Finite Group Databasebeta

← #16943983

Subgroups — #16943983

Order 4352.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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#14533980C211yesmaximal, characteristic
2#14527122C211yesmaximal, characteristic
3#14526729C212yesmaximal, complemented
4#14526727C212yesmaximal, complemented
5C17×#1459C211yesmaximal, characteristic
6C2×#10587556C411yescharacteristic
7#11762773—21no—
8#11762732—21no—
9#11762732—21no—
10#11762712C411yescharacteristic
11#11762712C411yescharacteristic
12#11762682—21no—
13#11762682—21no—
14#11762678C2211yescharacteristic
15#11762674C2211yescharacteristic
16C4×C4⋊Dic17C411yescharacteristic
17#11762535C2212yes—
18#11762533—21no—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×C22⋊C8—21no—
21C17×#324C2212yes—
22C17×#323—21no—
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C8×C17—41no—
27C4×D4×C17—41no—
28C4×D4×C17—41no—
29C2×C4⋊C4×C17C2311yescharacteristic
30C2×C22⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17D411yescharacteristic
32C2×C42×C17C2×C411yescharacteristic
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17C2×C411yescharacteristic
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×#63225—21no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—21no—
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17C2×C411yescharacteristic
46C2×#63223—41no—
47#10587556—41no—
48#10587556—41no—
49C17×C22⋊C8—22no—
50C17×C22⋊C8—41no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C22⋊#3622—22no—
55C22⋊#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C24×C17C22⋊C411yescharacteristic
58C2×D4×C17—22no—
59C2×D4×C17—22no—
60C2×D4×C17—41no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—81no—
66C22×C4×C17—81no—
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C2×C8×C17—42no—
77C2×C8×C17—82no—
78C4⋊C4×C17—41no—
79C22⋊C4×C17—41no—
80C22⋊C4×C17—41no—
81C42×C17—21no—
82C42×C17—21no—
83C22⋊Dic17—42no—
84C22⋊Dic17—42no—
85C22⋊Dic17—81no—
86C22⋊Dic17—81no—
87C4⋊Dic17—42no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90#63225—42no—
91#63225—41no—
92#63225—41no—
93#63225—81no—
94#63225—81no—
95C4×Dic17—22no—
96C4×Dic17—22no—
97#63223—82no—
98C2×#3622—42no—
99#11572—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17#10112yes—
110C23×C17C2×C22⋊C411yescharacteristic
111D4×C17—44no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—41no—
118C2×C4×C17—42no—
119C2×C4×C17—42no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—81no—
124C2×C4×C17—81no—
125C2×C4×C17#9911yescharacteristic
126C2×C4×C17#9911yescharacteristic
127C2×C4×C17#13112yes—
128C2×Dic17—22no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C8×C17—82no—
141#3622—82no—
142#2566—171no—
143#1465—171no—
144#1459D1711yescharacteristic
145#1325—172no—
146#1324—172no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—22no—
150C22×C17—42no—
151C22×C17—42no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17#40811yescharacteristic
160C22×C17C2×#9911yescharacteristic
161C22×C17C2×#10111yescharacteristic
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—22no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168Dic17—42no—
169Dic17—81no—
170Dic17—81no—
171Dic17—81no—
172C2×#125—171no—
173C2×C4×D4C2×D1711yescharacteristic
174#407—341no—
175C2×C22⋊C8—21no—
176#396—341no—
177#396—341no—
178#390—171no—
179#390—171no—
180#385—341no—
181#385—341no—
182#384—171no—
183#382—171no—
184C4×C4⋊C4—171no—
185#324—172no—
186#324C2×D1712yes—
187#323—21no—
188#323—341no—
189C2×C17—21no—
190C2×C17—21no—
191C2×C17—42no—
192C2×C17—81no—
193C2×C17#147211yescharacteristic
194C2×C17#212711yescharacteristic
195C2×C17#213211yescharacteristic
196C22×D4C4×D1711yescharacteristic
197C23×C4D6811yescharacteristic
198C23×C4C22⋊D1711yescharacteristic
199C2×M16—681no—
200C22×C8—41no—
201#125—681no—
202#125—681no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—171no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4—341no—
210C2×C4⋊C4—341no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4C22×D1711yescharacteristic
213C2×C22⋊C4—341no—
214C2×C22⋊C4—341no—
215C2×C22⋊C4—341no—
216C2×C22⋊C4—341no—
217C2×C22⋊C4D6811yescharacteristic
218C2×C22⋊C4C22⋊D1711yescharacteristic
219C2×C42—171no—
220C2×C42—171no—
221C2×C42C4×D1711yescharacteristic
222C22⋊C8—22no—
223C22⋊C8—41no—
224C22⋊C8—342no—
225C22⋊C8—681no—
226#95—341no—
227#95—341no—
228#95—341no—
229C17#1157211yescharacteristic, complemented, Sylow
230C24#6322711yescharacteristic
231C24#6322711yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—341no—
242C22×C4—341no—
243C22×C4—341no—
244C22×C4—341no—
245C22×C4#6322711yescharacteristic
246C22×C4#6322711yescharacteristic
247C22×C4C2×C4×D1711yescharacteristic
248C22×C4C2×D6811yescharacteristic
249C22×C4C2×C22⋊D1711yescharacteristic
250M16—1362no—
251C2×C8—42no—
252C2×C8—82no—
253C2×C8—682no—
254C4⋊C4—41no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C4⋊C4—682no—
258C4⋊C4—682no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—1361no—
262C4⋊C4—1361no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—682no—
266C22⋊C4—682no—
267C22⋊C4—1361no—
268C22⋊C4—1361no—
269C42—21no—
270C42—21no—
271C42—342no—
272C42—342no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1058749512yes—
283C23C2×#6322711yescharacteristic
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—342no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4—681no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—681no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4#1058747711yescharacteristic
311C2×C4#1058747711yescharacteristic
312C2×C4#1058758712yes—
313C8—82no—
314C8—1362no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22#1176277511yescharacteristic
328C22C2×#1058747711yescharacteristic
329C22C2×#1058749511yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—682no—
337C4—1361no—
338C4—1361no—
339C4—1361no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1452714711yescharacteristic
345C2#1453045111yescharacteristic
346C2#1453046711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1459C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1459D17
hypocenterC17#11572
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #14526729C2semidirect
4. #14526727C2semidirect
229. C17#11572semidirect

Maximal subgroups

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

subgroupindex
#145339802
#145271222
#145267292
#145267272
C17×#14592
#1157217