Finite Group Databasebeta

← C11×#24332 #14601525

Subgroups — C11×#24332 #14601525

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic
4C11×#2582C211yesmaximal, characteristic
5C11×#2059C212yesmaximal
6C11×#2026C212yesmaximal
7C11×#1990C211yesmaximal, characteristic
8C11×#1984C211yesmaximal, characteristic
9C11×#1878C212yesmaximal
10C11×#1865C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C11×#557—24no—
14C11×#557—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—22no—
18C2×C11×#125C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#475—24no—
25C4×C11×Q16—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C11×#398—22no—
35C11×#391—21no—
36C11×#391C2212yes—
37C11×#389—21no—
38C11×#389C2212yes—
39C11×#384C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16Q814yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—28no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yes—
58C11×#125—216no—
59C11×#125—24no—
60C11×#125—24no—
61C4×Q8×C11—28no—
62C4×Q8×C11—24no—
63C4×Q8×C11—24no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yes—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—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—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C11×#107—22no—
91C11×#106—24no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#103—24no—
95C11×#103—22no—
96C11×#103—24no—
97C4×C8×C11—22no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—22no—
101#24332C1111yesmaximal, characteristic, direct product factor, Sylow
102C2×Q8×C11—22no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×Q812yes—
118C2×Q8×C11C2×Q812yes—
119C2×Q8×C11#4112yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C11×Q16—28no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11C2×Q812yes—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
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—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—82no—
158C11×C4⋊C4C2×D414yes—
159C11×C4⋊C4C2×D412yes—
160C42×C11—28no—
161C42×C11—24no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—42no—
165C42×C11C2×D412yes—
166C42×C11C2×D412yes—
167C2×#557C2×C1111yescharacteristic
168C2×#475C2×C1111yescharacteristic
169C2×C4×Q16C2×C1111yescharacteristic
170#2582C2×C1111yescharacteristic
171#2059C2×C1112yes—
172#2026C2×C1112yes—
173#1990C2×C1111yescharacteristic
174#1984C2×C1111yescharacteristic
175#1878C2×C1112yes—
176#1865C2×C1112yes—
177#1803C2×C1111yescharacteristic
178C23×C11C22×D411yescharacteristic
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—44no—
187Q8×C11—48no—
188Q8×C11C22⋊Q814yes—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
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—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11#12012yes—
216C2×C4×C11#12012yes—
217C2×C4×C11#13512yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×Q811yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C8×C11—22no—
226C8×C11—41no—
227C8×C11—42no—
228C22×Q16C22×C1111yescharacteristic
229#557—24no—
230#557—24no—
231C2×C4⋊Q8—21no—
232C2×C4⋊Q8C22×C1111yescharacteristic
233C2×#125—22no—
234C2×#125C22×C1112yes—
235C2×C4×Q8—21no—
236C2×C4×Q8C22×C1111yescharacteristic
237C2×C4×Q8C22×C1112yes—
238C2×C4×Q8C22×C1111yescharacteristic
239C2×C4×Q8C22×C1111yescharacteristic
240#475—24no—
241C4×Q16—24no—
242C2×#107C22×C1111yescharacteristic
243C2×#106C22×C1112yes—
244C2×C4⋊C8C22×C1111yescharacteristic
245C2×#103C22×C1112yes—
246C2×#103C22×C1112yes—
247C2×#103C22×C1111yescharacteristic
248C2×#103C22×C1111yescharacteristic
249C2×C4×C8C22×C1111yescharacteristic
250#398—22no—
251#391—21no—
252#391C22×C1112yes—
253#389—21no—
254#389C22×C1112yes—
255#384C22×C1111yescharacteristic
256#340C22×C1112yes—
257#340C22×C1112yes—
258#340C22×C1112yes—
259#336C22×C1112yes—
260#336C22×C1112yes—
261C22×C11C2×#12011yescharacteristic
262C22×C11#54811yescharacteristic
263C22×C11D4×Q811yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11#45214yes—
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11#53611yescharacteristic
280C4×C11#54811yescharacteristic
281C4×C11D4×Q811yescharacteristic
282C22×Q8—21no—
283C22×Q8D4×C1111yescharacteristic
284C22×Q8C23×C1111yescharacteristic
285C22×Q8C23×C1111yescharacteristic
286C2×Q16—22no—
287C2×Q16—22no—
288C2×Q16Q8×C1114yescomplemented
289C22×C8C23×C1111yescharacteristic
290C22×C8C23×C1112yes—
291C22×C8C23×C1111yescharacteristic
292C4⋊Q8—28no—
293C4⋊Q8—22no—
294C4⋊Q8D4×C1114yes—
295#125—216no—
296#125—24no—
297#125—24no—
298C4×Q8—28no—
299C4×Q8—24no—
300C4×Q8—24no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8D4×C1114yes—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4D4×C1111yescharacteristic
317C2×C4⋊C4D4×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C4⋊C4C23×C1112yes—
322C2×C42—22no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42C23×C1112yes—
326C2×C42C23×C1111yescharacteristic
327#107—22no—
328#106—24no—
329C4⋊C8—22no—
330#103—22no—
331#103—24no—
332#103—22no—
333#103—24no—
334C4×C8—22no—
335#95—22no—
336#95—22no—
337#95—22no—
338C2×C11#240911yescharacteristic
339C2×C11C2×#45211yescharacteristic
340C2×C11#301311yescharacteristic
341C2×C11#336511yescharacteristic
342C2×C11#337411yescharacteristic
343C2×C11#338311yescharacteristic
344C2×C11#338711yescharacteristic
345C2×Q8—22no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—42no—
358C2×Q8—42no—
359C2×Q8C2×D4×C1112yes—
360C2×Q8C2×Q8×C1112yes—
361C2×Q8C2×Q8×C1112yes—
362C2×Q8C11×#4112yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1112yes—
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C24×C1111yescharacteristic
374Q16—28no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8C2×Q8×C1112yes—
384C4⋊C4—28no—
385C4⋊C4—28no—
386C4⋊C4—28no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—22no—
390C4⋊C4—24no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—81no—
400C4⋊C4—82no—
401C4⋊C4C2×D4×C1114yes—
402C4⋊C4C2×D4×C1112yes—
403C42—28no—
404C42—24no—
405C42—22no—
406C42—22no—
407C42—42no—
408C42C2×D4×C1112yes—
409C42C2×D4×C1112yes—
410C11#2433211yescharacteristic, direct product factor, Sylow
411C23C22×D4×C1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—22no—
415Q8—22no—
416Q8—22no—
417Q8—41no—
418Q8—41no—
419Q8—44no—
420Q8—48no—
421Q8C11×C22⋊Q814yes—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4C11×#12012yes—
449C2×C4C11×#12012yes—
450C2×C4C11×#13512yes—
451C2×C4C11×#13712yes—
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C22×Q8×C1111yescharacteristic
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C11×2−1+411yescharacteristic
457C2×C4C11×2−1+411yescharacteristic
458C8—22no—
459C8—41no—
460C8—42no—
461C22C2×C11×#12011yescharacteristic
462C22C11×#54811yescharacteristic
463C22D4×Q8×C1111yescharacteristic
464C22C2×C11×#13511yescharacteristic
465C22C2×C11×#13711yescharacteristic
466C22C11×#57711yescharacteristic
467C22C11×#57811yescharacteristic
468C4—24no—
469C4—22no—
470C4—42no—
471C4—42no—
472C4—44no—
473C4—42no—
474C4—42no—
475C4—81no—
476C4—82no—
477C4C11×#45214yes—
478C4C2×C11×C22⋊Q811yescharacteristic
479C4C11×#53611yescharacteristic
480C4C11×#54811yescharacteristic
481C4D4×Q8×C1111yescharacteristic
482C2C11×#240911yescharacteristic
483C2C2×C11×#45211yescharacteristic
484C2C11×#301311yescharacteristic
485C2C11×#336511yescharacteristic
486C2C11×#337411yescharacteristic
487C2C11×#338311yescharacteristic
488C2C11×#338711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
51. C2×C11×Q16Q8semidirect
101. #24332C11direct (N × H)
288. C2×Q16Q8×C11semidirect
410. C11#24332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4752
C2×C4×C11×Q162
C11×#25822
C11×#20592
C11×#20262
C11×#19902
C11×#19842
C11×#18782
C11×#18652
C11×#18032
#2433211