Finite Group Databasebeta

← C11×#15510 #14592703

Subgroups — C11×#15510 #14592703

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C212yesmaximal
2C2×C11×#391C212yesmaximal
3C11×#1446C211yesmaximal, characteristic
4C11×#1446C211yesmaximal, characteristic
5C11×#1444C212yesmaximal
6C11×#1444C211yesmaximal, characteristic
7C11×#1441C212yesmaximal
8C11×#1436C212yesmaximal
9C11×C4⋊#95C212yesmaximal
10C23×Q8×C11C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11C2212yes—
18C11×#395—28no—
19C11×#391—28no—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C22×Q8×C11—24no—
34C22×Q8×C11—24no—
35C22×Q8×C11—24no—
36C22×Q8×C11—22no—
37C22×Q8×C11—41no—
38C22×Q8×C11—41no—
39C22×Q8×C11—41no—
40C22×Q8×C11—42no—
41C22×Q8×C11—41no—
42C22×Q8×C11Q814yescomplemented
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—42no—
60C2×C11×C4⋊C4—42no—
61C2×C11×C4⋊C4—42no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4—41no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4Q818yescomplemented
66C2×C42×C11—24no—
67C2×C42×C11—24no—
68C2×C42×C11—42no—
69C11×#95—24no—
70C11×#95—24no—
71C11×#95—24no—
72C11×#95—24no—
73C11×#95—24no—
74C11×#95—24no—
75C11×#95—41no—
76C11×#95—42no—
77C11×#95—42no—
78C11×#95—41no—
79C11×#95—41no—
80C11×#95D418yes—
81C11×#95Q814yescomplemented
82#15510C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11C2411yescharacteristic
84C2×Q8×C11—216no—
85C2×Q8×C11—44no—
86C2×Q8×C11—44no—
87C2×Q8×C11—48no—
88C2×Q8×C11—44no—
89C2×Q8×C11—44no—
90C2×Q8×C11—48no—
91C2×Q8×C11—48no—
92C2×Q8×C11—44no—
93C2×Q8×C11—44no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
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—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×Q812yes—
143C22×C4×C11C2×Q814yes—
144C22×C4×C11C2×Q814yes—
145C22×C4×C11C2×Q812yes—
146C22×C4×C11C2×Q814yes—
147C22×C4×C11C2×Q814yes—
148C22×C4×C11C2×Q814yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4114yes—
151C11×C4⋊C4—48no—
152C11×C4⋊C4—48no—
153C11×C4⋊C4—48no—
154C11×C4⋊C4—48no—
155C11×C4⋊C4—44no—
156C42×C11—48no—
157C2×#395C2×C1112yes—
158C2×#391C2×C1112yes—
159#1446C2×C1111yescharacteristic
160#1446C2×C1111yescharacteristic
161#1444C2×C1111yescharacteristic
162#1444C2×C1112yes—
163#1441C2×C1112yes—
164#1436C2×C1112yes—
165C4⋊#95C2×C1112yes—
166C23×C11C22×D412yes—
167C23×C11C22×Q811yescharacteristic
168C23×C11C22×Q811yescharacteristic
169C23×C11C22×Q812yes—
170C23×C11C2×#4112yes—
171C23×C11C2×#4111yescharacteristic
172C23×C11H(5,𝔽2)11yescharacteristic
173C23×C11H(5,𝔽2)12yes—
174C23×C11H(5,𝔽2)11yescharacteristic
175C23×C11H(5,𝔽2)11yescharacteristic
176C23×C112−1+411yescharacteristic
177Q8×C11—416no—
178Q8×C11—416no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
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×C11C22⋊Q818yes—
235C2×C4×C11C4⋊Q818yes—
236C23×Q8C22×C1111yescharacteristic
237C23×Q8C22×C1111yescharacteristic
238C22×C4⋊C4C22×C1112yes—
239C22×C4⋊C4C22×C1112yes—
240C22×C4⋊C4C22×C1112yes—
241C22×C4⋊C4C22×C1111yescharacteristic
242C22×C4⋊C4C22×C1112yes—
243C22×C42C22×C1112yes—
244#395—28no—
245#391—28no—
246C2×#95C22×C1112yes—
247C2×#95C22×C1112yes—
248C2×#95C22×C1112yes—
249C2×#95C22×C1112yes—
250C2×#95C22×C1112yes—
251C2×#95C22×C1112yes—
252C2×#95C22×C1111yescharacteristic
253C2×#95C22×C1112yes—
254C2×#95C22×C1112yes—
255C2×#95C22×C1111yescharacteristic
256C2×#95C22×C1111yescharacteristic
257C2×#95C22×C1112yes—
258C2×#95C22×C1111yescharacteristic
259C22×C11C2×C22⋊Q812yes—
260C22×C11C2×C4⋊Q812yes—
261C22×C11#53312yes—
262C22×C11#53512yes—
263C22×C11#53811yescharacteristic
264C22×C11#54212yes—
265C22×C11#54312yes—
266C22×C11#54311yescharacteristic
267C22×C11#54411yescharacteristic
268C22×C11D4211yescharacteristic
269C22×C11#54612yes—
270C22×C11#54612yes—
271C22×C11D4×Q812yes—
272C22×C11#55111yescharacteristic
273C22×C11#55412yes—
274C22×C11#55412yes—
275C22×C11#55411yescharacteristic
276C22×C11#55711yescharacteristic
277C22×C11Q8211yescharacteristic
278C22×C11Q8212yes—
279C22×C11Q8211yescharacteristic
280C22×C11H(3,𝔽4)11yescharacteristic
281C22×C11#56211yescharacteristic
282C4×C11—28no—
283C4×C11—28no—
284C4×C11—44no—
285C4×C11—42no—
286C4×C11—44no—
287C4×C11—44no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—82no—
291C22×Q8—24no—
292C22×Q8—24no—
293C22×Q8—24no—
294C22×Q8—22no—
295C22×Q8—41no—
296C22×Q8—41no—
297C22×Q8—41no—
298C22×Q8—42no—
299C22×Q8—41no—
300C22×Q8Q8×C1114yescomplemented
301C23×C4C23×C1112yes—
302C23×C4C23×C1112yes—
303C23×C4C23×C1112yes—
304C23×C4C23×C1111yescharacteristic
305C23×C4C23×C1112yes—
306C23×C4C23×C1111yescharacteristic
307C23×C4C23×C1111yescharacteristic
308C23×C4C23×C1112yes—
309C23×C4C23×C1112yes—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4Q8×C1118yescomplemented
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—42no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—41no—
334#95—42no—
335#95—42no—
336#95—41no—
337#95—41no—
338#95D4×C1118yes—
339#95Q8×C1114yescomplemented
340C2×C11#243711yescharacteristic
341C2×C11#245112yes—
342C2×C11#254912yes—
343C2×C11#255111yescharacteristic
344C2×C11#256712yes—
345C2×C11#258611yescharacteristic
346C2×C11#267011yescharacteristic
347C2×C11#269212yes—
348C2×C11#276311yescharacteristic
349C2×C11#280611yescharacteristic
350C2×C11#281111yescharacteristic
351C24C24×C1111yescharacteristic
352C2×Q8—216no—
353C2×Q8—44no—
354C2×Q8—44no—
355C2×Q8—48no—
356C2×Q8—44no—
357C2×Q8—44no—
358C2×Q8—48no—
359C2×Q8—48no—
360C2×Q8—44no—
361C2×Q8—44no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4C2×D4×C1114yes—
408C22×C4C2×D4×C1114yes—
409C22×C4C2×D4×C1114yes—
410C22×C4C2×Q8×C1112yes—
411C22×C4C2×Q8×C1114yes—
412C22×C4C2×Q8×C1114yes—
413C22×C4C2×Q8×C1112yes—
414C22×C4C2×Q8×C1114yes—
415C22×C4C2×Q8×C1114yes—
416C22×C4C2×Q8×C1114yes—
417C22×C4C11×#4112yes—
418C22×C4C11×#4114yes—
419C4⋊C4—48no—
420C4⋊C4—48no—
421C4⋊C4—48no—
422C4⋊C4—48no—
423C4⋊C4—44no—
424C42—48no—
425C11#1551011yescharacteristic, direct product factor, Sylow
426C23C22×D4×C1112yes—
427C23C22×Q8×C1111yescharacteristic
428C23C22×Q8×C1111yescharacteristic
429C23C22×Q8×C1112yes—
430C23C2×C11×#4112yes—
431C23C2×C11×#4111yescharacteristic
432C23C11×H(5,𝔽2)11yescharacteristic
433C23C11×H(5,𝔽2)12yes—
434C23C11×H(5,𝔽2)11yescharacteristic
435C23C11×H(5,𝔽2)11yescharacteristic
436C23C11×2−1+411yescharacteristic
437Q8—416no—
438Q8—416no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4C11×C22⋊Q818yes—
495C2×C4C11×C4⋊Q818yes—
496C22C2×C11×C22⋊Q812yes—
497C22C2×C11×C4⋊Q812yes—
498C22C11×#53312yes—
499C22C11×#53512yes—
500C22C11×#53811yescharacteristic
501C22C11×#54212yes—
502C22C11×#54312yes—
503C22C11×#54311yescharacteristic
504C22C11×#54411yescharacteristic
505C22D42×C1111yescharacteristic
506C22C11×#54612yes—
507C22C11×#54612yes—
508C22D4×Q8×C1112yes—
509C22C11×#55111yescharacteristic
510C22C11×#55412yes—
511C22C11×#55412yes—
512C22C11×#55411yescharacteristic
513C22C11×#55711yescharacteristic
514C22Q82×C1112yes—
515C22Q82×C1111yescharacteristic
516C22Q82×C1111yescharacteristic
517C22C11×H(3,𝔽4)11yescharacteristic
518C22C11×#56211yescharacteristic
519C4—28no—
520C4—28no—
521C4—44no—
522C4—42no—
523C4—44no—
524C4—44no—
525C4—42no—
526C4—42no—
527C4—82no—
528C2C11×#243711yescharacteristic
529C2C11×#245112yes—
530C2C11×#254912yes—
531C2C11×#255111yescharacteristic
532C2C11×#256712yes—
533C2C11×#258611yescharacteristic
534C2C11×#267011yescharacteristic
535C2C11×#269212yes—
536C2C11×#276311yescharacteristic
537C2C11×#280611yescharacteristic
538C2C11×#281111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C24
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
42. C22×Q8×C11Q8semidirect
65. C2×C11×C4⋊C4Q8semidirect
81. C11×#95Q8semidirect
82. #15510C11direct (N × H)
300. C22×Q8Q8×C11semidirect
323. C2×C4⋊C4Q8×C11semidirect
339. #95Q8×C11semidirect
425. C11#15510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3952
C2×C11×#3912
C11×#14462
C11×#14442
C11×#14412
C11×#14362
C11×C4⋊#952
#1551011