Finite Group Databasebeta

← C11×#18949 #14596142

Subgroups — C11×#18949 #14596142

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic
2C11×#3246C211yesmaximal, characteristic
3C11×#3237C211yesmaximal, characteristic, complemented
4C11×#3231C211yesmaximal, characteristic, complemented
5C11×#1651C212yesmaximal, complemented
6C11×#1650C212yesmaximal, complemented
7C11×#1638C212yesmaximal, complemented
8C11×#1637C212yesmaximal, complemented
9C11×#1552C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#563—22no—
13C11×#559—21no—
14Q82×C11—21no—
15C11×#556—21no—
16C11×#556C2212yes—
17D4×Q8×C11—21no—
18D4×Q8×C11C2212yes—
19C11×#542—22no—
20C11×#542—22no—
21C11×#536—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#501—21no—
27C11×#500C2211yescharacteristic
28C11×#498C2211yescharacteristic
29C11×#491—21no—
30C11×#487C2211yescharacteristic
31C11×#487C2211yescharacteristic
32C11×#485—22no—
33C11×#485—22no—
34C11×#479—22no—
35C11×#477C2212yes—
36C11×#476C2212yes—
37C11×#475—21no—
38C11×#475C2212yes—
39C11×#465—22no—
40C11×#461C2212yes—
41C11×#460—21no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×D4⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C2×C11×#41—21no—
52C22×Q8×C11—22no—
53C2×C11×SD16—22no—
54C22×C8×C11—21no—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127D411yescharacteristic
66C11×#126—24no—
67C11×#126—24no—
68C11×#125—21no—
69C11×#125—21no—
70C11×#125D412yes—
71C11×#124—24no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#124—21no—
75C11×#123—24no—
76C11×#123—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8D412yes—
87C11×#121—21no—
88C11×#121D412yes—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11C2312yes—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—21no—
100C4×D4×C11C2312yes—
101C11×#117—21no—
102C11×#117—22no—
103C11×#117—21no—
104C11×#117D412yes—
105C2×C42×C11C2311yescharacteristic
106C11×#107—22no—
107C11×#107—22no—
108C11×#106—22no—
109C11×#106—22no—
110C11×#106—22no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18949C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—82no—
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—84no—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C11×SD16—82no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—81no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—41no—
182C42×C11—24no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—41no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190#3550C2×C1111yescharacteristic
191#3246C2×C1111yescharacteristic
192#3237C2×C1111yescharacteristic, complemented
193#3231C2×C1111yescharacteristic, complemented
194#1651C2×C1112yescomplemented
195#1650C2×C1112yescomplemented
196#1638C2×C1112yescomplemented
197#1637C2×C1112yescomplemented
198#1552C2×C1111yescharacteristic, complemented
199#1496C2×C1111yescharacteristic
200#1481C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11#12011yescharacteristic
203Q8×C11—24no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—41no—
207Q8×C11—42no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—41no—
211Q8×C11—81no—
212Q8×C11—84no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—42no—
216D4×C11—81no—
217D4×C11—82no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—44no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—84no—
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C8×C11—41no—
238C8×C11—41no—
239C8×C11—42no—
240C8×C11—42no—
241#563—22no—
242#559—21no—
243Q82—21no—
244#556—21no—
245#556C22×C1112yes—
246D4×Q8—21no—
247D4×Q8C22×C1112yes—
248#542—22no—
249#542—22no—
250#536—22no—
251#533C22×C1111yescharacteristic
252#533C22×C1111yescharacteristic
253#533C22×C1111yescharacteristic
254#532C22×C1111yescharacteristic
255#501—21no—
256#500C22×C1111yescharacteristic
257#498C22×C1111yescharacteristic
258#491—21no—
259#487C22×C1111yescharacteristic
260#487C22×C1111yescharacteristic
261#485—22no—
262#485—22no—
263#479—22no—
264#477C22×C1112yes—
265#476C22×C1112yes—
266#475—21no—
267#475C22×C1112yes—
268#465—22no—
269#461C22×C1112yes—
270#460—21no—
271#432C22×C1111yescharacteristic
272#431C22×C1111yescharacteristic
273C2×C4⋊C8C22×C1111yescharacteristic
274#332C22×C1112yes—
275#332C22×C1112yes—
276Q8⋊C8C22×C1112yes—
277Q8⋊C8C22×C1112yes—
278D4⋊C8C22×C1112yes—
279D4⋊C8C22×C1112yes—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11C2×#12011yescharacteristic
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11#57712yes—
299C4×C11#57711yescharacteristic
300C4×C11#57811yescharacteristic
301C2×#41—21no—
302C22×Q8—22no—
303C2×SD16—22no—
304C22×C8—21no—
305C4⋊Q8—24no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8D4×C1111yescharacteristic
309C4⋊Q8D4×C1111yescharacteristic
310C4⋊Q8D4×C1111yescharacteristic
311C4⋊Q8C23×C1111yescharacteristic
312C4⋊Q8C23×C1111yescharacteristic
313C4⋊Q8C23×C1111yescharacteristic
314C4⋊Q8C23×C1111yescharacteristic
315#127D4×C1111yescharacteristic
316#126—24no—
317#126—24no—
318#125—21no—
319#125—21no—
320#125D4×C1112yes—
321#124—24no—
322#124—22no—
323#124—22no—
324#124—21no—
325#123—24no—
326#123—24no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8D4×C1112yes—
337#121—21no—
338#121D4×C1112yes—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8C23×C1112yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—21no—
350C4×D4C23×C1112yes—
351#117—21no—
352#117—22no—
353#117—21no—
354#117D4×C1112yes—
355C2×C42C23×C1111yescharacteristic
356#107—22no—
357#107—22no—
358#106—22no—
359#106—22no—
360#106—22no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8C23×C1112yes—
364C4⋊C8C23×C1112yes—
365#103—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370#102—22no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373#97—21no—
374C4×C8C23×C1111yescharacteristic
375C4×C8C23×C1111yescharacteristic
376C2×C11—41no—
377C2×C11—82no—
378C2×C11#300911yescharacteristic
379C2×C11#301311yescharacteristic
380C2×C11#302011yescharacteristic
381#41—82no—
382C2×Q8—24no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—84no—
390C2×Q8C2×D4×C1112yes—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C2×D4×C1112yes—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400SD16—82no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—81no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4C2×D4×C1112yes—
425C4⋊C4C2×D4×C1112yes—
426C4⋊C4C2×D4×C1112yes—
427C4⋊C4C2×D4×C1112yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—41no—
436C42—24no—
437C42—22no—
438C42—22no—
439C42—41no—
440C42C2×D4×C1111yescharacteristic
441C42C2×D4×C1111yescharacteristic
442C42C2×D4×C1111yescharacteristic
443C42C24×C1111yescharacteristic
444C11#1894911yescharacteristic, direct product factor, Sylow
445C23—22no—
446C23C11×#12011yescharacteristic
447Q8—24no—
448Q8—42no—
449Q8—42no—
450Q8—41no—
451Q8—42no—
452Q8—41no—
453Q8—41no—
454Q8—41no—
455Q8—81no—
456Q8—84no—
457D4—22no—
458D4—22no—
459D4—42no—
460D4—81no—
461D4—82no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—84no—
475C2×C4C11×#12011yescharacteristic
476C2×C4C11×#12011yescharacteristic
477C2×C4C11×#12011yescharacteristic
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C22×D4×C1111yescharacteristic
480C2×C4C22×D4×C1111yescharacteristic
481C8—41no—
482C8—41no—
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22C2×C11×#12011yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—81no—
502C4—81no—
503C4C11×#57712yes—
504C4C11×#57711yescharacteristic
505C4C11×#57811yescharacteristic
506C2—41no—
507C2—82no—
508C2C11×#300911yescharacteristic
509C2C11×#301311yescharacteristic
510C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
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
3. C11×#3237C2semidirect
4. C11×#3231C2semidirect
5. C11×#1651C2semidirect
6. C11×#1650C2semidirect
7. C11×#1638C2semidirect
8. C11×#1637C2semidirect
9. C11×#1552C2semidirect
11. C11×#1481C2semidirect
126. #18949C11direct (N × H)
192. #3237C2×C11semidirect
193. #3231C2×C11semidirect
194. #1651C2×C11semidirect
195. #1650C2×C11semidirect
196. #1638C2×C11semidirect
197. #1637C2×C11semidirect
198. #1552C2×C11semidirect
200. #1481C2×C11semidirect
444. C11#18949direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#32462
C11×#32372
C11×#32312
C11×#16512
C11×#16502
C11×#16382
C11×#16372
C11×#15522
C11×#14962
C11×#14812
#1894911