Finite Group Databasebeta

← #14908462

Subgroups — #14908462

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079155C211yesmaximal, characteristic, complemented
2#13070773C212yesmaximal, complemented
3#13070773C212yesmaximal, complemented
4#13070763C212yesmaximal, complemented
5#13070753C212yesmaximal, complemented
6#13070405C211yesmaximal, characteristic, complemented
7#13070398C211yesmaximal, characteristic, complemented
8#13070375C211yesmaximal, characteristic, complemented
9#13070332C211yesmaximal, characteristic
10C2×#10622200C211yesmaximal, characteristic
11C11×#2948C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C11×#518—21no—
14#10623050—21no—
15C11×#442—22no—
16C4×C11×D8C2212yes—
17C4×C11×D8C2212yes—
18C11×#427C2211yescharacteristic
19C11×#418—21no—
20C11×#405C2211yescharacteristic
21#10622734—21no—
22#10622719C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622315—22no—
27#10622296C2212yescomplemented
28#10622295C2212yescomplemented
29#10622200C2212yes—
30#10622200C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33#10622128C2211yescharacteristic, complemented
34#10622128C2211yescharacteristic, complemented
35#10622128C2212yescomplemented
36#10622127C2211yescharacteristic, complemented
37#10622127C2211yescharacteristic, complemented
38#10622127C2212yescomplemented
39C4⋊(C11⋊C16)C2212yescomplemented
40C4⋊(C11⋊C16)C2212yescomplemented
41C22×D4×C11—21no—
42C2×C11×D8—21no—
43C2×C11×D8—22no—
44C2×C11×D8Q814yescomplemented
45C2×C11×D8C2312yes—
46C2×C11×M16D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C4×D4×C11—41no—
51C4×D4×C11—41no—
52C11×#117—21no—
53C11×#117D411yescharacteristic
54C2×C11×C22⋊C4—42no—
55#66979—21no—
56C2×C4⋊Dic11—21no—
57#66943—41no—
58#66941—41no—
59#66931—42no—
60#66923—22no—
61#66922—22no—
62C11×#107C2311yescharacteristic
63C11×#107C2311yescharacteristic
64C11×#106—21no—
65C11×#102—22no—
66C11×#102—22no—
67C11×#97D412yes—
68C4×C8×C11C2312yes—
69#66882—22no—
70#66882—21no—
71#66882C2311yescharacteristic
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66881—22no—
75#66881—21no—
76#66876—22no—
77C2×C11⋊C16—22no—
78C2×C11⋊C16C2311yescharacteristic
79C2×C11⋊C16C2312yes—
80C2×C11⋊C16C2311yescharacteristic
81#33631—111nomaximal, Sylow
82C24×C11—41no—
83C2×D4×C11—24no—
84C2×D4×C11—22no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—41no—
91C2×Dic22—42no—
92C11×D8—24no—
93C11×D8—22no—
94C11×D8C2×Q814yes—
95C11×M16—22no—
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×Q812yes—
99C2×C8×C11#4112yes—
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4D811yescharacteristic
104C11×C4⋊C4D811yescharacteristic
105C11×C22⋊C4—41no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4D812yes—
109C42×C11—41no—
110C42×C11C2×D412yes—
111C22⋊Dic11—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—42no—
116C4⋊Dic11—41no—
117Dic11⋊C4—42no—
118Dic11⋊C4—42no—
119C4×Dic11—41no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122C11⋊C16—22no—
123#3164—111no—
124#2948D1111yescharacteristic
125#2228—112no—
126#2228—112no—
127#2226—112no—
128#2224—112no—
129#2159—111no—
130#2158—111no—
131#2151—111no—
132#2140—111no—
133C2×#357—111no—
134C23×C11—42no—
135C23×C11—44no—
136C23×C11—161no—
137C23×C11—161no—
138C23×C11C2×D811yescharacteristic
139D4×C11—24no—
140D4×C11—42no—
141D4×C11—44no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—162no—
145C2×C4×C11—162no—
146C2×C4×C11C22⋊Q812yes—
147C2×C4×C11C2×D812yes—
148C2×C4×C11C2×D812yes—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11#13712yes—
151C2×C4×C11C22×D411yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—161no—
156Dic22—162no—
157C8×C11—22no—
158C8×C11C22⋊Q812yes—
159C8×C11C22×Q811yescharacteristic
160C8×C11C2×#4111yescharacteristic
161C22×D8C2×D1111yescharacteristic
162#544—221no—
163#518—21no—
164C2×M32—111no—
165C22×C16—111no—
166#501—222no—
167#500—112no—
168#499—112no—
169#442—22no—
170C4×D8C2×D1112yes—
171C4×D8C2×D1112yes—
172#428—221no—
173#427—111no—
174#427C2×D1111yescharacteristic
175C2×#107—111no—
176#418—21no—
177#405C2×D1111yescharacteristic
178#367—111no—
179#367—111no—
180#367—112no—
181#366—111no—
182#366—111no—
183#366—112no—
184C4⋊C16—112no—
185C4⋊C16—112no—
186#357—112no—
187#357—112no—
188#357—112no—
189#357—112no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—44no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—164no—
196C22×C11#47412yes—
197C22×C11C22×D811yescharacteristic
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#47412yes—
203C4×C11C2×C22⋊Q811yescharacteristic
204C4×C11C2×#13711yescharacteristic
205Dic11—81no—
206Dic11—82no—
207Dic11—81no—
208C22×D4—21no—
209C2×D8—22no—
210C2×D8—21no—
211C2×D8Dic2214yescomplemented
212C2×D8C22×D1112yes—
213C2×M16C22⋊D1111yescharacteristic
214C22×C8C22×D1111yescharacteristic
215C4⋊Q8—222no—
216C4⋊Q8—441no—
217#125—222no—
218#125—441no—
219C22⋊Q8—442no—
220C4×D4—22no—
221C4×D4—22no—
222C4×D4—41no—
223C4×D4—41no—
224#117—21no—
225#117—221no—
226#117C22⋊D1111yescharacteristic
227C2×C4⋊C4—221no—
228C2×C22⋊C4—42no—
229M32—222no—
230C2×C16—111no—
231C2×C16—112no—
232C2×C16—111no—
233C2×C16—222no—
234#107—112no—
235#107—111no—
236#107—111no—
237#107—221no—
238#107—222no—
239#107C22×D1111yescharacteristic
240#107C22×D1111yescharacteristic
241#106—21no—
242#106—221no—
243#106—222no—
244#102—22no—
245#102—22no—
246#97C22⋊D1112yes—
247C4×C8C22×D1112yes—
248C2×C11—22no—
249C2×C11—84no—
250C2×C11C2×#47411yescharacteristic
251C2×C11#341511yescharacteristic
252C2×C11#341611yescharacteristic
253C24—41no—
254C2×Q8—442no—
255C2×D4—24no—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—441no—
262C22×C4C2×C22⋊D1111yescharacteristic
263D8—24no—
264D8—22no—
265D8C2×Dic2214yes—
266M16—22no—
267C2×C8C2×Dic2212yes—
268C2×C8#433912yes—
269C2×C8C2×C22⋊D1112yes—
270C2×C8C2×C22⋊D1111yescharacteristic
271C2×C8C23×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—221no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4#432311yescharacteristic
282C4⋊C4#432311yescharacteristic
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—441no—
287C22⋊C4#432312yes—
288C42—41no—
289C42—441no—
290C42C2×C22⋊D1112yes—
291C16—221no—
292C16—221no—
293C16—222no—
294C11#3363111yescharacteristic, complemented, Sylow
295C23—42no—
296C23—44no—
297C23—161no—
298C23—161no—
299C23C2×#432311yescharacteristic
300Q8—1762no—
301D4—24no—
302D4—42no—
303D4—44no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—162no—
307C2×C4—162no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—1761no—
312C2×C4#6697712yes—
313C2×C4C2×#432312yes—
314C2×C4C2×#432312yes—
315C2×C4C2×#432311yescharacteristic
316C2×C4#6700412yes—
317C2×C4C22×C22⋊D1111yescharacteristic
318C8—22no—
319C8#6697712yes—
320C8C22×Dic2211yescharacteristic
321C8C2×#433911yescharacteristic
322C22—21no—
323C22—21no—
324C22—44no—
325C22—82no—
326C22—82no—
327C22—164no—
328C22#1062262012yes—
329C22C22×#432311yescharacteristic
330C4—22no—
331C4—22no—
332C4—81no—
333C4—81no—
334C4—882no—
335C4—881no—
336C4—881no—
337C4#1062262012yes—
338C4C2×#6697711yescharacteristic
339C4C2×#6700411yescharacteristic
340C2—22no—
341C2—84no—
342C2C2×#1062262011yescharacteristic
343C2#1308175511yescharacteristic
344C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2948C2
socleC22×C11C22×D8
prime radicalC22×C11×D8C22
hypercenter#2948D11
hypocenterC11#33631
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
1. #13079155C2semidirect
2. #13070773C2semidirect
3. #13070773C2semidirect
4. #13070763C2semidirect
5. #13070753C2semidirect
6. #13070405C2semidirect
7. #13070398C2semidirect
8. #13070375C2semidirect
27. #10622296C22semidirect
28. #10622295C22semidirect
33. #10622128C22semidirect
34. #10622128C22semidirect
35. #10622128C22semidirect
36. #10622127C22semidirect
37. #10622127C22semidirect
38. #10622127C22semidirect
39. C4⋊(C11⋊C16)C22semidirect
40. C4⋊(C11⋊C16)C22semidirect
44. C2×C11×D8Q8semidirect
211. C2×D8Dic22semidirect
294. C11#33631semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130707732
#130707632
#130707532
#130704052
#130703982
#130703752
#130703322
C2×#106222002
C11×#29482
#3363111