Finite Group Databasebeta

← C11×#24693 #14601886

Subgroups — C11×#24693 #14601886

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic, complemented
2C2×C11×#442C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic, complemented
5C11×#2073C212yesmaximal, complemented
6C11×#2054C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1949C212yesmaximal, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#474—24no—
17C11×#442—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#97C2211yescharacteristic
27C11×#393—21no—
28C11×#393—21no—
29C11×#390C2212yes—
30C11×#390C2212yes—
31C11×#388—22no—
32C11×#382C2212yes—
33C11×#382C2211yescharacteristic
34C11×#381—21no—
35C11×#380—22no—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C2×C11×D8—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11D414yes—
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—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C11×#107—24no—
76C11×#106—22no—
77C11×C4⋊C8—24no—
78C11×C4⋊C8—22no—
79C11×#102—22no—
80C11×#102—24no—
81C11×#102—24no—
82C11×#102—22no—
83C11×#97—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#24693C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C24×C11—21no—
94C2×Q8×C11—42no—
95C2×Q8×C11—82no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C2×D412yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—44no—
114C22×C4×C11—42no—
115C22×C4×C11—82no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C11×D8—28no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—44no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—82no—
145C11×C22⋊C4—82no—
146C11×C22⋊C4—82no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—82no—
150C42×C11C2×D412yes—
151C42×C11#4112yes—
152C2×#474C2×C1111yescharacteristic, complemented
153C2×#442C2×C1111yescharacteristic
154#2563C2×C1111yescharacteristic, complemented
155#2357C2×C1111yescharacteristic, complemented
156#2073C2×C1112yescomplemented
157#2054C2×C1112yes—
158#1993C2×C1111yescharacteristic, complemented
159#1949C2×C1112yescomplemented
160#1940C2×C1111yescharacteristic, complemented
161#1925C2×C1112yescomplemented
162#1804C2×C1111yescharacteristic, complemented
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11C22×D411yescharacteristic
174Q8×C11—84no—
175D4×C11—22no—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—41no—
180D4×C11—41no—
181D4×C11—41no—
182D4×C11—41no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—84no—
202C2×C4×C11—84no—
203C2×C4×C11#12112yes—
204C2×C4×C11#12112yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C8×C11—22no—
212C8×C11—42no—
213C8×C11—41no—
214C22×D8C22×C1111yescharacteristic
215C2×C4⋊Q8C22×C1111yescharacteristic
216C2×C4×D4C22×C1111yescharacteristic
217C2×C4×D4C22×C1111yescharacteristic
218#474—24no—
219#442—24no—
220C2×#107C22×C1112yes—
221C2×#106C22×C1111yescharacteristic
222C2×C4⋊C8C22×C1112yes—
223C2×C4⋊C8C22×C1111yescharacteristic
224C2×#102C22×C1112yes—
225C2×#102C22×C1112yes—
226C2×#102C22×C1111yescharacteristic
227C2×#102C22×C1111yescharacteristic
228C2×#97C22×C1111yescharacteristic
229#393—21no—
230#393—21no—
231#390C22×C1112yes—
232#390C22×C1112yes—
233#388—22no—
234#382C22×C1112yes—
235#382C22×C1111yescharacteristic
236#381—21no—
237#380—22no—
238C4×C4⋊C4C22×C1112yes—
239C4×C4⋊C4C22×C1111yescharacteristic
240C4×C22⋊C4—21no—
241#340C22×C1112yes—
242#340C22×C1112yes—
243#340C22×C1112yes—
244#336C22×C1112yes—
245C22×C11—44no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11C2×#12111yescharacteristic
256C22×C11#54711yescharacteristic
257C22×C11#54811yescharacteristic
258C22×C11#57512yes—
259C22×C11#57612yes—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11—82no—
268C4×C11#52511yescharacteristic
269C4×C11#53611yescharacteristic
270C4×C11#55211yescharacteristic
271C4×C11#55611yescharacteristic
272C22×Q8—21no—
273C22×D4C23×C1111yescharacteristic
274C22×D4C23×C1111yescharacteristic
275C23×C4—21no—
276C23×C4—21no—
277C2×D8—22no—
278C2×D8—22no—
279C2×D8—22no—
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1112yes—
282C22×C8C23×C1111yescharacteristic
283C4⋊Q8—22no—
284C4⋊Q8—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4D4×C1114yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4D4×C1112yes—
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C4⋊C4C23×C1112yes—
293C2×C4⋊C4C23×C1112yes—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C42—22no—
302C2×C42C23×C1112yes—
303C2×C42C23×C1111yescharacteristic
304#107—24no—
305#106—22no—
306C4⋊C8—24no—
307C4⋊C8—22no—
308#102—22no—
309#102—24no—
310#102—24no—
311#102—22no—
312#97—22no—
313#95—21no—
314#95—22no—
315#95—22no—
316#95—22no—
317#95—21no—
318#95D4×C1111yescharacteristic
319#95D4×C1111yescharacteristic
320C2×C11—82no—
321C2×C11—82no—
322C2×C11#241511yescharacteristic
323C2×C11#304011yescharacteristic
324C2×C11#304111yescharacteristic
325C2×C11#334712yes—
326C2×C11#337012yes—
327C24—21no—
328C24—21no—
329C2×Q8—42no—
330C2×Q8—82no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4C2×D4×C1112yes—
342C2×D4C11×#4112yes—
343C22×C4—21no—
344C22×C4—24no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—82no—
351C22×C4C2×D4×C1112yes—
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C24×C1111yescharacteristic
356D8—28no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8C11×#4112yes—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4C2×D4×C1112yes—
376C22⋊C4—24no—
377C22⋊C4—44no—
378C22⋊C4—42no—
379C22⋊C4—82no—
380C22⋊C4—82no—
381C22⋊C4—82no—
382C42—22no—
383C42—22no—
384C42—82no—
385C42C2×D4×C1112yes—
386C42C11×#4112yes—
387C11#2469311yescharacteristic, direct product factor, Sylow
388C23—22no—
389C23—22no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23C22×D4×C1111yescharacteristic
399Q8—84no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—22no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—41no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—84no—
427C2×C4—84no—
428C2×C4C11×#12112yes—
429C2×C4C11×#12112yes—
430C2×C4C22×D4×C1111yescharacteristic
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C2×C11×#4111yescharacteristic
433C2×C4C2×C11×#4111yescharacteristic
434C2×C4C11×2−1+411yescharacteristic
435C2×C4C11×2−1+411yescharacteristic
436C8—22no—
437C8—42no—
438C8—41no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—44no—
444C22—81no—
445C22—81no—
446C22—82no—
447C22—82no—
448C22—82no—
449C22C2×C11×#12111yescharacteristic
450C22C11×#54711yescharacteristic
451C22C11×#54811yescharacteristic
452C22C11×#57512yes—
453C22C11×#57612yes—
454C4—22no—
455C4—22no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—81no—
460C4—82no—
461C4—82no—
462C4C11×#52511yescharacteristic
463C4C11×#53611yescharacteristic
464C4C11×#55211yescharacteristic
465C4C11×#55611yescharacteristic
466C2—82no—
467C2—82no—
468C2C11×#241511yescharacteristic
469C2C11×#304011yescharacteristic
470C2C11×#304111yescharacteristic
471C2C11×#334712yes—
472C2C11×#337012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
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×#474C2semidirect
3. C11×#2563C2semidirect
4. C11×#2357C2semidirect
5. C11×#2073C2semidirect
7. C11×#1993C2semidirect
8. C11×#1949C2semidirect
9. C11×#1940C2semidirect
10. C11×#1925C2semidirect
11. C11×#1804C2semidirect
91. #24693C11direct (N × H)
152. C2×#474C2×C11semidirect
154. #2563C2×C11semidirect
155. #2357C2×C11semidirect
156. #2073C2×C11semidirect
158. #1993C2×C11semidirect
159. #1949C2×C11semidirect
160. #1940C2×C11semidirect
161. #1925C2×C11semidirect
162. #1804C2×C11semidirect
387. C11#24693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C2×C11×#4422
C11×#25632
C11×#23572
C11×#20732
C11×#20542
C11×#19932
C11×#19492
C11×#19402
C11×#19252
C11×#18042
#2469311