Finite Group Databasebeta

← C11×#18212 #14595405

Subgroups — C11×#18212 #14595405

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C11×#3101C212yesmaximal, complemented
3C11×#2535C211yesmaximal, characteristic
4C11×#1608C214yesmaximal, complemented
5C11×#1596C214yesmaximal, complemented
6C11×#1518C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C11×#554—22no—
9C11×#554—24no—
10D4×Q8×C11—22no—
11C11×#544—21no—
12C11×#543C2214yes—
13C11×#533C2212yes—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#121—21no—
16C11×#518—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#483C2214yes—
20C11×#476—22no—
21C11×#461—22no—
22C11×#450C2214yes—
23C4×C11×SD16—24no—
24C11×#431C2212yes—
25C11×#397C2212yes—
26C11×#392C2212yes—
27C11×#386—22no—
28C11×#382C2211yescharacteristic
29C11×#380—21no—
30C11×#328C2218yes—
31C11×#323C2214yes—
32C22×Q8×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11D411yescharacteristic
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11D412yes—
38C2×C11×SD16—24no—
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8D412yescomplemented
41C11×C4⋊Q8D412yescomplemented
42C11×#125—24no—
43C11×#125—22no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8C2314yes—
51C11×#121—44no—
52C4×Q8×C11—22no—
53C4×Q8×C11D414yescomplemented
54C4×D4×C11—24no—
55C4×D4×C11—24no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C11×#117—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4C2312yes—
71C2×C42×C11C2311yescharacteristic
72C11×#106—24no—
73C11×C4⋊C8—22no—
74C11×#103—24no—
75C11×#102—24no—
76C11×C22⋊C8C2314yes—
77C4×C8×C11—22no—
78C11×#95—22no—
79C11×#95—21no—
80C11×#95C2312yes—
81#18212C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C24×C11C2×D412yes—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—84no—
87C2×Q8×C11C2×D414yes—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—42no—
92C2×D4×C11—44no—
93C2×D4×C11—44no—
94C2×D4×C11—82no—
95C2×D4×C11SD1614yescomplemented
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—82no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C11×SD16—48no—
111C2×C8×C11—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4C2×D414yes—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—44no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—82no—
130C42×C11—24no—
131C42×C11C2×D412yes—
132C42×C11C2×D412yes—
133#3501C2×C1111yescharacteristic, complemented
134#3101C2×C1112yescomplemented
135#2535C2×C1111yescharacteristic
136#1608C2×C1114yescomplemented
137#1596C2×C1114yescomplemented
138#1518C2×C1112yescomplemented
139#1460C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C2×SD1614yes—
152C23×C11C22×D411yescharacteristic
153Q8×C11—44no—
154Q8×C11—44no—
155Q8×C11—84no—
156D4×C11—24no—
157D4×C11—28no—
158D4×C11—42no—
159D4×C11—88no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—44no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—82no—
174C2×C4×C11—84no—
175C2×C4×C11—84no—
176C2×C4×C11—84no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12012yes—
180C2×C4×C11C2×SD1612yes—
181C2×C4×C11#13712yes—
182C2×C4×C11C22×D412yes—
183C8×C11—44no—
184#554—22no—
185#554—24no—
186D4×Q8—22no—
187#544—21no—
188#543C22×C1114yes—
189#533C22×C1112yes—
190C2×C22⋊Q8—22no—
191C2×#121—21no—
192#518—21no—
193C2×C4×D4C22×C1111yescharacteristic
194C2×C4×D4C22×C1111yescharacteristic
195#483C22×C1114yes—
196#476—22no—
197#461—22no—
198#450C22×C1114yes—
199C4×SD16—24no—
200#431C22×C1112yes—
201#397C22×C1112yes—
202#392C22×C1112yes—
203#386—22no—
204#382C22×C1111yescharacteristic
205#380—21no—
206#328C22×C1118yes—
207#323C22×C1114yes—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—24no—
211C22×C11—44no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—82no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11C2×#12011yescharacteristic
223C22×C11C22×SD1611yescharacteristic
224C22×C11C2×#13711yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—42no—
229C4×C11—44no—
230C4×C11—44no—
231C4×C11—82no—
232C4×C11—81no—
233C4×C11#44814yes—
234C22×Q8—22no—
235C22×D4—22no—
236C22×D4D4×C1111yescharacteristic
237C22×D4C23×C1111yescharacteristic
238C23×C4—21no—
239C23×C4D4×C1112yes—
240C2×SD16—24no—
241C4⋊Q8—24no—
242C4⋊Q8D4×C1112yescomplemented
243C4⋊Q8D4×C1112yescomplemented
244#125—24no—
245#125—22no—
246C22⋊Q8—24no—
247C22⋊Q8—24no—
248C22⋊Q8—28no—
249C22⋊Q8—22no—
250C22⋊Q8—24no—
251C22⋊Q8—28no—
252C22⋊Q8C23×C1114yes—
253#121—44no—
254C4×Q8—22no—
255C4×Q8D4×C1114yescomplemented
256C4×D4—24no—
257C4×D4—24no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262#117—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C1111yescharacteristic
267C2×C4⋊C4C23×C1111yescharacteristic
268C2×C22⋊C4—24no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4C23×C1112yes—
273C2×C42C23×C1111yescharacteristic
274#106—24no—
275C4⋊C8—22no—
276#103—24no—
277#102—24no—
278C22⋊C8C23×C1114yes—
279C4×C8—22no—
280#95—22no—
281#95—21no—
282#95C23×C1112yes—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—44no—
286C2×C11—82no—
287C2×C11C2×#44811yescharacteristic
288C2×C11#301911yescharacteristic
289C2×C11#302511yescharacteristic
290C24—21no—
291C24C2×D4×C1112yes—
292C2×Q8—24no—
293C2×Q8—22no—
294C2×Q8—84no—
295C2×Q8C2×D4×C1114yes—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—82no—
303C2×D4C11×SD1614yescomplemented
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—82no—
314C22×C4C2×D4×C1112yes—
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C2×D4×C1111yescharacteristic
317C22×C4C24×C1111yescharacteristic
318SD16—48no—
319C2×C8—24no—
320C4⋊C4—24no—
321C4⋊C4—28no—
322C4⋊C4—22no—
323C4⋊C4—24no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4C2×D4×C1114yes—
331C22⋊C4—28no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—44no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—82no—
338C42—24no—
339C42C2×D4×C1112yes—
340C42C2×D4×C1112yes—
341C11#1821211yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—22no—
344C23—22no—
345C23—42no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23C2×C11×SD1614yes—
354C23C22×D4×C1111yescharacteristic
355Q8—44no—
356Q8—44no—
357Q8—84no—
358D4—24no—
359D4—28no—
360D4—42no—
361D4—88no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—84no—
377C2×C4—84no—
378C2×C4—84no—
379C2×C4C11×#12011yescharacteristic
380C2×C4C11×#12011yescharacteristic
381C2×C4C11×#12012yes—
382C2×C4C2×C11×SD1612yes—
383C2×C4C11×#13712yes—
384C2×C4C22×D4×C1112yes—
385C8—44no—
386C22—21no—
387C22—21no—
388C22—24no—
389C22—44no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—82no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22C2×C11×#12011yescharacteristic
401C22C22×C11×SD1611yescharacteristic
402C22C2×C11×#13711yescharacteristic
403C4—21no—
404C4—21no—
405C4—22no—
406C4—42no—
407C4—44no—
408C4—44no—
409C4—82no—
410C4—81no—
411C4C11×#44814yes—
412C2—21no—
413C2—21no—
414C2—44no—
415C2—82no—
416C2C2×C11×#44811yescharacteristic
417C2C11×#301911yescharacteristic
418C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3501C2semidirect
2. C11×#3101C2semidirect
4. C11×#1608C2semidirect
5. C11×#1596C2semidirect
6. C11×#1518C2semidirect
7. C11×#1460C2semidirect
40. C11×C4⋊Q8D4semidirect
41. C11×C4⋊Q8D4semidirect
53. C4×Q8×C11D4semidirect
81. #18212C11direct (N × H)
95. C2×D4×C11SD16semidirect
133. #3501C2×C11semidirect
134. #3101C2×C11semidirect
136. #1608C2×C11semidirect
137. #1596C2×C11semidirect
138. #1518C2×C11semidirect
139. #1460C2×C11semidirect
242. C4⋊Q8D4×C11semidirect
243. C4⋊Q8D4×C11semidirect
255. C4×Q8D4×C11semidirect
303. C2×D4C11×SD16semidirect
341. C11#18212direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#31012
C11×#25352
C11×#16082
C11×#15962
C11×#15182
C11×#14602
#1821211