Finite Group Databasebeta

← C11×#24303 #14601496

Subgroups — C11×#24303 #14601496

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#475C211yesmaximal, characteristic, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2026C212yesmaximal, complemented
7C11×#1988C211yesmaximal, characteristic, complemented
8C11×#1987C211yesmaximal, characteristic, complemented
9C11×#1873C212yesmaximal
10C11×#1854C212yesmaximal
11C11×#1797C211yesmaximal, characteristic
12C11×#533—24no—
13C11×#533—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C11×#117C2212yes—
24C22×C42×C11C2211yescharacteristic
25C11×#477—24no—
26C11×#475—24no—
27C2×C11×#107C2212yes—
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C11×#391C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#387—21no—
37C11×#385—21no—
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11C2311yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yes—
58C11×C4⋊Q8D414yes—
59C11×#125—24no—
60C11×#125—24no—
61C11×C22⋊Q8—28no—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8Q814yescomplemented
65C4×Q8×C11—28no—
66C4×Q8×C11—28no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C11×#117—24no—
70C11×#117—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11D411yescharacteristic
92C2×C42×C11D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C11×#107—24no—
96C11×#106—24no—
97C11×C4⋊C8—22no—
98C11×C4⋊C8—22no—
99C11×#103—24no—
100C11×#103—24no—
101C11×C22⋊C8—24no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107#24303C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11C2×D411yescharacteristic
109C2×Q8×C11—24no—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×Q812yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
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—21no—
134C22×C4×C11—21no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×Q812yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4C2×D414yes—
167C11×C4⋊C4C2×Q812yes—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—42no—
171C42×C11—28no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C42×C11—42no—
178C42×C11C2×D412yes—
179C42×C11C2×D412yes—
180C2×#533C2×C1111yescharacteristic
181C2×#477C2×C1111yescharacteristic, complemented
182C2×#475C2×C1111yescharacteristic, complemented
183C4×C22⋊Q8C2×C1111yescharacteristic
184#2059C2×C1112yescomplemented
185#2026C2×C1112yescomplemented
186#1988C2×C1111yescharacteristic, complemented
187#1987C2×C1111yescharacteristic, complemented
188#1873C2×C1112yes—
189#1854C2×C1112yes—
190#1797C2×C1111yescharacteristic
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11C22⋊Q812yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—48no—
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—48no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—44no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11#12012yes—
240C2×C4×C11#12012yes—
241C2×C4×C11C22⋊Q812yes—
242C2×C4×C11#13512yes—
243C2×C4×C11#13712yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C8×C11—42no—
251C8×C11—42no—
252#533—24no—
253#533—24no—
254C2×C4⋊Q8C22×C1111yescharacteristic
255C2×C4⋊Q8C22×C1111yescharacteristic
256C2×#125C22×C1112yes—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8C22×C1111yescharacteristic
260C2×C4×Q8—21no—
261C2×C4×Q8—21no—
262C2×C4×Q8C22×C1111yescharacteristic
263C2×#117C22×C1112yes—
264C22×C42C22×C1111yescharacteristic
265#477—24no—
266#475—24no—
267C2×#107C22×C1112yes—
268C2×#106C22×C1112yes—
269C2×C4⋊C8C22×C1111yescharacteristic
270C2×C4⋊C8C22×C1111yescharacteristic
271C2×#103C22×C1112yes—
272C2×#103C22×C1112yes—
273C2×C22⋊C8C22×C1112yes—
274#391C22×C1111yescharacteristic
275#389C22×C1111yescharacteristic
276#387—21no—
277#385—21no—
278#380C22×C1111yescharacteristic
279C4×C4⋊C4—21no—
280C4×C4⋊C4C22×C1111yescharacteristic
281C4×C22⋊C4—21no—
282#340C22×C1112yes—
283#340C22×C1112yes—
284#340C22×C1112yes—
285#340C22×C1112yes—
286#336C22×C1112yes—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×C22⋊Q811yescharacteristic
296C22×C11#53611yescharacteristic
297C22×C11C2×#13511yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11#57511yescharacteristic
300C22×C11#57511yescharacteristic
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—41no—
306C4×C11—44no—
307C4×C11—41no—
308C4×C11—44no—
309C4×C11—81no—
310C4×C11—81no—
311C4×C11#45214yes—
312C4×C11#54811yescharacteristic
313C4×C11#54811yescharacteristic
314C4×C11D4×Q811yescharacteristic
315C4×C11D4×Q811yescharacteristic
316C22×Q8—21no—
317C22×Q8—21no—
318C22×Q8C23×C1111yescharacteristic
319C23×C4D4×C1111yescharacteristic
320C23×C4D4×C1111yescharacteristic
321C23×C4C23×C1111yescharacteristic
322C22×C8C23×C1112yes—
323C22×C8C23×C1112yes—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8D4×C1114yes—
327C4⋊Q8D4×C1114yes—
328#125—24no—
329#125—24no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332C22⋊Q8—22no—
333C22⋊Q8Q8×C1114yescomplemented
334C4×Q8—28no—
335C4×Q8—28no—
336C4×Q8—22no—
337C4×Q8—22no—
338#117—24no—
339#117—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C22⋊C4—22no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42D4×C1111yescharacteristic
361C2×C42D4×C1111yescharacteristic
362C2×C42C23×C1111yescharacteristic
363C2×C42C23×C1111yescharacteristic
364#107—24no—
365#106—24no—
366C4⋊C8—22no—
367C4⋊C8—22no—
368#103—24no—
369#103—24no—
370C22⋊C8—24no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376C2×C11—42no—
377C2×C11#240911yescharacteristic
378C2×C11C2×#45211yescharacteristic
379C2×C11#300511yescharacteristic
380C2×C11#307611yescharacteristic
381C2×C11#307811yescharacteristic
382C2×C11#323311yescharacteristic
383C2×C11#323711yescharacteristic
384C24C2×D4×C1111yescharacteristic
385C2×Q8—24no—
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8C2×Q8×C1112yes—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×Q8×C1112yes—
419C22×C4C11×#4112yes—
420C22×C4C24×C1111yescharacteristic
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4C2×D4×C1114yes—
442C4⋊C4C2×D4×C1114yes—
443C4⋊C4C2×Q8×C1112yes—
444C22⋊C4—28no—
445C22⋊C4—24no—
446C22⋊C4—42no—
447C42—28no—
448C42—22no—
449C42—22no—
450C42—21no—
451C42—21no—
452C42—42no—
453C42—42no—
454C42C2×D4×C1112yes—
455C42C2×D4×C1112yes—
456C11#2430311yescharacteristic, direct product factor, Sylow
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23C11×C22⋊Q812yes—
464C23C22×D4×C1111yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—48no—
468Q8—41no—
469Q8—41no—
470Q8—48no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—44no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4C11×#12012yes—
506C2×C4C11×#12012yes—
507C2×C4C11×C22⋊Q812yes—
508C2×C4C11×#13512yes—
509C2×C4C11×#13712yes—
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C22×D4×C1111yescharacteristic
512C2×C4C22×Q8×C1111yescharacteristic
513C2×C4C2×C11×#4111yescharacteristic
514C2×C4C11×2−1+411yescharacteristic
515C2×C4C11×2−1+411yescharacteristic
516C8—42no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22C2×C11×#12011yescharacteristic
526C22C2×C11×C22⋊Q811yescharacteristic
527C22C11×#53611yescharacteristic
528C22C2×C11×#13511yescharacteristic
529C22C2×C11×#13711yescharacteristic
530C22C11×#57511yescharacteristic
531C22C11×#57511yescharacteristic
532C4—22no—
533C4—22no—
534C4—42no—
535C4—41no—
536C4—44no—
537C4—41no—
538C4—44no—
539C4—42no—
540C4—81no—
541C4—81no—
542C4C11×#45214yes—
543C4C11×#54811yescharacteristic
544C4C11×#54811yescharacteristic
545C4D4×Q8×C1111yescharacteristic
546C4D4×Q8×C1111yescharacteristic
547C2—42no—
548C2C11×#240911yescharacteristic
549C2C2×C11×#45211yescharacteristic
550C2C11×#300511yescharacteristic
551C2C11×#307611yescharacteristic
552C2C11×#307811yescharacteristic
553C2C11×#323311yescharacteristic
554C2C11×#323711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#477C2semidirect
3. C2×C11×#475C2semidirect
5. C11×#2059C2semidirect
6. C11×#2026C2semidirect
7. C11×#1988C2semidirect
8. C11×#1987C2semidirect
64. C11×C22⋊Q8Q8semidirect
107. #24303C11direct (N × H)
181. C2×#477C2×C11semidirect
182. C2×#475C2×C11semidirect
184. #2059C2×C11semidirect
185. #2026C2×C11semidirect
186. #1988C2×C11semidirect
187. #1987C2×C11semidirect
333. C22⋊Q8Q8×C11semidirect
456. C11#24303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4772
C2×C11×#4752
C4×C11×C22⋊Q82
C11×#20592
C11×#20262
C11×#19882
C11×#19872
C11×#18732
C11×#18542
C11×#17972
#2430311