Finite Group Databasebeta

← C11×#24968 #14602161

Subgroups — C11×#24968 #14602161

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2537C211yesmaximal, characteristic
2C11×#2354C211yesmaximal, characteristic, complemented
3C11×#2076C212yesmaximal, complemented
4C11×#2033C212yesmaximal, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1875C212yesmaximal, complemented
8C11×#1834C211yesmaximal, characteristic, complemented
9C11×#1825C212yesmaximal, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#117C2212yes—
17C2×C11×#107C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#394—22no—
26C11×#390—21no—
27C11×#388—22no—
28C11×#384C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C11×#380—21no—
31C11×#380C2212yes—
32C11×#380C2212yes—
33C4×C11×C4⋊C4—21no—
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—21no—
45C23×C4×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C11×#121—24no—
50C11×#121—42no—
51C11×#121—44no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C11×#117—24no—
57C11×#117—42no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D412yes—
74C2×C42×C11—22no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C11×#107—42no—
78C11×C4⋊C8—22no—
79C11×#102—22no—
80C11×#102—22no—
81C11×#102—42no—
82C11×C22⋊C8—42no—
83C11×C22⋊C8—42no—
84C4×C8×C11—22no—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88#24968C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—21no—
90C24×C11C2×D412yes—
91C2×D4×C11—22no—
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×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4#4112yes—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—82no—
151C42×C11—44no—
152C42×C11—42no—
153C42×C11#4112yes—
154C42×C11#4112yes—
155#2537C2×C1111yescharacteristic
156#2354C2×C1111yescharacteristic, complemented
157#2076C2×C1112yescomplemented
158#2033C2×C1112yescomplemented
159#1954C2×C1111yescharacteristic, complemented
160#1947C2×C1111yescharacteristic, complemented
161#1875C2×C1112yescomplemented
162#1834C2×C1111yescharacteristic, complemented
163#1825C2×C1112yescomplemented
164#1802C2×C1111yescharacteristic, complemented
165C4×#102C2×C1111yescharacteristic, complemented
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—44no—
186D4×C11—88no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—84no—
212C2×C4×C11#12312yes—
213C2×C4×C11#12312yes—
214C2×C4×C11#13512yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C8×C11—42no—
223C8×C11—41no—
224C8×C11—41no—
225C2×#121—21no—
226C2×#121C22×C1112yes—
227C2×C4×D4C22×C1111yescharacteristic
228C2×C4×D4C22×C1111yescharacteristic
229C2×#117C22×C1112yes—
230C2×#107C22×C1112yes—
231C2×C4⋊C8C22×C1111yescharacteristic
232C2×#102C22×C1111yescharacteristic
233C2×#102C22×C1111yescharacteristic
234C2×#102C22×C1112yes—
235C2×C22⋊C8C22×C1112yes—
236C2×C22⋊C8C22×C1112yes—
237C2×C4×C8C22×C1111yescharacteristic
238#394—22no—
239#390—21no—
240#388—22no—
241#384C22×C1111yescharacteristic
242#384C22×C1111yescharacteristic
243#380—21no—
244#380C22×C1112yes—
245#380C22×C1112yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C22×C1111yescharacteristic
248#340C22×C1112yes—
249#340C22×C1111yescharacteristic
250#340C22×C1112yes—
251#340C22×C1111yescharacteristic
252#340C22×C1112yes—
253#340C22×C1112yes—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11C2×#12311yescharacteristic
269C22×C11#54611yescharacteristic
270C22×C11#54611yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C11#57611yescharacteristic
274C22×C11#57811yescharacteristic
275C4×C11—22no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—81no—
279C4×C11—82no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11#48214yes—
283C4×C11#52911yescharacteristic
284C4×C11#54011yescharacteristic
285C4×C11#55311yescharacteristic
286C4×C11#55511yescharacteristic
287C22×D4—22no—
288C22×D4D4×C1111yescharacteristic
289C22×D4C23×C1111yescharacteristic
290C23×C4—21no—
291C23×C4C23×C1112yes—
292C22×C8C23×C1111yescharacteristic
293C22×C8C23×C1111yescharacteristic
294C22×C8C23×C1112yes—
295#121—24no—
296#121—42no—
297#121—44no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302#117—24no—
303#117—42no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4D4×C1111yescharacteristic
309C2×C4⋊C4C23×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C4⋊C4C23×C1112yes—
312C2×C4⋊C4C23×C1111yescharacteristic
313C2×C4⋊C4C23×C1111yescharacteristic
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4D4×C1112yes—
320C2×C42—22no—
321C2×C42—21no—
322C2×C42C23×C1111yescharacteristic
323#107—42no—
324C4⋊C8—22no—
325#102—22no—
326#102—22no—
327#102—42no—
328C22⋊C8—42no—
329C22⋊C8—42no—
330C4×C8—22no—
331#95—22no—
332#95—21no—
333#95—22no—
334C2×C11—82no—
335C2×C11—82no—
336C2×C11#242011yescharacteristic
337C2×C11C2×#48211yescharacteristic
338C2×C11#309811yescharacteristic
339C2×C11#330211yescharacteristic
340C2×C11#330511yescharacteristic
341C2×C11#332511yescharacteristic
342C2×C11#333011yescharacteristic
343C24—21no—
344C24C2×D4×C1112yes—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4—82no—
356C2×D4C11×#4112yes—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C24×C1111yescharacteristic
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—81no—
397C4⋊C4—81no—
398C4⋊C4C11×#4112yes—
399C22⋊C4—24no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—42no—
404C22⋊C4—82no—
405C42—44no—
406C42—42no—
407C42C11×#4112yes—
408C42C11×#4112yes—
409C11#2496811yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23C22×D4×C1111yescharacteristic
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429D4—44no—
430D4—88no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—84no—
456C2×C4C11×#12312yes—
457C2×C4C11×#12312yes—
458C2×C4C11×#13512yes—
459C2×C4C11×AGL(1,ℤ/8)12yes—
460C2×C4C2×C11×#4111yescharacteristic
461C2×C4C2×C11×#4111yescharacteristic
462C2×C4C2×C11×#4111yescharacteristic
463C2×C4C2×C11×#4111yescharacteristic
464C2×C4C11×H(5,𝔽2)11yescharacteristic
465C2×C4C11×H(5,𝔽2)11yescharacteristic
466C8—42no—
467C8—41no—
468C8—41no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×C11×#12311yescharacteristic
484C22C11×#54611yescharacteristic
485C22C11×#54611yescharacteristic
486C22C2×C11×#13511yescharacteristic
487C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
488C22C11×#57611yescharacteristic
489C22C11×#57811yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—82no—
495C4—81no—
496C4—81no—
497C4C11×#48214yes—
498C4C11×#52911yescharacteristic
499C4C11×#54011yescharacteristic
500C4C11×#55311yescharacteristic
501C4C11×#55511yescharacteristic
502C2—82no—
503C2—82no—
504C2C11×#242011yescharacteristic
505C2C2×C11×#48211yescharacteristic
506C2C11×#309811yescharacteristic
507C2C11×#330211yescharacteristic
508C2C11×#330511yescharacteristic
509C2C11×#332511yescharacteristic
510C2C11×#333011yescharacteristic
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. C11×#2354C2semidirect
3. C11×#2076C2semidirect
4. C11×#2033C2semidirect
5. C11×#1954C2semidirect
6. C11×#1947C2semidirect
7. C11×#1875C2semidirect
8. C11×#1834C2semidirect
9. C11×#1825C2semidirect
10. C11×#1802C2semidirect
11. C4×C11×#102C2semidirect
88. #24968C11direct (N × H)
156. #2354C2×C11semidirect
157. #2076C2×C11semidirect
158. #2033C2×C11semidirect
159. #1954C2×C11semidirect
160. #1947C2×C11semidirect
161. #1875C2×C11semidirect
162. #1834C2×C11semidirect
163. #1825C2×C11semidirect
164. #1802C2×C11semidirect
165. C4×#102C2×C11semidirect
409. C11#24968direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25372
C11×#23542
C11×#20762
C11×#20332
C11×#19542
C11×#19472
C11×#18752
C11×#18342
C11×#18252
C11×#18022
C4×C11×#1022
#2496811