Finite Group Databasebeta

← #17960855

Subgroups — #17960855

Order 4352.

628 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 102 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×#11763713C212yesmaximal
2C4×#10587539C212yesmaximal, complemented
3#14543879C212yesmaximal, complemented
4#14531506C211yesmaximal, characteristic
5C2×#10587539C2214yes—
6C4×C22⋊#595—22no—
7#11763713C418yescomplemented
8#11763687—22no—
9C2×#10587626C2211yescharacteristic
10C2×C4×D68C2211yescharacteristic
11#11762712C411yescharacteristic, complemented
12#11762710C2211yescharacteristic
13#11762688—22no—
14#11762685—22no—
15#11762674C411yescharacteristic, complemented
16#11762655C411yescharacteristic, complemented
17C2×C4×D4×C17C411yescharacteristic, complemented
18C22×D4×C17C2×C411yescharacteristic
19C23×C4×C17—21no—
20C22×C22⋊D17—22no—
21C22×D68C2311yescharacteristic
22C22×C4×D17D412yes—
23C2×C22⋊#595—24no—
24C2×C4×#595—42no—
25C4×D4×C17—42no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C22⋊C4×C17—21no—
28C2×C42×C17C2×C411yescharacteristic
29C2×C22⋊Dic17—22no—
30#10587626—22no—
31#10587626C2×C414yes—
32C2×#63227—22no—
33C2×#63227D412yes—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C4×Dic17C2×C411yescharacteristic
37C4×D68—42no—
38(C2×#595)⋊C4—42no—
39#10587539—24no—
40#10587539C2×C418yescomplemented
41#10587502—21no—
42#10587502—21no—
43#10587502—22no—
44C24×C17—21no—
45C23×D17C2×D412yes—
46C22×#595—44no—
47C2×D4×C17—21no—
48C2×D4×C17—41no—
49C2×D4×C17—41no—
50C2×D4×C17C4212yescomplemented
51C22×C4×C17—21no—
52C22×C4×C17—42no—
53C22×C4×C17—82no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C2×C22⋊D17—28no—
58C2×C22⋊D17—82no—
59C2×C22⋊D17—82no—
60C22×Dic17—21no—
61C22×Dic17—21no—
62C22×Dic17C22⋊C412yes—
63C2×D68—41no—
64C2×D68—41no—
65C2×D68C22×C412yes—
66C2×D68#4112yes—
67C2×C4×D17—22no—
68C2×C4×D17—22no—
69C2×C4×D17—82no—
70C22⋊#595—28no—
71C22⋊#595—44no—
72C4×#595—84no—
73C4⋊C4×C17—41no—
74C22⋊C4×C17—42no—
75C42×C17—22no—
76C22⋊Dic17—82no—
77#63227—42no—
78#63227—82no—
79C4⋊Dic17—41no—
80C4×Dic17—21no—
81C4×Dic17—41no—
82C4×Dic17C4212yescomplemented
83#12628—171nomaximal, Sylow
84C23×C17—22no—
85C23×C17—42no—
86C23×C17—42no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17C2×C22⋊C411yescharacteristic
90C22×D17—22no—
91C22×D17—22no—
92C22×D17—42no—
93C22×D17—42no—
94C22×D17C4×D414yes—
95C2×#595—48no—
96C2×#595—84no—
97C2×#595—84no—
98D4×C17—42no—
99D4×C17—42no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17—84no—
108C2×C4×C17#9912yes—
109C2×C4×C17C2×C4211yescharacteristic
110C2×C4×C17#11711yescharacteristic
111C22⋊D17—88no—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—42no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120D68—42no—
121D68—42no—
122C4×D17—44no—
123C4×D17—82no—
124#2328—171no—
125C2×#353—172no—
126C4×#99—172no—
127#1393—172no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—44no—
131C22×C17—42no—
132C22×C17—82no—
133C22×C17—81no—
134C22×C17—81no—
135C22×C17C4×C22⋊C411yescharacteristic
136C22×C17C2×#9911yescharacteristic
137C22×C17#41011yescharacteristic
138C2×D17—24no—
139C2×D17—42no—
140C2×D17—42no—
141C2×D17—44no—
142C2×D17—82no—
143#595—88no—
144C4×C17—22no—
145C4×C17—21no—
146C4×C17—21no—
147C4×C17—41no—
148C4×C17—81no—
149Dic17—42no—
150Dic17—42no—
151Dic17—81no—
152C2×#127—171no—
153C2×C4×D4—171no—
154C2×C4×D4#59511yescharacteristic, complemented
155C2×#99—174no—
156#390—171no—
157#390—171no—
158#386—342no—
159#386—342no—
160#382—171no—
161C4×C22⋊C4—342no—
162#376—171no—
163#353—178no—
164#342—342no—
165C2×C17—21no—
166C2×C17—21no—
167C2×C17—82no—
168C2×C17C4×#9911yescharacteristic
169C2×C17#212711yescharacteristic
170C2×C17#212811yescharacteristic
171D17—44no—
172C22×D4—171no—
173C22×D4—342no—
174C22×D4C2×#59511yescharacteristic
175C23×C4—21no—
176C23×C4—172no—
177#127—174no—
178#127—342no—
179C4×D4—42no—
180C4×D4—682no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4C2×#59511yescharacteristic
183C2×C22⋊C4—21no—
184C2×C22⋊C4—172no—
185C2×C22⋊C4—344no—
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—342no—
195#95—341no—
196#95—341no—
197#95—682no—
198C17#1262811yescharacteristic, complemented, Sylow
199C24—21no—
200C24—172no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—172no—
205C2×D4—172no—
206C2×D4—348no—
207C2×D4—681no—
208C2×D4—681no—
209C2×D4—1362no—
210C2×D4—1362no—
211C2×D4C4×#59512yescomplemented
212C22×C4—21no—
213C22×C4—42no—
214C22×C4—82no—
215C22×C4—172no—
216C22×C4—341no—
217C22×C4—342no—
218C22×C4—342no—
219C22×C4—341no—
220C22×C4—684no—
221C22×C4—1362no—
222C22×C4C22⋊#59511yescharacteristic
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22×#59511yescharacteristic
225C4⋊C4—41no—
226C4⋊C4—681no—
227C22⋊C4—42no—
228C22⋊C4—348no—
229C22⋊C4—682no—
230C22⋊C4—684no—
231C22⋊C4—1362no—
232C22⋊C4—1362no—
233C42—22no—
234C42—172no—
235C42—341no—
236C42—681no—
237C42—1364no—
238C23—22no—
239C23—42no—
240C23—42no—
241C23—41no—
242C23—41no—
243C23—174no—
244C23—342no—
245C23—342no—
246C23—682no—
247C23—682no—
248C23C2×C22⋊#59511yescharacteristic
249D4—42no—
250D4—42no—
251D4—682no—
252D4—682no—
253D4—1368no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—84no—
262C2×C4—342no—
263C2×C4—342no—
264C2×C4—684no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4—682no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—688no—
271C2×C4—681no—
272C2×C4—1362no—
273C2×C4—1364no—
274C2×C4—1364no—
275C2×C4#1058755112yes—
276C2×C4C2×C4×#59511yescharacteristic
277C2×C4#1058767711yescharacteristic
278C22—21no—
279C22—21no—
280C22—44no—
281C22—42no—
282C22—82no—
283C22—81no—
284C22—81no—
285C22—344no—
286C22—684no—
287C22—682no—
288C22—682no—
289C22—1362no—
290C22C4×C22⋊#59511yescharacteristic
291C22C2×#1058755111yescharacteristic
292C22#1176378811yescharacteristic
293C4—21no—
294C4—21no—
295C4—22no—
296C4—41no—
297C4—81no—
298C4—682no—
299C4—682no—
300C4—1361no—
301C4—1368no—
302C2—21no—
303C2—21no—
304C2—82no—
305C2—684no—
306C2C4×#1058755111yescharacteristic
307C2#1454505911yescharacteristic
308C2#1454506311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC22×C17C2×#99
prime radicalC2×#10587626C22
cosocleC22×D68C23
hypercenterC2×C4×D4#595
hypocenterC17#12628
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#10587539C2semidirect
3. #14543879C2semidirect
7. #11763713C4semidirect
11. #11762712C4semidirect
15. #11762674C4semidirect
16. #11762655C4semidirect
17. C2×C4×D4×C17C4semidirect
40. #10587539C2×C4semidirect
50. C2×D4×C17C42semidirect
82. C4×Dic17C42semidirect
154. C2×C4×D4#595semidirect
198. C17#12628semidirect
211. C2×D4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637132
C4×#105875392
#145438792
#145315062
#1262817