Finite Group Databasebeta

← C11×#24343 #14601536

Subgroups — C11×#24343 #14601536

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#2059C212yesmaximal, complemented
6C11×#2026C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1985C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal
10C11×#1864C212yesmaximal
11C11×#1804C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C11×#554—24no—
14C11×#554—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4—21no—
24C11×#475—24no—
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#400—21no—
35C11×#395—21no—
36C11×#391C2212yes—
37C11×#389C2212yes—
38C11×#387—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16Q814yescomplemented
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C11×#125—24no—
60C11×#125—24no—
61C11×C22⋊Q8—28no—
62C11×C22⋊Q8—216no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11D414yes—
71C2×C11×C4⋊C4—28no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C11×#107—22no—
89C11×#106—24no—
90C11×C4⋊C8—22no—
91C11×#103—22no—
92C11×#103—24no—
93C11×#102—22no—
94C11×#102—24no—
95C11×#97—22no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—22no—
101#24343C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—24no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—42no—
111C2×Q8×C11—82no—
112C2×Q8×C11C2×Q812yes—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C2×D412yes—
117C2×D4×C11C2×Q812yes—
118C2×D4×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—28no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—44no—
127C22×C4×C11—84no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C11×SD16—28no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11C2×Q812yes—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4C2×D414yes—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—42no—
163C42×C11C2×D412yes—
164C42×C11C2×D412yes—
165C2×#554C2×C1111yescharacteristic
166C2×#475C2×C1111yescharacteristic, complemented
167C2×#440C2×C1111yescharacteristic
168#2581C2×C1111yescharacteristic, complemented
169#2059C2×C1112yescomplemented
170#2026C2×C1112yescomplemented
171#1993C2×C1111yescharacteristic, complemented
172#1985C2×C1111yescharacteristic, complemented
173#1877C2×C1112yes—
174#1864C2×C1112yes—
175#1804C2×C1111yescharacteristic
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—44no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—84no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11C22⋊Q814yes—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—48no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—44no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—88no—
213C2×C4×C11#12012yes—
214C2×C4×C11#12012yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C8×C11—22no—
222C8×C11—41no—
223C8×C11—42no—
224C22×SD16C22×C1111yescharacteristic
225#554—24no—
226#554—24no—
227C2×C4⋊Q8C22×C1111yescharacteristic
228C2×#125C22×C1112yes—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—22no—
231C2×C4×Q8C22×C1111yescharacteristic
232C2×C4×Q8C22×C1111yescharacteristic
233C2×C4×D4C22×C1112yes—
234C2×C4×D4C22×C1111yescharacteristic
235C22×C4⋊C4—21no—
236#475—24no—
237#440—24no—
238C2×#107C22×C1111yescharacteristic
239C2×#106C22×C1112yes—
240C2×C4⋊C8C22×C1111yescharacteristic
241C2×#103C22×C1112yes—
242C2×#103C22×C1111yescharacteristic
243C2×#102C22×C1112yes—
244C2×#102C22×C1111yescharacteristic
245C2×#97C22×C1111yescharacteristic
246#400—21no—
247#395—21no—
248#391C22×C1112yes—
249#389C22×C1112yes—
250#387—22no—
251#382C22×C1111yescharacteristic
252#340C22×C1112yes—
253#340C22×C1112yes—
254#340C22×C1112yes—
255#336C22×C1112yes—
256#336C22×C1112yes—
257C22×C11—24no—
258C22×C11—44no—
259C22×C11—44no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11C2×#12011yescharacteristic
263C22×C11#54811yescharacteristic
264C22×C11D4×Q811yescharacteristic
265C22×C11#57512yes—
266C22×C11#57712yes—
267C4×C11—22no—
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—44no—
274C4×C11—82no—
275C4×C11—81no—
276C4×C11C2×C22⋊Q811yescharacteristic
277C4×C11#53611yescharacteristic
278C4×C11#54811yescharacteristic
279C4×C11D4×Q811yescharacteristic
280C22×Q8—21no—
281C22×Q8D4×C1111yescharacteristic
282C22×Q8C23×C1111yescharacteristic
283C22×D4C23×C1111yescharacteristic
284C23×C4—21no—
285C23×C4—22no—
286C2×SD16—22no—
287C2×SD16—22no—
288C2×SD16Q8×C1114yescomplemented
289C22×C8C23×C1111yescharacteristic
290C22×C8C23×C1112yes—
291C22×C8C23×C1111yescharacteristic
292C4⋊Q8—22no—
293C4⋊Q8D4×C1114yes—
294#125—24no—
295#125—24no—
296C22⋊Q8—28no—
297C22⋊Q8—216no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×D4—24no—
303C4×D4—24no—
304C4×D4—22no—
305C4×D4D4×C1114yes—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4D4×C1112yes—
314C2×C4⋊C4C23×C1111yescharacteristic
315C2×C4⋊C4C23×C1112yes—
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1112yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—21no—
320C2×C42—21no—
321C2×C42C23×C1112yes—
322C2×C42C23×C1111yescharacteristic
323#107—22no—
324#106—24no—
325C4⋊C8—22no—
326#103—22no—
327#103—24no—
328#102—22no—
329#102—24no—
330#97—22no—
331#95—21no—
332#95—21no—
333#95—22no—
334#95—22no—
335#95—22no—
336C2×C11—44no—
337C2×C11#240911yescharacteristic
338C2×C11#300511yescharacteristic
339C2×C11#300911yescharacteristic
340C2×C11#337612yes—
341C2×C11#338812yes—
342C24—21no—
343C2×Q8—22no—
344C2×Q8—24no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—42no—
351C2×Q8—82no—
352C2×Q8C2×Q8×C1112yes—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4C2×D4×C1112yes—
357C2×D4C2×Q8×C1112yes—
358C2×D4C11×#4112yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—28no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—44no—
367C22×C4—84no—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C24×C1111yescharacteristic
373SD16—28no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8C2×Q8×C1112yes—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—22no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4C2×D4×C1114yes—
397C4⋊C4C2×D4×C1112yes—
398C22⋊C4—28no—
399C22⋊C4—24no—
400C42—22no—
401C42—22no—
402C42—42no—
403C42C2×D4×C1112yes—
404C42C2×D4×C1112yes—
405C11#2434311yescharacteristic, direct product factor, Sylow
406C23—22no—
407C23—22no—
408C23—22no—
409C23—42no—
410C23—42no—
411C23C22×D4×C1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—44no—
415Q8—41no—
416Q8—41no—
417Q8—84no—
418D4—22no—
419D4—22no—
420D4—22no—
421D4C11×C22⋊Q814yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—48no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—88no—
443C2×C4C11×#12012yes—
444C2×C4C11×#12012yes—
445C2×C4C22×D4×C1111yescharacteristic
446C2×C4C22×D4×C1111yescharacteristic
447C2×C4C22×Q8×C1111yescharacteristic
448C2×C4C2×C11×#4111yescharacteristic
449C2×C4C11×2−1+411yescharacteristic
450C2×C4C11×2−1+411yescharacteristic
451C8—22no—
452C8—41no—
453C8—42no—
454C22—24no—
455C22—42no—
456C22—42no—
457C22—44no—
458C22—44no—
459C22C2×C11×#12011yescharacteristic
460C22C11×#54811yescharacteristic
461C22D4×Q8×C1111yescharacteristic
462C22C11×#57512yes—
463C22C11×#57712yes—
464C4—22no—
465C4—22no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—44no—
471C4—81no—
472C4—82no—
473C4C2×C11×C22⋊Q811yescharacteristic
474C4C11×#53611yescharacteristic
475C4C11×#54811yescharacteristic
476C4D4×Q8×C1111yescharacteristic
477C2—44no—
478C2C11×#240911yescharacteristic
479C2C11×#300511yescharacteristic
480C2C11×#300911yescharacteristic
481C2C11×#337612yes—
482C2C11×#338812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#475C2semidirect
4. C11×#2581C2semidirect
5. C11×#2059C2semidirect
6. C11×#2026C2semidirect
7. C11×#1993C2semidirect
8. C11×#1985C2semidirect
53. C2×C11×SD16Q8semidirect
101. #24343C11direct (N × H)
166. C2×#475C2×C11semidirect
168. #2581C2×C11semidirect
169. #2059C2×C11semidirect
170. #2026C2×C11semidirect
171. #1993C2×C11semidirect
172. #1985C2×C11semidirect
288. C2×SD16Q8×C11semidirect
405. C11#24343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4752
C2×C11×#4402
C11×#25812
C11×#20592
C11×#20262
C11×#19932
C11×#19852
C11×#18772
C11×#18642
C11×#18042
#2434311