Finite Group Databasebeta

← C11×#19004 #14596197

Subgroups — C11×#19004 #14596197

Order 2816.

896 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×#3531C211yesmaximal, characteristic, complemented
2C11×#3217C212yesmaximal, complemented
3C11×#3138C211yesmaximal, characteristic, complemented
4C11×#1658C212yesmaximal, complemented
5C11×#1657C214yesmaximal, complemented
6C11×#1656C212yesmaximal, complemented
7C11×#1537C211yesmaximal, characteristic, complemented
8C11×#1529C212yesmaximal, complemented
9C11×#564C2211yescharacteristic, complemented
10C11×#563—22no—
11C11×#563—22no—
12C11×#563C2212yescomplemented
13C11×#562—22no—
14C11×#562C2211yescharacteristic, complemented
15C11×#533—22no—
16C11×#533C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C11×#529—22no—
19C11×#529—22no—
20C11×#529C2212yes—
21C11×#496C2214yes—
22C11×#490C2212yes—
23C11×#490C2212yes—
24C11×#490C2214yes—
25C11×#486—22no—
26C11×#460—22no—
27C11×#459—22no—
28C11×#450—22no—
29C11×#447—22no—
30C11×#432C2212yes—
31C11×#418—22no—
32C4×C11×M16C2211yescharacteristic
33C11×#330C2212yescomplemented
34C11×#330C2212yescomplemented
35C11×#330C2214yescomplemented
36C11×#329C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C2×C11×SD16—24no—
40C2×C11×D8—24no—
41C2×C11×M16—21no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8D412yes—
45C11×#127—22no—
46C11×#127—21no—
47C11×#127C2312yes—
48C11×#126—22no—
49C11×#126—22no—
50C11×#126—22no—
51C11×#126—22no—
52C11×#126—22no—
53C11×#125—22no—
54C11×#125—22no—
55C11×#125—22no—
56C11×#125—22no—
57C11×#125C2312yes—
58C11×#125C2311yescharacteristic
59C11×#125C2311yescharacteristic
60C11×#124—22no—
61C11×#124—22no—
62C11×#124C2312yes—
63C11×#123—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8D412yes—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121D412yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11D412yes—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11D412yes—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117D412yes—
88C2×C42×C11—22no—
89C2×C42×C11C2311yescharacteristic
90C11×C4⋊C8—22no—
91C11×#102—24no—
92C11×#102—24no—
93C11×#102—24no—
94C11×#102—24no—
95C11×C22⋊C8—22no—
96C11×#97C2312yes—
97C11×#97C2314yes—
98C4×C8×C11—21no—
99#19004C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—41no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C2×D412yes—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—44no—
109C2×D4×C11—42no—
110C2×D4×C11—41no—
111C2×D4×C11—84no—
112C2×D4×C11C2×D412yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C11×SD16—84no—
119C11×D8—84no—
120C11×M16—42no—
121C2×C8×C11—22no—
122C2×C8×C11—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4C2×D412yes—
137C11×C4⋊C4C2×D412yes—
138C11×C4⋊C4C2×D412yes—
139C11×C4⋊C4C2×D412yes—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D412yes—
156C42×C11C2411yescharacteristic
157#3531C2×C1111yescharacteristic, complemented
158#3217C2×C1112yescomplemented
159#3138C2×C1111yescharacteristic, complemented
160#1658C2×C1112yescomplemented
161#1657C2×C1114yescomplemented
162#1656C2×C1112yescomplemented
163#1537C2×C1111yescharacteristic, complemented
164#1529C2×C1112yescomplemented
165C23×C11—22no—
166C23×C11—42no—
167C23×C11—82no—
168C23×C11—84no—
169C23×C11#12011yescharacteristic
170Q8×C11—42no—
171Q8×C11—82no—
172Q8×C11—82no—
173D4×C11—42no—
174D4×C11—44no—
175D4×C11—44no—
176D4×C11—44no—
177D4×C11—84no—
178D4×C11—82no—
179D4×C11—82no—
180D4×C11—82no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—44no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11#12012yes—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D412yes—
195C8×C11—42no—
196C8×C11—44no—
197#564C22×C1111yescharacteristic, complemented
198#563—22no—
199#563—22no—
200#563C22×C1112yescomplemented
201#562—22no—
202#562C22×C1111yescharacteristic, complemented
203#533—22no—
204#533C22×C1111yescharacteristic
205C2×#127C22×C1111yescharacteristic
206#529—22no—
207#529—22no—
208#529C22×C1112yes—
209#496C22×C1114yes—
210#490C22×C1112yes—
211#490C22×C1112yes—
212#490C22×C1114yes—
213#486—22no—
214#460—22no—
215#459—22no—
216#450—22no—
217#447—22no—
218#432C22×C1112yes—
219#418—22no—
220C4×M16C22×C1111yescharacteristic
221#330C22×C1112yescomplemented
222#330C22×C1112yescomplemented
223#330C22×C1114yescomplemented
224#329C22×C1114yescomplemented
225C22×C11—21no—
226C22×C11—22no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—82no—
231C22×C11—84no—
232C22×C11—164no—
233C22×C11C2×#12011yescharacteristic
234C4×C11—21no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—42no—
241C4×C11—42no—
242C4×C11#45412yes—
243C22×D4—21no—
244C22×D4—22no—
245C2×SD16—24no—
246C2×D8—24no—
247C2×M16—21no—
248C4⋊Q8—22no—
249C4⋊Q8—22no—
250C4⋊Q8D4×C1112yes—
251#127—22no—
252#127—21no—
253#127C23×C1112yes—
254#126—22no—
255#126—22no—
256#126—22no—
257#126—22no—
258#126—22no—
259#125—22no—
260#125—22no—
261#125—22no—
262#125—22no—
263#125C23×C1112yes—
264#125C23×C1111yescharacteristic
265#125C23×C1111yescharacteristic
266#124—22no—
267#124—22no—
268#124C23×C1112yes—
269#123—22no—
270#123—22no—
271#123—22no—
272#123—22no—
273#123—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8D4×C1112yes—
282#121—22no—
283#121—22no—
284#121D4×C1112yes—
285C4×Q8—22no—
286C4×Q8—22no—
287C4×Q8D4×C1112yes—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4D4×C1112yes—
291#117—22no—
292#117—22no—
293#117D4×C1112yes—
294C2×C42—22no—
295C2×C42C23×C1111yescharacteristic
296C4⋊C8—22no—
297#102—24no—
298#102—24no—
299#102—24no—
300#102—24no—
301C22⋊C8—22no—
302#97C23×C1112yes—
303#97C23×C1114yes—
304C4×C8—21no—
305C2×C11—41no—
306C2×C11—82no—
307C2×C11—162no—
308C2×C11C2×#45411yescharacteristic
309C2×C11#302112yes—
310C24—41no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8C2×D4×C1112yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—24no—
318C2×D4—44no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4—84no—
322C2×D4C2×D4×C1112yes—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4C2×D4×C1111yescharacteristic
327C22×C4C2×D4×C1112yes—
328SD16—84no—
329D8—84no—
330M16—42no—
331C2×C8—22no—
332C2×C8—24no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4C2×D4×C1112yes—
347C4⋊C4C2×D4×C1112yes—
348C4⋊C4C2×D4×C1112yes—
349C4⋊C4C2×D4×C1112yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42C2×D4×C1111yescharacteristic
365C42C2×D4×C1112yes—
366C42C24×C1111yescharacteristic
367C11#1900411yescharacteristic, direct product factor, Sylow
368C23—22no—
369C23—42no—
370C23—82no—
371C23—84no—
372C23C11×#12011yescharacteristic
373Q8—42no—
374Q8—82no—
375Q8—82no—
376D4—42no—
377D4—44no—
378D4—44no—
379D4—44no—
380D4—84no—
381D4—82no—
382D4—82no—
383D4—82no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4C11×#12012yes—
395C2×C4C11×#12011yescharacteristic
396C2×C4C22×D4×C1111yescharacteristic
397C2×C4C22×D4×C1112yes—
398C8—42no—
399C8—44no—
400C22—21no—
401C22—22no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—84no—
407C22—164no—
408C22C2×C11×#12011yescharacteristic
409C4—21no—
410C4—22no—
411C4—22no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4C11×#45412yes—
418C2—41no—
419C2—82no—
420C2—162no—
421C2C2×C11×#45411yescharacteristic
422C2C11×#302112yes—
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. C11×#3531C2semidirect
2. C11×#3217C2semidirect
3. C11×#3138C2semidirect
4. C11×#1658C2semidirect
5. C11×#1657C2semidirect
6. C11×#1656C2semidirect
7. C11×#1537C2semidirect
8. C11×#1529C2semidirect
9. C11×#564C22semidirect
12. C11×#563C22semidirect
14. C11×#562C22semidirect
33. C11×#330C22semidirect
34. C11×#330C22semidirect
35. C11×#330C22semidirect
36. C11×#329C22semidirect
99. #19004C11direct (N × H)
157. #3531C2×C11semidirect
158. #3217C2×C11semidirect
159. #3138C2×C11semidirect
160. #1658C2×C11semidirect
161. #1657C2×C11semidirect
162. #1656C2×C11semidirect
163. #1537C2×C11semidirect
164. #1529C2×C11semidirect
197. #564C22×C11semidirect
200. #563C22×C11semidirect
202. #562C22×C11semidirect
221. #330C22×C11semidirect
222. #330C22×C11semidirect
223. #330C22×C11semidirect
224. #329C22×C11semidirect
367. C11#19004direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35312
C11×#32172
C11×#31382
C11×#16582
C11×#16572
C11×#16562
C11×#15372
C11×#15292
#1900411