Finite Group Databasebeta

← C11×#18190 #14595383

Subgroups — C11×#18190 #14595383

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic, complemented
2C11×#3110C211yesmaximal, characteristic, complemented
3C11×#3109C211yesmaximal, characteristic, complemented
4C11×#2397C211yesmaximal, characteristic, complemented
5C11×#1618C214yesmaximal, complemented
6C11×#1600C214yesmaximal, complemented
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#1505C211yesmaximal, characteristic, complemented
9C11×#1466C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538C2214yes—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525—22no—
21C11×#520—21no—
22C2×C4×D4×C11—22no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#484C2212yes—
26C11×#481C2212yes—
27C11×#476—21no—
28C11×#474—21no—
29C11×#461—21no—
30C11×#459—21no—
31C11×#450C2212yes—
32C11×#447C2212yes—
33C11×#442—22no—
34C11×#440—22no—
35C11×#432C2211yescharacteristic
36C11×#432C2211yescharacteristic
37C11×#399—21no—
38C11×#399C2212yes—
39C11×#392—21no—
40C11×#392C2212yes—
41C11×#376C2211yescharacteristic
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#323C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D412yes—
52C2×C11×SD16—22no—
53C2×C11×D8—22no—
54C11×C4⋊Q8D411yescharacteristic, complemented
55C11×C4⋊Q8D411yescharacteristic, complemented
56C11×C4⋊Q8D411yescharacteristic, complemented
57C11×#127—22no—
58C11×#127D411yescharacteristic, complemented
59C11×#126—24no—
60C11×#125—21no—
61C11×#124—22no—
62C11×#124—24no—
63C11×#124—21no—
64C11×#123—24no—
65C11×#123—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8C2312yes—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—21no—
74C11×#121C2312yes—
75C11×#120—24no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11D412yescomplemented
79C4×D4×C11—22no—
80C4×D4×C11—24no—
81C4×D4×C11—24no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—48no—
92C4×D4×C11D412yescomplemented
93C11×#117—22no—
94C11×#117—22no—
95C11×#117—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4C2312yes—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C11×#107—22no—
107C11×#106—22no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×C22⋊C8C2312yes—
115C11×C22⋊C8C2312yes—
116C11×#97—21no—
117C11×#97—21no—
118C11×#95—21no—
119C11×#95C2312yes—
120#18190C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11C2×D412yes—
123C11×#41—44no—
124C11×#41—84no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—44no—
139C2×D4×C11—42no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C11×SD16—44no—
158C11×D8—44no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—44no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—44no—
184C11×C22⋊C4—44no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C42×C11—24no—
188C42×C11—24no—
189C42×C11—22no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194#3506C2×C1111yescharacteristic, complemented
195#3110C2×C1111yescharacteristic, complemented
196#3109C2×C1111yescharacteristic, complemented
197#2397C2×C1111yescharacteristic, complemented
198#1618C2×C1114yescomplemented
199#1600C2×C1114yescomplemented
200#1506C2×C1111yescharacteristic, complemented
201#1505C2×C1111yescharacteristic, complemented
202#1466C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11C22×D411yescharacteristic
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—42no—
226D4×C11—416no—
227D4×C11—44no—
228D4×C11—42no—
229D4×C11—84no—
230D4×C11—84no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11—84no—
249C2×C4×C11—82no—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C8×C11—42no—
257C8×C11—42no—
258#559—22no—
259#556—21no—
260#555—21no—
261#553—22no—
262#550—21no—
263#547—21no—
264#538C22×C1114yes—
265#535—21no—
266#533C22×C1111yescharacteristic
267#532C22×C1111yescharacteristic
268#525—22no—
269#520—21no—
270C2×C4×D4—22no—
271C2×C4×D4C22×C1111yescharacteristic
272C2×C4×D4C22×C1111yescharacteristic
273#484C22×C1112yes—
274#481C22×C1112yes—
275#476—21no—
276#474—21no—
277#461—21no—
278#459—21no—
279#450C22×C1112yes—
280#447C22×C1112yes—
281#442—22no—
282#440—22no—
283#432C22×C1111yescharacteristic
284#432C22×C1111yescharacteristic
285#399—21no—
286#399C22×C1112yes—
287#392—21no—
288#392C22×C1112yes—
289#376C22×C1111yescharacteristic
290#328C22×C1114yes—
291#327C22×C1114yes—
292#323C22×C1114yes—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11C2×#12011yescharacteristic
309C22×C11#57512yes—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—44no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—81no—
321C4×C11#45312yes—
322C2×#41—22no—
323C2×#41—21no—
324C22×D4—22no—
325C22×D4D4×C1111yescharacteristic
326C22×D4C23×C1111yescharacteristic
327C23×C4—21no—
328C23×C4D4×C1112yes—
329C2×SD16—22no—
330C2×D8—22no—
331C4⋊Q8D4×C1111yescharacteristic, complemented
332C4⋊Q8D4×C1111yescharacteristic, complemented
333C4⋊Q8D4×C1111yescharacteristic, complemented
334#127—22no—
335#127D4×C1111yescharacteristic, complemented
336#126—24no—
337#125—21no—
338#124—22no—
339#124—24no—
340#124—21no—
341#123—24no—
342#123—24no—
343C22⋊Q8—22no—
344C22⋊Q8—21no—
345C22⋊Q8C23×C1112yes—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—24no—
350#121—21no—
351#121C23×C1112yes—
352#120—24no—
353C4×Q8—22no—
354C4×Q8—21no—
355C4×Q8D4×C1112yescomplemented
356C4×D4—22no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—48no—
369C4×D4D4×C1112yescomplemented
370#117—22no—
371#117—22no—
372#117—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4D4×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4C23×C1112yes—
381C2×C42—21no—
382C2×C42C23×C1111yescharacteristic
383#107—22no—
384#106—22no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387#103—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391C22⋊C8C23×C1112yes—
392C22⋊C8C23×C1112yes—
393#97—21no—
394#97—21no—
395#95—21no—
396#95C23×C1112yes—
397C2×C11—22no—
398C2×C11—82no—
399C2×C11—82no—
400C2×C11—82no—
401C2×C11#300511yescharacteristic
402C2×C11C2×#45311yescharacteristic
403C2×C11#302511yescharacteristic
404C24—21no—
405C24C2×D4×C1112yes—
406#41—44no—
407#41—84no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C2×D4×C1112yes—
411C2×D4—22no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—42no—
421C2×D4—44no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4C2×D4×C1112yes—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1112yes—
439C22×C4C24×C1111yescharacteristic
440SD16—44no—
441D8—44no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—44no—
456C4⋊C4C2×D4×C1112yes—
457C4⋊C4C2×D4×C1112yes—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—24no—
471C42—24no—
472C42—22no—
473C42C2×D4×C1111yescharacteristic
474C42C2×D4×C1111yescharacteristic
475C42C2×D4×C1111yescharacteristic
476C42C2×D4×C1111yescharacteristic
477C11#1819011yescharacteristic, direct product factor, Sylow
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23C22×D4×C1111yescharacteristic
490Q8—42no—
491Q8—42no—
492Q8—42no—
493D4—22no—
494D4—22no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—416no—
502D4—44no—
503D4—42no—
504D4—84no—
505D4—84no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—84no—
524C2×C4—82no—
525C2×C4C11×#12011yescharacteristic
526C2×C4C11×#12011yescharacteristic
527C2×C4C11×#12011yescharacteristic
528C2×C4C11×#12011yescharacteristic
529C2×C4C22×D4×C1111yescharacteristic
530C2×C4C22×D4×C1111yescharacteristic
531C8—42no—
532C8—42no—
533C22—21no—
534C22—21no—
535C22—44no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22—81no—
547C22—81no—
548C22C2×C11×#12011yescharacteristic
549C22C11×#57512yes—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—81no—
561C4C11×#45312yes—
562C2—22no—
563C2—82no—
564C2—82no—
565C2—82no—
566C2C11×#300511yescharacteristic
567C2C2×C11×#45311yescharacteristic
568C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3506C2semidirect
2. C11×#3110C2semidirect
3. C11×#3109C2semidirect
4. C11×#2397C2semidirect
5. C11×#1618C2semidirect
6. C11×#1600C2semidirect
7. C11×#1506C2semidirect
8. C11×#1505C2semidirect
9. C11×#1466C2semidirect
54. C11×C4⋊Q8D4semidirect
55. C11×C4⋊Q8D4semidirect
56. C11×C4⋊Q8D4semidirect
58. C11×#127D4semidirect
78. C4×Q8×C11D4semidirect
92. C4×D4×C11D4semidirect
120. #18190C11direct (N × H)
194. #3506C2×C11semidirect
195. #3110C2×C11semidirect
196. #3109C2×C11semidirect
197. #2397C2×C11semidirect
198. #1618C2×C11semidirect
199. #1600C2×C11semidirect
200. #1506C2×C11semidirect
201. #1505C2×C11semidirect
202. #1466C2×C11semidirect
331. C4⋊Q8D4×C11semidirect
332. C4⋊Q8D4×C11semidirect
333. C4⋊Q8D4×C11semidirect
335. #127D4×C11semidirect
355. C4×Q8D4×C11semidirect
369. C4×D4D4×C11semidirect
477. C11#18190direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#31102
C11×#31092
C11×#23972
C11×#16182
C11×#16002
C11×#15062
C11×#15052
C11×#14662
#1819011