Finite Group Databasebeta

← #14721600

Subgroups — #14721600

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077657C211yesmaximal, characteristic
2#13071589C211yesmaximal, characteristic
3#13067180C212yesmaximal, complemented
4#13067149C214yesmaximal, complemented
5#13067136C214yesmaximal, complemented
6#13067115C212yesmaximal, complemented
7C11×#3501C211yesmaximal, characteristic
8C11×#554—24no—
9C11×#554C414yescomplemented
10D4×Q8×C11C414yescomplemented
11C11×#544—21no—
12C11×#543—22no—
13C11×#533C2212yes—
14C2×C11×C22⋊Q8C2214yes—
15C11×#518—21no—
16C2×C4×D4×C11C2211yescharacteristic
17#10622834—21no—
18#10622824C2212yes—
19C4×C22⋊Dic11C2212yes—
20#10622820C2214yes—
21#10622625—24no—
22C4⋊C4×Dic11—21no—
23#10622564—22no—
24#10622549C2211yescharacteristic
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2212yes—
27#10622176C2214yes—
28#10622176C2214yes—
29#10622176C2218yes—
30C22×Q8×C11C2×C414yes—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11C2312yes—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8C2×C412yes—
35C11×C4⋊Q8C2×C412yes—
36C11×#125—24no—
37C11×#125—22no—
38C11×C22⋊Q8—24no—
39C11×C22⋊Q8—24no—
40C11×C22⋊Q8—22no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8C2×C418yes—
44C11×C22⋊Q8C2314yes—
45C4×Q8×C11—22no—
46C4×Q8×C11C2×C414yes—
47C4×D4×C11—24no—
48C4×D4×C11—24no—
49C4×D4×C11C2×C414yes—
50C4×D4×C11D414yes—
51C11×#117—22no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—22no—
64C2×#4318—24no—
65C11⋊#95—21no—
66C11⋊#95—22no—
67C11⋊#95C2311yescharacteristic
68C11⋊#95C2311yescharacteristic
69C11⋊#95C2312yes—
70C22⋊(C11⋊C8)—24no—
71C22⋊(C11⋊C8)C2314yes—
72C4⋊(C11⋊C8)—22no—
73C4×C11⋊C8—22no—
74#17627—111nomaximal, Sylow
75C24×C11C2×D412yes—
76C2×Q8×C11—22no—
77C2×Q8×C11—24no—
78C2×Q8×C11—84no—
79C2×Q8×C11C22×C414yes—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11C22⋊C414yes—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—82no—
86C22×C4×C11C22×C414yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D414yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—22no—
94C22×Dic11—21no—
95C11×C4⋊C4—28no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4C22⋊C414yes—
103C11×C4⋊C4C22×C414yes—
104C11×C22⋊C4—28no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4C22⋊C418yes—
107C42×C11—24no—
108C42×C11C22×C412yes—
109C42×C11C2×D412yes—
110C22⋊Dic11—44no—
111C22⋊Dic11—82no—
112C4⋊Dic11—42no—
113C4⋊Dic11—42no—
114C4×Dic11—42no—
115C4×Dic11—82no—
116#4318—84no—
117C2×C11⋊C8—24no—
118#3501D1111yescharacteristic
119#2975—111no—
120#2357—111no—
121#1518—112no—
122#1511—114no—
123#1508—114no—
124#1503—112no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11C2×C22⋊C414yes—
130C23×C11C22×D411yescharacteristic
131Q8×C11—44no—
132Q8×C11—82no—
133Q8×C11—84no—
134D4×C11—28no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—44no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—44no—
142C2×C4×C11—84no—
143C2×C4×C11—84no—
144C2×C4×C11C2×C22⋊C412yes—
145C2×C4×C11C2×C22⋊C414yes—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11#13712yes—
148C2×C4×C11#13712yes—
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C11⋊C8—44no—
161#554—24no—
162#554Dic1114yescomplemented
163D4×Q8Dic1114yescomplemented
164#544—21no—
165#543—22no—
166#533C2×D1112yes—
167C2×C22⋊Q8C2×D1114yes—
168#518—21no—
169C2×C4×D4C2×D1111yescharacteristic
170#436—224no—
171#431—112no—
172#407—114no—
173#390—221no—
174#388—222no—
175#382—111no—
176#381—112no—
177C4×C4⋊C4—111no—
178C4×C4⋊C4—221no—
179C4×C22⋊C4—112no—
180#328—114no—
181#328—114no—
182#328—118no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—24no—
186C22×C11—24no—
187C22×C11—24no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11C22×C22⋊C411yescharacteristic
191C22×C11C2×#13711yescharacteristic
192C22×C11C2×#13711yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—24no—
196C4×C11—22no—
197C4×C11—44no—
198C4×C11—44no—
199C4×C11#41914yes—
200Dic11—42no—
201Dic11—81no—
202Dic11—82no—
203C22×Q8C2×Dic1114yes—
204C22×D4C22⋊D1111yescharacteristic
205C23×C4C22×D1112yes—
206C2×M16—224no—
207C4⋊Q8—24no—
208C4⋊Q8C2×Dic1112yes—
209C4⋊Q8C2×Dic1112yes—
210#125—24no—
211#125—22no—
212C22⋊Q8—24no—
213C22⋊Q8—24no—
214C22⋊Q8—22no—
215C22⋊Q8—28no—
216C22⋊Q8—28no—
217C22⋊Q8C2×Dic1118yes—
218C22⋊Q8C22×D1114yes—
219C4×Q8—22no—
220C4×Q8C2×Dic1114yes—
221C4×D4—24no—
222C4×D4—24no—
223C4×D4C2×Dic1114yes—
224C4×D4C22⋊D1114yes—
225#117—22no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4C2×Dic1114yes—
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4—24no—
232C2×C22⋊C4—222no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4C22⋊D1112yes—
235C2×C42—221no—
236C2×C42—222no—
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—222no—
239C22⋊C8—114no—
240C22⋊C8—224no—
241C4×C8—222no—
242#95—111no—
243#95—112no—
244#95—111no—
245#95—222no—
246#95—221no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—44no—
250C2×C11#288311yescharacteristic
251C2×C11C2×#41911yescharacteristic
252C2×C11#290111yescharacteristic
253C24C2×C22⋊D1112yes—
254C2×Q8—22no—
255C2×Q8—24no—
256C2×Q8—84no—
257C2×Q8C22×Dic1114yes—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4C22⋊Dic1114yes—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—82no—
264C22×C4—221no—
265C22×C4—222no—
266C22×C4—221no—
267C22×C4C22×Dic1114yes—
268C22×C4C2×C22⋊D1112yes—
269C22×C4C2×C22⋊D1111yescharacteristic
270C22×C4C2×C22⋊D1114yes—
271C22×C4C2×C22⋊D1111yescharacteristic
272C22×C4C23×D1111yescharacteristic
273M16—884no—
274C2×C8—224no—
275C4⋊C4—28no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4C22⋊Dic1114yes—
285C4⋊C4C22×Dic1114yes—
286C22⋊C4—28no—
287C22⋊C4—24no—
288C22⋊C4—444no—
289C22⋊C4—882no—
290C22⋊C4C22⋊Dic1118yes—
291C42—24no—
292C42—442no—
293C42—882no—
294C42C22×Dic1112yes—
295C42C2×C22⋊D1112yes—
296C11#1762711yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—42no—
300C23—42no—
301C23C2×C22⋊Dic1114yes—
302C23C22×C22⋊D1111yescharacteristic
303Q8—44no—
304Q8—82no—
305Q8—84no—
306D4—28no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—84no—
315C2×C4—84no—
316C2×C4—222no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4#6699512yes—
326C2×C4#6699512yes—
327C2×C4C2×C22⋊Dic1112yes—
328C2×C4C2×C22⋊Dic1114yes—
329C2×C4C2×C22⋊Dic1112yes—
330C2×C4C23×Dic1111yescharacteristic
331C2×C4C22×C22⋊D1111yescharacteristic
332C8—444no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—24no—
337C22—24no—
338C22—82no—
339C22—82no—
340C22C2×#6699511yescharacteristic
341C22C2×#6699511yescharacteristic
342C22C22×C22⋊Dic1111yescharacteristic
343C4—21no—
344C4—21no—
345C4—24no—
346C4—22no—
347C4—44no—
348C4—44no—
349C4—442no—
350C4—881no—
351C4—882no—
352C4#1062283814yes—
353C2—21no—
354C2—21no—
355C2—44no—
356C2#1307707711yescharacteristic
357C2C2×#1062283811yescharacteristic
358C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#3501D11
hypocenterC11#17627
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3501

Complements

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

NH ≅ G/Ntype
3. #13067180C2semidirect
4. #13067149C2semidirect
5. #13067136C2semidirect
6. #13067115C2semidirect
9. C11×#554C4semidirect
10. D4×Q8×C11C4semidirect
162. #554Dic11semidirect
163. D4×Q8Dic11semidirect
296. C11#17627semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130715892
#130671802
#130671492
#130671362
#130671152
C11×#35012
#1762711