Finite Group Databasebeta

← C11×#18370 #14595563

Subgroups — C11×#18370 #14595563

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic, complemented
2C11×#3215C211yesmaximal, characteristic, complemented
3C11×#3213C211yesmaximal, characteristic, complemented
4C11×#2631C211yesmaximal, characteristic, complemented
5C11×#1606C214yesmaximal, complemented
6C11×#1600C214yesmaximal, complemented
7C11×#1515C211yesmaximal, characteristic, complemented
8C11×#1514C211yesmaximal, 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
20C2×C11×#124C2211yescharacteristic
21C11×#525—22no—
22C11×#520—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#497—21no—
25C11×#496—21no—
26C11×#489—21no—
27C11×#489—21no—
28C11×#464—22no—
29C11×#463—22no—
30C11×#451C2212yes—
31C11×#450C2212yes—
32C11×#448C2212yes—
33C11×#447C2212yes—
34C11×#432C2211yescharacteristic
35C11×#432C2211yescharacteristic
36C11×#397—21no—
37C11×#393C2212yes—
38C11×#392—21no—
39C11×#392C2212yes—
40C11×#386—22no—
41C11×#383C2211yescharacteristic
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#323C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—22no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11D412yes—
52C2×C11×Q16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×D8—22no—
56C11×C4⋊Q8D411yescharacteristic, complemented
57C11×C4⋊Q8D411yescharacteristic, complemented
58C11×C4⋊Q8D411yescharacteristic, complemented
59C11×#127—22no—
60C11×#127D411yescharacteristic, complemented
61C11×#126—24no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—24no—
65C11×#124—21no—
66C11×#124—21no—
67C11×#124—21no—
68C11×#124—21no—
69C11×#124—21no—
70C11×#123—24no—
71C11×#123—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8C2312yes—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—24no—
79C11×#121—21no—
80C11×#121C2312yes—
81C11×#120—24no—
82C4×Q8×C11—22no—
83C4×Q8×C11—21no—
84C4×Q8×C11D412yescomplemented
85C4×D4×C11—22no—
86C4×D4×C11—24no—
87C4×D4×C11—24no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11D412yescomplemented
94C11×#117—22no—
95C11×#117—22no—
96C11×#117—21no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4C2312yes—
104C2×C42×C11C2311yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×C22⋊C8C2312yes—
112C11×C22⋊C8C2312yes—
113C11×#97—21no—
114C11×#97—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—22no—
118C11×#95C2312yes—
119#18370C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11C2×D412yes—
122C11×#41—44no—
123C11×#41—84no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—81no—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—42no—
140C2×D4×C11—44no—
141C2×D4×C11—81no—
142C2×D4×C11—82no—
143C2×D4×C11—82no—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—82no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C11×Q16—82no—
157C11×SD16—82no—
158C11×SD16—82no—
159C11×D8—82no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—82no—
186C11×C22⋊C4—82no—
187C42×C11—24no—
188C42×C11—22no—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193#3506C2×C1111yescharacteristic, complemented
194#3215C2×C1111yescharacteristic, complemented
195#3213C2×C1111yescharacteristic, complemented
196#2631C2×C1111yescharacteristic, complemented
197#1606C2×C1114yescomplemented
198#1600C2×C1114yescomplemented
199#1515C2×C1111yescharacteristic, complemented
200#1514C2×C1111yescharacteristic, complemented
201#1466C2×C1111yescharacteristic, complemented
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11C22×D411yescharacteristic
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—44no—
227D4×C11—84no—
228D4×C11—84no—
229D4×C11—88no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—82no—
246C2×C4×C11—84no—
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C8×C11—42no—
254C8×C11—42no—
255#559—22no—
256#556—21no—
257#555—21no—
258#553—22no—
259#550—21no—
260#547—21no—
261#538C22×C1114yes—
262#535—21no—
263#533C22×C1111yescharacteristic
264#532C22×C1111yescharacteristic
265C2×#124C22×C1111yescharacteristic
266#525—22no—
267#520—21no—
268C2×C4×D4C22×C1111yescharacteristic
269#497—21no—
270#496—21no—
271#489—21no—
272#489—21no—
273#464—22no—
274#463—22no—
275#451C22×C1112yes—
276#450C22×C1112yes—
277#448C22×C1112yes—
278#447C22×C1112yes—
279#432C22×C1111yescharacteristic
280#432C22×C1111yescharacteristic
281#397—21no—
282#393C22×C1112yes—
283#392—21no—
284#392C22×C1112yes—
285#386—22no—
286#383C22×C1111yescharacteristic
287#328C22×C1114yes—
288#327C22×C1114yes—
289#323C22×C1114yes—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11C2×#12011yescharacteristic
306C22×C11#57512yes—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11—81no—
319C2×#41—22no—
320C2×#41—21no—
321C22×Q8C23×C1111yescharacteristic
322C22×D4—22no—
323C22×D4D4×C1111yescharacteristic
324C22×D4C23×C1111yescharacteristic
325C23×C4D4×C1112yes—
326C2×Q16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C2×D8—22no—
330C4⋊Q8D4×C1111yescharacteristic, complemented
331C4⋊Q8D4×C1111yescharacteristic, complemented
332C4⋊Q8D4×C1111yescharacteristic, complemented
333#127—22no—
334#127D4×C1111yescharacteristic, complemented
335#126—24no—
336#125—21no—
337#124—22no—
338#124—24no—
339#124—21no—
340#124—21no—
341#124—21no—
342#124—21no—
343#124—21no—
344#123—24no—
345#123—24no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8C23×C1112yes—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—24no—
353#121—21no—
354#121C23×C1112yes—
355#120—24no—
356C4×Q8—22no—
357C4×Q8—21no—
358C4×Q8D4×C1112yescomplemented
359C4×D4—22no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4D4×C1112yescomplemented
368#117—22no—
369#117—22no—
370#117—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4D4×C1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4C23×C1112yes—
378C2×C42C23×C1111yescharacteristic
379C4⋊C8—21no—
380C4⋊C8—21no—
381#103—22no—
382#103—22no—
383#102—22no—
384#102—22no—
385C22⋊C8C23×C1112yes—
386C22⋊C8C23×C1112yes—
387#97—21no—
388#97—21no—
389#95—21no—
390#95—21no—
391#95—22no—
392#95C23×C1112yes—
393C2×C11—22no—
394C2×C11—82no—
395C2×C11—82no—
396C2×C11—161no—
397C2×C11#300511yescharacteristic
398C2×C11#301911yescharacteristic
399C2×C11#302711yescharacteristic
400C24—21no—
401C24C2×D4×C1112yes—
402#41—44no—
403#41—84no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—81no—
409C2×Q8C2×D4×C1112yes—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—81no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C2×D4×C1112yes—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—82no—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1112yes—
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C24×C1111yescharacteristic
436Q16—82no—
437SD16—82no—
438SD16—82no—
439D8—82no—
440C2×C8—22no—
441C2×C8—22no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4C2×D4×C1112yes—
452C4⋊C4C2×D4×C1112yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—82no—
466C22⋊C4—82no—
467C42—24no—
468C42—22no—
469C42C2×D4×C1111yescharacteristic
470C42C2×D4×C1111yescharacteristic
471C42C2×D4×C1111yescharacteristic
472C42C2×D4×C1111yescharacteristic
473C11#1837011yescharacteristic, direct product factor, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—42no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—41no—
484C23—42no—
485C23C22×D4×C1111yescharacteristic
486Q8—42no—
487Q8—42no—
488Q8—42no—
489Q8—42no—
490Q8—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—84no—
500D4—84no—
501D4—88no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4C11×#12011yescharacteristic
520C2×C4C11×#12011yescharacteristic
521C2×C4C11×#12011yescharacteristic
522C2×C4C11×#12011yescharacteristic
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C8—42no—
526C8—42no—
527C22—21no—
528C22—21no—
529C22—44no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22C2×C11×#12011yescharacteristic
543C22C11×#57512yes—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—42no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—81no—
556C2—22no—
557C2—82no—
558C2—82no—
559C2—161no—
560C2C11×#300511yescharacteristic
561C2C11×#301911yescharacteristic
562C2C11×#302711yescharacteristic
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×#3215C2semidirect
3. C11×#3213C2semidirect
4. C11×#2631C2semidirect
5. C11×#1606C2semidirect
6. C11×#1600C2semidirect
7. C11×#1515C2semidirect
8. C11×#1514C2semidirect
9. C11×#1466C2semidirect
56. C11×C4⋊Q8D4semidirect
57. C11×C4⋊Q8D4semidirect
58. C11×C4⋊Q8D4semidirect
60. C11×#127D4semidirect
84. C4×Q8×C11D4semidirect
93. C4×D4×C11D4semidirect
119. #18370C11direct (N × H)
193. #3506C2×C11semidirect
194. #3215C2×C11semidirect
195. #3213C2×C11semidirect
196. #2631C2×C11semidirect
197. #1606C2×C11semidirect
198. #1600C2×C11semidirect
199. #1515C2×C11semidirect
200. #1514C2×C11semidirect
201. #1466C2×C11semidirect
330. C4⋊Q8D4×C11semidirect
331. C4⋊Q8D4×C11semidirect
332. C4⋊Q8D4×C11semidirect
334. #127D4×C11semidirect
358. C4×Q8D4×C11semidirect
367. C4×D4D4×C11semidirect
473. C11#18370direct (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×#32152
C11×#32132
C11×#26312
C11×#16062
C11×#16002
C11×#15152
C11×#15142
C11×#14662
#1837011