Finite Group Databasebeta

← C11×#24135 #14601328

Subgroups — C11×#24135 #14601328

Order 2816.

1076 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#441C211yesmaximal, characteristic, complemented
4C11×#2536C211yesmaximal, characteristic
5C11×#2036C212yesmaximal, complemented
6C11×#2001C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic
9C11×#1873C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C11×#556—24no—
14C11×#556—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2212yes—
25C11×#477—24no—
26C11×#441—24no—
27C2×C11×#107C2212yes—
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#398—21no—
38C11×#394—21no—
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2312yes—
50C2×C11×Q16—22no—
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yes—
58C11×#126—216no—
59C11×#124—28no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—42no—
64C4×Q8×C11—28no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11D414yes—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C11×#117—24no—
72C11×#117—24no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—22no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#107—24no—
93C11×#106—22no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#103—42no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—42no—
101C11×#97—22no—
102C11×#95—22no—
103C11×#95—21no—
104C11×#95—21no—
105#24135C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11C2×D412yes—
107C2×Q8×C11—24no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—44no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11#4112yes—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C11×Q16—28no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11#4112yes—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—44no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D414yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—44no—
168C42×C11—28no—
169C42×C11—24no—
170C42×C11—42no—
171C42×C11C2×D412yes—
172C42×C11C2×D412yes—
173C2×#556C2×C1111yescharacteristic
174C2×#477C2×C1111yescharacteristic, complemented
175C2×#441C2×C1111yescharacteristic, complemented
176#2536C2×C1111yescharacteristic
177#2036C2×C1112yescomplemented
178#2001C2×C1112yescomplemented
179#1993C2×C1111yescharacteristic, complemented
180#1955C2×C1111yescharacteristic
181#1873C2×C1112yescomplemented
182#1854C2×C1112yescomplemented
183#1805C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11C22×D411yescharacteristic
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—48no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—41no—
201D4×C11—44no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12012yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C8×C11—22no—
235C8×C11—41no—
236C8×C11—42no—
237C22×Q16C22×C1111yescharacteristic
238#556—24no—
239#556—24no—
240C2×C4⋊Q8C22×C1111yescharacteristic
241C2×#126—22no—
242C2×#124—21no—
243C2×C22⋊Q8C22×C1112yes—
244C2×C22⋊Q8C22×C1112yes—
245C2×C4×Q8—21no—
246C2×C4×Q8C22×C1111yescharacteristic
247C2×C4×Q8C22×C1111yescharacteristic
248C2×C4×D4C22×C1111yescharacteristic
249C2×#117C22×C1112yes—
250#477—24no—
251#441—24no—
252C2×#107C22×C1112yes—
253C2×#106C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×#103C22×C1112yes—
256C2×#103C22×C1111yescharacteristic
257C2×#103C22×C1111yescharacteristic
258C2×#103C22×C1112yes—
259C2×C22⋊C8C22×C1112yes—
260C2×C22⋊C8C22×C1112yes—
261C2×#97C22×C1111yescharacteristic
262#398—21no—
263#394—21no—
264#388—22no—
265#382C22×C1111yescharacteristic
266#380C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269#340C22×C1112yes—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11C2×#12011yescharacteristic
278C22×C11#54611yescharacteristic
279C22×C11#54711yescharacteristic
280C22×C11#57512yes—
281C22×C11#57812yes—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—44no—
288C4×C11—42no—
289C4×C11—81no—
290C4×C11—82no—
291C4×C11#52511yescharacteristic
292C4×C11#53711yescharacteristic
293C4×C11#54811yescharacteristic
294C4×C11#55011yescharacteristic
295C22×Q8—21no—
296C22×Q8C23×C1111yescharacteristic
297C22×Q8C23×C1111yescharacteristic
298C22×D4D4×C1111yescharacteristic
299C23×C4C23×C1112yes—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×Q16—22no—
303C22×C8C23×C1111yescharacteristic
304C22×C8C23×C1112yes—
305C22×C8C23×C1111yescharacteristic
306C4⋊Q8—22no—
307C4⋊Q8D4×C1114yes—
308#126—216no—
309#124—28no—
310C22⋊Q8—24no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313C22⋊Q8—42no—
314C4×Q8—28no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8D4×C1114yes—
319C4×D4—22no—
320C4×D4—22no—
321#117—24no—
322#117—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4D4×C1111yescharacteristic
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C4⋊C4C23×C1112yes—
331C2×C4⋊C4C23×C1111yescharacteristic
332C2×C4⋊C4C23×C1112yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4D4×C1112yes—
338C2×C42—22no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42C23×C1111yescharacteristic
342#107—24no—
343#106—22no—
344C4⋊C8—22no—
345#103—22no—
346#103—22no—
347#103—24no—
348#103—42no—
349C22⋊C8—24no—
350C22⋊C8—42no—
351#97—22no—
352#95—22no—
353#95—21no—
354#95—21no—
355C2×C11—82no—
356C2×C11#240711yescharacteristic
357C2×C11#300511yescharacteristic
358C2×C11#301111yescharacteristic
359C2×C11#331312yes—
360C2×C11#334912yes—
361C24C2×D4×C1112yes—
362C2×Q8—24no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—44no—
374C2×Q8C2×D4×C1112yes—
375C2×Q8C11×#4112yes—
376C2×D4—22no—
377C2×D4—42no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4C2×D4×C1112yes—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C24×C1111yescharacteristic
394Q16—28no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—21no—
401C2×C8—22no—
402C2×C8—21no—
403C2×C8C11×#4112yes—
404C4⋊C4—28no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—44no—
415C4⋊C4—42no—
416C4⋊C4C2×D4×C1112yes—
417C4⋊C4C2×D4×C1114yes—
418C22⋊C4—28no—
419C22⋊C4—28no—
420C22⋊C4—24no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C42—28no—
424C42—24no—
425C42—42no—
426C42C2×D4×C1112yes—
427C42C2×D4×C1112yes—
428C11#2413511yescharacteristic, direct product factor, Sylow
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23C22×D4×C1111yescharacteristic
437Q8—22no—
438Q8—22no—
439Q8—22no—
440Q8—22no—
441Q8—48no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446D4—44no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4C11×#12012yes—
472C2×C4C11×#12012yes—
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C22×D4×C1111yescharacteristic
475C2×C4C2×C11×#4111yescharacteristic
476C2×C4C2×C11×#4111yescharacteristic
477C2×C4C11×H(5,𝔽2)11yescharacteristic
478C2×C4C11×2−1+411yescharacteristic
479C8—22no—
480C8—41no—
481C8—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22C2×C11×#12011yescharacteristic
490C22C11×#54611yescharacteristic
491C22C11×#54711yescharacteristic
492C22C11×#57512yes—
493C22C11×#57812yes—
494C4—22no—
495C4—22no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—44no—
500C4—42no—
501C4—81no—
502C4—82no—
503C4C11×#52511yescharacteristic
504C4C11×#53711yescharacteristic
505C4C11×#54811yescharacteristic
506C4C11×#55011yescharacteristic
507C2—82no—
508C2C11×#240711yescharacteristic
509C2C11×#300511yescharacteristic
510C2C11×#301111yescharacteristic
511C2C11×#331312yes—
512C2C11×#334912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
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. C2×C11×#477C2semidirect
3. C2×C11×#441C2semidirect
5. C11×#2036C2semidirect
6. C11×#2001C2semidirect
7. C11×#1993C2semidirect
9. C11×#1873C2semidirect
10. C11×#1854C2semidirect
11. C11×#1805C2semidirect
105. #24135C11direct (N × H)
174. C2×#477C2×C11semidirect
175. C2×#441C2×C11semidirect
177. #2036C2×C11semidirect
178. #2001C2×C11semidirect
179. #1993C2×C11semidirect
181. #1873C2×C11semidirect
182. #1854C2×C11semidirect
183. #1805C2×C11semidirect
428. C11#24135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4772
C2×C11×#4412
C11×#25362
C11×#20362
C11×#20012
C11×#19932
C11×#19552
C11×#18732
C11×#18542
C11×#18052
#2413511