Finite Group Databasebeta

← C11×#18223 #14595416

Subgroups — C11×#18223 #14595416

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#3104C211yesmaximal, characteristic, complemented
3C11×#3103C211yesmaximal, characteristic, complemented
4C11×#2580C211yesmaximal, characteristic, complemented
5C11×#1618C214yesmaximal, complemented
6C11×#1606C214yesmaximal, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#1517C211yesmaximal, characteristic, complemented
9C11×#1460C211yesmaximal, 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×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#484C2212yes—
25C11×#481C2212yes—
26C11×#477—21no—
27C11×#475—21no—
28C11×#462—21no—
29C11×#460—21no—
30C11×#451C2212yes—
31C11×#448C2212yes—
32C4×C11×Q16—22no—
33C4×C11×SD16—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C11×#399C2212yes—
37C11×#393C2212yes—
38C11×#390—21no—
39C11×#389—21no—
40C11×#385—22no—
41C11×#382C2211yescharacteristic
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#323C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11D412yes—
50C2×C11×Q16—22no—
51C2×C11×SD16—22no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#127—22no—
56C11×#127D411yescharacteristic
57C11×#126—24no—
58C11×#125—21no—
59C11×#124—22no—
60C11×#124—24no—
61C11×#124—21no—
62C11×#123—24no—
63C11×#123—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2312yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—24no—
71C11×#121—21no—
72C11×#121C2312yes—
73C11×#120—24no—
74C4×Q8×C11—22no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×D4×C11—22no—
82C4×D4×C11—24no—
83C4×D4×C11—24no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D412yes—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—21no—
93C2×C11×C4⋊C4—22no—
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⋊C4—22no—
101C2×C11×C22⋊C4C2312yes—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C11×#107—22no—
105C11×#106—22no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×C22⋊C8C2312yes—
113C11×C22⋊C8C2312yes—
114C4×C8×C11—21no—
115C4×C8×C11—21no—
116C11×#95—21no—
117C11×#95—22no—
118C11×#95C2312yes—
119#18223C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11C2×D412yes—
121C11×#41—42no—
122C11×#41—42no—
123C11×#41—84no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—42no—
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—22no—
138C2×D4×C11—22no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C11×Q16—44no—
153C11×SD16—44no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—82no—
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—44no—
182C11×C22⋊C4—82no—
183C42×C11—24no—
184C42×C11—22no—
185C42×C11—41no—
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191#3506C2×C1111yescharacteristic
192#3104C2×C1111yescharacteristic, complemented
193#3103C2×C1111yescharacteristic, complemented
194#2580C2×C1111yescharacteristic, complemented
195#1618C2×C1114yescomplemented
196#1606C2×C1114yescomplemented
197#1518C2×C1111yescharacteristic, complemented
198#1517C2×C1111yescharacteristic, complemented
199#1460C2×C1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11C22×D411yescharacteristic
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—42no—
210Q8×C11—41no—
211Q8×C11—41no—
212Q8×C11—42no—
213Q8×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—84no—
222D4×C11—84no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—44no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—82no—
242C2×C4×C11—84no—
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#13512yes—
248C2×C4×C11#13712yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C8×C11—42no—
252C8×C11—42no—
253#559—22no—
254#556—21no—
255#555—21no—
256#553—22no—
257#550—21no—
258#547—21no—
259#538C22×C1114yes—
260#535—21no—
261#533C22×C1111yescharacteristic
262#532C22×C1111yescharacteristic
263#525—22no—
264#520—21no—
265C2×C4×Q8C22×C1111yescharacteristic
266C2×C4×D4C22×C1111yescharacteristic
267#484C22×C1112yes—
268#481C22×C1112yes—
269#477—21no—
270#475—21no—
271#462—21no—
272#460—21no—
273#451C22×C1112yes—
274#448C22×C1112yes—
275C4×Q16—22no—
276C4×SD16—22no—
277#431C22×C1111yescharacteristic
278#431C22×C1111yescharacteristic
279#399C22×C1112yes—
280#393C22×C1112yes—
281#390—21no—
282#389—21no—
283#385—22no—
284#382C22×C1111yescharacteristic
285#328C22×C1114yes—
286#327C22×C1114yes—
287#323C22×C1114yes—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—82no—
298C22×C11C2×#12011yescharacteristic
299C22×C11C2×#13511yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—82no—
311C4×C11—81no—
312C4×C11#45212yes—
313C4×C11#45212yes—
314C2×#41—22no—
315C2×#41—21no—
316C22×Q8C23×C1111yescharacteristic
317C22×D4D4×C1111yescharacteristic
318C23×C4D4×C1112yes—
319C2×Q16—22no—
320C2×SD16—22no—
321C4⋊Q8D4×C1111yescharacteristic
322C4⋊Q8D4×C1111yescharacteristic
323C4⋊Q8D4×C1111yescharacteristic
324#127—22no—
325#127D4×C1111yescharacteristic
326#126—24no—
327#125—21no—
328#124—22no—
329#124—24no—
330#124—21no—
331#123—24no—
332#123—24no—
333C22⋊Q8—22no—
334C22⋊Q8—21no—
335C22⋊Q8C23×C1112yes—
336#121—22no—
337#121—22no—
338#121—22no—
339#121—24no—
340#121—21no—
341#121C23×C1112yes—
342#120—24no—
343C4×Q8—22no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8D4×C1112yes—
350C4×D4—22no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4D4×C1112yes—
359#117—22no—
360#117—22no—
361#117—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4D4×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4C23×C1112yes—
371C2×C42—21no—
372C2×C42C23×C1111yescharacteristic
373#107—22no—
374#106—22no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377#103—22no—
378#103—22no—
379#103—22no—
380#102—22no—
381C22⋊C8C23×C1112yes—
382C22⋊C8C23×C1112yes—
383C4×C8—21no—
384C4×C8—21no—
385#95—21no—
386#95—22no—
387#95C23×C1112yes—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—82no—
391C2×C11—82no—
392C2×C11C2×#45211yescharacteristic
393C2×C11#301911yescharacteristic
394C2×C11#302511yescharacteristic
395C24C2×D4×C1112yes—
396#41—42no—
397#41—42no—
398#41—84no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—42no—
404C2×Q8C2×D4×C1112yes—
405C2×D4—22no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4C2×D4×C1112yes—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—82no—
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C24×C1111yescharacteristic
427Q16—44no—
428SD16—44no—
429C2×C8—22no—
430C2×C8—22no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—42no—
445C4⋊C4—82no—
446C4⋊C4C2×D4×C1112yes—
447C4⋊C4C2×D4×C1112yes—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—44no—
457C22⋊C4—82no—
458C42—24no—
459C42—22no—
460C42—41no—
461C42—41no—
462C42C2×D4×C1111yescharacteristic
463C42C2×D4×C1111yescharacteristic
464C42C2×D4×C1111yescharacteristic
465C42C2×D4×C1111yescharacteristic
466C11#1822311yescharacteristic, direct product factor, Sylow
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—42no—
472C23—42no—
473C23C22×D4×C1111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—42no—
477Q8—41no—
478Q8—41no—
479Q8—42no—
480Q8—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—84no—
489D4—84no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4—84no—
510C2×C4C11×#12011yescharacteristic
511C2×C4C11×#12011yescharacteristic
512C2×C4C11×#12011yescharacteristic
513C2×C4C11×#12011yescharacteristic
514C2×C4C11×#13512yes—
515C2×C4C11×#13712yes—
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C22×D4×C1111yescharacteristic
518C8—42no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—44no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22C2×C11×#12011yescharacteristic
531C22C2×C11×#13511yescharacteristic
532C22C2×C11×#13711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—81no—
544C4C11×#45212yes—
545C4C11×#45212yes—
546C2—21no—
547C2—21no—
548C2—82no—
549C2—82no—
550C2C2×C11×#45211yescharacteristic
551C2C11×#301911yescharacteristic
552C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3506C2
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×#3104C2semidirect
3. C11×#3103C2semidirect
4. C11×#2580C2semidirect
5. C11×#1618C2semidirect
6. C11×#1606C2semidirect
7. C11×#1518C2semidirect
8. C11×#1517C2semidirect
9. C11×#1460C2semidirect
119. #18223C11direct (N × H)
192. #3104C2×C11semidirect
193. #3103C2×C11semidirect
194. #2580C2×C11semidirect
195. #1618C2×C11semidirect
196. #1606C2×C11semidirect
197. #1518C2×C11semidirect
198. #1517C2×C11semidirect
199. #1460C2×C11semidirect
466. C11#18223direct (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×#31042
C11×#31032
C11×#25802
C11×#16182
C11×#16062
C11×#15182
C11×#15172
C11×#14602
#1822311