Finite Group Databasebeta

← C11×#18371 #14595564

Subgroups — C11×#18371 #14595564

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic
2C11×#3238C212yesmaximal, complemented
3C11×#2621C211yesmaximal, characteristic, complemented
4C11×#1612C214yesmaximal, complemented
5C11×#1611C212yesmaximal, complemented
6C11×#1610C212yesmaximal, complemented
7C11×#1512C212yesmaximal, complemented
8C11×#1464C211yesmaximal, characteristic, complemented
9C11×#556—22no—
10C11×#555—22no—
11C11×#553—22no—
12C11×#552—22no—
13C11×#544C2211yescharacteristic
14C11×#538—21no—
15C11×#538C2212yes—
16C11×#537C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C11×#529—21no—
19C11×#529C2212yes—
20C11×#525—21no—
21C2×C11×C22⋊Q8—21no—
22C11×#520—21no—
23C2×C11×#117C2211yescharacteristic
24C11×#501—22no—
25C11×#489—22no—
26C11×#483C2214yes—
27C11×#480C2214yes—
28C11×#477—22no—
29C11×#476—22no—
30C11×#432C2212yes—
31C11×#398—21no—
32C11×#398C2212yes—
33C11×#397—21no—
34C11×#397C2212yes—
35C11×#391—21no—
36C11×#382C2211yescharacteristic
37C11×#328C2214yes—
38C11×#327C2214yes—
39C11×#324C2212yes—
40C11×#323C2212yes—
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C23×C4×C11D411yescharacteristic
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8—22no—
47C11×#126—22no—
48C11×#126—22no—
49C11×#126—22no—
50C11×#126—22no—
51C11×#125—21no—
52C11×#125—22no—
53C11×#125D412yes—
54C11×#124—21no—
55C11×#124—22no—
56C11×#124—22no—
57C11×#124D412yes—
58C11×#123—22no—
59C11×#123—22no—
60C11×#123—22no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—44no—
66C11×C22⋊Q8C2312yes—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—21no—
73C11×#121C2312yes—
74C11×#120—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11D412yes—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—21no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11D412yes—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—21no—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C11×C22⋊C4C2311yescharacteristic
101C2×C42×C11D411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C11×#107—24no—
104C11×#106—24no—
105C11×C4⋊C8—22no—
106C11×#103—24no—
107C11×#102—24no—
108C11×C22⋊C8C2314yes—
109C11×#97—22no—
110C11×#95—21no—
111C11×#95—22no—
112C11×#95—22no—
113C11×#95C2312yes—
114#18371C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11C2×D411yescharacteristic
116C11×#41—42no—
117C11×#41—42no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11—41no—
123C2×Q8×C11—41no—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C2×C8×C11—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—44no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—22no—
182C42×C11C2×D412yes—
183C42×C11C2×D412yes—
184#3493C2×C1111yescharacteristic
185#3238C2×C1112yescomplemented
186#2621C2×C1111yescharacteristic, complemented
187#1612C2×C1114yescomplemented
188#1611C2×C1112yescomplemented
189#1610C2×C1112yescomplemented
190#1512C2×C1112yescomplemented
191#1464C2×C1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11—22no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—82no—
202Q8×C11—82no—
203Q8×C11—81no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—82no—
209D4×C11—81no—
210D4×C11—82no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×D412yes—
240C8×C11—44no—
241#556—22no—
242#555—22no—
243#553—22no—
244#552—22no—
245#544C22×C1111yescharacteristic
246#538—21no—
247#538C22×C1112yes—
248#537C22×C1111yescharacteristic
249C2×C4⋊Q8C22×C1111yescharacteristic
250#529—21no—
251#529C22×C1112yes—
252#525—21no—
253C2×C22⋊Q8—21no—
254#520—21no—
255C2×#117C22×C1111yescharacteristic
256#501—22no—
257#489—22no—
258#483C22×C1114yes—
259#480C22×C1114yes—
260#477—22no—
261#476—22no—
262#432C22×C1112yes—
263#398—21no—
264#398C22×C1112yes—
265#397—21no—
266#397C22×C1112yes—
267#391—21no—
268#382C22×C1111yescharacteristic
269#328C22×C1114yes—
270#327C22×C1114yes—
271#324C22×C1112yes—
272#323C22×C1112yes—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—42no—
276C22×C11—41no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—41no—
280C22×C11—42no—
281C22×C11—41no—
282C22×C11—81no—
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—22no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—41no—
293C4×C11—42no—
294C4×C11—41no—
295C4×C11—42no—
296C4×C11—82no—
297C4×C11—82no—
298C2×#41—21no—
299C22×Q8—21no—
300C23×C4D4×C1111yescharacteristic
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304#126—22no—
305#126—22no—
306#126—22no—
307#126—22no—
308#125—21no—
309#125—22no—
310#125D4×C1112yes—
311#124—21no—
312#124—22no—
313#124—22no—
314#124D4×C1112yes—
315#123—22no—
316#123—22no—
317#123—22no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—22no—
322C22⋊Q8—44no—
323C22⋊Q8C23×C1112yes—
324#121—21no—
325#121—21no—
326#121—22no—
327#121—22no—
328#121—22no—
329#121—21no—
330#121C23×C1112yes—
331#120—22no—
332C4×Q8—22no—
333C4×Q8—21no—
334C4×Q8D4×C1112yes—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C1112yes—
342#117—22no—
343#117—22no—
344#117—21no—
345#117—22no—
346#117—22no—
347#117—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C1111yescharacteristic
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C22⋊C4—22no—
356C2×C22⋊C4D4×C1111yescharacteristic
357C2×C22⋊C4C23×C1111yescharacteristic
358C2×C42D4×C1111yescharacteristic
359C2×C42C23×C1111yescharacteristic
360#107—24no—
361#106—24no—
362C4⋊C8—22no—
363#103—24no—
364#102—24no—
365C22⋊C8C23×C1114yes—
366#97—22no—
367#95—21no—
368#95—22no—
369#95—22no—
370#95C23×C1112yes—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—82no—
374C2×C11—81no—
375C2×C11#300611yescharacteristic
376C2×C11#302211yescharacteristic
377C2×C11#302811yescharacteristic
378C24C2×D4×C1111yescharacteristic
379#41—42no—
380#41—42no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8C2×D4×C1112yes—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4C2×D4×C1112yes—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—41no—
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C24×C1111yescharacteristic
409C2×C8—24no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C4⋊C4—44no—
426C4⋊C4C2×D4×C1112yes—
427C4⋊C4C2×D4×C1112yes—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—44no—
440C42—22no—
441C42—22no—
442C42—21no—
443C42—21no—
444C42—22no—
445C42C2×D4×C1112yes—
446C42C2×D4×C1112yes—
447C11#1837111yescharacteristic, direct product factor, Sylow
448C23—21no—
449C23—22no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23C22×D4×C1111yescharacteristic
455Q8—42no—
456Q8—42no—
457Q8—82no—
458Q8—82no—
459Q8—81no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—82no—
465D4—81no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4C11×#12012yes—
492C2×C4C11×#12011yescharacteristic
493C2×C4C11×#12011yescharacteristic
494C2×C4C11×AGL(1,ℤ/8)12yes—
495C2×C4C22×D4×C1112yes—
496C8—44no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—42no—
503C22—41no—
504C22—42no—
505C22—41no—
506C22—81no—
507C22C2×C11×#12011yescharacteristic
508C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
509C22C11×#57511yescharacteristic
510C4—22no—
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—82no—
521C4—82no—
522C2—21no—
523C2—21no—
524C2—81no—
525C2—82no—
526C2C11×#300611yescharacteristic
527C2C11×#302211yescharacteristic
528C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3493C2
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×#3238C2semidirect
3. C11×#2621C2semidirect
4. C11×#1612C2semidirect
5. C11×#1611C2semidirect
6. C11×#1610C2semidirect
7. C11×#1512C2semidirect
8. C11×#1464C2semidirect
114. #18371C11direct (N × H)
185. #3238C2×C11semidirect
186. #2621C2×C11semidirect
187. #1612C2×C11semidirect
188. #1611C2×C11semidirect
189. #1610C2×C11semidirect
190. #1512C2×C11semidirect
191. #1464C2×C11semidirect
447. C11#18371direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#32382
C11×#26212
C11×#16122
C11×#16112
C11×#16102
C11×#15122
C11×#14642
#1837111