Finite Group Databasebeta

← C11×#24071 #14601264

Subgroups — C11×#24071 #14601264

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#541C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic
3C2×C11×#483C211yesmaximal, characteristic
4C11×#2317C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2043C212yesmaximal, complemented
7C11×#1873C211yesmaximal, characteristic
8C11×#1873C211yesmaximal, characteristic
9C11×#1865C212yesmaximal, complemented
10C11×#1863C212yesmaximal, complemented
11C11×#1818C211yesmaximal, characteristic
12C11×#541—24no—
13C11×#541—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—21no—
16C2×C11×#126—21no—
17C2×C11×#125—21no—
18C2×C11×#125—21no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#484—24no—
28C11×#483—24no—
29C2×C11×#107C2212yes—
30C2×C11×#106C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
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×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×#126—28no—
56C11×#126—28no—
57C11×#125—28no—
58C11×#125—28no—
59C11×#125—22no—
60C11×#125—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8D414yes—
64C11×C22⋊Q8D414yes—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—24no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
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⋊C4—22no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#107—24no—
102C11×#106—24no—
103C11×#103—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—24no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#95—22no—
110C11×#95—22no—
111#24071C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×D412yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2411yescharacteristic
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—82no—
162C11×C4⋊C4—82no—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4#4114yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11—24no—
173C42×C11—24no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C2×#541C2×C1111yescharacteristic
179C2×#484C2×C1111yescharacteristic
180C2×#483C2×C1111yescharacteristic
181#2317C2×C1111yescharacteristic
182#2059C2×C1112yescomplemented
183#2043C2×C1112yescomplemented
184#1873C2×C1111yescharacteristic
185#1873C2×C1111yescharacteristic
186#1865C2×C1112yescomplemented
187#1863C2×C1112yescomplemented
188#1818C2×C1111yescharacteristic
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11#12012yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—24no—
196Q8×C11—24no—
197Q8×C11—42no—
198Q8×C11—42no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—84no—
228C2×C4×C11#12012yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4112yes—
232C2×C4×C112−1+412yes—
233C8×C11—42no—
234C8×C11—42no—
235#541—24no—
236#541—24no—
237C2×C4⋊Q8C22×C1111yescharacteristic
238C2×#126—21no—
239C2×#126—21no—
240C2×#125—21no—
241C2×#125—21no—
242C2×#125C22×C1111yescharacteristic
243C2×C22⋊Q8C22×C1111yescharacteristic
244C2×C22⋊Q8C22×C1111yescharacteristic
245C2×C4×Q8C22×C1111yescharacteristic
246C2×C4×Q8C22×C1111yescharacteristic
247C2×#117C22×C1111yescharacteristic
248C2×#117C22×C1111yescharacteristic
249C22×C4⋊C4C22×C1111yescharacteristic
250#484—24no—
251#483—24no—
252C2×#107C22×C1112yes—
253C2×#106C22×C1112yes—
254C2×#103C22×C1112yes—
255C2×#103C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#103C22×C1112yes—
258C2×C22⋊C8C22×C1111yescharacteristic
259C2×C22⋊C8C22×C1111yescharacteristic
260#389C22×C1112yes—
261#389C22×C1112yes—
262#385—21no—
263#385—21no—
264#384—21no—
265#382—21no—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#336C22×C1112yes—
269#336C22×C1112yes—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11C2×#12011yescharacteristic
276C22×C11#52511yescharacteristic
277C22×C11#53611yescharacteristic
278C22×C11#57712yes—
279C22×C11#57812yes—
280C4×C11—22no—
281C4×C11—44no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—41no—
285C4×C11—41no—
286C4×C11—42no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11—42no—
290C4×C11—82no—
291C4×C11#54712yes—
292C4×C11#54712yes—
293C22×Q8C23×C1111yescharacteristic
294C22×Q8C23×C1111yescharacteristic
295C23×C4—21no—
296C23×C4C23×C1111yescharacteristic
297C22×C8C23×C1112yes—
298C22×C8C23×C1112yes—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301#126—28no—
302#126—28no—
303#125—28no—
304#125—28no—
305#125—22no—
306#125—22no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8D4×C1114yes—
310C22⋊Q8D4×C1114yes—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315#117—22no—
316#117—22no—
317#117—24no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4D4×C1111yescharacteristic
332C2×C4⋊C4D4×C1111yescharacteristic
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C4⋊C4C23×C1112yes—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4D4×C1111yescharacteristic
341C2×C22⋊C4D4×C1111yescharacteristic
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42C23×C1111yescharacteristic
346C2×C42C23×C1111yescharacteristic
347#107—24no—
348#106—24no—
349#103—24no—
350#103—24no—
351#103—24no—
352#103—24no—
353C22⋊C8—22no—
354C22⋊C8—22no—
355#95—22no—
356#95—22no—
357C2×C11—42no—
358C2×C11#240611yescharacteristic
359C2×C11#301011yescharacteristic
360C2×C11#301111yescharacteristic
361C2×C11#312012yes—
362C2×C11#324212yes—
363C24C2×D4×C1111yescharacteristic
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8C2×D4×C1112yes—
371C2×Q8C2×D4×C1112yes—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—42no—
381C22×C4—82no—
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1112yes—
388C22×C4C2×D4×C1112yes—
389C22×C4C24×C1111yescharacteristic
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—42no—
412C4⋊C4—82no—
413C4⋊C4—82no—
414C4⋊C4C2×D4×C1112yes—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C11×#4114yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C42—24no—
423C42—24no—
424C42—24no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—21no—
429C11#2407111yescharacteristic, direct product factor, Sylow
430C23—21no—
431C23—21no—
432C23—22no—
433C23—22no—
434C23C11×#12012yes—
435C23C22×D4×C1111yescharacteristic
436Q8—24no—
437Q8—24no—
438Q8—42no—
439Q8—42no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—84no—
469C2×C4C11×#12012yes—
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C22×D4×C1111yescharacteristic
472C2×C4C2×C11×#4112yes—
473C2×C4C11×2−1+412yes—
474C8—42no—
475C8—42no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—42no—
480C22—42no—
481C22C2×C11×#12011yescharacteristic
482C22C11×#52511yescharacteristic
483C22C11×#53611yescharacteristic
484C22C11×#57712yes—
485C22C11×#57812yes—
486C4—22no—
487C4—42no—
488C4—42no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—41no—
493C4—41no—
494C4—42no—
495C4—44no—
496C4—82no—
497C4C11×#54712yes—
498C4C11×#54712yes—
499C2—42no—
500C2C11×#240611yescharacteristic
501C2C11×#301011yescharacteristic
502C2C11×#301111yescharacteristic
503C2C11×#312012yes—
504C2C11×#324212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
5. C11×#2059C2semidirect
6. C11×#2043C2semidirect
9. C11×#1865C2semidirect
10. C11×#1863C2semidirect
111. #24071C11direct (N × H)
182. #2059C2×C11semidirect
183. #2043C2×C11semidirect
186. #1865C2×C11semidirect
187. #1863C2×C11semidirect
429. C11#24071direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C2×C11×#4842
C2×C11×#4832
C11×#23172
C11×#20592
C11×#20432
C11×#18732
C11×#18652
C11×#18632
C11×#18182
#2407111