Finite Group Databasebeta

← C11×#24965 #14602158

Subgroups — C11×#24965 #14602158

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2537C211yesmaximal, characteristic
2D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3C11×#2075C212yesmaximal, complemented
4C11×#2033C212yesmaximal, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1874C212yesmaximal, complemented
8C11×#1834C211yesmaximal, characteristic, complemented
9C11×#1823C212yesmaximal, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2212yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×C22⋊C8C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C11×#394—22no—
27C11×#389—21no—
28C11×#385—22no—
29C11×#384C2211yescharacteristic
30C11×#384C2211yescharacteristic
31C11×#380—21no—
32C11×#380C2212yes—
33C11×#380C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C11×#340C2212yes—
36C11×#340C2212yes—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C22×D4×C11—22no—
42C22×D4×C11D411yescharacteristic
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—21no—
46C23×C4×C11C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C11×#121—24no—
51C11×#121—42no—
52C11×#121—44no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—44no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C11×#107—42no—
79C11×C4⋊C8—22no—
80C11×#102—22no—
81C11×#102—22no—
82C11×#102—42no—
83C11×C22⋊C8—42no—
84C11×C22⋊C8—42no—
85C4×C8×C11—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89#24965C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C24×C11C2×D412yes—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—44no—
100C2×D4×C11—44no—
101C2×D4×C11—82no—
102C2×D4×C11D814yes—
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—82no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—81no—
148C11×C4⋊C4—81no—
149C11×C4⋊C4#4112yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—42no—
155C42×C11—42no—
156C42×C11#4112yes—
157C42×C11#4112yes—
158#2537C2×C1111yescharacteristic
159D4×C4⋊C4C2×C1111yescharacteristic, complemented
160#2075C2×C1112yescomplemented
161#2033C2×C1112yescomplemented
162#1954C2×C1111yescharacteristic, complemented
163#1947C2×C1111yescharacteristic, complemented
164#1874C2×C1112yescomplemented
165#1834C2×C1111yescharacteristic, complemented
166#1823C2×C1112yescomplemented
167#1802C2×C1111yescharacteristic, complemented
168C4×#102C2×C1111yescharacteristic, complemented
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11C2×D814yes—
183C23×C11C22×D411yescharacteristic
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—28no—
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—88no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—88no—
215C2×C4×C11—84no—
216C2×C4×C11#12312yes—
217C2×C4×C11#12312yes—
218C2×C4×C11C2×D812yes—
219C2×C4×C11#13712yes—
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C8×C11—42no—
227C8×C11—41no—
228C8×C11—41no—
229C2×#121—21no—
230C2×#121C22×C1112yes—
231C2×C4×D4—21no—
232C2×C4×D4C22×C1111yescharacteristic
233C2×C4×D4C22×C1111yescharacteristic
234C22×C4⋊C4C22×C1112yes—
235C2×#107C22×C1112yes—
236C2×C4⋊C8C22×C1111yescharacteristic
237C2×#102C22×C1111yescharacteristic
238C2×#102C22×C1111yescharacteristic
239C2×#102C22×C1112yes—
240C2×C22⋊C8C22×C1112yes—
241C2×C22⋊C8C22×C1112yes—
242C2×C4×C8C22×C1111yescharacteristic
243#394—22no—
244#389—21no—
245#385—22no—
246#384C22×C1111yescharacteristic
247#384C22×C1111yescharacteristic
248#380—21no—
249#380C22×C1112yes—
250#380C22×C1112yes—
251C4×C4⋊C4C22×C1111yescharacteristic
252#340C22×C1112yes—
253#340C22×C1111yescharacteristic
254#340C22×C1112yes—
255#340C22×C1111yescharacteristic
256#340C22×C1112yes—
257#340C22×C1112yes—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—24no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11C2×#12311yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11#54611yescharacteristic
275C22×C11C22×D811yescharacteristic
276C22×C11C2×#13711yescharacteristic
277C22×C11#57711yescharacteristic
278C22×C11#57711yescharacteristic
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—82no—
285C4×C11—82no—
286C4×C11#48014yes—
287C4×C11#52911yescharacteristic
288C4×C11#54011yescharacteristic
289C4×C11#55311yescharacteristic
290C4×C11#55511yescharacteristic
291C22×D4—22no—
292C22×D4D4×C1111yescharacteristic
293C22×D4C23×C1111yescharacteristic
294C23×C4—22no—
295C23×C4—21no—
296C23×C4C23×C1112yes—
297C22×C8C23×C1111yescharacteristic
298C22×C8C23×C1111yescharacteristic
299C22×C8C23×C1112yes—
300#121—24no—
301#121—42no—
302#121—44no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4—44no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4D4×C1111yescharacteristic
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1111yescharacteristic
318C2×C4⋊C4C23×C1112yes—
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4D4×C1112yes—
326C2×C42—21no—
327C2×C42C23×C1111yescharacteristic
328#107—42no—
329C4⋊C8—22no—
330#102—22no—
331#102—22no—
332#102—42no—
333C22⋊C8—42no—
334C22⋊C8—42no—
335C4×C8—22no—
336#95—21no—
337#95—22no—
338#95—22no—
339C2×C11—44no—
340C2×C11—82no—
341C2×C11#242011yescharacteristic
342C2×C11C2×#48011yescharacteristic
343C2×C11#309911yescharacteristic
344C2×C11#329411yescharacteristic
345C2×C11#329411yescharacteristic
346C2×C11#332911yescharacteristic
347C2×C11#333111yescharacteristic
348C24—21no—
349C24C2×D4×C1112yes—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—44no—
358C2×D4—44no—
359C2×D4—82no—
360C2×D4C11×D814yes—
361C2×D4C11×#4112yes—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—82no—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C24×C1111yescharacteristic
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—22no—
391C2×C8—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—44no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—81no—
406C4⋊C4—81no—
407C4⋊C4C11×#4112yes—
408C22⋊C4—24no—
409C22⋊C4—44no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—42no—
413C42—42no—
414C42C11×#4112yes—
415C42C11×#4112yes—
416C11#2496511yescharacteristic, direct product factor, Sylow
417C23—22no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23C2×C11×D814yes—
431C23C22×D4×C1111yescharacteristic
432D4—22no—
433D4—22no—
434D4—28no—
435D4—41no—
436D4—41no—
437D4—88no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—88no—
463C2×C4—84no—
464C2×C4C11×#12312yes—
465C2×C4C11×#12312yes—
466C2×C4C2×C11×D812yes—
467C2×C4C11×#13712yes—
468C2×C4C2×C11×#4111yescharacteristic
469C2×C4C2×C11×#4111yescharacteristic
470C2×C4C2×C11×#4111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C11×H(5,𝔽2)11yescharacteristic
473C2×C4C11×H(5,𝔽2)11yescharacteristic
474C8—42no—
475C8—41no—
476C8—41no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×C11×#12311yescharacteristic
492C22C11×#54611yescharacteristic
493C22C11×#54611yescharacteristic
494C22C22×C11×D811yescharacteristic
495C22C2×C11×#13711yescharacteristic
496C22C11×#57711yescharacteristic
497C22C11×#57711yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—82no—
502C4—82no—
503C4—81no—
504C4—81no—
505C4C11×#48014yes—
506C4C11×#52911yescharacteristic
507C4C11×#54011yescharacteristic
508C4C11×#55311yescharacteristic
509C4C11×#55511yescharacteristic
510C2—44no—
511C2—82no—
512C2C11×#242011yescharacteristic
513C2C2×C11×#48011yescharacteristic
514C2C11×#309911yescharacteristic
515C2C11×#329411yescharacteristic
516C2C11×#329411yescharacteristic
517C2C11×#332911yescharacteristic
518C2C11×#333111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C11×C4⋊C4C2semidirect
3. C11×#2075C2semidirect
4. C11×#2033C2semidirect
5. C11×#1954C2semidirect
6. C11×#1947C2semidirect
7. C11×#1874C2semidirect
8. C11×#1834C2semidirect
9. C11×#1823C2semidirect
10. C11×#1802C2semidirect
11. C4×C11×#102C2semidirect
89. #24965C11direct (N × H)
159. D4×C4⋊C4C2×C11semidirect
160. #2075C2×C11semidirect
161. #2033C2×C11semidirect
162. #1954C2×C11semidirect
163. #1947C2×C11semidirect
164. #1874C2×C11semidirect
165. #1834C2×C11semidirect
166. #1823C2×C11semidirect
167. #1802C2×C11semidirect
168. C4×#102C2×C11semidirect
416. C11#24965direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25372
D4×C11×C4⋊C42
C11×#20752
C11×#20332
C11×#19542
C11×#19472
C11×#18742
C11×#18342
C11×#18232
C11×#18022
C4×C11×#1022
#2496511