Finite Group Databasebeta

← C11×#24074 #14601267

Subgroups — C11×#24074 #14601267

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#542C211yesmaximal, characteristic
2C2×C11×#481C211yesmaximal, characteristic
3C2×C11×#483C211yesmaximal, characteristic, complemented
4C11×#2317C211yesmaximal, characteristic, complemented
5C11×#2058C212yesmaximal, complemented
6C11×#2042C212yesmaximal, complemented
7C11×#1875C211yesmaximal, characteristic
8C11×#1873C211yesmaximal, characteristic, complemented
9C11×#1865C212yesmaximal, complemented
10C11×#1864C212yesmaximal, complemented
11C11×#1818C211yesmaximal, characteristic, complemented
12C11×#542—24no—
13C11×#542—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—21no—
16C2×C11×#124—21no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#483—24no—
28C11×#481—24no—
29C2×C11×#106C2212yes—
30C2×C11×#106C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#389C2212yes—
38C11×#389C2212yes—
39C11×#385—21no—
40C11×#385—21no—
41C11×#384—21no—
42C11×#382—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#336C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×#126—28no—
59C11×#124—28no—
60C11×#124—22no—
61C11×#124—22no—
62C11×#123—28no—
63C11×C22⋊Q8—28no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D414yes—
66C11×#121—22no—
67C11×#121D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#106—24no—
102C11×#106—24no—
103C11×#103—24no—
104C11×#103—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#95—22no—
110C11×#95—22no—
111#24074C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C24×C11C2×D411yescharacteristic
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—82no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—24no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—82no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—82no—
136C22×C4×C11—82no—
137C22×C4×C11C2×D411yescharacteristic
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—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—82no—
163C11×C4⋊C4—82no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4#4114yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—24no—
175C42×C11—24no—
176C42×C11—24no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C2×#542C2×C1111yescharacteristic
182C2×#481C2×C1111yescharacteristic
183C2×#483C2×C1111yescharacteristic, complemented
184#2317C2×C1111yescharacteristic, complemented
185#2058C2×C1112yescomplemented
186#2042C2×C1112yescomplemented
187#1875C2×C1111yescharacteristic
188#1873C2×C1111yescharacteristic, complemented
189#1865C2×C1112yescomplemented
190#1864C2×C1112yescomplemented
191#1818C2×C1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11#12012yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—24no—
204Q8×C11—42no—
205Q8×C11—84no—
206D4×C11—24no—
207D4×C11—42no—
208D4×C11—84no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—84no—
235C2×C4×C11—84no—
236C2×C4×C11#12012yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4112yes—
240C2×C4×C112−1+412yes—
241C8×C11—42no—
242C8×C11—42no—
243#542—24no—
244#542—24no—
245C2×C4⋊Q8C22×C1111yescharacteristic
246C2×#126—21no—
247C2×#124—21no—
248C2×#124C22×C1111yescharacteristic
249C2×#123—21no—
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8C22×C1111yescharacteristic
252C2×#121C22×C1111yescharacteristic
253C2×C4×Q8C22×C1111yescharacteristic
254C2×C4×D4C22×C1111yescharacteristic
255C2×#117C22×C1111yescharacteristic
256C2×#117C22×C1111yescharacteristic
257C22×C4⋊C4C22×C1111yescharacteristic
258#483—24no—
259#481—24no—
260C2×#106C22×C1112yes—
261C2×#106C22×C1112yes—
262C2×#103C22×C1112yes—
263C2×#103C22×C1112yes—
264C2×#102C22×C1112yes—
265C2×#102C22×C1112yes—
266C2×C22⋊C8C22×C1111yescharacteristic
267C2×C22⋊C8C22×C1111yescharacteristic
268#389C22×C1112yes—
269#389C22×C1112yes—
270#385—21no—
271#385—21no—
272#384—21no—
273#382—21no—
274#340C22×C1112yes—
275#340C22×C1112yes—
276#336C22×C1112yes—
277#336C22×C1112yes—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#52511yescharacteristic
290C22×C11#53611yescharacteristic
291C22×C11#57712yes—
292C22×C11#57712yes—
293C4×C11—22no—
294C4×C11—44no—
295C4×C11—42no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—41no—
301C4×C11—41no—
302C4×C11—82no—
303C4×C11#54712yes—
304C4×C11#54712yes—
305C22×Q8—21no—
306C22×Q8C23×C1111yescharacteristic
307C22×D4—21no—
308C22×D4C23×C1111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4C23×C1111yescharacteristic
312C22×C8C23×C1112yes—
313C22×C8C23×C1112yes—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316#126—28no—
317#124—28no—
318#124—22no—
319#124—22no—
320#123—28no—
321C22⋊Q8—28no—
322C22⋊Q8—22no—
323C22⋊Q8D4×C1114yes—
324#121—22no—
325#121D4×C1114yes—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×D4—22no—
329C4×D4—22no—
330#117—22no—
331#117—22no—
332#117—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4D4×C1111yescharacteristic
342C2×C4⋊C4D4×C1111yescharacteristic
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C4⋊C4C23×C1112yes—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4D4×C1111yescharacteristic
354C2×C22⋊C4D4×C1111yescharacteristic
355C2×C42—21no—
356C2×C42—21no—
357C2×C42C23×C1111yescharacteristic
358C2×C42C23×C1111yescharacteristic
359#106—24no—
360#106—24no—
361#103—24no—
362#103—24no—
363#102—24no—
364#102—24no—
365C22⋊C8—22no—
366C22⋊C8—22no—
367#95—22no—
368#95—22no—
369C2×C11—42no—
370C2×C11—82no—
371C2×C11#240611yescharacteristic
372C2×C11#300911yescharacteristic
373C2×C11#301011yescharacteristic
374C2×C11#312512yes—
375C2×C11#324412yes—
376C24—21no—
377C24C2×D4×C1111yescharacteristic
378C2×Q8—24no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—82no—
383C2×Q8C2×D4×C1112yes—
384C2×D4—24no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—82no—
389C2×D4C2×D4×C1112yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—82no—
400C22×C4—82no—
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1112yes—
408C22×C4C24×C1111yescharacteristic
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—42no—
426C4⋊C4—82no—
427C4⋊C4—82no—
428C4⋊C4C2×D4×C1112yes—
429C4⋊C4C2×D4×C1112yes—
430C4⋊C4C11×#4114yes—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—24no—
439C42—24no—
440C42—24no—
441C42—21no—
442C42—21no—
443C42—21no—
444C42—21no—
445C11#2407411yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—21no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23C11×#12012yes—
456C23C22×D4×C1111yescharacteristic
457Q8—24no—
458Q8—42no—
459Q8—84no—
460D4—24no—
461D4—42no—
462D4—84no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—84no—
490C2×C4C11×#12012yes—
491C2×C4C22×D4×C1111yescharacteristic
492C2×C4C22×D4×C1111yescharacteristic
493C2×C4C2×C11×#4112yes—
494C2×C4C11×2−1+412yes—
495C8—42no—
496C8—42no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—82no—
506C22—82no—
507C22C2×C11×#12011yescharacteristic
508C22C11×#52511yescharacteristic
509C22C11×#53611yescharacteristic
510C22C11×#57712yes—
511C22C11×#57712yes—
512C4—22no—
513C4—42no—
514C4—41no—
515C4—41no—
516C4—42no—
517C4—42no—
518C4—41no—
519C4—41no—
520C4—44no—
521C4—82no—
522C4C11×#54712yes—
523C4C11×#54712yes—
524C2—42no—
525C2—82no—
526C2C11×#240611yescharacteristic
527C2C11×#300911yescharacteristic
528C2C11×#301011yescharacteristic
529C2C11×#312512yes—
530C2C11×#324412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#483C2semidirect
4. C11×#2317C2semidirect
5. C11×#2058C2semidirect
6. C11×#2042C2semidirect
8. C11×#1873C2semidirect
9. C11×#1865C2semidirect
10. C11×#1864C2semidirect
11. C11×#1818C2semidirect
111. #24074C11direct (N × H)
183. C2×#483C2×C11semidirect
184. #2317C2×C11semidirect
185. #2058C2×C11semidirect
186. #2042C2×C11semidirect
188. #1873C2×C11semidirect
189. #1865C2×C11semidirect
190. #1864C2×C11semidirect
191. #1818C2×C11semidirect
445. C11#24074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5422
C2×C11×#4812
C2×C11×#4832
C11×#23172
C11×#20582
C11×#20422
C11×#18752
C11×#18732
C11×#18652
C11×#18642
C11×#18182
#2407411