Finite Group Databasebeta

← C11×#24129 #14601322

Subgroups — C11×#24129 #14601322

Order 2816.

1204 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic, complemented
4C11×#2535C211yesmaximal, characteristic, complemented
5C11×#2033C212yesmaximal, complemented
6C11×#1999C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic, complemented
9C11×#1875C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#555—24no—
14C11×#555—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C2×C11×#117C2212yes—
25C11×#474—24no—
26C11×#442—24no—
27C2×C11×#107C2212yes—
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#397—21no—
38C11×#392—21no—
39C11×#386—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2312yes—
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yescomplemented
62C11×#124—216no—
63C11×#121—28no—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—42no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11D414yescomplemented
74C11×#117—28no—
75C11×#117—24no—
76C11×#117—24no—
77C2×C11×C4⋊C4—21no—
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—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11—22no—
91C2×C42×C11C2311yescharacteristic
92C11×#107—24no—
93C11×#106—22no—
94C11×C4⋊C8—22no—
95C11×#102—22no—
96C11×#102—22no—
97C11×#102—24no—
98C11×#102—42no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—42no—
101C11×#97—22no—
102C11×#95—22no—
103C11×#95—21no—
104C11×#95—21no—
105#24129C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11C2×D412yes—
109C2×Q8×C11—24no—
110C2×Q8×C11—82no—
111C2×D4×C11—28no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11—82no—
129C2×D4×C11C2×D412yes—
130C2×D4×C11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—44no—
143C22×C4×C11—42no—
144C22×C4×C11—82no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C11×D8—28no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11#4112yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D414yes—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—82no—
176C42×C11—28no—
177C42×C11C2×D412yes—
178C42×C11C2×D412yes—
179C2×#555C2×C1111yescharacteristic, complemented
180C2×#474C2×C1111yescharacteristic, complemented
181C2×#442C2×C1111yescharacteristic, complemented
182#2535C2×C1111yescharacteristic, complemented
183#2033C2×C1112yescomplemented
184#1999C2×C1112yescomplemented
185#1993C2×C1111yescharacteristic, complemented
186#1955C2×C1111yescharacteristic, complemented
187#1875C2×C1112yescomplemented
188#1854C2×C1112yescomplemented
189#1804C2×C1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11C22×D411yescharacteristic
208Q8×C11—84no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—44no—
214D4×C11—41no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—88no—
219D4×C11—88no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—48no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—84no—
241C2×C4×C11#12012yes—
242C2×C4×C11#12012yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C8×C11—22no—
250C8×C11—41no—
251C8×C11—42no—
252C22×D8C22×C1111yescharacteristic
253#555—24no—
254#555—24no—
255C2×C4⋊Q8C22×C1111yescharacteristic
256C2×#124—22no—
257C2×#121—21no—
258C2×#121C22×C1112yes—
259C2×#121C22×C1112yes—
260C2×C4×D4C22×C1111yescharacteristic
261C2×C4×D4C22×C1111yescharacteristic
262C2×C4×D4C22×C1111yescharacteristic
263C2×#117—21no—
264C2×#117C22×C1112yes—
265#474—24no—
266#442—24no—
267C2×#107C22×C1112yes—
268C2×#106C22×C1111yescharacteristic
269C2×C4⋊C8C22×C1111yescharacteristic
270C2×#102C22×C1111yescharacteristic
271C2×#102C22×C1112yes—
272C2×#102C22×C1111yescharacteristic
273C2×#102C22×C1112yes—
274C2×C22⋊C8C22×C1112yes—
275C2×C22⋊C8C22×C1112yes—
276C2×#97C22×C1111yescharacteristic
277#397—21no—
278#392—21no—
279#386—22no—
280#382C22×C1111yescharacteristic
281#380C22×C1112yes—
282#340C22×C1112yes—
283#340C22×C1112yes—
284#340C22×C1112yes—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—82no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11#54711yescharacteristic
305C22×C11#57512yes—
306C22×C11#57612yes—
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11—81no—
313C4×C11—82no—
314C4×C11#52511yescharacteristic
315C4×C11#53711yescharacteristic
316C4×C11#54811yescharacteristic
317C4×C11#55011yescharacteristic
318C22×Q8—21no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4D4×C1111yescharacteristic
322C22×D4C23×C1111yescharacteristic
323C22×D4C23×C1111yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C1112yes—
327C2×D8—22no—
328C2×D8—22no—
329C2×D8—22no—
330C22×C8C23×C1111yescharacteristic
331C22×C8C23×C1112yes—
332C22×C8C23×C1111yescharacteristic
333C4⋊Q8—22no—
334C4⋊Q8D4×C1114yescomplemented
335#124—216no—
336#121—28no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—42no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4D4×C1114yescomplemented
347#117—28no—
348#117—24no—
349#117—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4D4×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1112yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4D4×C1112yes—
363C2×C42—22no—
364C2×C42C23×C1111yescharacteristic
365#107—24no—
366#106—22no—
367C4⋊C8—22no—
368#102—22no—
369#102—22no—
370#102—24no—
371#102—42no—
372C22⋊C8—24no—
373C22⋊C8—42no—
374#97—22no—
375#95—22no—
376#95—21no—
377#95—21no—
378C2×C11—82no—
379C2×C11—82no—
380C2×C11—82no—
381C2×C11#240711yescharacteristic
382C2×C11#300511yescharacteristic
383C2×C11#300811yescharacteristic
384C2×C11#331912yes—
385C2×C11#334712yes—
386C24—21no—
387C24—21no—
388C24C2×D4×C1112yes—
389C2×Q8—24no—
390C2×Q8—82no—
391C2×D4—28no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—42no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—82no—
407C2×D4—82no—
408C2×D4—82no—
409C2×D4C2×D4×C1112yes—
410C2×D4C11×#4112yes—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—44no—
423C22×C4—42no—
424C22×C4—82no—
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C24×C1111yescharacteristic
429D8—28no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—22no—
437C2×C8—21no—
438C2×C8C11×#4112yes—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4C2×D4×C1112yes—
448C4⋊C4C2×D4×C1114yes—
449C22⋊C4—28no—
450C22⋊C4—28no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—82no—
456C42—28no—
457C42C2×D4×C1112yes—
458C42C2×D4×C1112yes—
459C11#2412911yescharacteristic, direct product factor, Sylow
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23C22×D4×C1111yescharacteristic
478Q8—84no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—22no—
483D4—44no—
484D4—41no—
485D4—41no—
486D4—41no—
487D4—41no—
488D4—88no—
489D4—88no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—84no—
511C2×C4C11×#12012yes—
512C2×C4C11×#12012yes—
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C2×C11×#4111yescharacteristic
517C2×C4C11×H(5,𝔽2)11yescharacteristic
518C2×C4C11×2−1+411yescharacteristic
519C8—22no—
520C8—41no—
521C8—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—44no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22C2×C11×#12011yescharacteristic
540C22C11×#54611yescharacteristic
541C22C11×#54711yescharacteristic
542C22C11×#57512yes—
543C22C11×#57612yes—
544C4—22no—
545C4—22no—
546C4—42no—
547C4—42no—
548C4—44no—
549C4—81no—
550C4—82no—
551C4C11×#52511yescharacteristic
552C4C11×#53711yescharacteristic
553C4C11×#54811yescharacteristic
554C4C11×#55011yescharacteristic
555C2—82no—
556C2—82no—
557C2—82no—
558C2C11×#240711yescharacteristic
559C2C11×#300511yescharacteristic
560C2C11×#300811yescharacteristic
561C2C11×#331912yes—
562C2C11×#334712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#555C2semidirect
2. C2×C11×#474C2semidirect
3. C2×C11×#442C2semidirect
4. C11×#2535C2semidirect
5. C11×#2033C2semidirect
6. C11×#1999C2semidirect
7. C11×#1993C2semidirect
8. C11×#1955C2semidirect
9. C11×#1875C2semidirect
10. C11×#1854C2semidirect
11. C11×#1804C2semidirect
61. C11×C4⋊Q8D4semidirect
73. C4×D4×C11D4semidirect
105. #24129C11direct (N × H)
179. C2×#555C2×C11semidirect
180. C2×#474C2×C11semidirect
181. C2×#442C2×C11semidirect
182. #2535C2×C11semidirect
183. #2033C2×C11semidirect
184. #1999C2×C11semidirect
185. #1993C2×C11semidirect
186. #1955C2×C11semidirect
187. #1875C2×C11semidirect
188. #1854C2×C11semidirect
189. #1804C2×C11semidirect
334. C4⋊Q8D4×C11semidirect
346. C4×D4D4×C11semidirect
459. C11#24129direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4742
C2×C11×#4422
C11×#25352
C11×#20332
C11×#19992
C11×#19932
C11×#19552
C11×#18752
C11×#18542
C11×#18042
#2412911