Finite Group Databasebeta

← #14911510

Subgroups — #14911510

Order 2816.

518 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#13081590C211yesmaximal, characteristic
2#13081505C211yesmaximal, characteristic, complemented
3#13070856C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070772C212yesmaximal, complemented
6#13070753C211yesmaximal, characteristic, complemented
7#13070656C211yesmaximal, characteristic, complemented
8#13070654C212yesmaximal, complemented
9#13070524C211yesmaximal, characteristic, complemented
10#13070483C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12#10623101—21no—
13#10623084—21no—
14C2×C11×SD32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17Q16×Dic11C2212yes—
18C2×#66892C2212yes—
19#10622764C2212yes—
20#10622633—21no—
21#10622628—21no—
22#10622491C2212yes—
23#10622485C2212yes—
24#10622409—22no—
25#10622399—22no—
26#10622308C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#367C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4339—41no—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46Q8×Dic11—22no—
47#66993—22no—
48C2×#4323—22no—
49#66983—41no—
50C2×D88—21no—
51C2×D88C2312yes—
52#66946—22no—
53#66943—22no—
54#66943—42no—
55#66937—42no—
56#66927—21no—
57#66922—21no—
58#66922—41no—
59C4×Dic22—41no—
60C4×Dic22D411yescharacteristic
61C11×SD32—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#103—21no—
67C11×#102—21no—
68C4×C8×C11C2311yescharacteristic
69#66899—22no—
70#66892—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66873—22no—
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33935—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85#4339—84no—
86C2×D44—22no—
87C2×D44—41no—
88C2×D44—41no—
89C2×C4×D11—42no—
90C2×Dic22—41no—
91C2×Dic22D811yescharacteristic
92C11×Q16—21no—
93C11×Q16#4112yescomplemented
94C11×D8—21no—
95C11×D8—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C42×C11C2×D411yescharacteristic
104#4323—82no—
105(C2×D11)⋊C4—42no—
106C4⋊Dic11—22no—
107C4⋊Dic11—42no—
108C4⋊Dic11—42no—
109C4⋊Dic11—41no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11—42no—
114C4×Dic11C2×D412yes—
115C2×C11⋊C8C2×D412yes—
116D88—22no—
117D88—22no—
118D88—81no—
119C11×C16—21no—
120C11×C16—21no—
121C11⋊C16—22no—
122#3391—111no—
123#3383—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2224—111no—
128#2207—112no—
129#2207—111no—
130#2183—111no—
131#2175—112no—
132C4×SD32D1111yescharacteristic, complemented
133C23×C11—41no—
134C22×D11—42no—
135Q8×C11—22no—
136Q8×C11—41no—
137D4×C11—41no—
138D4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—82no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—84no—
147C22⋊D11—162no—
148C2×Dic11—42no—
149C2×Dic11C2×D812yes—
150C2×Dic11C2×D812yes—
151D44—42no—
152D44—42no—
153D44—82no—
154D44—161no—
155C4×D11—84no—
156Dic22—22no—
157Dic22—82no—
158C8×C11—21no—
159C8×C11C2×#4111yescharacteristic
160C8×C112−1+411yescharacteristic
161C11⋊C8—22no—
162#557—221no—
163#550—221no—
164C2×SD32—112no—
165C2×SD32C2×D1111yescharacteristic
166#500—111no—
167#499—112no—
168#493—112no—
169#493—111no—
170#479—222no—
171#475—221no—
172#459—222no—
173#459—221no—
174C8×Q8—111no—
175C4×Q16—112no—
176C4×Q16C2×D1111yescharacteristic
177C4×D8—112no—
178C4×D8C2×D1111yescharacteristic
179#367C2×D1111yescharacteristic
180#366—112no—
181C4⋊C16—112no—
182C4⋊C16—111no—
183#358C2×D1111yescharacteristic
184#357—112no—
185#357—112no—
186#357—112no—
187#357—112no—
188#357C2×D1111yescharacteristic
189#346—112no—
190C4×C16C2×D1111yescharacteristic
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11C22×D811yescharacteristic
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—82no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#50912yes—
203C4×C11#54811yescharacteristic
204C4×C11#57711yescharacteristic
205Dic11—22no—
206Dic11—22no—
207Dic11—82no—
208C2×#41—441no—
209C2×Q16C22×D1111yescharacteristic
210C2×D8—112no—
211C2×D8—222no—
212C2×D8—221no—
213C2×D8C22×D1111yescharacteristic
214C4⋊Q8—221no—
215C4⋊Q8—441no—
216#127—222no—
217#127—221no—
218#125—222no—
219#125—442no—
220#121—442no—
221#121—441no—
222C4×Q8—21no—
223C4×Q8—111no—
224C4×Q8—222no—
225C4×Q8—441no—
226C4×D4—21no—
227C4×D4—222no—
228SD32—22no—
229SD32—224no—
230C2×C16—112no—
231C2×C16C22×D1111yescharacteristic
232C2×C16C22×D1111yescharacteristic
233#107—112no—
234#107—221no—
235#107C22×D1111yescharacteristic
236#107C22×D1111yescharacteristic
237#106—222no—
238C4⋊C8—112no—
239C4⋊C8—111no—
240#103—21no—
241#103—222no—
242#102—21no—
243#102—222no—
244C4×C8—112no—
245C4×C8C22×D1111yescharacteristic
246C2×C11—161no—
247C2×C11#335811yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341611yescharacteristic
250D11—162no—
251#41—884no—
252C2×Q8—21no—
253C2×Q8—111no—
254C2×Q8—441no—
255C2×D4—21no—
256C2×D4—222no—
257C2×D4—442no—
258C2×D4—442no—
259C2×D4—441no—
260C2×D4—441no—
261C22×C4—41no—
262C22×C4—442no—
263Q16—21no—
264Q16#433912yescomplemented
265D8—21no—
266D8—21no—
267D8—222no—
268D8—222no—
269D8—881no—
270D8—882no—
271C2×C8—112no—
272C2×C8D4×D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—111no—
278C4⋊C4—112no—
279C4⋊C4—222no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C22⋊C4—442no—
286C42—41no—
287C42—112no—
288C42—442no—
289C42D4×D1111yescharacteristic
290C16—21no—
291C16—21no—
292C16—222no—
293C11#3393511yescharacteristic, complemented, Sylow
294C23—41no—
295C23—442no—
296Q8—22no—
297Q8—41no—
298Q8—222no—
299Q8—882no—
300D4—41no—
301D4—41no—
302D4—442no—
303D4—442no—
304D4—884no—
305D4—882no—
306D4—1761no—
307D4—1762no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—112no—
313C2×C4—112no—
314C2×C4—442no—
315C2×C4—884no—
316C2×C4D8×D1111yescharacteristic
317C2×C4D8×D1111yescharacteristic
318C2×C4C2×D4×D1111yescharacteristic
319C8—21no—
320C8—222no—
321C8C2×#433911yescharacteristic
322C8#6704311yescharacteristic
323C22—81no—
324C22—81no—
325C22—81no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C2×D8×D1111yescharacteristic
330C4—21no—
331C4—42no—
332C4—81no—
333C4—81no—
334C4—222no—
335C4—222no—
336C4—882no—
337C4#1062252712yes—
338C4#1062308311yescharacteristic
339C4#1062330111yescharacteristic
340C2—161no—
341C2—1762no—
342C2#1308124911yescharacteristic
343C2C2×#1062252711yescharacteristic
344C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13081590C2
hypercenterC4×SD32D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #13081505C2semidirect
3. #13070856C2semidirect
4. #13070840C2semidirect
5. #13070772C2semidirect
6. #13070753C2semidirect
7. #13070656C2semidirect
8. #13070654C2semidirect
9. #13070524C2semidirect
10. #13070483C2semidirect
11. C4×C11×SD32C2semidirect
93. C11×Q16#41semidirect
132. C4×SD32D11semidirect
264. Q16#4339semidirect
293. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815902
#130815052
#130708562
#130708402
#130707722
#130707532
#130706562
#130706542
#130705242
#130704832
C4×C11×SD322
#3393511