Finite Group Databasebeta

← #14721599

Subgroups — #14721599

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#13082419C211yesmaximal, characteristic
2#13077657C211yesmaximal, characteristic
3#13067179C212yesmaximal, complemented
4#13067148C214yesmaximal, complemented
5#13067135C214yesmaximal, complemented
6#13067114C212yesmaximal, complemented
7C11×#2357C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623329—21no—
10C2×#66977C2214yes—
11#10623074C414yescomplemented
12#10623070—24no—
13D4×Dic22C414yescomplemented
14#10623031—21no—
15#10623014—22no—
16#10623001C2212yes—
17C11×#390—21no—
18C11×#388—22no—
19C11×#382C2211yescharacteristic
20C11×#381C2212yes—
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C4×C11×C22⋊C4C2212yes—
24#10622820C2214yes—
25#10622625—24no—
26#10622538C2212yes—
27#10622090C2214yes—
28#10622090C2214yes—
29#10622090C2218yes—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11C2312yes—
32C22×Dic22C2×C414yes—
33C4×D4×C11C2×C414yes—
34C4×D4×C11D414yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4D412yes—
41C2×C42×C11—21no—
42C2×C42×C11—22no—
43C2×C42×C11C2311yescharacteristic
44C2×C22⋊Dic11—24no—
45D4×Dic11—24no—
46D4×Dic11—24no—
47#66979—22no—
48C2×C4⋊Dic11C2×C414yes—
49#66977—22no—
50#66977—24no—
51#66977—24no—
52#66977C2×C418yes—
53#66977C2314yes—
54C2×Dic11⋊C4—24no—
55C2×#4318—24no—
56#66943—24no—
57#66941—24no—
58#66931—28no—
59#66931—28no—
60#66923—22no—
61#66922C2×C412yes—
62#66922C2×C412yes—
63C4×Dic22—22no—
64C4×Dic22C2×C414yes—
65C11×#95—22no—
66C11×#95—21no—
67C11×#95C2311yescharacteristic
68C11×#95C2312yes—
69C11×#95C2311yescharacteristic
70C22⋊(C11⋊C8)—24no—
71C22⋊(C11⋊C8)C2314yes—
72C4⋊(C11⋊C8)—22no—
73C4×C11⋊C8—22no—
74#17627—111nomaximal, Sylow
75C24×C11C2×D412yes—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11C22⋊C414yes—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—82no—
83C22×C4×C11C22×C414yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—24no—
90C22×Dic11—24no—
91C2×Dic22—22no—
92C2×Dic22—24no—
93C2×Dic22—84no—
94C2×Dic22C22×C414yes—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4C22⋊C414yes—
98C11×C22⋊C4—44no—
99C11×C22⋊C4—82no—
100C11×C22⋊C4C22⋊C418yes—
101C42×C11—42no—
102C42×C11—82no—
103C42×C11C22×C412yes—
104C42×C11C2×D412yes—
105C22⋊Dic11—28no—
106C22⋊Dic11—24no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—24no—
111C4⋊Dic11C22×C414yes—
112Dic11⋊C4—24no—
113Dic11⋊C4—28no—
114Dic11⋊C4—24no—
115C4×Dic11—24no—
116#4318—84no—
117C2×C11⋊C8—24no—
118#3501—111no—
119#2975—111no—
120#2357D1111yescharacteristic
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
131D4×C11—28no—
132C2×C4×C11—22no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—44no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C2×C22⋊C414yes—
148C2×C4×C11C2×C22⋊C412yes—
149C2×C4×C11#13712yes—
150C2×C4×C11#13712yes—
151C2×C4×C11C23×C411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×Dic11—24no—
154C2×Dic11—24no—
155C2×Dic11—84no—
156C2×Dic11—84no—
157Dic22—44no—
158Dic22—82no—
159Dic22—84no—
160C11⋊C8—44no—
161#554—114no—
162#554—224no—
163D4×Q8—114no—
164#544—221no—
165#543—222no—
166#533—112no—
167C2×C22⋊Q8—114no—
168#518—221no—
169C2×C4×D4C2×D1111yescharacteristic
170#436—224no—
171#431—112no—
172#407—114no—
173#390—21no—
174#388—22no—
175#382C2×D1111yescharacteristic
176#381C2×D1112yes—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C2×D1111yescharacteristic
179C4×C22⋊C4C2×D1112yes—
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—42no—
198C4×C11—81no—
199C4×C11—82no—
200C4×C11#41914yes—
201Dic11—44no—
202Dic11—44no—
203C22×Q8—114no—
204C22×D4C22⋊D1111yescharacteristic
205C23×C4C22×D1112yes—
206C2×M16—224no—
207C4⋊Q8—112no—
208C4⋊Q8—112no—
209C4⋊Q8—224no—
210#125—224no—
211#125—222no—
212C22⋊Q8—118no—
213C22⋊Q8—114no—
214C22⋊Q8—224no—
215C22⋊Q8—224no—
216C22⋊Q8—222no—
217C22⋊Q8—228no—
218C22⋊Q8—228no—
219C4×Q8—114no—
220C4×Q8—222no—
221C4×D4—224no—
222C4×D4—224no—
223C4×D4C4×D1114yes—
224C4×D4D4414yes—
225#117—222no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—114no—
229C2×C4⋊C4—224no—
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—224no—
234C2×C22⋊C4C22⋊D1112yes—
235C2×C42—21no—
236C2×C42—22no—
237C2×C42C22×D1111yescharacteristic
238C4⋊C8—222no—
239C22⋊C8—114no—
240C22⋊C8—224no—
241C4×C8—222no—
242#95—22no—
243#95—21no—
244#95C22×D1111yescharacteristic
245#95C22×D1112yes—
246#95C22×D1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—44no—
250C2×C11#288311yescharacteristic
251C2×C11C2×#41911yescharacteristic
252C2×C11#290111yescharacteristic
253C24C2×C22⋊D1112yes—
254C2×Q8—114no—
255C2×Q8—222no—
256C2×Q8—224no—
257C2×Q8—884no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4(C2×D11)⋊C414yes—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—82no—
265C22×C4—224no—
266C22×C4—224no—
267C22×C4C2×C4×D1114yes—
268C22×C4C2×D4414yes—
269C22×C4C2×C22⋊D1112yes—
270C22×C4C2×C22⋊D1111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272C22×C4C23×D1111yescharacteristic
273M16—884no—
274C2×C8—224no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—114no—
278C4⋊C4—224no—
279C4⋊C4—228no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—224no—
283C4⋊C4—222no—
284C4⋊C4—224no—
285C4⋊C4(C2×D11)⋊C414yes—
286C22⋊C4—44no—
287C22⋊C4—82no—
288C22⋊C4—228no—
289C22⋊C4—224no—
290C22⋊C4(C2×D11)⋊C418yes—
291C42—42no—
292C42—82no—
293C42—224no—
294C42C2×C4×D1112yes—
295C42C2×D4412yes—
296C11#1762711yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—42no—
300C23—42no—
301C23C2×(C2×D11)⋊C414yes—
302C23C22×C22⋊D1111yescharacteristic
303Q8—444no—
304Q8—884no—
305Q8—882no—
306D4—28no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—44no—
311C2×C4—41no—
312C2×C4—44no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—224no—
322C2×C4—224no—
323C2×C4—884no—
324C2×C4—884no—
325C2×C4C2×(C2×D11)⋊C412yes—
326C2×C4C2×(C2×D11)⋊C414yes—
327C2×C4C2×(C2×D11)⋊C412yes—
328C2×C4#6700412yes—
329C2×C4#6700412yes—
330C2×C4C22×C4×D1111yescharacteristic
331C2×C4C22×D4411yescharacteristic
332C8—444no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—24no—
337C22—24no—
338C22—82no—
339C22—82no—
340C22C22×(C2×D11)⋊C411yescharacteristic
341C22C2×#6700411yescharacteristic
342C22C2×#6700411yescharacteristic
343C4—21no—
344C4—21no—
345C4—24no—
346C4—22no—
347C4—42no—
348C4—81no—
349C4—82no—
350C4—444no—
351C4—444no—
352C4#1062261714yes—
353C2—21no—
354C2—21no—
355C2—44no—
356C2#1307707611yescharacteristic
357C2C2×#1062261711yescharacteristic
358C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2357C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#2357D11
hypocenterC11#17627
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2357

Complements

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

NH ≅ G/Ntype
3. #13067179C2semidirect
4. #13067148C2semidirect
5. #13067135C2semidirect
6. #13067114C2semidirect
11. #10623074C4semidirect
13. D4×Dic22C4semidirect
296. C11#17627semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130776572
#130671792
#130671482
#130671352
#130671142
C11×#23572
#1762711