Finite Group Databasebeta

← C11×#24095 #14601288

Subgroups — C11×#24095 #14601288

Order 2816.

1080 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C22×C11×#106C211yesmaximal, characteristic, complemented
4C11×#2487C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2035C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic
9C11×#1865C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C11×#552—24no—
14C11×#552—24no—
15C2×C11×#126—21no—
16C2×C11×#125—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C2×C11×#117C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#484—24no—
28C2×C11×#107C2212yes—
29C2×C11×#106—24no—
30C2×C11×#106C2212yes—
31C2×C11×#106C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#400—21no—
37C11×#399—21no—
38C11×#389C2212yes—
39C11×#386—21no—
40C11×#385—21no—
41C11×#380C2211yescharacteristic
42C11×#380C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11—22no—
54C22×C8×C11—24no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×#126—28no—
58C11×#125—28no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#123—28no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D414yes—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C11×#117—28no—
71C11×#117—22no—
72C11×#117—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D414yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×#107—24no—
102C11×#106—24no—
103C11×#106—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—24no—
108C11×#95—22no—
109C11×#95—21no—
110C11×#95—22no—
111#24095C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—82no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2411yescharacteristic
145C2×C8×C11—28no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11#4114yes—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—82no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—82no—
178C42×C11—24no—
179C42×C11—24no—
180C42×C11—21no—
181C42×C11—21no—
182C2×#552C2×C1111yescharacteristic
183C2×#484C2×C1111yescharacteristic, complemented
184C22×#106C2×C1111yescharacteristic, complemented
185#2487C2×C1111yescharacteristic
186#2059C2×C1112yescomplemented
187#2035C2×C1112yescomplemented
188#1892C2×C1111yescharacteristic, complemented
189#1869C2×C1111yescharacteristic
190#1865C2×C1112yescomplemented
191#1854C2×C1112yescomplemented
192#1823C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11#12012yes—
201C23×C11#13512yes—
202C23×C11#13712yes—
203C23×C11C22×D411yescharacteristic
204Q8×C11—24no—
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—44no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—84no—
240C2×C4×C11#12012yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4112yes—
244C2×C4×C112−1+412yes—
245C8×C11—24no—
246C8×C11—42no—
247C23×C8C22×C1111yescharacteristic
248#552—24no—
249#552—24no—
250C2×#126—21no—
251C2×#125—21no—
252C2×#125C22×C1111yescharacteristic
253C2×#123—21no—
254C2×C22⋊Q8C22×C1111yescharacteristic
255C2×C22⋊Q8C22×C1111yescharacteristic
256C2×C4×Q8C22×C1111yescharacteristic
257C2×C4×D4C22×C1111yescharacteristic
258C2×#117—21no—
259C2×#117C22×C1111yescharacteristic
260C22×C4⋊C4C22×C1111yescharacteristic
261C22×C4⋊C4C22×C1111yescharacteristic
262#484—24no—
263C2×#107C22×C1112yes—
264C2×#106—24no—
265C2×#106C22×C1112yes—
266C2×#106C22×C1112yes—
267C2×#103C22×C1112yes—
268C2×#103C22×C1112yes—
269C2×C22⋊C8C22×C1111yescharacteristic
270C2×C22⋊C8C22×C1112yes—
271#400—21no—
272#399—21no—
273#389C22×C1112yes—
274#386—21no—
275#385—21no—
276#380C22×C1111yescharacteristic
277#380C22×C1112yes—
278#340C22×C1112yes—
279#340C22×C1112yes—
280#340C22×C1112yes—
281#336C22×C1112yes—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11#45214yes—
292C22×C11C2×#12011yescharacteristic
293C22×C11#54712yes—
294C22×C11C2×#13511yescharacteristic
295C22×C11C2×#13711yescharacteristic
296C22×C11#57712yes—
297C4×C11—22no—
298C4×C11—41no—
299C4×C11—42no—
300C4×C11—41no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—41no—
304C4×C11—42no—
305C4×C11—82no—
306C4×C11—82no—
307C4×C11#52511yescharacteristic
308C4×C11#53611yescharacteristic
309C4×C11#54712yes—
310C22×Q8C23×C1111yescharacteristic
311C22×D4D4×C1111yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4C23×C1111yescharacteristic
315C23×C4C23×C1111yescharacteristic
316C22×C8—22no—
317C22×C8—24no—
318C22×C8C23×C1112yes—
319C22×C8C23×C1112yes—
320#126—28no—
321#125—28no—
322#125—22no—
323#125—22no—
324#123—28no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8D4×C1114yes—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×D4—22no—
332C4×D4—22no—
333#117—28no—
334#117—22no—
335#117—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4D4×C1111yescharacteristic
348C2×C4⋊C4D4×C1114yes—
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4D4×C1111yescharacteristic
360C2×C22⋊C4D4×C1111yescharacteristic
361C2×C42—21no—
362C2×C42—21no—
363C2×C42C23×C1111yescharacteristic
364#107—24no—
365#106—24no—
366#106—24no—
367#103—24no—
368#103—24no—
369C22⋊C8—22no—
370C22⋊C8—24no—
371#95—22no—
372#95—21no—
373#95—22no—
374C2×C11—24no—
375C2×C11—81no—
376C2×C11#240611yescharacteristic
377C2×C11C2×#45211yescharacteristic
378C2×C11#301011yescharacteristic
379C2×C11#333712yes—
380C2×C11#334412yes—
381C24C2×D4×C1111yescharacteristic
382C24C2×D4×C1111yescharacteristic
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8C2×D4×C1112yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1112yes—
412C22×C4C2×D4×C1112yes—
413C22×C4C24×C1111yescharacteristic
414C2×C8—28no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8C11×#4114yes—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—82no—
437C4⋊C4C2×D4×C1112yes—
438C4⋊C4C2×D4×C1112yes—
439C4⋊C4C2×D4×C1112yes—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—42no—
446C22⋊C4—82no—
447C42—24no—
448C42—24no—
449C42—21no—
450C42—21no—
451C11#2409511yescharacteristic, direct product factor, Sylow
452C23—22no—
453C23—22no—
454C23—21no—
455C23—22no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23C11×#12012yes—
460C23C11×#13512yes—
461C23C11×#13712yes—
462C23C22×D4×C1111yescharacteristic
463Q8—24no—
464Q8—41no—
465Q8—41no—
466D4—44no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—48no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—84no—
499C2×C4C11×#12012yes—
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C2×C4C2×C11×#4112yes—
503C2×C4C11×2−1+412yes—
504C8—24no—
505C8—42no—
506C22—22no—
507C22—22no—
508C22—24no—
509C22—24no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22C11×#45214yes—
516C22C2×C11×#12011yescharacteristic
517C22C11×#54712yes—
518C22C2×C11×#13511yescharacteristic
519C22C2×C11×#13711yescharacteristic
520C22C11×#57712yes—
521C4—22no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—82no—
530C4—82no—
531C4C11×#52511yescharacteristic
532C4C11×#53611yescharacteristic
533C4C11×#54712yes—
534C2—24no—
535C2—81no—
536C2C11×#240611yescharacteristic
537C2C2×C11×#45211yescharacteristic
538C2C11×#301011yescharacteristic
539C2C11×#333712yes—
540C2C11×#334412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#484C2semidirect
3. C22×C11×#106C2semidirect
5. C11×#2059C2semidirect
6. C11×#2035C2semidirect
7. C11×#1892C2semidirect
9. C11×#1865C2semidirect
10. C11×#1854C2semidirect
11. C11×#1823C2semidirect
111. #24095C11direct (N × H)
183. C2×#484C2×C11semidirect
184. C22×#106C2×C11semidirect
186. #2059C2×C11semidirect
187. #2035C2×C11semidirect
188. #1892C2×C11semidirect
190. #1865C2×C11semidirect
191. #1854C2×C11semidirect
192. #1823C2×C11semidirect
451. C11#24095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4842
C22×C11×#1062
C11×#24872
C11×#20592
C11×#20352
C11×#18922
C11×#18692
C11×#18652
C11×#18542
C11×#18232
#2409511