×C17C2×D414yes—
66C22×C4×C17C2411yescharacteristic
67C22×Dic17C22×C412yes—
68C22×Dic17C22×C412yes—
69C22×Dic17C22×C412yes—
70C22×Dic17C22×C412yes—
71C2×Dic34—28no—
72C2×Dic34—84no—
73M16×C17—28no—
74C2×C8×C17—24no—
75C4⋊C4×C17—24no—
76C4⋊C4×C17—22no—
77C4⋊C4×C17—22no—
78C22⋊Dic17—24no—
79C22⋊Dic17C22⋊C418yes—
80C4⋊Dic17—22no—
81C4⋊Dic17—22no—
82C4⋊Dic17—28no—
83C4⋊Dic17C22⋊C414yes—
84C4⋊Dic17C22⋊C414yes—
85#63225—28no—
86#63225—28no—
87C4×Dic17—24no—
88C4×Dic17C2×D414yes—
89C4×Dic17C2×D414yes—
90#63223—28no—
91C2×#3622—24no—
92#21832—171nomaximal, Sylow
93C23×C17—22no—
94C23×C17—41no—
95C23×C17—41no—
96C23×C17C2×C22⋊C412yes—
97C23×C17C23×C411yescharacteristic
98C2×C4×C17—22no—
99C2×C4×C17—28no—
100C2×C4×C17—24no—
101C2×C4×C17—44no—
102C2×C4×C17—84no—
103C2×C4×C17C2×C22⋊C412yes—
104C2×C4×C17C22×D412yes—
105C2×C4×C172−1+414yes—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17C2×C22⋊C414yes—
113C2×Dic17C2×C22⋊C414yes—
114Dic34—88no—
115C8×C17—44no—
116#3622—44no—
117C2×#544—171no—
118#2921—172no—
119#1998—174no—
120#1997—174no—
121#1822—172no—
122#1821—171no—
123#1821D1711yescharacteristic
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—22no—
127C22×C17—22no—
128C22×C17—22no—
129C22×C17—44no—
130C22×C17C22×C22⋊C411yescharacteristic
131C22×C17#51912yes—
132C4×C17—22no—
133C4×C17—44no—
134C4×C17#53614yes—
135Dic17—24no—
136Dic17—24no—
137Dic17—42no—
138Dic17—42no—
139#544—348no—
140C2×C4⋊Q8—172no—
141C2×C4⋊Q8—172no—
142C2×#125—172no—
143C2×#125—172no—
144C2×C22⋊Q8—174no—
145C2×#117—171no—
146C2×#117—171no—
147C22×C4⋊C4C2×D1711yescharacteristic
148#433—348no—
149#423—174no—
150#407—172no—
151#407C2×D1712yes—
152C4×M16—174no—
153#343—174no—
154#343—174no—
155#343—174no—
156#343C2×D1714yes—
157C2×C17—22no—
158C2×C17—42no—
159C2×C17#231011yescharacteristic
160C2×C17#288811yescharacteristic
161C2×C17#288911yescharacteristic
162C22×Q8—174no—
163C23×C4C4×D1712yes—
164C23×C4C22×D1711yescharacteristic
165C2×M16—174no—
166C2×M16C22×D1714yes—
167C4⋊Q8—344no—
168C4⋊Q8—344no—
169C4⋊Q8—348no—
170#125—344no—
171#125—344no—
172#125—348no—
173C22⋊Q8—3416no—
174#117—178no—
175#117—344no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—171no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—174no—
180C2×C4⋊C4—174no—
181C2×C4⋊C4—174no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4C4×D1712yes—
185C2×C4⋊C4C22×D1712yes—
186C2×C22⋊C4—172no—
187C2×C22⋊C4—172no—
188C2×C42—172no—
189C2×C42—172no—
190C4⋊C8—348no—
191C22⋊C8—24no—
192C22⋊C8—344no—
193#97—344no—
194C4×C8—344no—
195C17#2183211yescharacteristic, complemented, Sylow
196C24C2×C4×D1711yescharacteristic
197C2×Q8—348no—
198C2×Q8—1364no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—82no—
202C22×C4—172no—
203C22×C4—172no—
204C22×C4—172no—
205C22×C4—172no—
206C22×C4C2×C4×D1711yescharacteristic
207C22×C4C2×C4×D1714yes—
208C22×C4D4×D1714yes—
209C22×C4C23×D1711yescharacteristic
210M16—28no—
211M16—348no—
212C2×C8—24no—
213C2×C8—344no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—24no—
217C4⋊C4—174no—
218C4⋊C4—174no—
219C4⋊C4—348no—
220C4⋊C4—348no—
221C4⋊C4—348no—
222C4⋊C4—342no—
223C4⋊C4—342no—
224C22⋊C4—178no—
225C22⋊C4—344no—
226C42—174no—
227C42—174no—
228C42—344no—
229C23—22no—
230C23—41no—
231C23—41no—
232C23C22⋊C4×D1712yes—
233C23C22×C4×D1711yescharacteristic
234Q8—1368no—
235C2×C4—22no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—44no—
239C2×C4—84no—
240C2×C4—174no—
241C2×C4—174no—
242C2×C4—342no—
243C2×C4—342no—
244C2×C4—682no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4—682no—
248C2×C4C22⋊C4×D1712yes—
249C2×C4C2×D4×D1712yes—
250C2×C4#1058769714yes—
251C8—44no—
252C8—684no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—44no—
259C22C2×C22⋊C4×D1711yescharacteristic
260C22#1176328612yes—
261C4—22no—
262C4—44no—
263C4—344no—
264C4—344no—
265C4—682no—
266C4—682no—
267C4#1176338114yes—
268C2—22no—
269C2—42no—
270C2#1453136911yescharacteristic
271C2#1453726011yescharacteristic
272C2#1453726411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1821C2
socleC22×C17C22×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenter#1821D17
hypocenterC17#21832
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #14529775C2semidirect
4. #14529771C2semidirect
195. C17#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#117634402
#145374192
#145297752
#145297712
#145288652
#145288642
C17×#18212
#2183217