Finite Group Databasebeta

← C11×#24694 #14601887

Subgroups — C11×#24694 #14601887

Order 2816.

836 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, complemented
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic, complemented
5C11×#2072C212yesmaximal, complemented
6C11×#2055C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1947C212yesmaximal, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal
11C11×#1804C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—22no—
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C11×#477—24no—
18C11×#440—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#97C2211yescharacteristic
28C11×#399—21no—
29C11×#399—21no—
30C11×#391C2212yes—
31C11×#390C2212yes—
32C11×#387—22no—
33C11×#384C2212yes—
34C11×#383—21no—
35C11×#382C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#376—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×C22⋊Q8—48no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
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×#102—24no—
83C11×#102—22no—
84C11×#97—22no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95D411yescharacteristic
91C11×#95D411yescharacteristic
92#24694C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×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—44no—
100C2×Q8×C11—42no—
101C2×Q8×C11C2×D412yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—44no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2411yescharacteristic
120C11×SD16—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11#4112yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—44no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—44no—
146C42×C11—24no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—44no—
150C42×C11C2×D412yes—
151C42×C11#4112yes—
152C2×#477C2×C1111yescharacteristic, complemented
153C2×#440C2×C1111yescharacteristic
154#2542C2×C1111yescharacteristic
155#2356C2×C1111yescharacteristic, complemented
156#2072C2×C1112yescomplemented
157#2055C2×C1112yes—
158#1993C2×C1111yescharacteristic, complemented
159#1947C2×C1112yescomplemented
160#1940C2×C1111yescharacteristic, complemented
161#1925C2×C1112yes—
162#1804C2×C1111yescharacteristic
163C23×C11—22no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11C22×D411yescharacteristic
169Q8×C11—22no—
170Q8×C11—22no—
171Q8×C11—41no—
172Q8×C11—41no—
173Q8×C11—84no—
174D4×C11—22no—
175D4×C11—22no—
176D4×C11—41no—
177D4×C11—41no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—84no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11AGL(1,ℤ/8)14yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C8×C11—22no—
209C8×C11—42no—
210C8×C11—41no—
211C22×SD16C22×C1111yescharacteristic
212C2×C4⋊Q8C22×C1111yescharacteristic
213C2×C22⋊Q8—22no—
214C2×C4×Q8C22×C1111yescharacteristic
215C2×C4×D4C22×C1111yescharacteristic
216#477—24no—
217#440—24no—
218C2×#107C22×C1112yes—
219C2×#107C22×C1111yescharacteristic
220C2×C4⋊C8C22×C1111yescharacteristic
221C2×C4⋊C8C22×C1112yes—
222C2×#103C22×C1112yes—
223C2×#103C22×C1111yescharacteristic
224C2×#102C22×C1112yes—
225C2×#102C22×C1111yescharacteristic
226C2×#97C22×C1111yescharacteristic
227#399—21no—
228#399—21no—
229#391C22×C1112yes—
230#390C22×C1112yes—
231#387—22no—
232#384C22×C1112yes—
233#383—21no—
234#382C22×C1111yescharacteristic
235C4×C4⋊C4C22×C1112yes—
236C4×C4⋊C4C22×C1111yescharacteristic
237#376—21no—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#336C22×C1112yes—
242C22×C11—44no—
243C22×C11—42no—
244C22×C11—82no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11C2×#12111yescharacteristic
248C22×C11#54711yescharacteristic
249C22×C11#54811yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)12yes—
251C22×C11#57812yes—
252C4×C11—24no—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—82no—
259C4×C11—81no—
260C4×C11—82no—
261C4×C11#52511yescharacteristic
262C4×C11#53611yescharacteristic
263C4×C11#55211yescharacteristic
264C4×C11#55611yescharacteristic
265C22×Q8—21no—
266C22×Q8C23×C1111yescharacteristic
267C22×D4C23×C1111yescharacteristic
268C23×C4—21no—
269C2×SD16—22no—
270C2×SD16—22no—
271C2×SD16—22no—
272C22×C8C23×C1111yescharacteristic
273C22×C8C23×C1112yes—
274C22×C8C23×C1111yescharacteristic
275C4⋊Q8—22no—
276C4⋊Q8—22no—
277C22⋊Q8—48no—
278C4×Q8—22no—
279C4×Q8D4×C1114yes—
280C4×D4—22no—
281C4×D4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4D4×C1112yes—
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C4⋊C4C23×C1112yes—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C42—21no—
295C2×C42—22no—
296C2×C42C23×C1112yes—
297C2×C42C23×C1111yescharacteristic
298#107—22no—
299#107—24no—
300C4⋊C8—24no—
301C4⋊C8—22no—
302#103—22no—
303#103—24no—
304#102—24no—
305#102—22no—
306#97—22no—
307#95—21no—
308#95—22no—
309#95—22no—
310#95—21no—
311#95—22no—
312#95D4×C1111yescharacteristic
313#95D4×C1111yescharacteristic
314C2×C11—82no—
315C2×C11#241511yescharacteristic
316C2×C11#303811yescharacteristic
317C2×C11#304411yescharacteristic
318C2×C11#334312yes—
319C2×C11#336712yes—
320C24—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—44no—
327C2×Q8—42no—
328C2×Q8C2×D4×C1112yes—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4C11×#4112yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—44no—
341C22×C4—42no—
342C22×C4C2×D4×C1112yes—
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1112yes—
346C22×C4C24×C1111yescharacteristic
347SD16—28no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8C11×#4112yes—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—44no—
367C4⋊C4—42no—
368C4⋊C4—44no—
369C4⋊C4C2×D4×C1112yes—
370C22⋊C4—44no—
371C22⋊C4—42no—
372C22⋊C4—44no—
373C42—24no—
374C42—22no—
375C42—22no—
376C42—44no—
377C42C2×D4×C1112yes—
378C42C11×#4112yes—
379C11#2469411yescharacteristic, direct product factor, Sylow
380C23—22no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23C22×D4×C1111yescharacteristic
386Q8—22no—
387Q8—22no—
388Q8—41no—
389Q8—41no—
390Q8—84no—
391D4—22no—
392D4—22no—
393D4—41no—
394D4—41no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—84no—
416C2×C4C11×#12112yes—
417C2×C4C11×#12112yes—
418C2×C4C11×AGL(1,ℤ/8)14yes—
419C2×C4C22×D4×C1111yescharacteristic
420C2×C4C2×C11×#4111yescharacteristic
421C2×C4C2×C11×#4111yescharacteristic
422C2×C4C2×C11×#4111yescharacteristic
423C2×C4C11×2−1+411yescharacteristic
424C2×C4C11×2−1+411yescharacteristic
425C8—22no—
426C8—42no—
427C8—41no—
428C22—42no—
429C22—44no—
430C22—81no—
431C22—81no—
432C22—82no—
433C22C2×C11×#12111yescharacteristic
434C22C11×#54711yescharacteristic
435C22C11×#54811yescharacteristic
436C22C2×C11×AGL(1,ℤ/8)12yes—
437C22C11×#57812yes—
438C4—22no—
439C4—22no—
440C4—24no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—82no—
446C4—82no—
447C4C11×#52511yescharacteristic
448C4C11×#53611yescharacteristic
449C4C11×#55211yescharacteristic
450C4C11×#55611yescharacteristic
451C2—82no—
452C2C11×#241511yescharacteristic
453C2C11×#303811yescharacteristic
454C2C11×#304411yescharacteristic
455C2C11×#334312yes—
456C2C11×#336712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
1. C2×C11×#477C2semidirect
4. C11×#2356C2semidirect
5. C11×#2072C2semidirect
7. C11×#1993C2semidirect
8. C11×#1947C2semidirect
9. C11×#1940C2semidirect
92. #24694C11direct (N × H)
152. C2×#477C2×C11semidirect
155. #2356C2×C11semidirect
156. #2072C2×C11semidirect
158. #1993C2×C11semidirect
159. #1947C2×C11semidirect
160. #1940C2×C11semidirect
379. C11#24694direct (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×C11×#4402
C11×#25422
C11×#23562
C11×#20722
C11×#20552
C11×#19932
C11×#19472
C11×#19402
C11×#19252
C11×#18042
#2469411