Finite Group Databasebeta

← C11×#18950 #14596143

Subgroups — C11×#18950 #14596143

Order 2816.

824 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×#3556C211yesmaximal, characteristic, complemented
2C11×#3246C211yesmaximal, characteristic
3C11×#3228C211yesmaximal, characteristic
4C11×#3216C211yesmaximal, characteristic
5C11×#1653C212yesmaximal, complemented
6C11×#1648C212yesmaximal, complemented
7C11×#1626C212yesmaximal, complemented
8C11×#1626C212yesmaximal, complemented
9C11×#1552C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#564—22no—
13C11×#557—21no—
14C11×#557—21no—
15C11×#557—21no—
16C11×#557—21no—
17C11×#557C2212yes—
18C11×#557C2212yes—
19C11×#541—22no—
20C11×#541—22no—
21C11×#541—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#500C2211yescharacteristic
27C11×#498C2211yescharacteristic
28C11×#497—21no—
29C11×#489—21no—
30C11×#486C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#482—22no—
33C11×#478—22no—
34C11×#476—21no—
35C11×#475C2212yes—
36C11×#465—22no—
37C11×#462C2212yes—
38C11×#461—21no—
39C11×#460C2212yes—
40C11×#460C2212yes—
41C11×#452—22no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×Q8⋊C8C2212yes—
51C2×C11×#41—21no—
52C2×C11×Q16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#126—24no—
68C11×#126—24no—
69C11×#125—22no—
70C11×#125—24no—
71C11×#125—24no—
72C11×#125—24no—
73C11×#125—24no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125—24no—
77C11×#125—24no—
78C11×#125—21no—
79C11×#125—21no—
80C11×#125D412yes—
81C11×#124—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8D412yes—
87C11×C22⋊Q8D412yes—
88C11×#121—21no—
89C11×#121—21no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11C2312yes—
101C4×Q8×C11C2312yes—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#117D412yes—
107C2×C42×C11C2311yescharacteristic
108C11×#107—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×#102—22no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18950C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—82no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C11×Q16—82no—
144C11×SD16—82no—
145C11×SD16—82no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—81no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
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—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11—24no—
183C42×C11—24no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2411yescharacteristic
191#3556C2×C1111yescharacteristic, complemented
192#3246C2×C1111yescharacteristic
193#3228C2×C1111yescharacteristic
194#3216C2×C1111yescharacteristic
195#1653C2×C1112yescomplemented
196#1648C2×C1112yescomplemented
197#1626C2×C1112yescomplemented
198#1626C2×C1112yescomplemented
199#1552C2×C1111yescharacteristic, complemented
200#1497C2×C1111yescharacteristic, complemented
201#1481C2×C1111yescharacteristic, complemented
202C23×C11—41no—
203C23×C11#12011yescharacteristic
204Q8×C11—22no—
205Q8×C11—22no—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—41no—
212Q8×C11—41no—
213Q8×C11—42no—
214D4×C11—42no—
215D4×C11—41no—
216D4×C11—42no—
217D4×C11—41no—
218D4×C11—82no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
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—82no—
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#564—22no—
242#557—21no—
243#557—21no—
244#557—21no—
245#557—21no—
246#557C22×C1112yes—
247#557C22×C1112yes—
248#541—22no—
249#541—22no—
250#541—22no—
251#533C22×C1111yescharacteristic
252#533C22×C1111yescharacteristic
253#533C22×C1111yescharacteristic
254#532C22×C1111yescharacteristic
255#500C22×C1111yescharacteristic
256#498C22×C1111yescharacteristic
257#497—21no—
258#489—21no—
259#486C22×C1111yescharacteristic
260#486C22×C1111yescharacteristic
261#482—22no—
262#478—22no—
263#476—21no—
264#475C22×C1112yes—
265#465—22no—
266#462C22×C1112yes—
267#461—21no—
268#460C22×C1112yes—
269#460C22×C1112yes—
270#452—22no—
271#432C22×C1111yescharacteristic
272#431C22×C1111yescharacteristic
273C2×C4⋊C8C22×C1111yescharacteristic
274#332C22×C1112yes—
275#332C22×C1112yes—
276Q8⋊C8C22×C1112yes—
277Q8⋊C8C22×C1112yes—
278Q8⋊C8C22×C1112yes—
279Q8⋊C8C22×C1112yes—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
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—42no—
297C4×C11—81no—
298C4×C11#57712yes—
299C4×C11#57711yescharacteristic
300C4×C11#57811yescharacteristic
301C2×#41—21no—
302C2×Q16—22no—
303C2×SD16—22no—
304C2×SD16—22no—
305C22×C8—21no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8D4×C1111yescharacteristic
310C4⋊Q8D4×C1111yescharacteristic
311C4⋊Q8D4×C1111yescharacteristic
312C4⋊Q8D4×C1111yescharacteristic
313C4⋊Q8C23×C1111yescharacteristic
314C4⋊Q8C23×C1111yescharacteristic
315C4⋊Q8C23×C1111yescharacteristic
316#127C23×C1111yescharacteristic
317#126—24no—
318#126—24no—
319#125—22no—
320#125—24no—
321#125—24no—
322#125—24no—
323#125—24no—
324#125—22no—
325#125—22no—
326#125—24no—
327#125—24no—
328#125—21no—
329#125—21no—
330#125D4×C1112yes—
331#124—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8D4×C1112yes—
337C22⋊Q8D4×C1112yes—
338#121—21no—
339#121—21no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8C23×C1112yes—
351C4×Q8C23×C1112yes—
352C4×D4—21no—
353C4×D4—21no—
354#117—21no—
355#117—21no—
356#117D4×C1112yes—
357C2×C42C23×C1111yescharacteristic
358#107—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#102—22no—
368#102—22no—
369#102—22no—
370#102—22no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373#97—21no—
374C4×C8C23×C1111yescharacteristic
375C4×C8C23×C1111yescharacteristic
376C2×C11—41no—
377C2×C11—161no—
378C2×C11#301011yescharacteristic
379C2×C11#301311yescharacteristic
380C2×C11#302011yescharacteristic
381#41—82no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8C2×D4×C1112yes—
388C2×Q8C2×D4×C1112yes—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C22×C4—41no—
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1111yescharacteristic
397Q16—82no—
398SD16—82no—
399SD16—82no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—81no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4C2×D4×C1112yes—
428C4⋊C4C2×D4×C1112yes—
429C4⋊C4C2×D4×C1112yes—
430C4⋊C4C2×D4×C1112yes—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C42—24no—
437C42—24no—
438C42—22no—
439C42—22no—
440C42—22no—
441C42C2×D4×C1111yescharacteristic
442C42C2×D4×C1111yescharacteristic
443C42C2×D4×C1111yescharacteristic
444C42C24×C1111yescharacteristic
445C11#1895011yescharacteristic, direct product factor, Sylow
446C23—41no—
447C23C11×#12011yescharacteristic
448Q8—22no—
449Q8—22no—
450Q8—22no—
451Q8—22no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—41no—
456Q8—41no—
457Q8—42no—
458D4—42no—
459D4—41no—
460D4—42no—
461D4—41no—
462D4—82no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
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—81no—
489C22—81no—
490C22—81no—
491C22C2×C11×#12011yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—81no—
503C4C11×#57712yes—
504C4C11×#57711yescharacteristic
505C4C11×#57811yescharacteristic
506C2—41no—
507C2—161no—
508C2C11×#301011yescharacteristic
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
1. C11×#3556C2semidirect
5. C11×#1653C2semidirect
6. C11×#1648C2semidirect
7. C11×#1626C2semidirect
8. C11×#1626C2semidirect
9. C11×#1552C2semidirect
10. C11×#1497C2semidirect
11. C11×#1481C2semidirect
126. #18950C11direct (N × H)
191. #3556C2×C11semidirect
195. #1653C2×C11semidirect
196. #1648C2×C11semidirect
197. #1626C2×C11semidirect
198. #1626C2×C11semidirect
199. #1552C2×C11semidirect
200. #1497C2×C11semidirect
201. #1481C2×C11semidirect
445. C11#18950direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35562
C11×#32462
C11×#32282
C11×#32162
C11×#16532
C11×#16482
C11×#16262
C11×#15522
C11×#14972
C11×#14812
#1895011