Finite Group Databasebeta

← #14758129

Subgroups — #14758129

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071267C212yesmaximal
2#13069488C211yesmaximal, characteristic
3#13069478C211yesmaximal, characteristic
4#13069360C211yesmaximal, characteristic
5#13069345C211yesmaximal, characteristic
6#13069308C212yesmaximal
7#13069294C212yesmaximal
8#13068513C211yesmaximal, characteristic
9C4×#66899C212yesmaximal
10#13068304C211yesmaximal, characteristic
11C2×C11×#441C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C11×#441C418yescomplemented
15C2×C11×#106C2211yescharacteristic
16C2×C11×#103C2212yes—
17C2×C11×#97C2211yescharacteristic
18#10622843C2212yes—
19#10622843C2212yes—
20C2×#66899C2212yes—
21C2×#66899C2212yes—
22C2×#66882C2211yescharacteristic
23C2×#66881C2211yescharacteristic
24C2×#66879C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622598C2212yes—
29#10622598C2212yes—
30#10622594—22no—
31#10622594—22no—
32#10622550—22no—
33#10622549—22no—
34C4×C4⋊Dic11C2212yes—
35#10622545C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C22×Q8×C11C2312yes—
41C2×C11×Q16—22no—
42C2×C11×Q16—22no—
43C2×C11×Q16C2×C414yes—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C4×Q8×C11—24no—
47C4×Q8×C11C2×C418yes—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11—22no—
51C2×C42×C11C2311yescharacteristic
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×C4×Dic11—22no—
57C2×C4×Dic11C2311yescharacteristic
58C2×C4×Dic11C2311yescharacteristic
59C22×C11⋊C8C2311yescharacteristic
60C22×C11⋊C8C2311yescharacteristic
61C11×#106C2×C414yes—
62C11×#103C2×C418yes—
63C11×#97C2×C414yes—
64#66899—24no—
65#66899—24no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95D412yes—
74C11⋊#95D412yes—
75#66882—22no—
76#66881—22no—
77#66879—22no—
78#66879—22no—
79C8×Dic11—22no—
80C8×Dic11—22no—
81C4×C11⋊C8—22no—
82#21289—111nomaximal, Sylow
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11C22×C414yes—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2411yescharacteristic
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11C2×D411yescharacteristic
96C22×Dic11C2×D412yes—
97C22×Dic11C2×D411yescharacteristic
98C11×Q16—28no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11C22×C412yes—
102C2×C8×C11C22×C412yes—
103C2×C8×C11#4112yes—
104C2×C8×C11#4112yes—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4C22×C414yes—
108C42×C11—28no—
109C42×C11C22×C412yes—
110C42×C11#4112yes—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—22no—
115C4⋊Dic11—82no—
116C4⋊Dic11—82no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—82no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8#4112yes—
127C2×C11⋊C8#4112yes—
128C2×#441D1111yescharacteristic
129#2320—112no—
130#1971—111no—
131#1969—111no—
132#1944—111no—
133#1941—111no—
134#1935—112no—
135#1933—112no—
136#1776—111no—
137C4×#103—112no—
138#1726—111no—
139C23×C11C22×D411yescharacteristic
140Q8×C11—24no—
141Q8×C11—24no—
142Q8×C11—42no—
143Q8×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11C4×D414yes—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C8×C11—22no—
173C8×C11#11714yes—
174C11⋊C8—22no—
175C11⋊C8—22no—
176C22×Q16C2×D1111yescharacteristic
177C2×C4×Q8C2×D1112yes—
178#441Dic1118yescomplemented
179C2×#107—111no—
180C2×#106—111no—
181C2×#106C2×D1111yescharacteristic
182C2×#103—112no—
183C2×#103—112no—
184C2×#103C2×D1112yes—
185C2×#97—111no—
186C2×#97—111no—
187C2×#97C2×D1111yescharacteristic
188C2×C4×C8—111no—
189C2×C4×C8—111no—
190C2×C4×C8—111no—
191#391—112no—
192#391—112no—
193#389—112no—
194#389—112no—
195#387—222no—
196#387—222no—
197#383—222no—
198#382—222no—
199C4×C4⋊C4—112no—
200#376—111no—
201#340—112no—
202#340—112no—
203#340—112no—
204C22×C11C2×C4×D411yescharacteristic
205C22×C11#53211yescharacteristic
206C22×C11#53211yescharacteristic
207C22×C11#57712yes—
208C22×C11#57812yes—
209C4×C11—24no—
210C4×C11—44no—
211C4×C11—44no—
212C4×C11C2×#11711yescharacteristic
213C4×C11C4×#4111yescharacteristic
214C4×C11#52911yescharacteristic
215C4×C11#52911yescharacteristic
216Dic11—41no—
217Dic11—41no—
218Dic11—42no—
219Dic11—82no—
220Dic11—82no—
221C22×Q8C22×D1112yes—
222C2×Q16—22no—
223C2×Q16—22no—
224C2×Q16C2×Dic1114yes—
225C22×C8—111no—
226C22×C8—111no—
227C22×C8C22×D1111yescharacteristic
228C22×C8C22×D1111yescharacteristic
229C4×Q8—24no—
230C4×Q8C2×Dic1118yes—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4—222no—
236C2×C4⋊C4C22×D1112yes—
237C2×C42—22no—
238C2×C42—111no—
239C2×C42—111no—
240C2×C42—222no—
241C2×C42C22×D1111yescharacteristic
242#107—222no—
243#106—222no—
244#106C2×Dic1114yes—
245#103—224no—
246#103—224no—
247#103C2×Dic1118yes—
248#97—222no—
249#97—222no—
250#97C2×Dic1114yes—
251C4×C8—222no—
252C4×C8—222no—
253C4×C8—222no—
254#95—112no—
255#95—112no—
256#95—222no—
257#95—222no—
258#95—222no—
259#95—222no—
260#95—222no—
261#95—222no—
262#95—222no—
263C2×C11#229311yescharacteristic
264C2×C11#294712yes—
265C2×C11#317311yescharacteristic
266C2×C11#317711yescharacteristic
267C2×C11#317812yes—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8C22×Dic1114yes—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—111no—
277C22×C4—112no—
278C22×C4—111no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4D4×D1112yes—
282C22×C4C23×D1111yescharacteristic
283Q16—28no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—112no—
287C2×C8—112no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—221no—
291C2×C8—221no—
292C2×C8#433912yes—
293C2×C8#433912yes—
294C2×C8C22×Dic1112yes—
295C2×C8C22×Dic1112yes—
296C4⋊C4—28no—
297C4⋊C4—22no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—882no—
303C4⋊C4—882no—
304C4⋊C4C22×Dic1114yes—
305C42—28no—
306C42—221no—
307C42—221no—
308C42—221no—
309C42—221no—
310C42—882no—
311C42#434112yes—
312C42C22×Dic1112yes—
313C11#2128911yescharacteristic, complemented, Sylow
314C23C2×D4×D1111yescharacteristic
315Q8—24no—
316Q8—24no—
317Q8—42no—
318Q8—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—222no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4D4×Dic1114yes—
341C2×C4C2×#433911yescharacteristic
342C2×C4C2×#433911yescharacteristic
343C2×C4C2×#434111yescharacteristic
344C2×C4#41×D1111yescharacteristic
345C2×C4#41×D1111yescharacteristic
346C2×C4C23×Dic1111yescharacteristic
347C8—22no—
348C8—222no—
349C8—222no—
350C8#6697914yes—
351C22#1062307911yescharacteristic
352C22#1062307911yescharacteristic
353C22#1062330912yes—
354C22#1062331012yes—
355C22C2×D4×Dic1111yescharacteristic
356C4—24no—
357C4—44no—
358C4—44no—
359C4—441no—
360C4—441no—
361C4—442no—
362C4—882no—
363C4—882no—
364C4#1062308811yescharacteristic
365C4#1062308811yescharacteristic
366C4C2×#6697911yescharacteristic
367C4#41×Dic1111yescharacteristic
368C2#1307108111yescharacteristic
369C2#1307746012yes—
370C2#1307923611yescharacteristic
371C2#1307927311yescharacteristic
372C2#1307929012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#441D11
hypocenterC11#21289
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
14. C11×#441C4semidirect
178. #441Dic11semidirect
313. C11#21289semidirect

Maximal subgroups

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

subgroupindex
#130712672
#130694882
#130694782
#130693602
#130693452
#130693082
#130692942
#130685132
C4×#668992
#130683042
C2×C11×#4412
#2128911