Finite Group Databasebeta

← C11×#18372 #14595565

Subgroups — C11×#18372 #14595565

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic
2C11×#3239C212yesmaximal, complemented
3C11×#2628C211yesmaximal, characteristic, complemented
4C11×#1618C214yesmaximal, complemented
5C11×#1617C212yesmaximal, complemented
6C11×#1616C212yesmaximal, 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×#501—22no—
24C11×#489—22no—
25C11×#484C2214yes—
26C11×#481C2214yes—
27C11×#475—22no—
28C11×#474—22no—
29C11×#432C2212yes—
30C11×#400C2212yes—
31C11×#399C2212yes—
32C11×#395—21no—
33C11×#393—21no—
34C11×#389—21no—
35C11×#382C2211yescharacteristic
36C11×#380—21no—
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⋊Q8C2312yes—
66C11×#121—21no—
67C11×#121—21no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—21no—
72C11×#121C2312yes—
73C11×#120—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—21no—
76C4×Q8×C11D412yes—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—21no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11D412yes—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—21no—
87C11×#117—22no—
88C11×#117—22no—
89C11×#117—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C11×C22⋊C4C2311yescharacteristic
100C2×C42×C11D411yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107—24no—
103C11×#106—24no—
104C11×C4⋊C8—22no—
105C11×#103—24no—
106C11×#102—24no—
107C11×C22⋊C8C2314yes—
108C11×#97—22no—
109C11×#95—22no—
110C11×#95—21no—
111C11×#95—22no—
112C11×#95C2312yes—
113#18372C1111yesmaximal, 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—42no—
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
143C2×C8×C11—24no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—82no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
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—82no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—22no—
180C42×C11C2×D412yes—
181C42×C11C2×D412yes—
182#3493C2×C1111yescharacteristic
183#3239C2×C1112yescomplemented
184#2628C2×C1111yescharacteristic, complemented
185#1618C2×C1114yescomplemented
186#1617C2×C1112yescomplemented
187#1616C2×C1112yescomplemented
188#1512C2×C1112yescomplemented
189#1464C2×C1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C22×D411yescharacteristic
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—84no—
200Q8×C11—81no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—82no—
206D4×C11—81no—
207D4×C11—82no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—82no—
231C2×C4×C11—82no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12012yes—
235C2×C4×C11#13712yes—
236C2×C4×C11C22×D412yes—
237C8×C11—44no—
238#556—22no—
239#555—22no—
240#553—22no—
241#552—22no—
242#544C22×C1111yescharacteristic
243#538—21no—
244#538C22×C1112yes—
245#537C22×C1111yescharacteristic
246C2×C4⋊Q8C22×C1111yescharacteristic
247#529—21no—
248#529C22×C1112yes—
249#525—21no—
250#520—21no—
251C2×#117C22×C1111yescharacteristic
252#501—22no—
253#489—22no—
254#484C22×C1114yes—
255#481C22×C1114yes—
256#475—22no—
257#474—22no—
258#432C22×C1112yes—
259#400C22×C1112yes—
260#399C22×C1112yes—
261#395—21no—
262#393—21no—
263#389—21no—
264#382C22×C1111yescharacteristic
265#380—21no—
266#328C22×C1114yes—
267#327C22×C1114yes—
268#324C22×C1112yes—
269#323C22×C1112yes—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—42no—
273C22×C11—41no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—41no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—81no—
280C22×C11C2×#12011yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11#57511yescharacteristic
283C4×C11—22no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—42no—
289C4×C11—41no—
290C4×C11—42no—
291C4×C11—41no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11—82no—
295C2×#41—21no—
296C22×Q8—21no—
297C23×C4D4×C1111yescharacteristic
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301#126—22no—
302#126—22no—
303#126—22no—
304#126—22no—
305#125—21no—
306#125—22no—
307#125D4×C1112yes—
308#124—21no—
309#124—22no—
310#124—22no—
311#124D4×C1112yes—
312#123—22no—
313#123—22no—
314#123—22no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—22no—
319C22⋊Q8C23×C1112yes—
320#121—21no—
321#121—21no—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—21no—
326#121C23×C1112yes—
327#120—22no—
328C4×Q8—22no—
329C4×Q8—21no—
330C4×Q8D4×C1112yes—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—21no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4D4×C1112yes—
338#117—22no—
339#117—22no—
340#117—21no—
341#117—22no—
342#117—22no—
343#117—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C22⋊C4—22no—
352C2×C22⋊C4D4×C1111yescharacteristic
353C2×C22⋊C4C23×C1111yescharacteristic
354C2×C42D4×C1111yescharacteristic
355C2×C42C23×C1111yescharacteristic
356#107—24no—
357#106—24no—
358C4⋊C8—22no—
359#103—24no—
360#102—24no—
361C22⋊C8C23×C1114yes—
362#97—22no—
363#95—22no—
364#95—21no—
365#95—22no—
366#95C23×C1112yes—
367C2×C11—21no—
368C2×C11—21no—
369C2×C11—82no—
370C2×C11—81no—
371C2×C11#300711yescharacteristic
372C2×C11#302111yescharacteristic
373C2×C11#302811yescharacteristic
374C24C2×D4×C1111yescharacteristic
375#41—42no—
376#41—42no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—82no—
381C2×Q8C2×D4×C1112yes—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4C2×D4×C1112yes—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C24×C1111yescharacteristic
403C2×C8—24no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—24no—
417C4⋊C4—42no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—82no—
421C4⋊C4C2×D4×C1112yes—
422C4⋊C4C2×D4×C1112yes—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—82no—
435C42—22no—
436C42—22no—
437C42—21no—
438C42—21no—
439C42—22no—
440C42C2×D4×C1112yes—
441C42C2×D4×C1112yes—
442C11#1837211yescharacteristic, direct product factor, Sylow
443C23—21no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23C22×D4×C1111yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—84no—
453Q8—81no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—81no—
460D4—82no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4C11×#12011yescharacteristic
486C2×C4C11×#12011yescharacteristic
487C2×C4C11×#12012yes—
488C2×C4C11×#13712yes—
489C2×C4C22×D4×C1112yes—
490C8—44no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—81no—
501C22C2×C11×#12011yescharacteristic
502C22C2×C11×#13711yescharacteristic
503C22C11×#57511yescharacteristic
504C4—22no—
505C4—21no—
506C4—21no—
507C4—22no—
508C4—22no—
509C4—42no—
510C4—41no—
511C4—42no—
512C4—41no—
513C4—42no—
514C4—82no—
515C4—82no—
516C2—21no—
517C2—21no—
518C2—81no—
519C2—82no—
520C2C11×#300711yescharacteristic
521C2C11×#302111yescharacteristic
522C2C11×#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×#3239C2semidirect
3. C11×#2628C2semidirect
4. C11×#1618C2semidirect
5. C11×#1617C2semidirect
6. C11×#1616C2semidirect
7. C11×#1512C2semidirect
8. C11×#1464C2semidirect
113. #18372C11direct (N × H)
183. #3239C2×C11semidirect
184. #2628C2×C11semidirect
185. #1618C2×C11semidirect
186. #1617C2×C11semidirect
187. #1616C2×C11semidirect
188. #1512C2×C11semidirect
189. #1464C2×C11semidirect
442. C11#18372direct (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×#32392
C11×#26282
C11×#16182
C11×#16172
C11×#16162
C11×#15122
C11×#14642
#1837211