Finite Group Databasebeta

← #17952442

Subgroups — #17952442

Order 4352.

1482 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 164 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#14544674C212yesmaximal, complemented
2C2×#11763653C214yesmaximal, complemented
3C22×#10587579C211yesmaximal, characteristic
4C2×C22⋊#3624C2214yes—
5#11763675—24no—
6#11763653—28no—
7C23×D68C411yescharacteristic
8C23×C4×D17C412yes—
9C2×#10587579—28no—
10C2×#10587579—24no—
11C22×#63227C2212yes—
12C22×C4×Dic17C2211yescharacteristic
13C22×C4⋊C4×C17C411yescharacteristic
14C24×D17C2×C412yes—
15C23×C4×C17C2×C411yescharacteristic
16C23×C4×C17C2×C412yes—
17C23×Dic17C2×C411yescharacteristic
18C23×Dic17C2311yescharacteristic
19C22×D68—24no—
20C22×D68—24no—
21C22×D68—22no—
22C22×D68—22no—
23C22×D68C814yescomplemented
24C22×C4×D17—24no—
25C22×C4×D17—24no—
26C22×C4×D17—24no—
27C22×C4×D17—48no—
28C22×#3624—24no—
29C2×C4⋊C4×C17—24no—
30C2×C4⋊C4×C17—22no—
31C2×#63227—24no—
32C2×#63227—24no—
33C2×#63227D418yes—
34C2×C4×Dic17—24no—
35C2×C4×Dic17D414yes—
36#10587579—232no—
37C22⋊#3624—28no—
38C24×C17C22×C411yescharacteristic
39C23×D17—22no—
40C23×D17—22no—
41C23×D17—22no—
42C23×D17—22no—
43C23×D17—44no—
44C23×D17—44no—
45C23×D17C22⋊C414yes—
46C23×D17C2×C814yes—
47C23×D17M1614yes—
48C22×C4×C17—22no—
49C22×C4×C17—22no—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17—44no—
53C22×C4×C17C22⋊C412yes—
54C22×C4×C17C22⋊C414yes—
55C22×C4×C17C2×C812yes—
56C22×C4×C17M1612yes—
57C22×Dic17—22no—
58C22×Dic17—24no—
59C22×Dic17—42no—
60C22×Dic17C22⋊C412yes—
61C22×Dic17C2×D412yes—
62C22×Dic17C2×D414yes—
63C2×D68—28no—
64C2×D68—216no—
65C2×D68—28no—
66C2×D68—216no—
67C2×D68—28no—
68C2×C4×D17—216no—
69C2×C4×D17—416no—
70C2×C4×D17—416no—
71C2×C4×D17—48no—
72C2×C4×D17—48no—
73C2×#3624—48no—
74C2×#3624—44no—
75C4⋊C4×C17—28no—
76#63227—216no—
77C4×Dic17—28no—
78#8302—171nomaximal, Sylow
79C23×C17—22no—
80C23×C17—22no—
81C23×C17C2×C22⋊C412yes—
82C23×C17C2×C22⋊C411yescharacteristic
83C23×C17C22×C811yescharacteristic
84C23×C17C2×M1611yescharacteristic
85C23×C17C2×M1612yes—
86C22×D17—24no—
87C22×D17—24no—
88C22×D17—24no—
89C22×D17—24no—
90C22×D17—24no—
91C22×D17—24no—
92C22×D17—44no—
93C22×D17—48no—
94C22×D17—48no—
95C22×D17—44no—
96C22×D17—44no—
97C22×D17—44no—
98C22×D17—44no—
99C22×D17—44no—
100C22×D17—48no—
101C22×D17—48no—
102C22×D17C22⋊C818yes—
103C2×C4×C17—22no—
104C2×C4×C17—24no—
105C2×C4×C17—22no—
106C2×C4×C17—24no—
107C2×C4×C17—24no—
108C2×C4×C17—44no—
109C2×C4×C17—44no—
110C2×C4×C17—44no—
111C2×C4×C17C22⋊C814yes—
112C2×Dic17—28no—
113C2×Dic17—22no—
114C2×Dic17—24no—
115C2×Dic17—22no—
116C2×Dic17—44no—
117C2×Dic17#10014yes—
118C2×Dic17#12014yes—
119D68—232no—
120C4×D17—432no—
121#3624—84no—
122C22×C4×D4—171no—
123#1817—172no—
124C2×#323—174no—
125C22×C17—22no—
126C22×C17—22no—
127C22×C17—24no—
128C22×C17—22no—
129C22×C17—22no—
130C22×C17#37911yescharacteristic
131C22×C17C2×C22⋊C812yes—
132C22×C17C2×C22⋊C811yescharacteristic
133C22×C17#40712yes—
134C22×C17#40711yescharacteristic
135C22×C17#41012yes—
136C22×C17C2×#10012yes—
137C2×D17—28no—
138C2×D17—48no—
139C2×D17—48no—
140C2×D17—48no—
141C2×D17—48no—
142C2×D17—48no—
143C2×D17—44no—
144C2×D17—44no—
145C2×D17—48no—
146C4×C17—24no—
147C4×C17—44no—
148Dic17—24no—
149Dic17—24no—
150C23×D4—171no—
151C24×C4—172no—
152C2×C4×D4—344no—
153C2×C4×D4—348no—
154C22×C4⋊C4#59511yescharacteristic
155C22×C22⋊C4—172no—
156C22×C42—171no—
157C2×C22⋊C8—174no—
158#336—344no—
159#323—348no—
160C2×C17—22no—
161C2×C17—22no—
162C2×C17#146012yes—
163C2×C17#146612yes—
164C2×C17#177911yescharacteristic
165C2×C17#178211yescharacteristic
166C2×C17#178311yescharacteristic
167D17—48no—
168C25—172no—
169C22×D4—174no—
170C22×D4—344no—
171C22×D4—344no—
172C22×D4—342no—
173C22×D4—342no—
174C23×C4—171no—
175C23×C4—171no—
176C23×C4—344no—
177C23×C4—344no—
178C23×C4—344no—
179C23×C4—688no—
180C23×C4C2×#59512yes—
181C23×C4C2×#59511yescharacteristic
182C22×C8—344no—
183C4×D4—3432no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—22no—
186C2×C22⋊C4—178no—
187C2×C22⋊C4—344no—
188C2×C22⋊C4—344no—
189C2×C42—174no—
190C2×C42—344no—
191C22⋊C8—348no—
192C17#830211yescharacteristic, complemented, Sylow
193C24—174no—
194C24—174no—
195C24—174no—
196C24—342no—
197C24—342no—
198C24—342no—
199C24—342no—
200C24—684no—
201C24—684no—
202C24C22×#59511yescharacteristic
203C2×D4—3416no—
204C2×D4—348no—
205C2×D4—3416no—
206C2×D4—348no—
207C2×D4—348no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—44no—
213C22×C4—172no—
214C22×C4—172no—
215C22×C4—174no—
216C22×C4—3416no—
217C22×C4—344no—
218C22×C4—342no—
219C22×C4—688no—
220C22×C4—6816no—
221C22×C4—688no—
222C22×C4—6816no—
223C22×C4—682no—
224C22×C4#6324212yes—
225C22×C4#6324312yes—
226C22×C4C22⋊#59512yes—
227C22×C4C22⋊#59514yes—
228C2×C8—684no—
229C2×C8—688no—
230C4⋊C4—28no—
231C22⋊C4—3416no—
232C42—348no—
233C23—22no—
234C23—22no—
235C23—178no—
236C23—344no—
237C23—344no—
238C23—344no—
239C23—344no—
240C23—344no—
241C23—344no—
242C23—684no—
243C23—688no—
244C23—688no—
245C23—684no—
246C23—684no—
247C23—688no—
248C23—688no—
249C23—684no—
250C23—684no—
251C23—684no—
252C23C2×#6324211yescharacteristic
253C23C2×#6324311yescharacteristic
254C23D17⋊M1612yes—
255C23C2×C22⋊#59512yes—
256C23C2×C22⋊#59511yescharacteristic
257D4—3432no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—174no—
267C2×C4—174no—
268C2×C4—348no—
269C2×C4—342no—
270C2×C4—344no—
271C2×C4—342no—
272C2×C4—6832no—
273C2×C4—684no—
274C2×C4#1058754314yes—
275C8—1364no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—22no—
280C22—22no—
281C22—348no—
282C22—688no—
283C22—688no—
284C22—688no—
285C22—688no—
286C22—688no—
287C22—688no—
288C22—684no—
289C22—684no—
290C22#1176375011yescharacteristic
291C22#1176377712yes—
292C22C2×#1058754311yescharacteristic
293C22#1176378012yes—
294C22#1176378111yescharacteristic
295C22#1176379012yes—
296C22D17⋊#10012yes—
297C4—24no—
298C4—44no—
299C4—344no—
300C4—344no—
301C2—22no—
302C2—22no—
303C2—688no—
304C2#1454402512yes—
305C2#1454404512yes—
306C2#1454460711yescharacteristic
307C2#1454461511yescharacteristic
308C2#1454461711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D68C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8302
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544674C2semidirect
2. C2×#11763653C2semidirect
23. C22×D68C8semidirect
192. C17#8302semidirect

Maximal subgroups

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

subgroupindex
#145446742
C2×#117636532
C22×#105875792
#830217