Finite Group Databasebeta

← C11×#18211 #14595404

Subgroups — C11×#18211 #14595404

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C11×#3103C212yesmaximal, complemented
3C11×#2580C211yesmaximal, characteristic, complemented
4C11×#1613C214yesmaximal, complemented
5C11×#1601C214yesmaximal, complemented
6C11×#1517C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537—21no—
13C11×#534C2214yes—
14C11×#532C2212yes—
15C2×C11×#121—22no—
16C2×C4×Q8×C11C2211yescharacteristic, complemented
17C2×C4×D4×C11C2211yescharacteristic
18C11×#481C2214yescomplemented
19C11×#475—22no—
20C11×#460—22no—
21C11×#448C2214yescomplemented
22C4×C11×SD16—24no—
23C11×#431C2212yescomplemented
24C11×#399C2212yescomplemented
25C11×#393C2212yescomplemented
26C11×#390—21no—
27C11×#389—21no—
28C11×#385—22no—
29C11×#382C2211yescharacteristic, complemented
30C11×#327C2218yescomplemented
31C11×#323C2214yescomplemented
32C11×H(5,𝔽2)—44no—
33C11×H(5,𝔽2)—44no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×Q8×C11C2311yescharacteristic
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—22no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11D412yes—
42C2×C11×SD16—24no—
43C11×C4⋊Q8D412yes—
44C11×#127D412yes—
45C11×#124—22no—
46C11×#123—28no—
47C11×C22⋊Q8—24no—
48C11×#121—24no—
49C11×#121—24no—
50C11×#121—24no—
51C11×#121—22no—
52C11×#121—24no—
53C11×#121C2314yes—
54C11×#120—28no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4C2312yes—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C11×#106—24no—
74C11×C4⋊C8—22no—
75C11×#103—24no—
76C11×#102—24no—
77C11×C22⋊C8C2314yes—
78C4×C8×C11—22no—
79C11×#95—21no—
80C11×#95—22no—
81C11×#95C2312yes—
82#18211C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—24no—
84C24×C11C2×D412yes—
85C11×#41—416no—
86C11×#41—44no—
87C11×#41—44no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—42no—
91C2×D4×C11—28no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—416no—
99C2×D4×C11—48no—
100C2×D4×C11—48no—
101C2×D4×C11—84no—
102C2×D4×C11SD1614yescomplemented
103C2×D4×C11C2×D414yes—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—82no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C11×SD16—48no—
117C2×C8×C11—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—82no—
126C11×C4⋊C4C2×D414yes—
127C11×C22⋊C4—28no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—44no—
132C11×C22⋊C4—82no—
133C42×C11—42no—
134C42×C11C2×D412yes—
135C42×C11C2×D412yes—
136#3496C2×C1111yescharacteristic
137#3103C2×C1112yescomplemented
138#2580C2×C1111yescharacteristic, complemented
139#1613C2×C1114yescomplemented
140#1601C2×C1114yescomplemented
141#1517C2×C1112yescomplemented
142#1460C2×C1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—48no—
149C23×C11—84no—
150C23×C11—84no—
151C23×C11C2×SD1614yes—
152C23×C11C22×D411yescharacteristic
153Q8×C11—24no—
154Q8×C11—42no—
155Q8×C11—44no—
156D4×C11—28no—
157D4×C11—44no—
158D4×C11—44no—
159D4×C11—416no—
160D4×C11—44no—
161D4×C11—44no—
162D4×C11—44no—
163D4×C11—84no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—44no—
170C2×C4×C11—48no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—48no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—82no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12012yes—
185C2×C4×C11C2×SD1612yes—
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11C22×D412yes—
188C8×C11—44no—
189C2×H(5,𝔽2)—21no—
190#547—22no—
191#546—24no—
192D42—22no—
193#537—21no—
194#534C22×C1114yes—
195#532C22×C1112yes—
196C2×#121—22no—
197C2×C4×Q8C22×C1111yescharacteristic, complemented
198C2×C4×D4C22×C1111yescharacteristic
199#481C22×C1114yescomplemented
200#475—22no—
201#460—22no—
202#448C22×C1114yescomplemented
203C4×SD16—24no—
204#431C22×C1112yescomplemented
205#399C22×C1112yescomplemented
206#393C22×C1112yescomplemented
207#390—21no—
208#389—21no—
209#385—22no—
210#382C22×C1111yescharacteristic, complemented
211#327C22×C1118yescomplemented
212#323C22×C1114yescomplemented
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—44no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—44no—
220C22×C11—44no—
221C22×C11—44no—
222C22×C11—82no—
223C22×C11—168no—
224C22×C11C2×#12011yescharacteristic
225C22×C11C22×SD1611yescharacteristic
226C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—22no—
230C4×C11—44no—
231C4×C11—42no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11#45014yes—
236H(5,𝔽2)—44no—
237H(5,𝔽2)—44no—
238C2×#41—24no—
239C2×#41—22no—
240C22×Q8C23×C1111yescharacteristic
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4D4×C1111yescharacteristic
245C23×C4D4×C1112yes—
246C2×SD16—24no—
247C4⋊Q8D4×C1112yes—
248#127D4×C1112yes—
249#124—22no—
250#123—28no—
251C22⋊Q8—24no—
252#121—24no—
253#121—24no—
254#121—24no—
255#121—22no—
256#121—24no—
257#121C23×C1114yes—
258#120—28no—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4D4×C1114yes—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4D4×C1111yescharacteristic
270C2×C4⋊C4C23×C1111yescharacteristic
271C2×C22⋊C4—24no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4C23×C1112yes—
275C2×C42—21no—
276C2×C42C23×C1111yescharacteristic
277#106—24no—
278C4⋊C8—22no—
279#103—24no—
280#102—24no—
281C22⋊C8C23×C1114yes—
282C4×C8—22no—
283#95—21no—
284#95—22no—
285#95C23×C1112yes—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—44no—
289C2×C11—84no—
290C2×C11C2×#45011yescharacteristic
291C2×C11#301911yescharacteristic
292C2×C11#302511yescharacteristic
293C24—24no—
294C24C2×D4×C1112yes—
295#41—416no—
296#41—44no—
297#41—44no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—42no—
301C2×D4—28no—
302C2×D4—24no—
303C2×D4—24no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—416no—
309C2×D4—48no—
310C2×D4—48no—
311C2×D4—84no—
312C2×D4C11×SD1614yescomplemented
313C2×D4C2×D4×C1114yes—
314C22×C4—24no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—82no—
322C22×C4C2×D4×C1112yes—
323C22×C4C2×D4×C1111yescharacteristic
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C24×C1111yescharacteristic
326SD16—48no—
327C2×C8—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—82no—
336C4⋊C4C2×D4×C1114yes—
337C22⋊C4—28no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—44no—
342C22⋊C4—82no—
343C42—42no—
344C42C2×D4×C1112yes—
345C42C2×D4×C1112yes—
346C11#1821111yescharacteristic, direct product factor, Sylow
347C23—22no—
348C23—22no—
349C23—24no—
350C23—42no—
351C23—42no—
352C23—48no—
353C23—84no—
354C23—84no—
355C23C2×C11×SD1614yes—
356C23C22×D4×C1111yescharacteristic
357Q8—24no—
358Q8—42no—
359Q8—44no—
360D4—28no—
361D4—44no—
362D4—44no—
363D4—416no—
364D4—44no—
365D4—44no—
366D4—44no—
367D4—84no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—44no—
374C2×C4—48no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—48no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—82no—
386C2×C4C11×#12011yescharacteristic
387C2×C4C11×#12011yescharacteristic
388C2×C4C11×#12012yes—
389C2×C4C2×C11×SD1612yes—
390C2×C4C11×AGL(1,ℤ/8)12yes—
391C2×C4C22×D4×C1112yes—
392C8—44no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—44no—
397C22—42no—
398C22—42no—
399C22—44no—
400C22—44no—
401C22—44no—
402C22—82no—
403C22—168no—
404C22C2×C11×#12011yescharacteristic
405C22C22×C11×SD1611yescharacteristic
406C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
407C4—21no—
408C4—21no—
409C4—22no—
410C4—44no—
411C4—42no—
412C4—42no—
413C4—82no—
414C4—81no—
415C4C11×#45014yes—
416C2—21no—
417C2—21no—
418C2—44no—
419C2—84no—
420C2C2×C11×#45011yescharacteristic
421C2C11×#301911yescharacteristic
422C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3496C2
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
2. C11×#3103C2semidirect
3. C11×#2580C2semidirect
4. C11×#1613C2semidirect
5. C11×#1601C2semidirect
6. C11×#1517C2semidirect
7. C11×#1460C2semidirect
16. C2×C4×Q8×C11C22semidirect
18. C11×#481C22semidirect
21. C11×#448C22semidirect
23. C11×#431C22semidirect
24. C11×#399C22semidirect
25. C11×#393C22semidirect
29. C11×#382C22semidirect
30. C11×#327C22semidirect
31. C11×#323C22semidirect
82. #18211C11direct (N × H)
102. C2×D4×C11SD16semidirect
137. #3103C2×C11semidirect
138. #2580C2×C11semidirect
139. #1613C2×C11semidirect
140. #1601C2×C11semidirect
141. #1517C2×C11semidirect
142. #1460C2×C11semidirect
197. C2×C4×Q8C22×C11semidirect
199. #481C22×C11semidirect
202. #448C22×C11semidirect
204. #431C22×C11semidirect
205. #399C22×C11semidirect
206. #393C22×C11semidirect
210. #382C22×C11semidirect
211. #327C22×C11semidirect
212. #323C22×C11semidirect
312. C2×D4C11×SD16semidirect
346. C11#18211direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#31032
C11×#25802
C11×#16132
C11×#16012
C11×#15172
C11×#14602
#1821111