Finite Group Databasebeta

← #14909017

Subgroups — #14909017

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#13077527C211yesmaximal, characteristic, complemented
2#13070833C211yesmaximal, characteristic, complemented
3#13070828C211yesmaximal, characteristic, complemented
4#13070789C212yesmaximal, complemented
5#13070682C212yesmaximal, complemented
6#13070566C211yesmaximal, characteristic, complemented
7#13070561C211yesmaximal, characteristic
8#13070512C212yesmaximal, complemented
9#13070505C212yesmaximal, complemented
10#13070428C211yesmaximal, characteristic, complemented
11C11×#3183C211yesmaximal, characteristic, complemented
12C11×#529—21no—
13#10623279C2211yescharacteristic
14#10623276—21no—
15C11×#499C2211yescharacteristic, complemented
16C11×#495C2211yescharacteristic, complemented
17C11×#488—21no—
18C11×#470C2211yescharacteristic
19C11×#469C2211yescharacteristic
20C11×#468—21no—
21C11×#442C2211yescharacteristic, complemented
22C11×#441C2211yescharacteristic, complemented
23C11×#440—21no—
24C4×C11×M16C2211yescharacteristic
25#10622792C2212yes—
26#10622760C2212yes—
27#10622738C2211yescharacteristic
28C2×#66869—21no—
29#10622330—21no—
30#10622330C2212yes—
31#10622313—21no—
32#10622313C2212yes—
33#10622203C2212yescomplemented
34#10622201C2212yescomplemented
35#10622191C2211yescharacteristic
36#10622191C2211yescharacteristic
37#10622126C2212yes—
38#10622126C2212yes—
39#10622125C2212yescomplemented
40#10622125C2212yescomplemented
41#10622104C2212yescomplemented
42#10622101C2212yescomplemented
43C2×#4339—21no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C2×C11×M16D411yescharacteristic
48C2×C11×M16C2311yescharacteristic
49C11×#126—41no—
50C11×#125—21no—
51C11×#124—21no—
52C11×#123—41no—
53C11×C22⋊Q8—21no—
54C11×#121—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—41no—
58C11×#117—41no—
59C2×C42×C11D411yescharacteristic
60C2×#4318—21no—
61#66962—22no—
62#66961—22no—
63#66960—42no—
64M16×D11—42no—
65#66957—21no—
66#66957C2312yes—
67#66954—22no—
68#66954—22no—
69C11×#107—21no—
70C11×#106C2311yescharacteristic
71C11×#106C2311yescharacteristic
72C11×#103—21no—
73C11×#103—21no—
74C11×#102—21no—
75C11×#102—21no—
76C11×#97D411yescharacteristic
77C11×#97C2311yescharacteristic
78C4×C8×C11D411yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66893—22no—
81#66892—22no—
82#66891—22no—
83#66890—22no—
84#66883—21no—
85#66883C2312yes—
86#66876C2312yes—
87#66876C2312yes—
88#66869—22no—
89#66869—22no—
90#33690—111nomaximal, Sylow
91C2×Q8×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—41no—
98#4339—22no—
99#4339—22no—
100#4339—41no—
101#4339—41no—
102C2×D44—21no—
103C2×C4×D11—41no—
104C2×Dic22—21no—
105C11×Q16—22no—
106C11×SD16—42no—
107C11×D8—22no—
108C11×M16—22no—
109C11×M16—22no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2411yescharacteristic
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—21no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129#4318—22no—
130#4318—41no—
131C2×C11⋊C8—41no—
132Dic44—21no—
133Dic44#4112yes—
134D88—21no—
135D88#4112yes—
136#4314—22no—
137#4314—22no—
138#4313—42no—
139#4313—42no—
140C8×D11—42no—
141C8×D11—42no—
142C11⋊C16—22no—
143C11⋊C16—22no—
144#3183D1111yescharacteristic, complemented
145#2956—111no—
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—41no—
159Q8×C11—41no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—82no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—82no—
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C22⋊D11—42no—
175C22⋊D11—42no—
176C2×Dic11—41no—
177D44—22no—
178D44—41no—
179C4×D11—42no—
180C4×D11—42no—
181Dic22—22no—
182Dic22—41no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11AGL(1,ℤ/8)12yes—
186C8×C11C2×#4112yes—
187C11⋊C8—42no—
188#575—111no—
189#568—221no—
190#529—21no—
191#510—112no—
192#509—112no—
193#499C2×D1111yescharacteristic, complemented
194#495C2×D1111yescharacteristic, complemented
195#488—21no—
196#470C2×D1111yescharacteristic
197#469C2×D1111yescharacteristic
198#468—21no—
199#444—112no—
200#444—221no—
201#443—112no—
202#443—221no—
203#442C2×D1111yescharacteristic, complemented
204#441C2×D1111yescharacteristic, complemented
205#440—21no—
206#430—111no—
207C2×#104—221no—
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—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
225C2×D11—42no—
226C2×D11—161no—
227C4×C11—21no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11#52511yescharacteristic
234C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
235Dic11—42no—
236C2×#41—221no—
237#137—222no—
238AGL(1,ℤ/8)—222no—
239#135—112no—
240#135—221no—
241C2×Q16C22×D1111yescharacteristic
242C2×SD16—21no—
243C2×D8C22×D1111yescharacteristic
244#131—222no—
245#131—222no—
246#131—442no—
247C2×M16—221no—
248C2×M16—442no—
249C2×M16C22⋊D1111yescharacteristic
250C2×M16C22×D1111yescharacteristic
251#126—41no—
252#125—21no—
253#124—21no—
254#123—41no—
255C22⋊Q8—21no—
256#121—21no—
257C4×Q8—21no—
258C4×D4—21no—
259C4×D4—41no—
260#117—41no—
261C2×C42C22⋊D1111yescharacteristic
262Q32—222no—
263SD32—222no—
264SD32—222no—
265D16—222no—
266M32—112no—
267M32—112no—
268#108—112no—
269#108—221no—
270#107—21no—
271#106C22×D1111yescharacteristic
272#106C22×D1111yescharacteristic
273#104—222no—
274#104—222no—
275#103—21no—
276#103—21no—
277#102—21no—
278#102—21no—
279#97C22⋊D1111yescharacteristic
280#97C22×D1111yescharacteristic
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—161no—
286C2×C11#310911yescharacteristic
287D11—82no—
288#41—222no—
289#41—222no—
290#41—441no—
291#41—441no—
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—22no—
303Q16—112no—
304Q16—221no—
305SD16—42no—
306SD16—222no—
307SD16—222no—
308D8—22no—
309D8—112no—
310D8—221no—
311M16—22no—
312M16—22no—
313M16—222no—
314M16—442no—
315M16—441no—
316M16—442no—
317C2×C8—442no—
318C2×C8—441no—
319C2×C8—442no—
320C2×C8C2×C22⋊D1111yescharacteristic
321C2×C8C2×C22⋊D1111yescharacteristic
322C2×C8C2×C22⋊D1111yescharacteristic
323C2×C8C23×D1111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—21no—
336C42—41no—
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C16—222no—
340C16—222no—
341C11#3369011yescharacteristic, complemented, Sylow
342C23—41no—
343C23—441no—
344C23#6698511yescharacteristic
345Q8—41no—
346Q8—41no—
347Q8—222no—
348Q8—441no—
349D4—41no—
350D4—41no—
351D4—82no—
352D4—222no—
353D4—441no—
354D4—442no—
355D4—442no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—82no—
365C2×C4—442no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4#6698511yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—21no—
371C8—21no—
372C8—442no—
373C8#6700212yes—
374C8#41×D1112yes—
375C22—21no—
376C22—41no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—442no—
381C22—1761no—
382C22C2×#6698511yescharacteristic
383C4—21no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—442no—
390C4C2×#6700211yescharacteristic
391C4#1062335911yescharacteristic
392C2—21no—
393C2—41no—
394C2—161no—
395C2—882no—
396C2#1307870311yescharacteristic
subgroupG/H
centerC2#13078703
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3183C2
socleC2×C11#3109
prime radical#13070561C2
hypercenter#3183D11
hypocenterC11#33690
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3183

Complements

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

NH ≅ G/Ntype
1. #13077527C2semidirect
2. #13070833C2semidirect
3. #13070828C2semidirect
4. #13070789C2semidirect
5. #13070682C2semidirect
6. #13070566C2semidirect
8. #13070512C2semidirect
9. #13070505C2semidirect
10. #13070428C2semidirect
11. C11×#3183C2semidirect
15. C11×#499C22semidirect
16. C11×#495C22semidirect
21. C11×#442C22semidirect
22. C11×#441C22semidirect
33. #10622203C22semidirect
34. #10622201C22semidirect
39. #10622125C22semidirect
40. #10622125C22semidirect
41. #10622104C22semidirect
42. #10622101C22semidirect
144. #3183D11semidirect
193. #499C2×D11semidirect
194. #495C2×D11semidirect
203. #442C2×D11semidirect
204. #441C2×D11semidirect
341. C11#33690semidirect

Maximal subgroups

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

subgroupindex
#130775272
#130708332
#130708282
#130707892
#130706822
#130705662
#130705612
#130705122
#130705052
#130704282
C11×#31832
#3369011