Finite Group Databasebeta

← C11×#18196 #14595389

Subgroups — C11×#18196 #14595389

Order 2816.

1370 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C2×C11×#450C212yesmaximal, complemented
3C11×#2408C211yesmaximal, characteristic
4C11×#1599C214yesmaximal, complemented
5C11×#1596C214yesmaximal, complemented
6C11×#1520C212yesmaximal, complemented
7C11×#1459C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×SD16—22no—
10C11×#554—24no—
11C11×#554—22no—
12D4×Q8×C11—22no—
13C11×#544C2212yescomplemented
14C11×#543—21no—
15C11×#543C2212yescomplemented
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C11×#120—21no—
21C11×#518—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#450—24no—
24C11×#450C2218yes—
25C2×C11×#102—22no—
26C2×C11×C22⋊C8C2212yes—
27C11×#394C2212yes—
28C11×#392C2212yes—
29C11×#390—21no—
30C11×#380C2211yescharacteristic
31C11×#379—21no—
32C11×#328C2218yescomplemented
33C11×#324C2212yescomplemented
34C11×#323C2212yescomplemented
35C25×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11D412yescomplemented
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—44no—
43C22×D4×C11D411yescharacteristic
44C22×D4×C11C2312yes—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C2×C11×SD16—28no—
48C2×C11×SD16—48no—
49C22×C8×C11—22no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—24no—
53C11×#125—22no—
54C11×#125—24no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8D414yescomplemented
66C11×C22⋊Q8C2314yes—
67C11×#121—44no—
68C11×#120—44no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D412yescomplemented
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4C2311yescharacteristic
90C2×C42×C11D411yescharacteristic
91C11×#102—28no—
92C11×C22⋊C8—22no—
93C11×C22⋊C8C2314yes—
94C11×#95C2312yes—
95#18196C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—22no—
97C24×C11—44no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—82no—
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—44no—
108C2×Q8×C11—82no—
109C2×Q8×C11C2×D414yes—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—28no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—42no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11—48no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—82no—
124C2×D4×C11SD1614yescomplemented
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2411yescharacteristic
141C11×SD16—416no—
142C2×C8×C11—24no—
143C2×C8×C11—44no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—82no—
165C42×C11—24no—
166C42×C11—21no—
167C42×C11—21no—
168#3501C2×C1111yescharacteristic, complemented
169C2×#450C2×C1112yescomplemented
170#2408C2×C1111yescharacteristic
171#1599C2×C1114yescomplemented
172#1596C2×C1114yescomplemented
173#1520C2×C1112yescomplemented
174#1459C2×C1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—24no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—48no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—84no—
190C23×C11—88no—
191C23×C11—88no—
192C23×C11—84no—
193C23×C11#12012yes—
194C23×C11C2×SD1612yes—
195C23×C11C2×SD1612yescomplemented
196C23×C11#13712yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—44no—
199Q8×C11—44no—
200Q8×C11—82no—
201Q8×C11—82no—
202D4×C11—28no—
203D4×C11—28no—
204D4×C11—44no—
205D4×C11—44no—
206D4×C11—44no—
207D4×C11—88no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—81no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11—82no—
228C2×C4×C11—82no—
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11C2×SD1612yescomplemented
232C2×C4×C11C22×D412yes—
233C8×C11—44no—
234C23×D4C22×C1111yescharacteristic
235C22×SD16—22no—
236#554—24no—
237#554—22no—
238D4×Q8—22no—
239#544C22×C1112yescomplemented
240#543—21no—
241#543C22×C1112yescomplemented
242#533—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C22×C1112yes—
245C2×#121—21no—
246C2×#120—21no—
247#518—21no—
248C2×C4×D4C22×C1111yescharacteristic
249#450—24no—
250#450C22×C1118yes—
251C2×#102—22no—
252C2×C22⋊C8C22×C1112yes—
253#394C22×C1112yes—
254#392C22×C1112yes—
255#390—21no—
256#380C22×C1111yescharacteristic
257#379—21no—
258#328C22×C1118yescomplemented
259#324C22×C1112yescomplemented
260#323C22×C1112yescomplemented
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—21no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—44no—
274C22×C11—81no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—816no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11#44814yes—
281C22×C11C2×#12011yescharacteristic
282C22×C11C22×SD1611yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C4×C11—22no—
285C4×C11—21no—
286C4×C11—22no—
287C4×C11—41no—
288C4×C11—44no—
289C4×C11—41no—
290C4×C11—44no—
291C4×C11—82no—
292C4×C11B(4,𝔽2)12yes—
293C25—21no—
294C22×Q8—21no—
295C22×Q8D4×C1112yescomplemented
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—22no—
300C22×D4—44no—
301C22×D4D4×C1111yescharacteristic
302C22×D4C23×C1112yes—
303C23×C4D4×C1111yescharacteristic
304C23×C4C23×C1111yescharacteristic
305C2×SD16—28no—
306C2×SD16—48no—
307C22×C8—22no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—24no—
311#125—22no—
312#125—24no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8D4×C1114yescomplemented
324C22⋊Q8C23×C1114yes—
325#121—44no—
326#120—44no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4—22no—
333#117—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4D4×C1112yescomplemented
339C2×C4⋊C4C23×C1111yescharacteristic
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4D4×C1111yescharacteristic
347C2×C22⋊C4C23×C1111yescharacteristic
348C2×C42D4×C1111yescharacteristic
349#102—28no—
350C22⋊C8—22no—
351C22⋊C8C23×C1114yes—
352#95C23×C1112yes—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—24no—
356C2×C11—42no—
357C2×C11—84no—
358C2×C11C2×#44811yescharacteristic
359C2×C11#302111yescharacteristic
360C2×C11C2×B(4,𝔽2)11yescharacteristic
361C24—22no—
362C24—44no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24—82no—
367C24C2×D4×C1111yescharacteristic
368C24C2×D4×C1111yescharacteristic
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—44no—
373C2×Q8—82no—
374C2×Q8C2×D4×C1114yes—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—28no—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—42no—
381C2×D4—44no—
382C2×D4—44no—
383C2×D4—48no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—82no—
389C2×D4C11×SD1614yescomplemented
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1112yes—
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1112yes—
405C22×C4C24×C1111yescharacteristic
406SD16—416no—
407C2×C8—24no—
408C2×C8—44no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4C2×D4×C1114yes—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—44no—
427C22⋊C4—42no—
428C22⋊C4—44no—
429C22⋊C4—82no—
430C42—24no—
431C42—21no—
432C42—21no—
433C11#1819611yescharacteristic, direct product factor, Sylow
434C23—21no—
435C23—21no—
436C23—24no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—42no—
442C23—48no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—84no—
449C23—88no—
450C23—88no—
451C23—84no—
452C23C11×#12012yes—
453C23C2×C11×SD1612yes—
454C23C2×C11×SD1612yescomplemented
455C23C11×#13712yes—
456C23C22×D4×C1111yescharacteristic
457Q8—44no—
458Q8—44no—
459Q8—82no—
460Q8—82no—
461D4—28no—
462D4—28no—
463D4—44no—
464D4—44no—
465D4—44no—
466D4—88no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—81no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4C11×#12011yescharacteristic
489C2×C4C11×#12011yescharacteristic
490C2×C4C2×C11×SD1612yescomplemented
491C2×C4C22×D4×C1112yes—
492C8—44no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—44no—
502C22—44no—
503C22—41no—
504C22—41no—
505C22—44no—
506C22—81no—
507C22—82no—
508C22—82no—
509C22—816no—
510C22—82no—
511C22—82no—
512C22C11×#44814yes—
513C22C2×C11×#12011yescharacteristic
514C22C22×C11×SD1611yescharacteristic
515C22C2×C11×#13711yescharacteristic
516C4—22no—
517C4—22no—
518C4—21no—
519C4—41no—
520C4—44no—
521C4—41no—
522C4—44no—
523C4—82no—
524C4C11×B(4,𝔽2)12yes—
525C2—21no—
526C2—21no—
527C2—24no—
528C2—42no—
529C2—84no—
530C2C2×C11×#44811yescharacteristic
531C2C11×#302111yescharacteristic
532C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2408C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3501C2semidirect
2. C2×C11×#450C2semidirect
4. C11×#1599C2semidirect
5. C11×#1596C2semidirect
6. C11×#1520C2semidirect
7. C11×#1459C2semidirect
13. C11×#544C22semidirect
15. C11×#543C22semidirect
32. C11×#328C22semidirect
33. C11×#324C22semidirect
34. C11×#323C22semidirect
37. C22×Q8×C11D4semidirect
65. C11×C22⋊Q8D4semidirect
80. C2×C11×C4⋊C4D4semidirect
95. #18196C11direct (N × H)
124. C2×D4×C11SD16semidirect
168. #3501C2×C11semidirect
169. C2×#450C2×C11semidirect
171. #1599C2×C11semidirect
172. #1596C2×C11semidirect
173. #1520C2×C11semidirect
174. #1459C2×C11semidirect
195. C23×C11C2×SD16semidirect
231. C2×C4×C11C2×SD16semidirect
239. #544C22×C11semidirect
241. #543C22×C11semidirect
258. #328C22×C11semidirect
259. #324C22×C11semidirect
260. #323C22×C11semidirect
295. C22×Q8D4×C11semidirect
323. C22⋊Q8D4×C11semidirect
338. C2×C4⋊C4D4×C11semidirect
389. C2×D4C11×SD16semidirect
433. C11#18196direct (N × H)
454. C23C2×C11×SD16semidirect
490. C2×C4C2×C11×SD16semidirect

Maximal subgroups

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

subgroupindex
C11×#35012
C2×C11×#4502
C11×#24082
C11×#15992
C11×#15962
C11×#15202
C11×#14592
#1819611