Finite Group Databasebeta

← #14911512

Subgroups — #14911512

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#13081591C211yesmaximal, characteristic
2#13070859C212yesmaximal, complemented
3#13070841C211yesmaximal, characteristic, complemented
4#13070770C212yesmaximal, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070656C212yesmaximal, complemented
7#13070656C211yesmaximal, characteristic, complemented
8#13070525C211yesmaximal, characteristic, complemented
9#13070478C212yesmaximal, complemented
10C4×#66892C211yesmaximal, characteristic, complemented
11C11×#3383C211yesmaximal, characteristic, complemented
12C11×#557—21no—
13#10623108—21no—
14C11×#500C2211yescharacteristic
15C11×#499C2212yes—
16C11×#479—22no—
17C11×#475—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×Q16C2212yes—
21C2×#66892C2211yescharacteristic
22C2×#66892C2212yes—
23#10622456—21no—
24#10622456—22no—
25#10622308C2212yes—
26#10622308C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C4×D88C2212yes—
29#10622202C2211yescharacteristic
30#10622129C2211yescharacteristic
31#10622129C2212yes—
32#10622129C2212yes—
33#10622129C2212yes—
34#10622129C2212yes—
35#10622128C2211yescharacteristic
36#10622127C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×#4343—41no—
42C2×C11×Q16C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—41no—
45C11×#125—22no—
46C11×#125—42no—
47C4×Q8×C11—21no—
48C4×Q8×C11—22no—
49C4×Q8×C11—41no—
50C4×Q8×C11D411yescharacteristic
51C2×D88—22no—
52C2×D88—21no—
53C2×D88C2311yescharacteristic
54C2×D88C2312yes—
55#66948—41no—
56#66948—42no—
57#66927—22no—
58#66927—21no—
59C4×D44—22no—
60C4×D44—21no—
61C11×#107—21no—
62C11×#107C2311yescharacteristic
63C11×#107C2312yes—
64C11×#106—22no—
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—21no—
69C4×C8×C11C2312yes—
70C4×C8×C11C2311yescharacteristic
71#66892—22no—
72#66892—24no—
73#66885—22no—
74#66885—21no—
75#66882C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33935—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11D811yescharacteristic
83#4343—84no—
84C2×D44—22no—
85C2×D44—21no—
86C2×D44—42no—
87C2×D44—41no—
88C2×D44—42no—
89C2×D44—41no—
90C2×C4×D11—42no—
91C2×C4×D11—41no—
92C11×Q16—21no—
93C11×Q16#4112yescomplemented
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4D811yescharacteristic
105C11×C4⋊C4D812yes—
106C42×C11—42no—
107C42×C11—41no—
108C42×C11C2×D412yes—
109C42×C11C2×D411yescharacteristic
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113D88—21no—
114D88—22no—
115D88—21no—
116D88—22no—
117D88—82no—
118D88—81no—
119C11⋊C16—21no—
120C11⋊C16—22no—
121C11⋊C16—21no—
122#3391—111no—
123#3383D1111yescharacteristic, complemented
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×SD32—111no—
133C22×D11—42no—
134C22×D11—41no—
135Q8×C11—22no—
136Q8×C11—22no—
137Q8×C11—41no—
138Q8×C11—82no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×Dic11—41no—
148D44—41no—
149D44—42no—
150D44—41no—
151D44—42no—
152D44—84no—
153D44—82no—
154D44—162no—
155D44—161no—
156C4×D11—84no—
157C4×D11—82no—
158C8×C11—22no—
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#557—21no—
163#550—221no—
164C2×SD32—111no—
165C2×SD32—112no—
166#500C2×D1111yescharacteristic
167#499C2×D1112yes—
168#493—111no—
169#493—112no—
170#479—22no—
171#475—21no—
172#459—221no—
173#459—222no—
174C8×Q8C2×D1111yescharacteristic
175C4×Q16C2×D1111yescharacteristic
176C4×Q16C2×D1112yes—
177C4×D8—111no—
178C4×D8—112no—
179#367—111no—
180#366—112no—
181C4⋊C16—111no—
182C4⋊C16—112no—
183#358—111no—
184#357—111no—
185#357—112no—
186#357—112no—
187#357—112no—
188#357—112no—
189#346—112no—
190C4×C16—111no—
191C22×C11C22×D811yescharacteristic
192C2×D11—82no—
193C2×D11—81no—
194C2×D11—82no—
195C2×D11—81no—
196C2×D11—82no—
197C2×D11—81no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—42no—
202C4×C11—82no—
203C4×C11—81no—
204C4×C11#50912yes—
205C4×C11#54811yescharacteristic
206C4×C11#57711yescharacteristic
207Dic11—81no—
208C2×#41—441no—
209C2×Q16C22×D1111yescharacteristic
210C2×D8—111no—
211C2×D8—112no—
212C2×D8—222no—
213C2×D8—221no—
214C4⋊Q8—21no—
215C4⋊Q8—41no—
216#127—222no—
217#127—221no—
218#125—22no—
219#125—42no—
220#121—441no—
221#121—442no—
222C4×Q8—21no—
223C4×Q8—22no—
224C4×Q8—41no—
225C4×Q8C22⋊D1111yescharacteristic
226C4×D4—222no—
227C4×D4—221no—
228SD32—222no—
229SD32—224no—
230C2×C16—111no—
231C2×C16—111no—
232C2×C16—112no—
233#107—21no—
234#107—111no—
235#107C22×D1112yes—
236#107C22×D1111yescharacteristic
237#106—22no—
238C4⋊C8C22⋊D1111yescharacteristic
239C4⋊C8C22⋊D1112yes—
240#103—22no—
241#103—21no—
242#102—222no—
243#102—221no—
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11#335811yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341611yescharacteristic
249D11—162no—
250D11—161no—
251#41—884no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8#432311yescharacteristic
255C2×D4—222no—
256C2×D4—221no—
257C2×D4—442no—
258C2×D4—441no—
259C2×D4—442no—
260C2×D4—441no—
261C22×C4—442no—
262C22×C4—441no—
263Q16—21no—
264Q16#434312yescomplemented
265D8—221no—
266D8—222no—
267D8—221no—
268D8—222no—
269D8—882no—
270D8—881no—
271C2×C8C2×C22⋊D1112yes—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—221no—
282C4⋊C4#432311yescharacteristic
283C4⋊C4#432312yes—
284C22⋊C4—442no—
285C22⋊C4—441no—
286C42—42no—
287C42—41no—
288C42C2×C22⋊D1112yes—
289C42C2×C22⋊D1111yescharacteristic
290C16—221no—
291C16—222no—
292C16—221no—
293C11#3393511yescharacteristic, complemented, Sylow
294C23—442no—
295C23—441no—
296Q8—22no—
297Q8—22no—
298Q8—41no—
299Q8—82no—
300D4—441no—
301D4—442no—
302D4—441no—
303D4—442no—
304D4—884no—
305D4—882no—
306D4—1762no—
307D4—1761no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—441no—
312C2×C4—884no—
313C2×C4—882no—
314C2×C4C2×#432312yes—
315C2×C4C2×#432311yescharacteristic
316C2×C4C2×#432312yes—
317C2×C4C2×#432311yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—22no—
320C8—21no—
321C8C2×#434311yescharacteristic
322C8#6704011yescharacteristic
323C22—882no—
324C22—881no—
325C22—882no—
326C22—881no—
327C22—882no—
328C22—881no—
329C22C22×#432311yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—42no—
334C4—82no—
335C4—81no—
336C4—881no—
337C4#1062280612yes—
338C4#1062334811yescharacteristic
339C4#1062336811yescharacteristic
340C2—1762no—
341C2—1761no—
342C2#1308125111yescharacteristic
343C2C2×#1062280611yescharacteristic
344C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3383C2
socleC22×C11C22×D8
prime radical#13081591C2
hypercenter#3383D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
2. #13070859C2semidirect
3. #13070841C2semidirect
4. #13070770C2semidirect
5. #13070750C2semidirect
6. #13070656C2semidirect
7. #13070656C2semidirect
8. #13070525C2semidirect
9. #13070478C2semidirect
10. C4×#66892C2semidirect
11. C11×#3383C2semidirect
93. C11×Q16#41semidirect
123. #3383D11semidirect
264. Q16#4343semidirect
293. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815912
#130708592
#130708412
#130707702
#130707502
#130706562
#130705252
#130704782
C4×#668922
C11×#33832
#3393511