Finite Group Databasebeta

← #17961569

Subgroups — #17961569

Order 4352.

638 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544619C212yesmaximal
2#14543882C212yesmaximal, complemented
3#14543881C212yesmaximal, complemented
4D17×#391C211yesmaximal, characteristic
5C2×#10587545—22no—
6C2×#10587545C2214yes—
7#11763781—22no—
8C22×Q8×D17C2211yescharacteristic
9C2×C4⋊C4×D17C411yescharacteristic
10C2×C42×D17C411yescharacteristic
11#11762716C411yescharacteristic
12#11762715C2211yescharacteristic
13#11762714C2211yescharacteristic
14#11762713—22no—
15#95×D17—22no—
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C2×Q8×D17—24no—
19C2×Q8×D17—42no—
20C2×Q8×D17—41no—
21C2×Q8×D17—41no—
22C22×C4×D17—21no—
23C22×C4×D17—21no—
24C22×C4×D17C2×C411yescharacteristic
25C22×C4×D17D412yes—
26C22×Dic34D412yes—
27C22×Dic34C2311yescharacteristic
28C2×#63247—24no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225—21no—
33C2×C4×Dic17—21no—
34C2×C4×Dic17C2×C411yescharacteristic
35C4⋊C4×D17—41no—
36C4⋊C4×D17—41no—
37C42×D17—42no—
38#10587545—28no—
39#10587545—44no—
40#10587543—42no—
41#10587543—42no—
42C17×#95—22no—
43#10587502—22no—
44#10587502—22no—
45#10587502—22no—
46C23×D17C22⋊C411yescharacteristic
47C2×Q8×C17—22no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17C22⋊C412yes—
53C22×C4×C17C22×C411yescharacteristic
54C22×Dic17—21no—
55C22×Dic17—21no—
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C2×D412yes—
58Q8×D17—48no—
59Q8×D17—48no—
60C2×C4×D17—21no—
61C2×C4×D17—21no—
62C2×C4×D17—22no—
63C2×C4×D17—22no—
64C2×C4×D17—24no—
65C2×C4×D17—22no—
66C2×C4×D17—22no—
67C2×C4×D17—24no—
68C2×C4×D17—42no—
69C2×C4×D17—42no—
70C2×C4×D17—42no—
71C2×C4×D17—44no—
72C2×C4×D17—41no—
73C2×C4×D17—41no—
74C2×Dic34—24no—
75C2×Dic34—24no—
76C2×Dic34—42no—
77C2×Dic34—41no—
78C2×Dic34—41no—
79C2×Dic34#4114yes—
80#63247—44no—
81#63247—44no—
82C2×#3624—44no—
83C4⋊C4×C17—41no—
84C42×C17—41no—
85C4⋊Dic17—41no—
86#63225—42no—
87C4×Dic17—42no—
88C4×Dic17—41no—
89#12860—171nomaximal, Sylow
90C23×C17C2×C22⋊C411yescharacteristic
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—22no—
94C22×D17—22no—
95C22×D17#9911yescharacteristic
96C22×D17#9911yescharacteristic
97Q8×C17—44no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—22no—
101C2×C4×C17—22no—
102C2×C4×C17—22no—
103C2×C4×C17—22no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17—41no—
108C2×C4×C17#11712yes—
109C2×Dic17—21no—
110C2×Dic17—22no—
111C2×Dic17—22no—
112C2×Dic17—21no—
113C2×Dic17—22no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—42no—
117C2×Dic17—41no—
118C2×Dic17#9912yes—
119C2×Dic17#12314yes—
120C4×D17—24no—
121C4×D17—24no—
122C4×D17—44no—
123C4×D17—44no—
124C4×D17—48no—
125C4×D17—82no—
126C4×D17—82no—
127Dic34—44no—
128Dic34—48no—
129#3624—84no—
130C2×#391—171no—
131#1784—172no—
132#1394—172no—
133#1394—172no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17#38111yescharacteristic
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#9911yescharacteristic
139C2×D17—24no—
140C2×D17—24no—
141C2×D17—21no—
142C2×D17—21no—
143C2×D17—21no—
144C2×D17—21no—
145C2×D17#35512yes—
146C2×D17#35612yes—
147C4×C17—22no—
148C4×C17—42no—
149C4×C17—42no—
150C4×C17—81no—
151Dic17—24no—
152Dic17—22no—
153Dic17—42no—
154Dic17—81no—
155C23×Q8—171no—
156C22×C4⋊C4—171no—
157C22×C42—171no—
158C2×#101—174no—
159C2×#101—342no—
160#407—342no—
161#391—171no—
162#391—171no—
163#391—171no—
164#391—342no—
165#391#59511yescharacteristic
166C2×#95—342no—
167C2×C17—21no—
168C2×C17—21no—
169C2×C17#181911yescharacteristic
170C2×C17C2×#35511yescharacteristic
171C2×C17C2×#35611yescharacteristic
172D17—22no—
173D17—22no—
174C22×Q8—172no—
175C22×Q8—171no—
176C22×Q8—344no—
177C22×Q8—681no—
178C22×Q8—681no—
179C22×Q8—682no—
180C22×Q8C2×#59511yescharacteristic
181C23×C4—171no—
182C23×C4—172no—
183C23×C4—341no—
184C23×C4—341no—
185C2×M16—344no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—681no—
189C2×C4⋊C4—681no—
190C2×C4⋊C4C2×#59511yescharacteristic
191C2×C42—171no—
192C2×C42—341no—
193C2×C42—682no—
194C2×C42C2×#59511yescharacteristic
195#101—348no—
196#101—684no—
197C22⋊C8—682no—
198C22⋊C8—682no—
199#95—22no—
200#95—342no—
201#95—342no—
202#95—342no—
203C17#1286011yescharacteristic, complemented, Sylow
204C24—171no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—174no—
209C2×Q8—344no—
210C2×Q8—344no—
211C2×Q8—681no—
212C2×Q8—681no—
213C2×Q8—682no—
214C2×Q8—688no—
215C2×Q8—688no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—171no—
219C22×C4—172no—
220C22×C4—342no—
221C22×C4—344no—
222C22×C4—341no—
223C22×C4—341no—
224C22×C4—342no—
225C22×C4—342no—
226C22×C4—344no—
227C22×C4—342no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—682no—
231C22×C4—682no—
232C22×C4—682no—
233C22×C4—681no—
234C22×C4—681no—
235C22×C4—684no—
236C22×C4C22⋊#59512yes—
237C22×C4C22×#59511yescharacteristic
238M16—684no—
239M16—684no—
240C2×C8—684no—
241C4⋊C4—41no—
242C4⋊C4—681no—
243C4⋊C4—682no—
244C42—41no—
245C42—681no—
246C42—682no—
247C23—171no—
248C23—171no—
249C23—342no—
250C23—342no—
251C23—341no—
252C23—341no—
253C23C2×C22⋊#59511yescharacteristic
254Q8—44no—
255Q8—684no—
256Q8—688no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—174no—
268C2×C4—172no—
269C2×C4—344no—
270C2×C4—344no—
271C2×C4—341no—
272C2×C4—342no—
273C2×C4—341no—
274C2×C4—342no—
275C2×C4—342no—
276C2×C4—684no—
277C2×C4—684no—
278C2×C4—688no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—682no—
282C2×C4—681no—
283C2×C4—1362no—
284C2×C4—1362no—
285C2×C4#1058767712yes—
286C8—1364no—
287C22—21no—
288C22—21no—
289C22—172no—
290C22—172no—
291C22—344no—
292C22—344no—
293C22—341no—
294C22—341no—
295C22—341no—
296C22—341no—
297C22#1176375211yescharacteristic
298C22D17⋊#9911yescharacteristic
299C22D17⋊#9911yescharacteristic
300C4—22no—
301C4—42no—
302C4—42no—
303C4—81no—
304C4—344no—
305C4—342no—
306C4—682no—
307C4—1361no—
308C2—21no—
309C2—21no—
310C2—342no—
311C2—342no—
312C2#1454468011yescharacteristic
313C2D17⋊#35511yescharacteristic
314C2D17⋊#35611yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC22×Dic34C23
hypercenter#391#595
hypocenterC17#12860
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #14543882C2semidirect
3. #14543881C2semidirect
203. C17#12860semidirect

Maximal subgroups

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

subgroupindex
#145446192
#145438822
#145438812
D17×#3912
#1286017