Finite Group Databasebeta

← #16932296

Subgroups — #16932296

Order 4352.

522 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 103 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#14537825C211yesmaximal, characteristic
2#14533101C211yesmaximal, characteristic
3#14528862C212yesmaximal, complemented
4#14526691C212yesmaximal, complemented
5C17×#1465C211yesmaximal, characteristic
6C22×C4⋊Dic17C2211yescharacteristic
7#11762887—24no—
8#11762862—21no—
9#11762773—21no—
10#11762773C2212yes—
11#11762748—21no—
12#11762745—21no—
13#11762707—21no—
14#11762689C412yes—
15#11762681C412yes—
16#11762669—21no—
17#11762669C2211yescharacteristic
18#11762577—24no—
19C2×C4×D4×C17C2211yescharacteristic
20C17×#407C2212yes—
21C17×#324—21no—
22C17×#323—21no—
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17C2311yescharacteristic
26C23×Dic17C2×C412yes—
27C2×M16×C17—22no—
28C4×D4×C17—22no—
29C4×D4×C17—22no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17D411yescharacteristic
33C2×C42×C17D411yescharacteristic
34C2×C22⋊Dic17—22no—
35C2×C22⋊Dic17C2×C412yes—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—22no—
40C2×C4⋊Dic17—22no—
41C2×#63225—22no—
42C2×#63223—22no—
43C2×#63223D414yes—
44C17×C22⋊C8—22no—
45C17×C22⋊C8—22no—
46#10587502—22no—
47#10587502—22no—
48#10587502—21no—
49C22⋊#3622—22no—
50C22⋊#3622—22no—
51C22⋊#3622—22no—
52C4⋊#3622—22no—
53C4×#3622—22no—
54C24×C17C22⋊C411yescharacteristic
55C24×C17C22×C411yescharacteristic
56C2×D4×C17—22no—
57C2×D4×C17—22no—
58C2×D4×C17—41no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—42no—
62C22×C4×C17—42no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×C4×C17C2×D412yes—
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17#4112yes—
70C22×Dic17—22no—
71C22×Dic17—22no—
72C22×Dic17—24no—
73C22×Dic17—82no—
74M16×C17—44no—
75C2×C8×C17—42no—
76C4⋊C4×C17—22no—
77C22⋊C4×C17—22no—
78C22⋊C4×C17—22no—
79C42×C17—21no—
80C42×C17—21no—
81C22⋊Dic17—42no—
82C22⋊Dic17—82no—
83C4⋊Dic17—42no—
84C4⋊Dic17—41no—
85C4⋊Dic17—42no—
86C4⋊Dic17—41no—
87#63225—82no—
88#63223—44no—
89#63223—82no—
90C2×#3622—24no—
91#9510—171nomaximal, Sylow
92C23×C17—21no—
93C23×C17—21no—
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—41no—
98C23×C17—41no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17C2×C22⋊C411yescharacteristic
102C23×C17C4×D412yes—
103D4×C17—44no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—24no—
107C2×C4×C17—22no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—81no—
116C2×C4×C17#10112yes—
117C2×C4×C17#12011yescharacteristic
118C2×C4×C17#12112yes—
119C2×C4×C17#12311yescharacteristic
120C2×Dic17—42no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17—42no—
125C2×Dic17—42no—
126C2×Dic17—84no—
127C8×C17—82no—
128#3622—44no—
129#2975—171no—
130#2487—171no—
131#1821—172no—
132#1465D1711yescharacteristic
133#1305—172no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—22no—
137C22×C17—22no—
138C22×C17—22no—
139C22×C17—42no—
140C22×C17—42no—
141C22×C17—42no—
142C22×C17—41no—
143C22×C17—41no—
144C22×C17—41no—
145C22×C17—81no—
146C22×C17#38611yescharacteristic
147C22×C17C2×#10111yescharacteristic
148C22×C17#41311yescharacteristic
149C4×C17—22no—
150C4×C17—21no—
151C4×C17—22no—
152C4×C17—41no—
153C4×C17—41no—
154C4×C17#45812yes—
155Dic17—82no—
156Dic17—82no—
157C2×C4×D4C2×D1711yescharacteristic
158C22×C4⋊C4—171no—
159#436—344no—
160#431—341no—
161#407—172no—
162#407—341no—
163#407C2×D1712yes—
164#400—341no—
165#399—341no—
166#389—341no—
167#386—172no—
168#385—172no—
169#380—171no—
170#380—341no—
171#343—344no—
172#324—21no—
173#323—21no—
174C2×C17—21no—
175C2×C17—21no—
176C2×C17—42no—
177C2×C17—81no—
178C2×C17#189011yescharacteristic
179C2×C17#190111yescharacteristic
180C2×C17#191411yescharacteristic
181C22×D4C4×D1711yescharacteristic
182C23×C4—172no—
183C23×C4D6811yescharacteristic
184C23×C4C22×D1711yescharacteristic
185C2×M16—22no—
186C2×M16—174no—
187C2×M16—342no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4—341no—
192C2×C4⋊C4—342no—
193C2×C4⋊C4—342no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4—342no—
196C2×C4⋊C4C22⋊D1711yescharacteristic
197C2×C22⋊C4—172no—
198C2×C22⋊C4—342no—
199C2×C22⋊C4C4×D1711yescharacteristic
200C2×C22⋊C4C22⋊D1711yescharacteristic
201C2×C42D6811yescharacteristic
202C4⋊C8—342no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—342no—
206C22⋊C8—342no—
207C22⋊C8—342no—
208C4×C8—342no—
209#95—341no—
210#95—342no—
211#95—342no—
212C17#951011yescharacteristic, complemented, Sylow
213C24#6322711yescharacteristic
214C24C2×C4×D1711yescharacteristic
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—342no—
223C22×C4—342no—
224C22×C4—344no—
225C22×C4—1362no—
226C22×C4#6322711yescharacteristic
227C22×C4#6322711yescharacteristic
228C22×C4#6322711yescharacteristic
229C22×C4C2×D6811yescharacteristic
230C22×C4D4×D1712yes—
231C22×C4#6325412yes—
232C22×C4C2×C22⋊D1711yescharacteristic
233M16—44no—
234M16—684no—
235M16—1362no—
236C2×C8—42no—
237C2×C8—344no—
238C4⋊C4—22no—
239C4⋊C4—682no—
240C4⋊C4—681no—
241C4⋊C4—681no—
242C4⋊C4—682no—
243C4⋊C4—1362no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—682no—
247C22⋊C4—1362no—
248C42—21no—
249C42—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23#1058756712yes—
260C23C2×#6322711yescharacteristic
261D4—44no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—682no—
275C2×C4—682no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—682no—
279C2×C4—682no—
280C2×C4—1364no—
281C2×C4#1058749512yes—
282C2×C4#1058756811yescharacteristic
283C2×C4#1058757211yescharacteristic
284C2×C4#1058762512yes—
285C8—82no—
286C8—684no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22#1176268611yescharacteristic
300C22C2×#1058749511yescharacteristic
301C22#1176279111yescharacteristic
302C4—22no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—1362no—
308C4—1362no—
309C4#1176300012yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1452919511yescharacteristic
315C2#1452925011yescharacteristic
316C2#1452932911yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC24×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1465C2
socleC22×C17#386
prime radicalC22×D4×C17C2×C4
cosocleC23×C4×C17C23
hypercenter#1465D17
hypocenterC17#9510
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #14528862C2semidirect
4. #14526691C2semidirect
212. C17#9510semidirect

Maximal subgroups

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

subgroupindex
#145378252
#145331012
#145288622
#145266912
C17×#14652
#951017