Finite Group Databasebeta

← #14911511

Subgroups — #14911511

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#13081509C211yesmaximal, characteristic, complemented
3#13070856C212yesmaximal, complemented
4#13070841C211yesmaximal, characteristic, complemented
5#13070776C212yesmaximal, complemented
6#13070657C211yesmaximal, characteristic, complemented
7#13070655C212yesmaximal, complemented
8#13070521C211yesmaximal, characteristic, complemented
9#13070479C212yesmaximal, complemented
10C4×#66891C211yesmaximal, characteristic, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12#10623252—21no—
13#10623084—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622764C2212yes—
17C2×#66891C2211yescharacteristic
18#10622707—21no—
19#10622628—21no—
20C2×#66864C2212yes—
21#10622491C2212yes—
22#10622490—22no—
23#10622486C2212yes—
24#10622485C2212yes—
25#10622399—22no—
26C4×Dic44C2211yescharacteristic
27#10622308C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622147C2212yes—
34#10622140C2212yes—
35Dic11⋊C16C2212yes—
36#10622130C2211yescharacteristic
37#10622129C2212yes—
38#10622129C2212yes—
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4339—41no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×D4×C11—21no—
45Q8×Dic11—41no—
46#66997—41no—
47#66993—22no—
48C2×#4323—22no—
49#66983—41no—
50C2×Dic44C2311yescharacteristic
51C2×D88—21no—
52C2×D88C2312yes—
53#66946—22no—
54#66943—22no—
55#66942—42no—
56#66940—22no—
57#66937—42no—
58#66927—21no—
59C4×Dic22—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2312yes—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2311yescharacteristic
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66891—22no—
68#66882C2311yescharacteristic
69#66880—21no—
70Dic11⋊C8D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66874—22no—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—24no—
79#33935—111nomaximal, Sylow
80C2×Q8×C11—41no—
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—21no—
91C2×Dic22D811yescharacteristic
92C11×D8—21no—
93C11×D8—21no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101#4323—82no—
102(C2×D11)⋊C4—42no—
103C4⋊Dic11—21no—
104C4⋊Dic11—42no—
105C4⋊Dic11D811yescharacteristic
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4D812yes—
110C4×Dic11—42no—
111C4×Dic11—41no—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114Dic44—21no—
115Dic44#4112yescomplemented
116D88—22no—
117D88—22no—
118D88—81no—
119C11×C16—22no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122#3391—111no—
123#3383—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2224D1111yescharacteristic, complemented
128#2207—111no—
129#2207—112no—
130#2183—111no—
131#2175—112no—
132C4×SD32—111no—
133C23×C11—41no—
134C22×D11—42no—
135Q8×C11—82no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—82no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C22⋊D11—84no—
145C22⋊D11—162no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11C2×D812yes—
149C2×Dic11C2×D812yes—
150D44—42no—
151D44—42no—
152D44—82no—
153D44—161no—
154C4×D11—84no—
155Dic22—22no—
156Dic22—22no—
157Dic22—41no—
158C8×C11—21no—
159C8×C11C2×#4111yescharacteristic
160C8×C112−1+411yescharacteristic
161C11⋊C8—22no—
162#557—221no—
163#550—221no—
164C2×SD32—111no—
165C2×SD32—112no—
166#500C2×D1111yescharacteristic
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×Q16—111no—
177C4×D8—112no—
178C4×D8C2×D1111yescharacteristic
179#367—111no—
180#366C2×D1112yes—
181C4⋊C16—112no—
182C4⋊C16C2×D1111yescharacteristic
183#358—111no—
184#357—111no—
185#357—112no—
186#357—112no—
187#357—112no—
188#357C2×D1112yes—
189#346—112no—
190C4×C16—111no—
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—81no—
200C4×C11—82no—
201C4×C11#50912yes—
202C4×C11#54811yescharacteristic
203C4×C11#57711yescharacteristic
204Dic11—22no—
205Dic11—22no—
206Dic11—42no—
207Dic11—81no—
208C2×#41—441no—
209C2×Q16—111no—
210C2×D8—112no—
211C2×D8—222no—
212C2×D8—221no—
213C2×D8C22×D1111yescharacteristic
214C4⋊Q8—21no—
215C4⋊Q8—441no—
216#127—222no—
217#127—221no—
218#125—222no—
219#125—442no—
220#121—442no—
221#121—441no—
222C4×Q8—111no—
223C4×Q8—222no—
224C4×Q8—221no—
225C4×Q8—441no—
226C4×D4—21no—
227C4×D4—222no—
228SD32—224no—
229SD32—222no—
230C2×C16—111no—
231C2×C16—111no—
232C2×C16C22×D1112yes—
233#107—21no—
234#107—111no—
235#107C22×D1112yes—
236#107C22×D1111yescharacteristic
237#106—222no—
238C4⋊C8—112no—
239C4⋊C8—111no—
240#103—222no—
241#103—221no—
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—41no—
253C2×Q8—111no—
254C2×Q8—221no—
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—112no—
264Q16—221no—
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—22no—
276C4⋊C4—41no—
277C4⋊C4—111no—
278C4⋊C4—112no—
279C4⋊C4—221no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C22⋊C4—442no—
286C42—112no—
287C42—442no—
288C42—441no—
289C42D4×D1111yescharacteristic
290C16—22no—
291C16—221no—
292C16—221no—
293C11#3393511yescharacteristic, complemented, Sylow
294C23—41no—
295C23—442no—
296Q8—82no—
297Q8—222no—
298Q8—222no—
299Q8—441no—
300D4—41no—
301D4—41no—
302D4—442no—
303D4—442no—
304D4—884no—
305D4—882no—
306D4—1761no—
307D4—1762no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—82no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—884no—
316C2×C4D8×D1111yescharacteristic
317C2×C4D8×D1111yescharacteristic
318C2×C4C2×D4×D1111yescharacteristic
319C8—21no—
320C8—222no—
321C8#6704011yescharacteristic
322C8#41×D1111yescharacteristic
323C22—81no—
324C22—81no—
325C22—81no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C2×D8×D1111yescharacteristic
330C4—21no—
331C4—81no—
332C4—82no—
333C4—222no—
334C4—222no—
335C4—442no—
336C4—881no—
337C4#1062252412yes—
338C4#1062316411yescharacteristic
339C4#1062330911yescharacteristic
340C2—161no—
341C2—1762no—
342C2#1308125011yescharacteristic
343C2C2×#1062252411yescharacteristic
344C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
prime radical#13081590C2
hypercenter#2224D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. #13081509C2semidirect
3. #13070856C2semidirect
4. #13070841C2semidirect
5. #13070776C2semidirect
6. #13070657C2semidirect
7. #13070655C2semidirect
8. #13070521C2semidirect
9. #13070479C2semidirect
10. C4×#66891C2semidirect
11. C11×#2224C2semidirect
115. Dic44#41semidirect
127. #2224D11semidirect
293. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815902
#130815092
#130708562
#130708412
#130707762
#130706572
#130706552
#130705212
#130704792
C4×#668912
C11×#22242
#3393511