Finite Group Databasebeta

← #17960856

Subgroups — #17960856

Order 4352.

628 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 100 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×#11763714C212yesmaximal
2#14544529C212yesmaximal, complemented
3#14543879C212yesmaximal, complemented
4#14531507C211yesmaximal, characteristic
5C2×#10587539C2214yes—
6C4×C22⋊#595—22no—
7#11763714C418yescomplemented
8#11763687—22no—
9C2×#10587560C2211yescharacteristic
10C2×#10587579C411yescharacteristic, complemented
11C2×#10587579C2211yescharacteristic
12#11762710C411yescharacteristic, complemented
13#11762710C2211yescharacteristic
14#11762687—22no—
15#11762687—22no—
16#11762655C411yescharacteristic, complemented
17C17×#382C411yescharacteristic, complemented
18C22×D68—22no—
19C22×D68C2×C411yescharacteristic
20C22×D68C2311yescharacteristic
21C22×C4×D17—21no—
22C22×C4×D17D412yes—
23C2×C22⋊#595—24no—
24C2×C4×#595—42no—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×#63227—22no—
29C2×#63227—22no—
30C2×#63227—21no—
31C2×#63227D412yes—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17C2×C411yescharacteristic
34#10587579—42no—
35#10587579—42no—
36#10587560—22no—
37#10587560C2×C414yes—
38(C2×#595)⋊C4—42no—
39#10587539—24no—
40#10587539C2×C418yescomplemented
41C17×#95—22no—
42#10587502—21no—
43#10587502—21no—
44C23×D17—21no—
45C23×D17C2×D412yes—
46C22×#595—44no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C412yes—
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17C22⋊C411yescharacteristic
53C22×Dic17C22⋊C411yescharacteristic
54C2×D68—21no—
55C2×D68—28no—
56C2×D68—41no—
57C2×D68—41no—
58C2×D68—41no—
59C2×D68—41no—
60C2×D68—82no—
61C2×D68—82no—
62C2×D68C4212yescomplemented
63C2×D68C22×C412yes—
64C2×D68#4112yes—
65C2×C4×D17—22no—
66C2×C4×D17—22no—
67C2×C4×D17—42no—
68C2×C4×D17—82no—
69C2×C4×D17—82no—
70C22⋊#595—28no—
71C22⋊#595—44no—
72C4×#595—84no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C42×C17—21no—
76C42×C17C4212yescomplemented
77#63227—42no—
78#63227—42no—
79#63227—82no—
80#63227—82no—
81C4×Dic17—22no—
82C4×Dic17—41no—
83#12628—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85C22×D17—22no—
86C22×D17—22no—
87C22×D17—22no—
88C22×D17—42no—
89C22×D17—42no—
90C22×D17—42no—
91C22×D17—42no—
92C22×D17—41no—
93C22×D17—41no—
94C22×D17C4×D414yes—
95C2×#595—48no—
96C2×#595—84no—
97C2×#595—84no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—22no—
101C2×C4×C17—22no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17C2×C4211yescharacteristic
108C2×C4×C17#11711yescharacteristic
109C2×Dic17—21no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17#9912yes—
116D68—42no—
117D68—42no—
118D68—42no—
119D68—42no—
120D68—88no—
121C4×D17—44no—
122C4×D17—82no—
123C4×D17—84no—
124#2328—171no—
125C2×#353—172no—
126C4×#99—172no—
127#1393—172no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17C4×C22⋊C411yescharacteristic
131C22×C17C2×#9911yescharacteristic
132C22×C17#41011yescharacteristic
133C2×D17—24no—
134C2×D17—42no—
135C2×D17—42no—
136C2×D17—44no—
137C2×D17—44no—
138C2×D17—42no—
139C2×D17—82no—
140C2×D17—82no—
141C2×D17—81no—
142C2×D17—81no—
143#595—88no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17—42no—
147C4×C17—42no—
148C4×C17—81no—
149Dic17—22no—
150Dic17—41no—
151Dic17—81no—
152C2×#127—171no—
153C2×C4×D4—171no—
154C2×C4×D4—171no—
155C2×#99—174no—
156#390—171no—
157#390—171no—
158#386—342no—
159#386—342no—
160#382#59511yescharacteristic, complemented
161C4×C22⋊C4—342no—
162#376—171no—
163#353—178no—
164#342—342no—
165C2×C17—21no—
166C2×C17—21no—
167C2×C17C4×#9911yescharacteristic
168C2×C17#212711yescharacteristic
169C2×C17#212811yescharacteristic
170D17—44no—
171D17—82no—
172C22×D4—171no—
173C22×D4—171no—
174C22×D4—342no—
175C23×C4—172no—
176C23×C4—341no—
177#127—174no—
178#127—342no—
179C4×D4—682no—
180C4×D4—682no—
181C2×C4⋊C4C2×#59511yescharacteristic
182C2×C4⋊C4C2×#59511yescharacteristic
183C2×C22⋊C4—172no—
184C2×C22⋊C4—344no—
185C2×C22⋊C4—341no—
186C2×C22⋊C4—342no—
187C2×C22⋊C4—342no—
188C2×C42—171no—
189C2×C42—171no—
190C2×C42—682no—
191C2×C42C2×#59511yescharacteristic
192#99—178no—
193#99—344no—
194#95—22no—
195#95—341no—
196#95—341no—
197#95—682no—
198C17#1262811yescharacteristic, complemented, Sylow
199C24—172no—
200C24—341no—
201C2×D4—172no—
202C2×D4—172no—
203C2×D4—172no—
204C2×D4—348no—
205C2×D4—341no—
206C2×D4—681no—
207C2×D4—681no—
208C2×D4—681no—
209C2×D4—681no—
210C2×D4—1362no—
211C2×D4—1362no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—342no—
217C22×C4—342no—
218C22×C4—341no—
219C22×C4—682no—
220C22×C4—684no—
221C22×C4—1362no—
222C22×C4—1362no—
223C22×C4C22⋊#59512yes—
224C22×C4C22×#59511yescharacteristic
225C4⋊C4—41no—
226C4⋊C4—41no—
227C22⋊C4—348no—
228C22⋊C4—682no—
229C22⋊C4—682no—
230C22⋊C4—684no—
231C22⋊C4—1362no—
232C22⋊C4—1362no—
233C42—21no—
234C42—342no—
235C42—681no—
236C42—1364no—
237C42C4×#59512yescomplemented
238C23—174no—
239C23—342no—
240C23—342no—
241C23—342no—
242C23—682no—
243C23—682no—
244C23—682no—
245C23—682no—
246C23—681no—
247C23—681no—
248C23C2×C22⋊#59511yescharacteristic
249D4—682no—
250D4—682no—
251D4—682no—
252D4—682no—
253D4—1368no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—172no—
264C2×C4—341no—
265C2×C4—684no—
266C2×C4—681no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—688no—
271C2×C4—681no—
272C2×C4—1362no—
273C2×C4—1364no—
274C2×C4—1364no—
275C2×C4—1364no—
276C2×C4C2×C4×#59511yescharacteristic
277C2×C4#1058767711yescharacteristic
278C22—21no—
279C22—21no—
280C22—344no—
281C22—684no—
282C22—684no—
283C22—682no—
284C22—682no—
285C22—682no—
286C22—1362no—
287C22—1362no—
288C22—1361no—
289C22—1361no—
290C22C4×C22⋊#59511yescharacteristic
291C22D17⋊#9911yescharacteristic
292C22#1176379011yescharacteristic
293C4—21no—
294C4—21no—
295C4—42no—
296C4—42no—
297C4—81no—
298C4—342no—
299C4—681no—
300C4—1361no—
301C4—1368no—
302C2—21no—
303C2—21no—
304C2—684no—
305C2—1362no—
306C2#1454452911yescharacteristic
307C2#1454506211yescharacteristic
308C2#1454506411yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC22×C17C2×#99
prime radicalC2×#10587560C22
cosocleC22×D68C23
hypercenter#382#595
hypocenterC17#12628
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14544529C2semidirect
3. #14543879C2semidirect
7. #11763714C4semidirect
10. C2×#10587579C4semidirect
12. #11762710C4semidirect
16. #11762655C4semidirect
17. C17×#382C4semidirect
40. #10587539C2×C4semidirect
62. C2×D68C42semidirect
76. C42×C17C42semidirect
160. #382#595semidirect
198. C17#12628semidirect
237. C42C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637142
#145445292
#145438792
#145315072
#1262817