Finite Group Databasebeta

← C11×#24695 #14601888

Subgroups — C11×#24695 #14601888

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#475C211yesmaximal, characteristic, complemented
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic, complemented
5C11×#2074C212yesmaximal, complemented
6C11×#2055C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1949C212yesmaximal, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1926C212yesmaximal
11C11×#1804C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#475—24no—
17C11×#440—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#97C2211yescharacteristic
27C11×#393—21no—
28C11×#393—21no—
29C11×#391C2212yes—
30C11×#390C2212yes—
31C11×#387—22no—
32C11×#383—21no—
33C11×#382C2212yes—
34C11×#382C2211yescharacteristic
35C11×#380—22no—
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—
55C4×Q8×C11—22no—
56C4×Q8×C11D414yes—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—21no—
70C2×C42×C11—22no—
71C2×C42×C11C2312yes—
72C2×C42×C11C2311yescharacteristic
73C11×#107—22no—
74C11×#106—24no—
75C11×C4⋊C8—24no—
76C11×C4⋊C8—22no—
77C11×#103—22no—
78C11×#103—24no—
79C11×#102—24no—
80C11×#102—22no—
81C11×#97—22no—
82C11×#95—21no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—21no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#24695C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×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—42no—
99C2×Q8×C11—82no—
100C2×Q8×C11C2×D412yes—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11#4112yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C11×SD16—28no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11#4112yes—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
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⋊C4C2×D412yes—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—82no—
142C11×C22⋊C4—82no—
143C42×C11—24no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—44no—
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149C2×#475C2×C1111yescharacteristic, complemented
150C2×#440C2×C1111yescharacteristic
151#2563C2×C1111yescharacteristic
152#2356C2×C1111yescharacteristic, complemented
153#2074C2×C1112yescomplemented
154#2055C2×C1112yes—
155#1993C2×C1111yescharacteristic, complemented
156#1949C2×C1112yescomplemented
157#1940C2×C1111yescharacteristic, complemented
158#1926C2×C1112yes—
159#1804C2×C1111yescharacteristic
160C23×C11—22no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11C22×D411yescharacteristic
166Q8×C11—22no—
167Q8×C11—22no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—84no—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—41no—
174D4×C11—41no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
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—22no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—84no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C8×C11—22no—
206C8×C11—42no—
207C8×C11—41no—
208C22×SD16C22×C1111yescharacteristic
209C2×C4⋊Q8C22×C1111yescharacteristic
210C2×C4×Q8C22×C1111yescharacteristic
211C2×C4×D4C22×C1111yescharacteristic
212#475—24no—
213#440—24no—
214C2×#107C22×C1111yescharacteristic
215C2×#106C22×C1112yes—
216C2×C4⋊C8C22×C1111yescharacteristic
217C2×C4⋊C8C22×C1112yes—
218C2×#103C22×C1112yes—
219C2×#103C22×C1111yescharacteristic
220C2×#102C22×C1112yes—
221C2×#102C22×C1111yescharacteristic
222C2×#97C22×C1111yescharacteristic
223#393—21no—
224#393—21no—
225#391C22×C1112yes—
226#390C22×C1112yes—
227#387—22no—
228#383—21no—
229#382C22×C1112yes—
230#382C22×C1111yescharacteristic
231#380—22no—
232C4×C4⋊C4C22×C1112yes—
233C4×C4⋊C4C22×C1111yescharacteristic
234#376—21no—
235#340C22×C1112yes—
236#340C22×C1112yes—
237#340C22×C1112yes—
238#336C22×C1112yes—
239C22×C11—44no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11C2×#12111yescharacteristic
245C22×C11#54711yescharacteristic
246C22×C11#54811yescharacteristic
247C22×C11#57512yes—
248C22×C11#57712yes—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—82no—
256C4×C11—81no—
257C4×C11—82no—
258C4×C11#52511yescharacteristic
259C4×C11#53611yescharacteristic
260C4×C11#55211yescharacteristic
261C4×C11#55611yescharacteristic
262C22×Q8—21no—
263C22×Q8C23×C1111yescharacteristic
264C22×D4C23×C1111yescharacteristic
265C23×C4—21no—
266C2×SD16—22no—
267C2×SD16—22no—
268C2×SD16—22no—
269C22×C8C23×C1111yescharacteristic
270C22×C8C23×C1112yes—
271C22×C8C23×C1111yescharacteristic
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4×Q8—22no—
275C4×Q8D4×C1114yes—
276C4×D4—22no—
277C4×D4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4D4×C1112yes—
281C2×C4⋊C4C23×C1111yescharacteristic
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1112yes—
284C2×C4⋊C4C23×C1111yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C42—21no—
289C2×C42—22no—
290C2×C42C23×C1112yes—
291C2×C42C23×C1111yescharacteristic
292#107—22no—
293#106—24no—
294C4⋊C8—24no—
295C4⋊C8—22no—
296#103—22no—
297#103—24no—
298#102—24no—
299#102—22no—
300#97—22no—
301#95—21no—
302#95—22no—
303#95—22no—
304#95—22no—
305#95—22no—
306#95—21no—
307#95—22no—
308#95D4×C1111yescharacteristic
309#95D4×C1111yescharacteristic
310C2×C11—82no—
311C2×C11#241511yescharacteristic
312C2×C11#304011yescharacteristic
313C2×C11#304311yescharacteristic
314C2×C11#334812yes—
315C2×C11#337612yes—
316C24—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—42no—
323C2×Q8—82no—
324C2×Q8C2×D4×C1112yes—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4C11×#4112yes—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—44no—
337C22×C4—42no—
338C22×C4C2×D4×C1112yes—
339C22×C4C2×D4×C1112yes—
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C24×C1111yescharacteristic
343SD16—28no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8C11×#4112yes—
353C4⋊C4—24no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4C2×D4×C1112yes—
364C22⋊C4—42no—
365C22⋊C4—82no—
366C22⋊C4—82no—
367C42—24no—
368C42—22no—
369C42—22no—
370C42—44no—
371C42C2×D4×C1112yes—
372C42C11×#4112yes—
373C11#2469511yescharacteristic, direct product factor, Sylow
374C23—22no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—42no—
379C23C22×D4×C1111yescharacteristic
380Q8—22no—
381Q8—22no—
382Q8—41no—
383Q8—41no—
384Q8—84no—
385D4—22no—
386D4—22no—
387D4—41no—
388D4—41no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4C11×#12112yes—
412C2×C4C11×#12112yes—
413C2×C4C22×D4×C1111yescharacteristic
414C2×C4C2×C11×#4111yescharacteristic
415C2×C4C2×C11×#4111yescharacteristic
416C2×C4C2×C11×#4111yescharacteristic
417C2×C4C11×2−1+411yescharacteristic
418C2×C4C11×2−1+411yescharacteristic
419C8—22no—
420C8—42no—
421C8—41no—
422C22—42no—
423C22—44no—
424C22—81no—
425C22—81no—
426C22—82no—
427C22C2×C11×#12111yescharacteristic
428C22C11×#54711yescharacteristic
429C22C11×#54811yescharacteristic
430C22C11×#57512yes—
431C22C11×#57712yes—
432C4—22no—
433C4—22no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—81no—
439C4—82no—
440C4—82no—
441C4C11×#52511yescharacteristic
442C4C11×#53611yescharacteristic
443C4C11×#55211yescharacteristic
444C4C11×#55611yescharacteristic
445C2—82no—
446C2C11×#241511yescharacteristic
447C2C11×#304011yescharacteristic
448C2C11×#304311yescharacteristic
449C2C11×#334812yes—
450C2C11×#337612yes—
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×#475C2semidirect
4. C11×#2356C2semidirect
5. C11×#2074C2semidirect
7. C11×#1993C2semidirect
8. C11×#1949C2semidirect
9. C11×#1940C2semidirect
91. #24695C11direct (N × H)
149. C2×#475C2×C11semidirect
152. #2356C2×C11semidirect
153. #2074C2×C11semidirect
155. #1993C2×C11semidirect
156. #1949C2×C11semidirect
157. #1940C2×C11semidirect
373. C11#24695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4752
C2×C11×#4402
C11×#25632
C11×#23562
C11×#20742
C11×#20552
C11×#19932
C11×#19492
C11×#19402
C11×#19262
C11×#18042
#2469511