Finite Group Databasebeta

← #14649713

Subgroups — #14649713

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078088C211yesmaximal, characteristic
2#13071537C211yesmaximal, characteristic, complemented
3#13067177C211yesmaximal, characteristic
4#13067112C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×Q8×Dic11—21no—
10C2×#66995—21no—
11#10623008C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622644C412yescomplemented
15#10622641—22no—
16#10622640C412yescomplemented
17#10622598—21no—
18#10622598—22no—
19#10622579—21no—
20#10622549—21no—
21#10622549C2211yescharacteristic
22C4×C4⋊Dic11—21no—
23C4×C4⋊Dic11C2211yescharacteristic
24#10622537C2211yescharacteristic
25C11×Q8⋊C8—22no—
26#10622108—21no—
27#10622108—21no—
28#10622108—22no—
29C22×Q8×C11D411yescharacteristic
30C2×#4339—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11C2×C412yes—
34C4×Q8×C11D412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39Q8×Dic11—42no—
40Q8×Dic11—42no—
41C2×#4326—22no—
42#66995—42no—
43#66995—42no—
44C2×#4325—22no—
45#66983—21no—
46#66983—21no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4×Dic11—22no—
52C2×C4×Dic11—21no—
53C2×#4318—21no—
54#66928—21no—
55#66927C2×C411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922C2×C411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64C4×C8×C11—21no—
65C11⋊#95—22no—
66C11⋊#95—21no—
67C11⋊#95D411yescharacteristic
68C11⋊#95D411yescharacteristic
69C11⋊#95D412yes—
70#66874—22no—
71#66873—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)C2×C412yes—
74#9180—111nomaximal, Sylow
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11C22⋊C412yes—
79C2×Q8×C11D812yes—
80C2×Q8×C11SD1612yes—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—41no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—22no—
90#4339—41no—
91#4339—41no—
92#4339—41no—
93#4339—41no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4C22⋊C412yes—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11C22×C411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111#4326—44no—
112#4325—44no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—44no—
118C4⋊Dic11—42no—
119C4⋊Dic11—44no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4×Dic11—44no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128#3037—111no—
129#2351—111no—
130#1517—111no—
131#1502—111no—
132#1479D1111yescharacteristic, complemented
133#1303—111no—
134#1286—111no—
135C23×C11#12011yescharacteristic
136C22×D11—41no—
137Q8×C11—22no—
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11#10214yes—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C22⋊D11—81no—
159C22⋊D11—81no—
160C2×Dic11—22no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170D44—41no—
171D44—41no—
172D44—81no—
173D44—81no—
174C4×D11—81no—
175C4×D11—81no—
176Dic22—41no—
177Dic22—41no—
178C8×C11—81no—
179C8×C11—81no—
180C11⋊C8—42no—
181C2×#137—221no—
182#532—111no—
183C2×C4×Q8—221no—
184C2×C4×Q8C2×D1111yescharacteristic
185#464—222no—
186#462—112no—
187#460—112no—
188#431C2×D1111yescharacteristic
189#431C2×D1111yescharacteristic
190#423—111no—
191#417—221no—
192#389—222no—
193#389—221no—
194#382—111no—
195#382—221no—
196C4×C4⋊C4—111no—
197C4×C4⋊C4—221no—
198#327—221no—
199#327—221no—
200#327—222no—
201Q8⋊C8—22no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11#38611yescharacteristic
205C22×C11#44711yescharacteristic
206C22×C11#44811yescharacteristic
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11C2×#10211yescharacteristic
217C4×C11#41711yescharacteristic
218C4×C11#48011yescharacteristic
219C4×C11#48111yescharacteristic
220Dic11—42no—
221Dic11—82no—
222Dic11—81no—
223Dic11—81no—
224C2×#41—221no—
225C22×Q8D4411yescharacteristic
226#137—442no—
227#137—442no—
228C2×Q16—222no—
229C2×SD16—222no—
230C2×M16—221no—
231C4⋊Q8—111no—
232#127—111no—
233#124—221no—
234#121—221no—
235#121—221no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—442no—
239C4×Q8—442no—
240C4×Q8C4×D1112yes—
241C4×Q8C22⋊D1112yes—
242C4×D4—221no—
243C4×D4—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4D4411yescharacteristic
250C2×C42—21no—
251C2×C42—222no—
252C2×C42—221no—
253C2×C42C22×D1111yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258#103—222no—
259#102—222no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C4×C8—21no—
263C4×C8—21no—
264#95—111no—
265#95—111no—
266#95—112no—
267#95—222no—
268#95—221no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11#187411yescharacteristic
272C2×C11#190511yescharacteristic
273C2×C11#190611yescharacteristic
274D11—161no—
275#41—441no—
276#41—441no—
277#41—441no—
278#41—441no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—221no—
283C2×Q8#431412yes—
284C2×Q8D8812yes—
285C2×Q8(C2×D11)⋊C412yes—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4—441no—
296C22×C4C2×D4411yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299Q16—444no—
300SD16—444no—
301M16—441no—
302M16—441no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—222no—
306C4⋊C4—22no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—444no—
312C4⋊C4—442no—
313C4⋊C4—444no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4(C2×D11)⋊C412yes—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C42—22no—
320C42—22no—
321C42—444no—
322C42—441no—
323C42—441no—
324C42C2×C4×D1111yescharacteristic
325C42#434111yescharacteristic
326C42#434111yescharacteristic
327C42C2×C22⋊D1111yescharacteristic
328C11#918011yescharacteristic, complemented, Sylow
329C23—441no—
330C23#6693511yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—22no—
334Q8—441no—
335Q8—441no—
336Q8#6688514yes—
337D4—441no—
338D4—441no—
339D4—881no—
340D4—881no—
341D4—881no—
342D4—881no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—222no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—441no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—442no—
359C2×C4—441no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4(C22⋊D11)⋊C411yescharacteristic
363C2×C4(C22⋊D11)⋊C411yescharacteristic
364C2×C4#6693911yescharacteristic
365C2×C4C2×#431411yescharacteristic
366C2×C4C2×D8811yescharacteristic
367C2×C4#6696111yescharacteristic
368C2×C4#6696211yescharacteristic
369C2×C4C2×(C2×D11)⋊C411yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6699211yescharacteristic
372C8—81no—
373C8—81no—
374C8—442no—
375C22—21no—
376C22—21no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22#1062234511yescharacteristic
381C22#1062235111yescharacteristic
382C22#1062257111yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—24no—
388C4—42no—
389C4—442no—
390C4—882no—
391C4—881no—
392C4—881no—
393C4#1062234811yescharacteristic
394C4#1062234911yescharacteristic
395C4C2×#6688511yescharacteristic
396C4#1062274611yescharacteristic
397C2—21no—
398C2—21no—
399C2—1761no—
400C2#1306893111yescharacteristic
401C2#1306910811yescharacteristic
402C2#1306911511yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1479D11
hypocenterC11#9180
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #13071537C2semidirect
5. #13066518C2semidirect
6. #13066475C2semidirect
7. C11×#1479C2semidirect
14. #10622644C4semidirect
16. #10622640C4semidirect
132. #1479D11semidirect
328. C11#9180semidirect

Maximal subgroups

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

subgroupindex
#130780882
#130715372
#130671772
#130671122
#130665182
#130664752
C11×#14792
#918011