Finite Group Databasebeta

← #14908707

Subgroups — #14908707

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079203C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic
3#13070815C212yesmaximal, complemented
4#13070760C211yesmaximal, characteristic, complemented
5#13070662C211yesmaximal, characteristic, complemented
6#13070661C211yesmaximal, characteristic, complemented
7#13070546C212yesmaximal
8#13070471C212yesmaximal, complemented
9#13070467C212yesmaximal, complemented
10#13070414C211yesmaximal, characteristic, complemented
11C11×#2226C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic
13#10623259—21no—
14C4×D4×D11—21no—
15C11×#500C2211yescharacteristic, complemented
16C4×C11×D8C2211yescharacteristic
17D8×Dic11C2211yescharacteristic
18C2×#66891C2212yes—
19#10622706—21no—
20C4×#4323—21no—
21C2×#66864C2212yes—
22#10622500—21no—
23#10622500C2212yes—
24D11×#107C2211yescharacteristic
25#10622486—21no—
26#10622486C2212yescomplemented
27#10622485C2211yescharacteristic
28D11×#102—21no—
29#10622369—21no—
30#10622312C2211yescharacteristic, complemented
31C4×D88C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33C11×#367C2212yescomplemented
34C11×C4⋊C16C2211yescharacteristic, complemented
35C11×#357C2212yes—
36(C2×D11)⋊C16C2212yes—
37#10622141C2212yescomplemented
38C16×Dic11C2212yescomplemented
39#10622130C2212yescomplemented
40#10622129C2212yes—
41#10622128C2212yescomplemented
42C4⋊(C11⋊C16)C2211yescharacteristic, complemented
43C2×D4×D11—21no—
44C22×C4×D11—41no—
45C2×C11×D8C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C4×D4×C11—21no—
48#66999—41no—
49Q8×Dic11—41no—
50D4×Dic11—21no—
51C2×#4323—21no—
52C4×C22⋊D11—41no—
53D8×D11—22no—
54D8×D11—22no—
55C2×Dic44—21no—
56C2×Dic44C2312yes—
57C2×D88C2311yescharacteristic
58C2×C8×D11D411yescharacteristic
59C2×C8×D11C2311yescharacteristic
60#66950—22no—
61#66946—21no—
62#66945—41no—
63C4⋊C4×D11—21no—
64#66943—41no—
65#66940—22no—
66(C22⋊D11)⋊C4—41no—
67C22⋊C4×D11—41no—
68C4×D44—21no—
69C42×D11D411yescharacteristic
70#66922—21no—
71C2×C11×C16C2312yes—
72C11×#107—21no—
73C11×#107C2312yes—
74C11×#107C2311yescharacteristic
75C11×#102—21no—
76C4×C8×C11C2311yescharacteristic
77#66896—21no—
78#66891—24no—
79#66885—21no—
80#66882C2311yescharacteristic
81C8×Dic11D411yescharacteristic
82C8×Dic11C2311yescharacteristic
83C2×C11⋊C16C2312yes—
84#66874—22no—
85#66874—22no—
86#66873—21no—
87#66871—21no—
88C4×C11⋊C8D411yescharacteristic
89#66864—24no—
90#33661—111nomaximal, Sylow
91C23×D11—41no—
92C2×Q8×C11—41no—
93C2×D4×C11—21no—
94C22×C4×C11—41no—
95C2×C22⋊D11—41no—
96C22×Dic11—41no—
97D4×D11—24no—
98D4×D11—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—84no—
104C2×C4×D11D811yescharacteristic
105C2×C4×D11D811yescharacteristic
106C2×C4×D11C2×D411yescharacteristic
107C2×Dic22—22no—
108C11×D8—21no—
109C11×D8#4112yes—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C22⋊Dic11—41no—
118#4323—24no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—42no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—42no—
128C4×Dic11—42no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134Dic44—22no—
135Dic44—22no—
136Dic44—42no—
137D88—21no—
138D88#4112yes—
139C8×D11—21no—
140C8×D11—21no—
141C8×D11—41no—
142C11×C16—22no—
143C11⋊C16—22no—
144#3170—111no—
145C2×C4×D8—111no—
146#2235—112no—
147#2226—111no—
148#2226D1111yescharacteristic, complemented
149#2208—111no—
150#2208—111no—
151#2187—112no—
152C4×SD32—112no—
153C4×SD32—112no—
154#2162—111no—
155C23×C11—41no—
156C22×D11—44no—
157C22×D11—41no—
158C22×D11—82no—
159C22×D11—82no—
160C22×D11C2×D811yescharacteristic
161Q8×C11—82no—
162D4×C11—22no—
163D4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—82no—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C22⋊D11—44no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—82no—
174C2×Dic11C2×D811yescharacteristic
175C2×Dic11C2×D811yescharacteristic
176C2×Dic11C2×D811yescharacteristic
177D44—22no—
178D44—41no—
179C4×D11—21no—
180C4×D11—21no—
181C4×D11—41no—
182C4×D11—82no—
183C4×D11—82no—
184C4×D11—82no—
185C4×D11SD3214yescomplemented
186Dic22—42no—
187Dic22—42no—
188C8×C11—21no—
189C8×C11C2×#4111yescharacteristic
190C8×C11C2×#4111yescharacteristic
191C11⋊C8—21no—
192C11⋊C8—21no—
193C22×D8—111no—
194#533—221no—
195C2×C4×D4—221no—
196C2×SD32—112no—
197C2×SD32—112no—
198#500C2×D1111yescharacteristic, complemented
199#494—111no—
200#487—221no—
201#467—112no—
202#467—221no—
203C4×Q16—112no—
204C4×Q16—221no—
205C4×D8—111no—
206C4×D8—111no—
207C4×D8—111no—
208C4×D8—221no—
209C4×D8—221no—
210C4×D8C2×D1111yescharacteristic
211C2×#107—111no—
212C2×#102—221no—
213C2×C4×C8—111no—
214#367—112no—
215#367C2×D1112yescomplemented
216C4⋊C16—111no—
217C4⋊C16C2×D1111yescharacteristic, complemented
218#358—112no—
219#358—112no—
220#357—112no—
221#357C2×D1112yes—
222C22⋊C16—112no—
223C4×C16—112no—
224C22×C11—42no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11C22×D811yescharacteristic
228C2×D11—21no—
229C2×D11—21no—
230C2×D11—42no—
231C2×D11—88no—
232C2×D11—81no—
233C2×D11—81no—
234C2×D11C2×SD3212yes—
235C4×C11—21no—
236C4×C11—81no—
237C4×C11—82no—
238C4×C11C2×SD3212yes—
239C4×C11#52511yescharacteristic
240C4×C11#57511yescharacteristic
241Dic11—21no—
242Dic11—21no—
243Dic11—82no—
244Dic11—81no—
245Dic11C2×SD3212yes—
246C22×D4—221no—
247C23×C4—441no—
248C2×Q16—112no—
249C2×Q16—221no—
250C2×D8—111no—
251C2×D8—221no—
252C2×D8—222no—
253C2×D8—222no—
254C2×D8C22×D1111yescharacteristic
255C22×C8—111no—
256C22×C8—111no—
257C4⋊Q8—21no—
258C4⋊Q8—221no—
259#125—441no—
260C22⋊Q8—222no—
261C22⋊Q8—441no—
262C4×Q8—222no—
263C4×Q8—441no—
264C4×D4—21no—
265C4×D4—221no—
266C4×D4—221no—
267C4×D4—221no—
268C4×D4—441no—
269C4×D4—441no—
270#117—441no—
271C2×C4⋊C4—221no—
272C2×C22⋊C4—441no—
273C2×C42—111no—
274SD32—224no—
275SD32—224no—
276C2×C16—112no—
277C2×C16C22×D1112yes—
278#107—21no—
279#107—111no—
280#107—221no—
281#107C22×D1112yes—
282#107C22×D1111yescharacteristic
283#103—222no—
284#103—222no—
285#102—21no—
286#102—221no—
287#102—221no—
288#102—221no—
289C4×C8—111no—
290C4×C8—111no—
291C4×C8—111no—
292C4×C8C22×D1111yescharacteristic
293C2×C11—82no—
294C2×C11#310011yescharacteristic
295C2×C11C22×SD3211yescharacteristic
296C2×C11#341411yescharacteristic
297D11—22no—
298D11—82no—
299C24—441no—
300C2×Q8—41no—
301C2×Q8—222no—
302C2×D4—21no—
303C2×D4—224no—
304C2×D4—221no—
305C2×D4—441no—
306C2×D4—442no—
307C22×C4—41no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—884no—
316Q16—222no—
317Q16—222no—
318Q16—442no—
319D8—21no—
320D8—112no—
321D8—224no—
322D8—221no—
323D8#434312yes—
324C2×C8—111no—
325C2×C8—111no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8—441no—
329C2×C8D4×D1111yescharacteristic
330C2×C8C23×D1111yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—41no—
334C4⋊C4—221no—
335C4⋊C4—441no—
336C4⋊C4—442no—
337C4⋊C4—442no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C22⋊C4—442no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C42—111no—
346C42—111no—
347C42—111no—
348C42—442no—
349C42D4×D1111yescharacteristic
350C16—22no—
351C16—222no—
352C11#3366111yescharacteristic, complemented, Sylow
353C23—41no—
354C23—111no—
355C23—444no—
356C23—441no—
357C23—882no—
358C23—882no—
359Q8—82no—
360Q8—442no—
361Q8—442no—
362D4—22no—
363D4—41no—
364D4—222no—
365D4—444no—
366D4—441no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—82no—
370C2×C4—111no—
371C2×C4—114no—
372C2×C4—111no—
373C2×C4—111no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—441no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—882no—
380C2×C4—882no—
381C2×C4—882no—
382C2×C4—882no—
383C2×C4D8×D1111yescharacteristic
384C2×C4D8×D1111yescharacteristic
385C2×C4C2×D4×D1111yescharacteristic
386C8—21no—
387C8—221no—
388C8—221no—
389C8C2×#434311yescharacteristic
390C8#41×D1111yescharacteristic
391C22—42no—
392C22—81no—
393C22—81no—
394C22—112no—
395C22—221no—
396C22—221no—
397C22—442no—
398C22—888no—
399C22—881no—
400C22—881no—
401C22C2×D8×D1111yescharacteristic
402C4—21no—
403C4—81no—
404C4—82no—
405C4—112no—
406C4—221no—
407C4—221no—
408C4—882no—
409C4—881no—
410C4D11×SD3212yes—
411C4#1062315811yescharacteristic
412C4#1062330811yescharacteristic
413C2—82no—
414C2—222no—
415C2—882no—
416C2#1307861811yescharacteristic
417C2C2×D11×SD3211yescharacteristic
418C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2226D11
hypocenterC11#33661
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13079203C2semidirect
3. #13070815C2semidirect
4. #13070760C2semidirect
5. #13070662C2semidirect
6. #13070661C2semidirect
8. #13070471C2semidirect
9. #13070467C2semidirect
10. #13070414C2semidirect
11. C11×#2226C2semidirect
15. C11×#500C22semidirect
26. #10622486C22semidirect
30. #10622312C22semidirect
33. C11×#367C22semidirect
34. C11×C4⋊C16C22semidirect
37. #10622141C22semidirect
38. C16×Dic11C22semidirect
39. #10622130C22semidirect
41. #10622128C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
148. #2226D11semidirect
185. C4×D11SD32semidirect
198. #500C2×D11semidirect
215. #367C2×D11semidirect
217. C4⋊C16C2×D11semidirect
352. C11#33661semidirect

Maximal subgroups

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

subgroupindex
#130792032
C4×D8×D112
#130708152
#130707602
#130706622
#130706612
#130705462
#130704712
#130704672
#130704142
C11×#22262
#3366111