Finite Group Databasebeta

← #14909021

Subgroups — #14909021

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079345C211yesmaximal, characteristic, complemented
2#13070835C211yesmaximal, characteristic, complemented
3#13070830C211yesmaximal, characteristic, complemented
4#13070792C212yesmaximal, complemented
5#13070685C212yesmaximal, complemented
6#13070567C211yesmaximal, characteristic, complemented
7#13070562C211yesmaximal, characteristic
8#13070514C212yesmaximal, complemented
9#13070507C212yesmaximal, complemented
10#13070428C211yesmaximal, characteristic, complemented
11C11×#2956C211yesmaximal, characteristic, complemented
12C11×#575C2211yescharacteristic
13C11×#568—21no—
14#10623010—21no—
15C11×#444—21no—
16C11×#444C2212yes—
17C11×#443—21no—
18C11×#443C2212yes—
19C11×#430C2211yescharacteristic
20C2×C11×#104—21no—
21C4×C11×M16C2211yescharacteristic
22#10622808C2212yes—
23#10622806C2212yes—
24#10622750C2211yescharacteristic
25#10622748C2211yescharacteristic
26#10622747—21no—
27#10622329C2211yescharacteristic, complemented
28#10622324C2211yescharacteristic, complemented
29#10622323—21no—
30#10622310—21no—
31#10622309C2211yescharacteristic, complemented
32#10622296C2211yescharacteristic, complemented
33#10622204C2212yes—
34#10622204C2212yes—
35#10622191C2211yescharacteristic
36#10622191C2211yescharacteristic
37#10622134C2212yescomplemented
38#10622133C2212yescomplemented
39#10622132C2212yescomplemented
40#10622132C2212yescomplemented
41#10622104C2212yescomplemented
42#10622101C2212yescomplemented
43C2×C11×#41—21no—
44C11×#137—22no—
45C11×AGL(1,ℤ/8)—22no—
46C11×#135—21no—
47C11×#135C2312yes—
48C11×#131—22no—
49C11×#131—22no—
50C11×#131—42no—
51C2×C11×M16—21no—
52C2×C11×M16—42no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16C2311yescharacteristic
55C2×C42×C11D411yescharacteristic
56#66983—21no—
57#66982—41no—
58C4×C22⋊D11—41no—
59#66977—21no—
60C2×Dic44C2311yescharacteristic
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63#66929—41no—
64#66928—21no—
65C4×D44—21no—
66#66925—41no—
67#66923—21no—
68C4×Dic22—21no—
69C11×#108—21no—
70C11×#108C2312yes—
71C11×#104—22no—
72C11×#104—22no—
73C11×#97D411yescharacteristic
74C11×#97C2311yescharacteristic
75C4×C8×C11D411yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66893—22no—
78#66892—22no—
79#66891—22no—
80#66890—22no—
81#66885—21no—
82#66885—21no—
83#66882—21no—
84#66881C2311yescharacteristic
85#66881C2311yescharacteristic
86#66880—21no—
87#66880—21no—
88#66876C2312yes—
89#66876C2312yes—
90#33690—111nomaximal, Sylow
91C11×#41—22no—
92C11×#41—22no—
93C11×#41—41no—
94C11×#41—41no—
95C2×Q8×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C2×C22⋊D11—41no—
102C2×D44—21no—
103C2×C4×D11—41no—
104C2×Dic22—21no—
105C11×Q16—21no—
106C11×Q16#4112yes—
107C11×SD16—22no—
108C11×SD16—22no—
109C11×D8—21no—
110C11×D8#4112yes—
111C11×M16—22no—
112C11×M16—22no—
113C11×M16—22no—
114C11×M16—41no—
115C11×M16—42no—
116C11×M16—42no—
117C2×C8×C11—41no—
118C2×C8×C11—42no—
119C2×C8×C11—42no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C42×C11—21no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C22⋊Dic11—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138C4×Dic11—41no—
139Dic44—22no—
140D88—22no—
141#4314—42no—
142C11⋊C16—22no—
143C11⋊C16—22no—
144#3183—111no—
145#2956D1111yescharacteristic, complemented
146#2239—111no—
147#2238—111no—
148#2231—112no—
149#2212—112no—
150#2191—111no—
151#2190—111no—
152AGL(1,ℤ/16)—112no—
153#2180—112no—
154#2165—111no—
155C23×C11—41no—
156C23×C11AGL(1,ℤ/8)11yescharacteristic
157C22×D11—41no—
158Q8×C11—22no—
159Q8×C11—41no—
160D4×C11—22no—
161D4×C11—41no—
162D4×C11—42no—
163D4×C11—42no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—81no—
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C22⋊D11—82no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178D44—41no—
179D44—41no—
180C4×D11—82no—
181Dic22—41no—
182Dic22—41no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11—42no—
186C8×C11AGL(1,ℤ/8)12yes—
187C8×C11C2×#4112yes—
188#575C2×D1111yescharacteristic
189#568—21no—
190#529—221no—
191#510—112no—
192#509—112no—
193#499—111no—
194#495—111no—
195#488—221no—
196#470—111no—
197#469—111no—
198#468—221no—
199#444—21no—
200#444C2×D1112yes—
201#443—21no—
202#443C2×D1112yes—
203#442—111no—
204#441—111no—
205#440—221no—
206#430C2×D1111yescharacteristic
207C2×#104—21no—
208C4×M16C2×D1111yescharacteristic
209#365—112no—
210#365—112no—
211#364—112no—
212#362—112no—
213#361—112no—
214#360—112no—
215#360—112no—
216#349—111no—
217#349—111no—
218#347—112no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—42no—
222C22×C11—161no—
223C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C4×C11—21no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—42no—
231C4×C11#52511yescharacteristic
232C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
233Dic11—81no—
234Dic11—81no—
235Dic11—81no—
236C2×#41—21no—
237#137—22no—
238AGL(1,ℤ/8)—22no—
239#135—21no—
240#135C22×D1112yes—
241C2×Q16—111no—
242C2×SD16—221no—
243C2×D8—111no—
244#131—22no—
245#131—22no—
246#131—42no—
247C2×M16—21no—
248C2×M16—42no—
249C2×M16C22⋊D1111yescharacteristic
250C2×M16C22×D1111yescharacteristic
251#126—441no—
252#125—221no—
253#124—221no—
254#123—441no—
255C22⋊Q8—221no—
256#121—221no—
257C4×Q8—221no—
258C4×D4—221no—
259C4×D4—441no—
260#117—441no—
261C2×C42C22⋊D1111yescharacteristic
262Q32—222no—
263SD32—222no—
264SD32—222no—
265D16—222no—
266M32—112no—
267M32—112no—
268#108—21no—
269#108C22×D1112yes—
270#107—221no—
271#106—111no—
272#106—111no—
273#104—22no—
274#104—22no—
275#103—221no—
276#103—221no—
277#102—221no—
278#102—221no—
279#97C22⋊D1111yescharacteristic
280#97C22×D1111yescharacteristic
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—82no—
286C2×C11#310911yescharacteristic
287D11—161no—
288#41—22no—
289#41—22no—
290#41—41no—
291#41—41no—
292C2×Q8—21no—
293C2×Q8—221no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—221no—
297C2×D4—441no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—441no—
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—21no—
303Q16—222no—
304Q16#433912yes—
305SD16—22no—
306SD16—22no—
307SD16—442no—
308D8—21no—
309D8—222no—
310D8#433912yes—
311M16—22no—
312M16—22no—
313M16—22no—
314M16—42no—
315M16—41no—
316M16—42no—
317C2×C8—42no—
318C2×C8—41no—
319C2×C8—42no—
320C2×C8C2×C22⋊D1111yescharacteristic
321C2×C8C2×C22⋊D1111yescharacteristic
322C2×C8C2×C22⋊D1111yescharacteristic
323C2×C8C23×D1111yescharacteristic
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42—21no—
336C42—441no—
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C16—222no—
340C16—222no—
341C11#3369011yescharacteristic, complemented, Sylow
342C23—41no—
343C23—441no—
344C23#6700211yescharacteristic
345Q8—22no—
346Q8—41no—
347Q8—441no—
348Q8—441no—
349D4—22no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—441no—
354D4—441no—
355D4—882no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—81no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—882no—
368C2×C4#6700211yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—21no—
371C8—21no—
372C8—42no—
373C8#6698512yes—
374C8C2×#433912yes—
375C22—21no—
376C22—41no—
377C22—42no—
378C22—161no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22C2×#6700211yescharacteristic
383C4—21no—
384C4—41no—
385C4—41no—
386C4—42no—
387C4—881no—
388C4—881no—
389C4—881no—
390C4#1062332211yescharacteristic
391C4C2×#6698511yescharacteristic
392C2—21no—
393C2—41no—
394C2—82no—
395C2—1761no—
396C2#1307870711yescharacteristic
subgroupG/H
centerC2#13078707
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2956C2
socleC2×C11#3109
prime radical#13070562C2
hypercenter#2956D11
hypocenterC11#33690
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2956

Complements

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

NH ≅ G/Ntype
1. #13079345C2semidirect
2. #13070835C2semidirect
3. #13070830C2semidirect
4. #13070792C2semidirect
5. #13070685C2semidirect
6. #13070567C2semidirect
8. #13070514C2semidirect
9. #13070507C2semidirect
10. #13070428C2semidirect
11. C11×#2956C2semidirect
27. #10622329C22semidirect
28. #10622324C22semidirect
31. #10622309C22semidirect
32. #10622296C22semidirect
37. #10622134C22semidirect
38. #10622133C22semidirect
39. #10622132C22semidirect
40. #10622132C22semidirect
41. #10622104C22semidirect
42. #10622101C22semidirect
145. #2956D11semidirect
341. C11#33690semidirect

Maximal subgroups

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

subgroupindex
#130793452
#130708352
#130708302
#130707922
#130706852
#130705672
#130705622
#130705142
#130705072
#130704282
C11×#29562
#3369011