Finite Group Databasebeta

← C11×#19171 #14596364

Subgroups — C11×#19171 #14596364

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3152C211yesmaximal, characteristic
2C11×#3103C211yesmaximal, characteristic
3C2×C11×#475C211yesmaximal, characteristic, complemented
4Q8×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1690C212yesmaximal, complemented
6C11×#1686C212yesmaximal, complemented
7C11×#1670C212yesmaximal, complemented
8C11×#1666C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1547C211yesmaximal, characteristic
11C11×#1546C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#137—21no—
14C11×#532C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C11×#497—22no—
18C11×#494C2212yes—
19C11×#492C2212yes—
20C11×#481—21no—
21C11×#475—21no—
22C11×#475—21no—
23C11×#475C2212yes—
24C11×#475C2211yescharacteristic
25C11×#475C2212yes—
26C11×#475C2211yescharacteristic
27C11×#460C2211yescharacteristic
28C11×#460C2211yescharacteristic
29C11×#448—21no—
30C11×#446—22no—
31C11×#446C2212yes—
32C8×Q8×C11C2212yes—
33C4×C11×SD16—21no—
34C4×C11×SD16—21no—
35C11×#431C2211yescharacteristic
36C2×C11×#106—21no—
37C11×#423—21no—
38C11×#423C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#103—21no—
41C4×C11×M16—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yes—
44C11×#334C2212yes—
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11D411yescharacteristic
52C11×#137—44no—
53C11×#137—44no—
54C2×C11×Q16—22no—
55C2×C11×Q16—22no—
56C2×C11×SD16—21no—
57C2×C11×SD16—21no—
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×M16—21no—
61C2×C11×M16D411yescharacteristic
62C2×C11×M16D411yescharacteristic
63C22×C8×C11—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2311yescharacteristic
69C11×#127C2311yescharacteristic
70C11×#124—21no—
71C11×#121—21no—
72C11×#121—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C11×#106—22no—
88C11×#106—22no—
89C11×#106—21no—
90C11×#106—21no—
91C11×C4⋊C8—22no—
92C11×C4⋊C8—22no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8C2312yes—
96C11×C4⋊C8C2312yes—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—21no—
102C11×#103—21no—
103C11×#102—21no—
104C11×#102—21no—
105C11×C22⋊C8—21no—
106C11×#97—22no—
107C11×#97D412yes—
108C4×C8×C11—22no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#19171C1111yesmaximal, characteristic, direct product factor, Sylow
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11C2×D411yescharacteristic
123C2×Q8×C11C2×D411yescharacteristic
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—41no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C11×Q16—44no—
136C11×Q16—44no—
137C11×SD16—42no—
138C11×SD16—44no—
139C11×SD16—44no—
140C11×SD16—42no—
141C11×M16—22no—
142C11×M16—42no—
143C11×M16SD1614yescomplemented
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—42no—
149C2×C8×C11C2×D412yes—
150C2×C8×C11C2×D412yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4C2×D411yescharacteristic
163C11×C4⋊C4C2×D411yescharacteristic
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11#4111yescharacteristic
173C42×C11C2411yescharacteristic
174#3152C2×C1111yescharacteristic
175#3103C2×C1111yescharacteristic
176C2×#475C2×C1111yescharacteristic, complemented
177Q8×M16C2×C1111yescharacteristic, complemented
178#1690C2×C1112yescomplemented
179#1686C2×C1112yescomplemented
180#1670C2×C1112yescomplemented
181#1666C2×C1112yescomplemented
182#1565C2×C1111yescharacteristic, complemented
183#1547C2×C1111yescharacteristic
184#1546C2×C1111yescharacteristic, complemented
185C23×C11—41no—
186C23×C11#12111yescharacteristic
187Q8×C11—21no—
188Q8×C11—21no—
189Q8×C11—21no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—41no—
193Q8×C11—42no—
194Q8×C11—41no—
195Q8×C11—82no—
196Q8×C11#13712yescomplemented
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—81no—
202D4×C11—82no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—81no—
214C2×C4×C11—82no—
215C2×C4×C11—82no—
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11C2×SD1612yes—
220C2×C4×C11AGL(1,ℤ/8)12yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C8×C11—22no—
225C8×C11—42no—
226C8×C11—41no—
227C8×C11—42no—
228C8×C11—41no—
229C8×C11C2×SD1614yes—
230C2×#137—21no—
231C2×#137—21no—
232#532C22×C1111yescharacteristic
233C2×C4⋊Q8C22×C1111yescharacteristic
234C2×C4×Q8C22×C1111yescharacteristic
235#497—22no—
236#494C22×C1112yes—
237#492C22×C1112yes—
238#481—21no—
239#475—21no—
240#475—21no—
241#475C22×C1112yes—
242#475C22×C1112yes—
243#475C22×C1111yescharacteristic
244#475C22×C1111yescharacteristic
245#460C22×C1111yescharacteristic
246#460C22×C1111yescharacteristic
247#448—21no—
248#446—22no—
249#446C22×C1112yes—
250C8×Q8C22×C1112yes—
251C4×SD16—21no—
252C4×SD16—21no—
253#431C22×C1111yescharacteristic
254C2×#106—21no—
255#423—21no—
256#423C22×C1111yescharacteristic
257C2×C4⋊C8C22×C1111yescharacteristic
258C2×#103—21no—
259C4×M16—21no—
260C4×M16C22×C1111yescharacteristic
261#335C22×C1112yes—
262#334C22×C1112yes—
263#332C22×C1112yes—
264#332C22×C1112yes—
265#332C22×C1112yes—
266#331C22×C1112yes—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11#46012yes—
273C22×C11C2×#12111yescharacteristic
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11—81no—
282C4×C11—82no—
283C4×C11#46012yes—
284C4×C11C22×SD1611yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×#13711yescharacteristic
287C4×C11#57511yescharacteristic
288C2×#41—21no—
289C22×Q8—21no—
290C22×Q8D4×C1111yescharacteristic
291#137—44no—
292#137—44no—
293C2×Q16—22no—
294C2×Q16—22no—
295C2×SD16—21no—
296C2×SD16—21no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×M16—21no—
300C2×M16D4×C1111yescharacteristic
301C2×M16D4×C1111yescharacteristic
302C22×C8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C23×C1112yes—
307C4⋊Q8C23×C1111yescharacteristic
308#127C23×C1111yescharacteristic
309#124—21no—
310#121—21no—
311#121—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C1111yescharacteristic
315C4×Q8D4×C1111yescharacteristic
316C4×Q8C23×C1111yescharacteristic
317C4×Q8C23×C1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4D4×C1111yescharacteristic
324C2×C42—21no—
325C2×C42C23×C1111yescharacteristic
326#106—22no—
327#106—22no—
328#106—21no—
329#106—21no—
330C4⋊C8—22no—
331C4⋊C8—22no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8C23×C1112yes—
335C4⋊C8C23×C1112yes—
336C4⋊C8C23×C1111yescharacteristic
337C4⋊C8C23×C1111yescharacteristic
338#103—22no—
339#103—22no—
340#103—21no—
341#103—21no—
342#102—21no—
343#102—21no—
344C22⋊C8—21no—
345#97—22no—
346#97D4×C1112yes—
347C4×C8—22no—
348C4×C8—21no—
349C4×C8C23×C1112yes—
350C2×C11—22no—
351C2×C11—161no—
352C2×C11C2×#46011yescharacteristic
353C2×C11#305611yescharacteristic
354C2×C11#306911yescharacteristic
355#41—42no—
356#41—42no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×Q8C2×D4×C1111yescharacteristic
366C2×Q8C2×D4×C1111yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—41no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C11×#4111yescharacteristic
378Q16—44no—
379Q16—44no—
380SD16—44no—
381SD16—42no—
382SD16—42no—
383SD16—44no—
384M16—22no—
385M16—42no—
386M16C11×SD1614yescomplemented
387C2×C8—22no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—22no—
391C2×C8—42no—
392C2×C8C2×D4×C1112yes—
393C2×C8C2×D4×C1112yes—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4C2×D4×C1111yescharacteristic
406C4⋊C4C2×D4×C1111yescharacteristic
407C22⋊C4—41no—
408C22⋊C4—41no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42C2×D4×C1111yescharacteristic
414C42C2×D4×C1111yescharacteristic
415C42C11×#4111yescharacteristic
416C42C24×C1111yescharacteristic
417C11#1917111yescharacteristic, direct product factor, Sylow
418C23—41no—
419C23C11×#12111yescharacteristic
420Q8—21no—
421Q8—21no—
422Q8—21no—
423Q8—42no—
424Q8—42no—
425Q8—41no—
426Q8—42no—
427Q8—41no—
428Q8—82no—
429Q8C11×#13712yescomplemented
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4C11×#12111yescharacteristic
450C2×C4C11×#12111yescharacteristic
451C2×C4C11×#12111yescharacteristic
452C2×C4C2×C11×SD1612yes—
453C2×C4C11×AGL(1,ℤ/8)12yes—
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C22×D4×C1111yescharacteristic
456C2×C4C2×C11×#4111yescharacteristic
457C8—22no—
458C8—42no—
459C8—41no—
460C8—42no—
461C8—41no—
462C8C2×C11×SD1614yes—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C11×#46012yes—
469C22C2×C11×#12111yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C11×#46012yes—
480C4C22×C11×SD1611yescharacteristic
481C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
482C4C2×C11×#13711yescharacteristic
483C4C11×#57511yescharacteristic
484C2—22no—
485C2—161no—
486C2C2×C11×#46011yescharacteristic
487C2C11×#305611yescharacteristic
488C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
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
3. C2×C11×#475C2semidirect
4. Q8×C11×M16C2semidirect
5. C11×#1690C2semidirect
6. C11×#1686C2semidirect
7. C11×#1670C2semidirect
8. C11×#1666C2semidirect
9. C11×#1565C2semidirect
11. C11×#1546C2semidirect
111. #19171C11direct (N × H)
143. C11×M16SD16semidirect
176. C2×#475C2×C11semidirect
177. Q8×M16C2×C11semidirect
178. #1690C2×C11semidirect
179. #1686C2×C11semidirect
180. #1670C2×C11semidirect
181. #1666C2×C11semidirect
182. #1565C2×C11semidirect
184. #1546C2×C11semidirect
196. Q8×C11#137semidirect
386. M16C11×SD16semidirect
417. C11#19171direct (N × H)
429. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#31522
C11×#31032
C2×C11×#4752
Q8×C11×M162
C11×#16902
C11×#16862
C11×#16702
C11×#16662
C11×#15652
C11×#15472
C11×#15462
#1917111