Finite Group Databasebeta

← C11×#24682 #14601875

Subgroups — C11×#24682 #14601875

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic
3C11×#2567C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic
5C11×#2072C212yesmaximal
6C11×#2056C212yesmaximal
7C11×#1990C211yesmaximal, characteristic
8C11×#1947C212yesmaximal
9C11×#1939C211yesmaximal, characteristic
10C11×#1928C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#477—24no—
17C4×C11×Q16—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#395—22no—
28C11×#391C2212yes—
29C11×#391C2212yes—
30C11×#389—21no—
31C11×#389—21no—
32C11×#387—22no—
33C11×#384C2212yes—
34C11×#384C2211yescharacteristic
35C11×#382—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C11×#107—22no—
77C11×#107—24no—
78C11×C4⋊C8—24no—
79C11×C4⋊C8—22no—
80C11×#103—22no—
81C11×#103—24no—
82C11×#103—24no—
83C11×#103—22no—
84C4×C8×C11—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D412yes—
91#24682C1111yesmaximal, characteristic, direct product factor, Sylow
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—42no—
103C2×Q8×C11—81no—
104C2×Q8×C11—81no—
105C2×Q8×C11C2×D412yes—
106C2×Q8×C11#4112yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C11×Q16—28no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11#4112yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—82no—
141C11×C4⋊C4—81no—
142C11×C4⋊C4—82no—
143C11×C4⋊C4Q1614yescomplemented
144C11×C4⋊C4C2×D412yes—
145C42×C11—24no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—42no—
149C42×C11—82no—
150C42×C11C2×D412yes—
151C42×C11#4112yes—
152C2×#477C2×C1111yescharacteristic
153C2×C4×Q16C2×C1111yescharacteristic
154#2567C2×C1111yescharacteristic
155#2355C2×C1111yescharacteristic
156#2072C2×C1112yes—
157#2056C2×C1112yes—
158#1990C2×C1111yescharacteristic
159#1947C2×C1112yes—
160#1939C2×C1111yescharacteristic
161#1928C2×C1112yes—
162#1803C2×C1111yescharacteristic
163C23×C11C22×D411yescharacteristic
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11—22no—
167Q8×C11—22no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—41no—
171Q8×C11—41no—
172Q8×C11—84no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11C2×Q1614yes—
201C2×C4×C11C2×Q1612yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C8×C11—22no—
210C8×C11—42no—
211C8×C11—41no—
212C22×Q16C22×C1111yescharacteristic
213C2×C4⋊Q8C22×C1111yescharacteristic
214C2×C4×Q8C22×C1111yescharacteristic
215C2×C4×Q8C22×C1111yescharacteristic
216#477—24no—
217C4×Q16—24no—
218C2×#107C22×C1112yes—
219C2×#107C22×C1111yescharacteristic
220C2×C4⋊C8C22×C1111yescharacteristic
221C2×C4⋊C8C22×C1112yes—
222C2×#103C22×C1112yes—
223C2×#103C22×C1112yes—
224C2×#103C22×C1111yescharacteristic
225C2×#103C22×C1111yescharacteristic
226C2×C4×C8C22×C1111yescharacteristic
227#395—22no—
228#391C22×C1112yes—
229#391C22×C1112yes—
230#389—21no—
231#389—21no—
232#387—22no—
233#384C22×C1112yes—
234#384C22×C1111yescharacteristic
235#382—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4C22×C1112yes—
238C4×C4⋊C4C22×C1111yescharacteristic
239#340C22×C1112yes—
240#340C22×C1112yes—
241#340C22×C1112yes—
242#336C22×C1112yes—
243C22×C11C2×#12111yescharacteristic
244C22×C11#54711yescharacteristic
245C22×C11#54811yescharacteristic
246C22×C11C22×Q1611yescharacteristic
247C22×C11C2×#13711yescharacteristic
248C22×C11#57611yescharacteristic
249C22×C11#57711yescharacteristic
250C4×C11—24no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11—81no—
258C4×C11—82no—
259C4×C11#46214yes—
260C4×C11#52511yescharacteristic
261C4×C11#53611yescharacteristic
262C4×C11#55211yescharacteristic
263C4×C11#55611yescharacteristic
264C22×Q8—21no—
265C22×Q8C23×C1111yescharacteristic
266C22×Q8C23×C1111yescharacteristic
267C2×Q16—22no—
268C2×Q16—22no—
269C2×Q16—22no—
270C22×C8C23×C1111yescharacteristic
271C22×C8C23×C1112yes—
272C22×C8C23×C1111yescharacteristic
273C4⋊Q8—22no—
274C4⋊Q8—22no—
275C4×Q8—22no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×Q8D4×C1114yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4D4×C1111yescharacteristic
287C2×C4⋊C4D4×C1111yescharacteristic
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—22no—
295C2×C42C23×C1112yes—
296C2×C42C23×C1111yescharacteristic
297#107—22no—
298#107—24no—
299C4⋊C8—24no—
300C4⋊C8—22no—
301#103—22no—
302#103—24no—
303#103—24no—
304#103—22no—
305C4×C8—22no—
306#95—22no—
307#95—22no—
308#95—22no—
309#95—22no—
310#95—22no—
311#95D4×C1112yes—
312C2×C11#241511yescharacteristic
313C2×C11C2×#46211yescharacteristic
314C2×C11#304511yescharacteristic
315C2×C11#333811yescharacteristic
316C2×C11#335611yescharacteristic
317C2×C11#336311yescharacteristic
318C2×C11#337511yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—42no—
330C2×Q8—81no—
331C2×Q8—81no—
332C2×Q8C2×D4×C1112yes—
333C2×Q8C11×#4112yes—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4C2×D4×C1112yes—
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C2×D4×C1112yes—
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C24×C1111yescharacteristic
345Q16—28no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C11×#4112yes—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—82no—
368C4⋊C4—81no—
369C4⋊C4—82no—
370C4⋊C4C11×Q1614yescomplemented
371C4⋊C4C2×D4×C1112yes—
372C42—24no—
373C42—22no—
374C42—22no—
375C42—42no—
376C42—82no—
377C42C2×D4×C1112yes—
378C42C11×#4112yes—
379C11#2468211yescharacteristic, direct product factor, Sylow
380C23C22×D4×C1111yescharacteristic
381Q8—22no—
382Q8—22no—
383Q8—22no—
384Q8—22no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388Q8—41no—
389Q8—84no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4C11×#12112yes—
416C2×C4C11×#12112yes—
417C2×C4C2×C11×Q1614yes—
418C2×C4C2×C11×Q1612yes—
419C2×C4C11×#13712yes—
420C2×C4C22×D4×C1111yescharacteristic
421C2×C4C2×C11×#4111yescharacteristic
422C2×C4C2×C11×#4111yescharacteristic
423C2×C4C2×C11×#4111yescharacteristic
424C2×C4C11×2−1+411yescharacteristic
425C2×C4C11×2−1+411yescharacteristic
426C8—22no—
427C8—42no—
428C8—41no—
429C22C2×C11×#12111yescharacteristic
430C22C11×#54711yescharacteristic
431C22C11×#54811yescharacteristic
432C22C22×C11×Q1611yescharacteristic
433C22C2×C11×#13711yescharacteristic
434C22C11×#57611yescharacteristic
435C22C11×#57711yescharacteristic
436C4—22no—
437C4—24no—
438C4—42no—
439C4—42no—
440C4—42no—
441C4—42no—
442C4—82no—
443C4—81no—
444C4—82no—
445C4C11×#46214yes—
446C4C11×#52511yescharacteristic
447C4C11×#53611yescharacteristic
448C4C11×#55211yescharacteristic
449C4C11×#55611yescharacteristic
450C2C11×#241511yescharacteristic
451C2C2×C11×#46211yescharacteristic
452C2C11×#304511yescharacteristic
453C2C11×#333811yescharacteristic
454C2C11×#335611yescharacteristic
455C2C11×#336311yescharacteristic
456C2C11×#337511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
91. #24682C11direct (N × H)
143. C11×C4⋊C4Q16semidirect
370. C4⋊C4C11×Q16semidirect
379. C11#24682direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C2×C4×C11×Q162
C11×#25672
C11×#23552
C11×#20722
C11×#20562
C11×#19902
C11×#19472
C11×#19392
C11×#19282
C11×#18032
#2468211