Finite Group Databasebeta

← C11×#18898 #14596091

Subgroups — C11×#18898 #14596091

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic
4C2×C11×#460C211yesmaximal, characteristic, complemented
5C11×#1628C214yesmaximal, complemented
6C11×#1622C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C11×#559—21no—
12C11×#557—21no—
13C11×#556—22no—
14C11×#556C2212yescomplemented
15C11×#554C2212yescomplemented
16C11×#552—22no—
17C11×#539—22no—
18C11×#536—21no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#493—21no—
26C11×#492C2212yes—
27C11×#486—21no—
28C11×#486C2212yes—
29C11×#460—22no—
30C11×#460—22no—
31C11×#460C2214yes—
32C11×#459C2214yes—
33C11×#450—22no—
34C11×#447—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#333C2212yescomplemented
40C11×#332C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C2×C11×#41—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—44no—
51C2×C11×D8—24no—
52C22×C8×C11—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127D411yescharacteristic
61C11×#127C2312yes—
62C11×#126—24no—
63C11×#126—24no—
64C11×#125—24no—
65C11×#125—22no—
66C11×#125—21no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124—21no—
70C11×#123—24no—
71C11×#123—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8D412yes—
77C11×#121—21no—
78C11×#121D412yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11D412yes—
85C4×Q8×C11D412yes—
86C4×Q8×C11C2312yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11C2312yes—
92C11×#117—24no—
93C11×#117—21no—
94C11×#117—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18898C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—41no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—82no—
134C2×D4×C11—82no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C11×SD16—48no—
144C11×SD16—84no—
145C11×D8—84no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2411yescharacteristic
179#3507C2×C1111yescharacteristic, complemented
180#3208C2×C1111yescharacteristic, complemented
181#3205C2×C1111yescharacteristic
182C2×#460C2×C1111yescharacteristic, complemented
183#1628C2×C1114yescomplemented
184#1622C2×C1114yescomplemented
185#1542C2×C1111yescharacteristic, complemented
186#1480C2×C1111yescharacteristic, complemented
187#1479C2×C1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—42no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11#12011yescharacteristic
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—42no—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—42no—
200D4×C11—24no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—44no—
206D4×C11—42no—
207D4×C11—81no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11—82no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—81no—
222C2×C4×C11—84no—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#13512yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C8×C11—42no—
232C8×C11—42no—
233C8×C11—42no—
234C22×SD16—21no—
235#559—21no—
236#557—21no—
237#556—22no—
238#556C22×C1112yescomplemented
239#554C22×C1112yescomplemented
240#552—22no—
241#539—22no—
242#536—21no—
243#533C22×C1111yescharacteristic
244#532C22×C1111yescharacteristic
245C2×#127C22×C1111yescharacteristic
246#529—22no—
247#520—21no—
248C2×C4×Q8C22×C1111yescharacteristic
249#493—21no—
250#492C22×C1112yes—
251#486—21no—
252#486C22×C1112yes—
253#460—22no—
254#460—22no—
255#460C22×C1114yes—
256#459C22×C1114yes—
257#450—22no—
258#447—22no—
259#431C22×C1111yescharacteristic
260#431C22×C1111yescharacteristic
261C2×C4⋊C8C22×C1111yescharacteristic
262C2×#102—21no—
263#333C22×C1112yescomplemented
264#332C22×C1112yescomplemented
265Q8⋊C8C22×C1114yescomplemented
266D4⋊C8C22×C1114yescomplemented
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—164no—
276C22×C11#44912yes—
277C22×C11C2×#12011yescharacteristic
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11#44912yes—
287C4×C11C2×#13511yescharacteristic
288C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C11#57712yes—
290C2×#41—21no—
291C22×Q8D4×C1111yescharacteristic
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C2×SD16—24no—
296C2×SD16—24no—
297C2×SD16—44no—
298C2×D8—24no—
299C22×C8—21no—
300C4⋊Q8—22no—
301C4⋊Q8D4×C1111yescharacteristic
302C4⋊Q8C23×C1111yescharacteristic
303C4⋊Q8C23×C1111yescharacteristic
304#127—21no—
305#127—21no—
306#127—21no—
307#127D4×C1111yescharacteristic
308#127C23×C1112yes—
309#126—24no—
310#126—24no—
311#125—24no—
312#125—22no—
313#125—21no—
314#124—22no—
315#124—22no—
316#124—21no—
317#123—24no—
318#123—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—21no—
323C22⋊Q8D4×C1112yes—
324#121—21no—
325#121D4×C1112yes—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8D4×C1112yes—
332C4×Q8D4×C1112yes—
333C4×Q8C23×C1112yes—
334C4×D4—24no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—21no—
338C4×D4C23×C1112yes—
339#117—24no—
340#117—21no—
341#117—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4D4×C1111yescharacteristic
345C2×C42—21no—
346C2×C42C23×C1111yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8C23×C1112yes—
350C4⋊C8C23×C1112yes—
351#102—24no—
352#102—24no—
353#102—24no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C4×C8—21no—
357C4×C8C23×C1112yes—
358C2×C11—22no—
359C2×C11—82no—
360C2×C11—162no—
361C2×C11C2×#44911yescharacteristic
362C2×C11#301011yescharacteristic
363C2×C11#302111yescharacteristic
364C24—41no—
365#41—42no—
366#41—42no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8C2×D4×C1112yes—
373C2×Q8C2×D4×C1112yes—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—82no—
386C2×D4—82no—
387C2×D4C2×D4×C1112yes—
388C22×C4—21no—
389C22×C4—24no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395SD16—48no—
396SD16—84no—
397D8—84no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—42no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4C2×D4×C1112yes—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C2×D4×C1112yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C42—24no—
424C42—22no—
425C42—22no—
426C42—22no—
427C42C2×D4×C1111yescharacteristic
428C42C2×D4×C1111yescharacteristic
429C42C2×D4×C1111yescharacteristic
430C42C24×C1111yescharacteristic
431C11#1889811yescharacteristic, direct product factor, Sylow
432C23—22no—
433C23—42no—
434C23—82no—
435C23—82no—
436C23—82no—
437C23C11×#12011yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444D4—24no—
445D4—44no—
446D4—44no—
447D4—42no—
448D4—42no—
449D4—44no—
450D4—42no—
451D4—81no—
452D4—82no—
453D4—82no—
454D4—82no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—81no—
466C2×C4—84no—
467C2×C4C11×#12011yescharacteristic
468C2×C4C11×#12011yescharacteristic
469C2×C4C11×#12011yescharacteristic
470C2×C4C11×#13512yes—
471C2×C4C11×AGL(1,ℤ/8)12yes—
472C2×C4C22×D4×C1111yescharacteristic
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C22×D4×C1111yescharacteristic
475C8—42no—
476C8—42no—
477C8—42no—
478C22—21no—
479C22—21no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—164no—
487C22C11×#44912yes—
488C22C2×C11×#12011yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4C11×#44912yes—
498C4C2×C11×#13511yescharacteristic
499C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
500C4C11×#57712yes—
501C2—22no—
502C2—82no—
503C2—162no—
504C2C2×C11×#44911yescharacteristic
505C2C11×#301011yescharacteristic
506C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3205C2
LCSG ▷ C42 ▷ 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×#3507C2semidirect
2. C11×#3208C2semidirect
4. C2×C11×#460C2semidirect
5. C11×#1628C2semidirect
6. C11×#1622C2semidirect
7. C11×#1542C2semidirect
8. C11×#1480C2semidirect
9. C11×#1479C2semidirect
14. C11×#556C22semidirect
15. C11×#554C22semidirect
39. C11×#333C22semidirect
40. C11×#332C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
111. #18898C11direct (N × H)
179. #3507C2×C11semidirect
180. #3208C2×C11semidirect
182. C2×#460C2×C11semidirect
183. #1628C2×C11semidirect
184. #1622C2×C11semidirect
185. #1542C2×C11semidirect
186. #1480C2×C11semidirect
187. #1479C2×C11semidirect
238. #556C22×C11semidirect
239. #554C22×C11semidirect
263. #333C22×C11semidirect
264. #332C22×C11semidirect
265. Q8⋊C8C22×C11semidirect
266. D4⋊C8C22×C11semidirect
431. C11#18898direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32082
C11×#32052
C2×C11×#4602
C11×#16282
C11×#16222
C11×#15422
C11×#14802
C11×#14792
#1889811