Finite Group Databasebeta

← C11×#18992 #14596185

Subgroups — C11×#18992 #14596185

Order 2816.

1152 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×H(3,𝔽4)C211yesmaximal, characteristic, complemented
2C11×#3213C212yesmaximal, complemented
3C11×#3153C211yesmaximal, characteristic, complemented
4C11×#1659C214yesmaximal, complemented
5C11×#1655C214yesmaximal, complemented
6C11×#1533C211yesmaximal, characteristic, complemented
7C11×#1527C212yesmaximal, complemented
8C2×C11×#137—21no—
9C2×C11×AGL(1,ℤ/8)—21no—
10C11×H(3,𝔽4)—22no—
11C11×H(3,𝔽4)—24no—
12C11×H(3,𝔽4)C2214yes—
13C11×#532C2211yescharacteristic, complemented
14C2×C11×#124—21no—
15C2×C11×#124—22no—
16C2×C11×#124C2211yescharacteristic
17C2×C11×#124C2212yes—
18C2×C11×#120—21no—
19C2×C11×#120—22no—
20C11×#497C2212yescomplemented
21C11×#496C2212yescomplemented
22C11×#496C2214yescomplemented
23C11×#495—22no—
24C11×#489C2214yescomplemented
25C11×#463—24no—
26C11×#448—22no—
27C11×#447—22no—
28C11×#432C2212yescomplemented
29C4×C11×M16C2211yescharacteristic, complemented
30C11×#329C2218yescomplemented
31C11×#329C2214yescomplemented
32C25×C11—21no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C22×Q8×C11D412yes—
36C22×D4×C11—22no—
37C22×D4×C11—21no—
38C22×D4×C11D411yescharacteristic
39C22×D4×C11D412yes—
40C11×#137—44no—
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×Q16—22no—
43C2×C11×SD16—22no—
44C2×C11×SD16—22no—
45C2×C11×SD16—24no—
46C2×C11×D8—22no—
47C2×C11×D8—24no—
48C2×C11×M16—21no—
49C11×C4⋊Q8C2311yescharacteristic, complemented
50C11×#127C2311yescharacteristic, complemented
51C11×#124—28no—
52C11×#124—24no—
53C11×#124—28no—
54C11×#124—24no—
55C11×#124—22no—
56C11×#124—22no—
57C11×#124—22no—
58C11×#124—21no—
59C11×#124D412yes—
60C11×#124D414yes—
61C11×#124C2314yes—
62C11×#124C2312yes—
63C11×#121—22no—
64C11×#120—28no—
65C11×#120—24no—
66C11×#120—28no—
67C11×#120—24no—
68C4×D4×C11—22no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C11×C4⋊C8—22no—
77C11×#103—24no—
78C11×#102—24no—
79C11×C22⋊C8—22no—
80C11×#97C2314yescomplemented
81C11×#97C2312yescomplemented
82C4×C8×C11—21no—
83#18992C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—24no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—84no—
88C24×C11—82no—
89C11×#41—42no—
90C11×#41—42no—
91C2×Q8×C11—22no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—42no—
95C2×Q8×C11—82no—
96C2×Q8×C11C2×D414yes—
97C2×Q8×C11C2×D412yes—
98C2×D4×C11—24no—
99C2×D4×C11—28no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—42no—
105C2×D4×C11—41no—
106C2×D4×C11—82no—
107C2×D4×C11—84no—
108C2×D4×C11—82no—
109C2×D4×C11C2×D414yes—
110C2×D4×C11C2×D412yes—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C11×Q16—44no—
117C11×SD16—44no—
118C11×SD16—44no—
119C11×SD16—84no—
120C11×D8—44no—
121C11×D8—84no—
122C11×M16—24no—
123C2×C8×C11—22no—
124C2×C8×C11—24no—
125C11×C4⋊C4—22no—
126C11×C22⋊C4—28no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—42no—
135C42×C11—24no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D412yes—
138C42×C11C2411yescharacteristic
139C2×H(3,𝔽4)C2×C1111yescharacteristic, complemented
140#3213C2×C1112yescomplemented
141#3153C2×C1111yescharacteristic, complemented
142#1659C2×C1114yescomplemented
143#1655C2×C1114yescomplemented
144#1533C2×C1111yescharacteristic, complemented
145#1527C2×C1112yescomplemented
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—44no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—42no—
152C23×C11—44no—
153C23×C11—41no—
154C23×C11—84no—
155C23×C11—88no—
156C23×C11—816no—
157C23×C11#12011yescharacteristic
158Q8×C11—42no—
159Q8×C11—44no—
160Q8×C11—41no—
161Q8×C11—41no—
162Q8×C11—81no—
163Q8×C11—82no—
164D4×C11—42no—
165D4×C11—44no—
166D4×C11—41no—
167D4×C11—44no—
168D4×C11—41no—
169D4×C11—81no—
170D4×C11—82no—
171D4×C11—84no—
172D4×C11—88no—
173D4×C11—82no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—82no—
182C2×C4×C11#12012yes—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11C22×D412yes—
185C2×C4×C11C22×D411yescharacteristic
186C8×C11—24no—
187C8×C11—44no—
188C2×#137—21no—
189C2×AGL(1,ℤ/8)—21no—
190H(3,𝔽4)—24no—
191H(3,𝔽4)—22no—
192H(3,𝔽4)C22×C1114yes—
193#532C22×C1111yescharacteristic, complemented
194C2×#124—21no—
195C2×#124—22no—
196C2×#124C22×C1111yescharacteristic
197C2×#124C22×C1112yes—
198C2×#120—21no—
199C2×#120—22no—
200#497C22×C1112yescomplemented
201#496C22×C1112yescomplemented
202#496C22×C1114yescomplemented
203#495—22no—
204#489C22×C1114yescomplemented
205#463—24no—
206#448—22no—
207#447—22no—
208#432C22×C1112yescomplemented
209C4×M16C22×C1111yescharacteristic, complemented
210#329C22×C1118yescomplemented
211#329C22×C1114yescomplemented
212C22×C11—22no—
213C22×C11—42no—
214C22×C11—44no—
215C22×C11—44no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—84no—
219C22×C11—88no—
220C22×C11—816no—
221C22×C11—81no—
222C22×C11—82no—
223C22×C11#45312yes—
224C22×C11C2×#12011yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—42no—
230C4×C11—44no—
231C4×C11—81no—
232C25—21no—
233C2×#41—21no—
234C22×Q8D4×C1111yescharacteristic
235C22×Q8D4×C1112yes—
236C22×D4—22no—
237C22×D4—21no—
238C22×D4D4×C1111yescharacteristic
239C22×D4D4×C1112yes—
240#137—44no—
241AGL(1,ℤ/8)—44no—
242C2×Q16—22no—
243C2×SD16—22no—
244C2×SD16—22no—
245C2×SD16—24no—
246C2×D8—22no—
247C2×D8—24no—
248C2×M16—21no—
249C4⋊Q8C23×C1111yescharacteristic, complemented
250#127C23×C1111yescharacteristic, complemented
251#124—28no—
252#124—24no—
253#124—28no—
254#124—24no—
255#124—22no—
256#124—22no—
257#124—22no—
258#124—21no—
259#124D4×C1114yes—
260#124D4×C1112yes—
261#124C23×C1114yes—
262#124C23×C1112yes—
263#121—22no—
264#120—28no—
265#120—24no—
266#120—28no—
267#120—24no—
268C4×D4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C42—21no—
275C2×C42C23×C1111yescharacteristic
276C4⋊C8—22no—
277#103—24no—
278#102—24no—
279C22⋊C8—22no—
280#97C23×C1112yescomplemented
281#97C23×C1114yescomplemented
282C4×C8—21no—
283C2×C11—22no—
284C2×C11—82no—
285C2×C11—84no—
286C2×C11—161no—
287C2×C11C2×#45311yescharacteristic
288C2×C11#301912yes—
289C24—24no—
290C24—21no—
291C24—22no—
292C24—84no—
293C24—82no—
294#41—42no—
295#41—42no—
296C2×Q8—22no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—42no—
300C2×Q8—82no—
301C2×Q8C2×D4×C1114yes—
302C2×Q8C2×D4×C1112yes—
303C2×D4—24no—
304C2×D4—28no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—82no—
312C2×D4—84no—
313C2×D4—82no—
314C2×D4C2×D4×C1114yes—
315C2×D4C2×D4×C1112yes—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4C2×D4×C1111yescharacteristic
320C22×C4C2×D4×C1112yes—
321Q16—44no—
322SD16—44no—
323SD16—44no—
324SD16—84no—
325D8—44no—
326D8—84no—
327M16—24no—
328C2×C8—22no—
329C2×C8—24no—
330C4⋊C4—22no—
331C22⋊C4—28no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—42no—
340C42—24no—
341C42C2×D4×C1111yescharacteristic
342C42C2×D4×C1112yes—
343C42C24×C1111yescharacteristic
344C11#1899211yescharacteristic, direct product factor, Sylow
345C23—22no—
346C23—24no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—42no—
351C23—44no—
352C23—41no—
353C23—84no—
354C23—88no—
355C23—816no—
356C23C11×#12011yescharacteristic
357Q8—42no—
358Q8—44no—
359Q8—41no—
360Q8—41no—
361Q8—81no—
362Q8—82no—
363D4—42no—
364D4—44no—
365D4—41no—
366D4—44no—
367D4—41no—
368D4—81no—
369D4—82no—
370D4—84no—
371D4—88no—
372D4—82no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—82no—
381C2×C4C11×#12012yes—
382C2×C4C11×#12011yescharacteristic
383C2×C4C22×D4×C1112yes—
384C2×C4C22×D4×C1111yescharacteristic
385C8—24no—
386C8—44no—
387C22—22no—
388C22—42no—
389C22—44no—
390C22—44no—
391C22—44no—
392C22—44no—
393C22—84no—
394C22—88no—
395C22—816no—
396C22—81no—
397C22—82no—
398C22C11×#45312yes—
399C22C2×C11×#12011yescharacteristic
400C4—21no—
401C4—21no—
402C4—22no—
403C4—22no—
404C4—42no—
405C4—44no—
406C4—81no—
407C2—22no—
408C2—82no—
409C2—84no—
410C2—161no—
411C2C2×C11×#45311yescharacteristic
412C2C11×#301912yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×H(3,𝔽4)C2semidirect
2. C11×#3213C2semidirect
3. C11×#3153C2semidirect
4. C11×#1659C2semidirect
5. C11×#1655C2semidirect
6. C11×#1533C2semidirect
7. C11×#1527C2semidirect
13. C11×#532C22semidirect
20. C11×#497C22semidirect
21. C11×#496C22semidirect
22. C11×#496C22semidirect
24. C11×#489C22semidirect
28. C11×#432C22semidirect
29. C4×C11×M16C22semidirect
30. C11×#329C22semidirect
31. C11×#329C22semidirect
49. C11×C4⋊Q8C23semidirect
50. C11×#127C23semidirect
80. C11×#97C23semidirect
81. C11×#97C23semidirect
83. #18992C11direct (N × H)
139. C2×H(3,𝔽4)C2×C11semidirect
140. #3213C2×C11semidirect
141. #3153C2×C11semidirect
142. #1659C2×C11semidirect
143. #1655C2×C11semidirect
144. #1533C2×C11semidirect
145. #1527C2×C11semidirect
193. #532C22×C11semidirect
200. #497C22×C11semidirect
201. #496C22×C11semidirect
202. #496C22×C11semidirect
204. #489C22×C11semidirect
208. #432C22×C11semidirect
209. C4×M16C22×C11semidirect
210. #329C22×C11semidirect
211. #329C22×C11semidirect
249. C4⋊Q8C23×C11semidirect
250. #127C23×C11semidirect
280. #97C23×C11semidirect
281. #97C23×C11semidirect
344. C11#18992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×H(3,𝔽4)2
C11×#32132
C11×#31532
C11×#16592
C11×#16552
C11×#15332
C11×#15272
#1899211