Finite Group Databasebeta

← C11×#18367 #14595560

Subgroups — C11×#18367 #14595560

Order 2816.

928 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×#3218C212yesmaximal, complemented
3C11×#2628C211yesmaximal, characteristic, complemented
4C11×#1606C214yesmaximal, complemented
5C11×#1605C212yesmaximal, complemented
6C11×#1604C212yesmaximal, 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—
21C11×#520—21no—
22C2×C11×#117C2211yescharacteristic
23C11×#497—22no—
24C11×#491—22no—
25C11×#462—22no—
26C11×#461—22no—
27C11×#451C2214yes—
28C11×#448C2214yes—
29C11×#432C2212yes—
30C11×#400—21no—
31C11×#399—21no—
32C11×#395C2212yes—
33C11×#393C2212yes—
34C11×#389—21no—
35C11×#382C2211yescharacteristic
36C11×#380—21no—
37C11×#328C2214yes—
38C11×#327C2214yes—
39C11×#324C2212yes—
40C11×#323C2212yes—
41C2×C11×#41—21no—
42C22×Q8×C11C2312yes—
43C23×C4×C11D411yescharacteristic
44C2×C11×Q16—24no—
45C2×C11×SD16—24no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×#126—22no—
50C11×#126—22no—
51C11×#126—22no—
52C11×#126—22no—
53C11×#125—21no—
54C11×#125—22no—
55C11×#125D412yes—
56C11×#124—21no—
57C11×#124—22no—
58C11×#124—22no—
59C11×#124D412yes—
60C11×#123—22no—
61C11×#123—22no—
62C11×#123—22no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8C2312yes—
68C11×#121—21no—
69C11×#121—21no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—21no—
74C11×#121C2312yes—
75C11×#120—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11D412yes—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—21no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11D412yes—
86C11×#117—22no—
87C11×#117—22no—
88C11×#117—21no—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4C2311yescharacteristic
102C2×C42×C11D411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C11×C4⋊C8—22no—
105C11×#103—24no—
106C11×#103—24no—
107C11×C22⋊C8C2314yes—
108C11×#97—22no—
109C11×#95—22no—
110C11×#95—21no—
111C11×#95—22no—
112C11×#95C2312yes—
113#18367C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11C2×D411yescharacteristic
115C11×#41—42no—
116C11×#41—42no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—24no—
120C2×Q8×C11—82no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11C2×D412yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C11×Q16—84no—
144C11×SD16—84no—
145C2×C8×C11—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—82no—
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—82no—
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#3218C2×C1112yescomplemented
186#2628C2×C1111yescharacteristic, complemented
187#1606C2×C1114yescomplemented
188#1605C2×C1112yescomplemented
189#1604C2×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—44no—
202Q8×C11—44no—
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#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12012yes—
238C2×C4×C11#13712yes—
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—
253#520—21no—
254C2×#117C22×C1111yescharacteristic
255#497—22no—
256#491—22no—
257#462—22no—
258#461—22no—
259#451C22×C1114yes—
260#448C22×C1114yes—
261#432C22×C1112yes—
262#400—21no—
263#399—21no—
264#395C22×C1112yes—
265#393C22×C1112yes—
266#389—21no—
267#382C22×C1111yescharacteristic
268#380—21no—
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×#13711yescharacteristic
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×Q8C23×C1112yes—
300C23×C4D4×C1111yescharacteristic
301C2×Q16—24no—
302C2×SD16—24no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#126—22no—
307#126—22no—
308#126—22no—
309#126—22no—
310#125—21no—
311#125—22no—
312#125D4×C1112yes—
313#124—21no—
314#124—22no—
315#124—22no—
316#124D4×C1112yes—
317#123—22no—
318#123—22no—
319#123—22no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—22no—
324C22⋊Q8C23×C1112yes—
325#121—21no—
326#121—21no—
327#121—22no—
328#121—22no—
329#121—22no—
330#121—21no—
331#121C23×C1112yes—
332#120—22no—
333C4×Q8—22no—
334C4×Q8—21no—
335C4×Q8D4×C1112yes—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—21no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4D4×C1112yes—
343#117—22no—
344#117—22no—
345#117—21no—
346#117—22no—
347#117—22no—
348#117—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4D4×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C22⋊C4—22no—
357C2×C22⋊C4D4×C1111yescharacteristic
358C2×C22⋊C4C23×C1111yescharacteristic
359C2×C42D4×C1111yescharacteristic
360C2×C42C23×C1111yescharacteristic
361C4⋊C8—22no—
362#103—24no—
363#103—24no—
364C22⋊C8C23×C1114yes—
365#97—22no—
366#95—22no—
367#95—21no—
368#95—22no—
369#95C23×C1112yes—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—82no—
373C2×C11—81no—
374C2×C11#300711yescharacteristic
375C2×C11#302211yescharacteristic
376C2×C11#302711yescharacteristic
377C24C2×D4×C1111yescharacteristic
378#41—42no—
379#41—42no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—24no—
383C2×Q8—82no—
384C2×Q8C2×D4×C1112yes—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4C2×D4×C1112yes—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C24×C1111yescharacteristic
406Q16—84no—
407SD16—84no—
408C2×C8—24no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—42no—
425C4⋊C4—82no—
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—82no—
440C42—22no—
441C42—22no—
442C42—21no—
443C42—21no—
444C42—22no—
445C42C2×D4×C1112yes—
446C42C2×D4×C1112yes—
447C11#1836711yescharacteristic, direct product factor, Sylow
448C23—21no—
449C23—22no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23C22×D4×C1111yescharacteristic
455Q8—42no—
456Q8—42no—
457Q8—44no—
458Q8—44no—
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×#12011yescharacteristic
492C2×C4C11×#12011yescharacteristic
493C2×C4C11×#12012yes—
494C2×C4C11×#13712yes—
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×#13711yescharacteristic
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×#300711yescharacteristic
527C2C11×#302211yescharacteristic
528C2C11×#302711yescharacteristic
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×#3218C2semidirect
3. C11×#2628C2semidirect
4. C11×#1606C2semidirect
5. C11×#1605C2semidirect
6. C11×#1604C2semidirect
7. C11×#1512C2semidirect
8. C11×#1464C2semidirect
113. #18367C11direct (N × H)
185. #3218C2×C11semidirect
186. #2628C2×C11semidirect
187. #1606C2×C11semidirect
188. #1605C2×C11semidirect
189. #1604C2×C11semidirect
190. #1512C2×C11semidirect
191. #1464C2×C11semidirect
447. C11#18367direct (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×#32182
C11×#26282
C11×#16062
C11×#16052
C11×#16042
C11×#15122
C11×#14642
#1836711