Finite Group Databasebeta

← C11×#18923 #14596116

Subgroups — C11×#18923 #14596116

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3227C211yesmaximal, characteristic, complemented
3C11×#3206C211yesmaximal, characteristic, complemented
4C2×C11×#475C211yesmaximal, characteristic, complemented
5C11×#1651C214yesmaximal, complemented
6C11×#1642C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C2×C11×2−1+4—21no—
11C11×#550—21no—
12C11×#550C2212yes—
13D4×Q8×C11—21no—
14D4×Q8×C11C2212yes—
15C11×#548—22no—
16C11×#548—22no—
17C11×#537—22no—
18C11×#537—21no—
19C11×#532—22no—
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#498C2212yes—
25C11×#492—21no—
26C11×#487—21no—
27C11×#486C2212yes—
28C11×#481—22no—
29C11×#476—22no—
30C11×#475—22no—
31C11×#475C2214yes—
32C11×#461C2214yes—
33C11×#448—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C2×C11×#106—21no—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#332C2212yes—
40C11×#331C2212yes—
41C11×Q8⋊C8C2214yes—
42C11×D4⋊C8C2214yes—
43C11×2−1+4—44no—
44C11×2−1+4—44no—
45C2×C11×#41—24no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—21no—
53C22×Q8×C11D411yescharacteristic
54C2×C11×SD16—24no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127—22no—
64C11×#127D411yescharacteristic
65C11×#127C2311yescharacteristic
66C11×#124—24no—
67C11×#124—21no—
68C11×#124—21no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—24no—
73C11×#121—24no—
74C11×#121—22no—
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—22no—
80C11×#121D412yes—
81C11×#121D412yes—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11D412yes—
85C4×Q8×C11C2312yes—
86C4×D4×C11—24no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11D412yes—
92C4×D4×C11C2312yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99C11×#106—24no—
100C11×#106—24no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2312yes—
104C11×C4⋊C8C2312yes—
105C11×#103—24no—
106C11×#103—24no—
107C11×#102—24no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C4×C8×C11—21no—
111C4×C8×C11C2312yes—
112#18923C1111yesmaximal, characteristic, direct product factor, Sylow
113C11×#41—416no—
114C11×#41—44no—
115C11×#41—48no—
116C11×#41—44no—
117C11×#41—42no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11—48no—
129C2×Q8×C11—44no—
130C2×Q8×C11—41no—
131C2×Q8×C11—82no—
132C2×Q8×C11SD1614yescomplemented
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×D412yes—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—41no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C11×SD16—84no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—42no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2411yescharacteristic
184#3497C2×C1111yescharacteristic
185#3227C2×C1111yescharacteristic, complemented
186#3206C2×C1111yescharacteristic, complemented
187C2×#475C2×C1111yescharacteristic, complemented
188#1651C2×C1114yescomplemented
189#1642C2×C1114yescomplemented
190#1540C2×C1111yescharacteristic, complemented
191#1480C2×C1111yescharacteristic, complemented
192#1479C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11#12011yescharacteristic
196Q8×C11—22no—
197Q8×C11—24no—
198Q8×C11—48no—
199Q8×C11—41no—
200Q8×C11—41no—
201Q8×C11—42no—
202Q8×C11—44no—
203Q8×C11—82no—
204Q8×C11C2×SD1614yes—
205D4×C11—24no—
206D4×C11—42no—
207D4×C11—48no—
208D4×C11—44no—
209D4×C11—44no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—81no—
215D4×C11—84no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—48no—
224C2×C4×C11—48no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—81no—
230C2×C4×C11—82no—
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11C2×SD1612yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C8×C11—42no—
240C8×C11—42no—
241C8×C11—42no—
242C2×2−1+4—21no—
243#550—21no—
244#550C22×C1112yes—
245D4×Q8—21no—
246D4×Q8C22×C1112yes—
247#548—22no—
248#548—22no—
249#537—22no—
250#537—21no—
251#532—22no—
252#532C22×C1111yescharacteristic
253#532C22×C1111yescharacteristic
254C2×C4⋊Q8C22×C1111yescharacteristic
255C2×C4×Q8C22×C1111yescharacteristic
256#498C22×C1112yes—
257#492—21no—
258#487—21no—
259#486C22×C1112yes—
260#481—22no—
261#476—22no—
262#475—22no—
263#475C22×C1114yes—
264#461C22×C1114yes—
265#448—22no—
266#431C22×C1111yescharacteristic
267#431C22×C1111yescharacteristic
268C2×#106—21no—
269C2×C4⋊C8C22×C1111yescharacteristic
270C2×#103—21no—
271#332C22×C1112yes—
272#331C22×C1112yes—
273Q8⋊C8C22×C1114yes—
274D4⋊C8C22×C1114yes—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11#45012yes—
284C22×C11C2×#12011yescharacteristic
285C4×C11—24no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—82no—
293C4×C11#45012yes—
294C4×C11C22×SD1611yescharacteristic
295C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C11#57712yes—
2972−1+4—44no—
2982−1+4—44no—
299C2×#41—24no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—21no—
303C2×#41—21no—
304C22×Q8—22no—
305C22×Q8—22no—
306C22×Q8—21no—
307C22×Q8D4×C1111yescharacteristic
308C2×SD16—24no—
309C22×C8—21no—
310C4⋊Q8—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8D4×C1111yescharacteristic
315C4⋊Q8C23×C1112yes—
316C4⋊Q8C23×C1111yescharacteristic
317#127—22no—
318#127D4×C1111yescharacteristic
319#127C23×C1111yescharacteristic
320#124—24no—
321#124—21no—
322#124—21no—
323C22⋊Q8—22no—
324C22⋊Q8—24no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327#121—24no—
328#121—22no—
329#121—24no—
330#121—24no—
331#121—21no—
332#121—21no—
333#121—22no—
334#121D4×C1112yes—
335#121D4×C1112yes—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8D4×C1112yes—
339C4×Q8C23×C1112yes—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4D4×C1112yes—
346C4×D4C23×C1112yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C42—21no—
352C2×C42C23×C1111yescharacteristic
353#106—24no—
354#106—24no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8C23×C1112yes—
358C4⋊C8C23×C1112yes—
359#103—24no—
360#103—24no—
361#102—24no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C4×C8—21no—
365C4×C8C23×C1112yes—
366C2×C11—22no—
367C2×C11—82no—
368C2×C11—82no—
369C2×C11C2×#45011yescharacteristic
370C2×C11#301011yescharacteristic
371C2×C11#302211yescharacteristic
372#41—416no—
373#41—44no—
374#41—48no—
375#41—44no—
376#41—42no—
377#41—42no—
378#41—42no—
379#41—42no—
380C2×Q8—24no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—44no—
387C2×Q8—48no—
388C2×Q8—44no—
389C2×Q8—41no—
390C2×Q8—82no—
391C2×Q8C11×SD1614yescomplemented
392C2×Q8C2×D4×C1112yes—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4C2×D4×C1112yes—
402C2×D4C2×D4×C1112yes—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—41no—
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413SD16—84no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—42no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4C2×D4×C1112yes—
429C4⋊C4C2×D4×C1112yes—
430C4⋊C4C2×D4×C1112yes—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C42—22no—
438C42—22no—
439C42C2×D4×C1111yescharacteristic
440C42C2×D4×C1111yescharacteristic
441C42C2×D4×C1111yescharacteristic
442C42C24×C1111yescharacteristic
443C11#1892311yescharacteristic, direct product factor, Sylow
444C23—22no—
445C23—22no—
446C23C11×#12011yescharacteristic
447Q8—22no—
448Q8—24no—
449Q8—48no—
450Q8—41no—
451Q8—41no—
452Q8—42no—
453Q8—44no—
454Q8—82no—
455Q8C2×C11×SD1614yes—
456D4—24no—
457D4—42no—
458D4—48no—
459D4—44no—
460D4—44no—
461D4—41no—
462D4—41no—
463D4—42no—
464D4—42no—
465D4—81no—
466D4—84no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—48no—
475C2×C4—48no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—42no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4C11×#12011yescharacteristic
483C2×C4C11×#12011yescharacteristic
484C2×C4C11×#12011yescharacteristic
485C2×C4C2×C11×SD1612yes—
486C2×C4C11×AGL(1,ℤ/8)12yes—
487C2×C4C22×D4×C1111yescharacteristic
488C2×C4C22×D4×C1111yescharacteristic
489C2×C4C22×D4×C1111yescharacteristic
490C8—42no—
491C8—42no—
492C8—42no—
493C22—21no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22C11×#45012yes—
502C22C2×C11×#12011yescharacteristic
503C4—24no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4C11×#45012yes—
512C4C22×C11×SD1611yescharacteristic
513C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
514C4C11×#57712yes—
515C2—22no—
516C2—82no—
517C2—82no—
518C2C2×C11×#45011yescharacteristic
519C2C11×#301011yescharacteristic
520C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3497C2
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
2. C11×#3227C2semidirect
3. C11×#3206C2semidirect
4. C2×C11×#475C2semidirect
5. C11×#1651C2semidirect
6. C11×#1642C2semidirect
7. C11×#1540C2semidirect
8. C11×#1480C2semidirect
9. C11×#1479C2semidirect
112. #18923C11direct (N × H)
132. C2×Q8×C11SD16semidirect
185. #3227C2×C11semidirect
186. #3206C2×C11semidirect
187. C2×#475C2×C11semidirect
188. #1651C2×C11semidirect
189. #1642C2×C11semidirect
190. #1540C2×C11semidirect
191. #1480C2×C11semidirect
192. #1479C2×C11semidirect
391. C2×Q8C11×SD16semidirect
443. C11#18923direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34972
C11×#32272
C11×#32062
C2×C11×#4752
C11×#16512
C11×#16422
C11×#15402
C11×#14802
C11×#14792
#1892311