Finite Group Databasebeta

← C11×#15511 #14592704

Subgroups — C11×#15511 #14592704

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#398C212yesmaximal
2C2×C11×#391C212yesmaximal
3C11×#1446C211yesmaximal, characteristic
4C11×#1445C211yesmaximal, characteristic
5C11×#1444C212yesmaximal
6C11×#1442C211yesmaximal, characteristic
7C11×#1441C212yesmaximal
8C11×#1436C212yesmaximal
9C11×#1434C212yesmaximal
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2212yes—
17C11×#398—28no—
18C11×#391—28no—
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C22×Q8×C11—24no—
34C22×Q8×C11—24no—
35C22×Q8×C11—41no—
36C22×Q8×C11—41no—
37C22×Q8×C11Q814yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4—41no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4—41no—
60C2×C11×C4⋊C4—41no—
61C2×C42×C11—24no—
62C2×C42×C11—24no—
63C2×C42×C11—42no—
64C11×#95—24no—
65C11×#95—24no—
66C11×#95—24no—
67C11×#95—24no—
68C11×#95—24no—
69C11×#95—24no—
70C11×#95—24no—
71C11×#95—24no—
72C11×#95—41no—
73C11×#95—42no—
74C11×#95—41no—
75C11×#95—41no—
76C11×#95D418yes—
77C11×#95Q814yescomplemented
78#15511C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11C2411yescharacteristic
80C2×Q8×C11—216no—
81C2×Q8×C11—44no—
82C2×Q8×C11—44no—
83C2×Q8×C11—48no—
84C2×Q8×C11—44no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
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—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
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—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×Q814yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11C2×Q814yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4114yes—
141C22×C4×C11#4114yes—
142C11×C4⋊C4—48no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—48no—
145C11×C4⋊C4—48no—
146C11×C4⋊C4—44no—
147C42×C11—48no—
148C2×#398C2×C1112yes—
149C2×#391C2×C1112yes—
150#1446C2×C1111yescharacteristic
151#1445C2×C1111yescharacteristic
152#1444C2×C1112yes—
153#1442C2×C1111yescharacteristic
154#1441C2×C1112yes—
155#1436C2×C1112yes—
156#1434C2×C1112yes—
157C23×C11C22×D412yes—
158C23×C11C22×Q811yescharacteristic
159C23×C11C22×Q811yescharacteristic
160C23×C11C2×#4112yes—
161C23×C11C2×#4111yescharacteristic
162C23×C11C2×#4112yes—
163C23×C11H(5,𝔽2)11yescharacteristic
164C23×C11H(5,𝔽2)11yescharacteristic
165C23×C11H(5,𝔽2)11yescharacteristic
166C23×C112−1+411yescharacteristic
167C23×C112−1+412yes—
168Q8×C11—416no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
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—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11C22⋊Q818yes—
226C23×Q8C22×C1111yescharacteristic
227C22×C4⋊C4C22×C1111yescharacteristic
228C22×C4⋊C4C22×C1112yes—
229C22×C4⋊C4C22×C1112yes—
230C22×C4⋊C4C22×C1112yes—
231C22×C4⋊C4C22×C1111yescharacteristic
232C22×C42C22×C1112yes—
233#398—28no—
234#391—28no—
235C2×#95C22×C1112yes—
236C2×#95C22×C1112yes—
237C2×#95C22×C1112yes—
238C2×#95C22×C1112yes—
239C2×#95C22×C1112yes—
240C2×#95C22×C1112yes—
241C2×#95C22×C1112yes—
242C2×#95C22×C1112yes—
243C2×#95C22×C1112yes—
244C2×#95C22×C1111yescharacteristic
245C2×#95C22×C1111yescharacteristic
246C2×#95C22×C1111yescharacteristic
247C2×#95C22×C1112yes—
248C2×#95C22×C1111yescharacteristic
249C22×C11C2×C22⋊Q812yes—
250C22×C11#53212yes—
251C22×C11#53312yes—
252C22×C11#53612yes—
253C22×C11#53811yescharacteristic
254C22×C11#53912yes—
255C22×C11#54212yes—
256C22×C11#54311yescharacteristic
257C22×C11#54411yescharacteristic
258C22×C11D4211yescharacteristic
259C22×C11#54612yes—
260C22×C11#54612yes—
261C22×C11D4×Q812yes—
262C22×C11#55111yescharacteristic
263C22×C11#55212yes—
264C22×C11#55212yes—
265C22×C11#55411yescharacteristic
266C22×C11#55511yescharacteristic
267C22×C11#55711yescharacteristic
268C22×C11#55712yes—
269C22×C11Q8211yescharacteristic
270C22×C11#56211yescharacteristic
271C22×C11#56311yescharacteristic
272C4×C11—28no—
273C4×C11—42no—
274C4×C11—44no—
275C4×C11—44no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—44no—
279C4×C11—44no—
280C4×C11—82no—
281C22×Q8—24no—
282C22×Q8—24no—
283C22×Q8—41no—
284C22×Q8—41no—
285C22×Q8Q8×C1114yes—
286C23×C4C23×C1112yes—
287C23×C4C23×C1112yes—
288C23×C4C23×C1112yes—
289C23×C4C23×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291C23×C4C23×C1112yes—
292C23×C4C23×C1112yes—
293C23×C4C23×C1111yescharacteristic
294C23×C4C23×C1112yes—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C42—24no—
310C2×C42—24no—
311C2×C42—42no—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—41no—
321#95—42no—
322#95—41no—
323#95—41no—
324#95D4×C1118yes—
325#95Q8×C1114yescomplemented
326C2×C11#243711yescharacteristic
327C2×C11#245112yes—
328C2×C11#255511yescharacteristic
329C2×C11#255612yes—
330C2×C11#256512yes—
331C2×C11#261211yescharacteristic
332C2×C11#267711yescharacteristic
333C2×C11#268712yes—
334C2×C11#276411yescharacteristic
335C2×C11#280611yescharacteristic
336C2×C11#280911yescharacteristic
337C24C24×C1111yescharacteristic
338C2×Q8—216no—
339C2×Q8—44no—
340C2×Q8—44no—
341C2×Q8—48no—
342C2×Q8—44no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
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—22no—
390C22×C4C2×D4×C1114yes—
391C22×C4C2×D4×C1114yes—
392C22×C4C2×D4×C1114yes—
393C22×C4C2×Q8×C1114yes—
394C22×C4C2×Q8×C1112yes—
395C22×C4C2×Q8×C1112yes—
396C22×C4C2×Q8×C1114yes—
397C22×C4C11×#4112yes—
398C22×C4C11×#4114yes—
399C22×C4C11×#4114yes—
400C4⋊C4—48no—
401C4⋊C4—44no—
402C4⋊C4—48no—
403C4⋊C4—48no—
404C4⋊C4—44no—
405C42—48no—
406C11#1551111yescharacteristic, direct product factor, Sylow
407C23C22×D4×C1112yes—
408C23C22×Q8×C1111yescharacteristic
409C23C22×Q8×C1111yescharacteristic
410C23C2×C11×#4112yes—
411C23C2×C11×#4111yescharacteristic
412C23C2×C11×#4112yes—
413C23C11×H(5,𝔽2)11yescharacteristic
414C23C11×H(5,𝔽2)11yescharacteristic
415C23C11×H(5,𝔽2)11yescharacteristic
416C23C11×2−1+411yescharacteristic
417C23C11×2−1+412yes—
418Q8—416no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4C11×C22⋊Q818yes—
476C22C2×C11×C22⋊Q812yes—
477C22C11×#53212yes—
478C22C11×#53312yes—
479C22C11×#53612yes—
480C22C11×#53811yescharacteristic
481C22C11×#53912yes—
482C22C11×#54212yes—
483C22C11×#54311yescharacteristic
484C22C11×#54411yescharacteristic
485C22D42×C1111yescharacteristic
486C22C11×#54612yes—
487C22C11×#54612yes—
488C22D4×Q8×C1112yes—
489C22C11×#55111yescharacteristic
490C22C11×#55212yes—
491C22C11×#55212yes—
492C22C11×#55411yescharacteristic
493C22C11×#55511yescharacteristic
494C22C11×#55712yes—
495C22C11×#55711yescharacteristic
496C22Q82×C1111yescharacteristic
497C22C11×#56211yescharacteristic
498C22C11×#56311yescharacteristic
499C4—28no—
500C4—42no—
501C4—44no—
502C4—44no—
503C4—42no—
504C4—42no—
505C4—44no—
506C4—44no—
507C4—82no—
508C2C11×#243711yescharacteristic
509C2C11×#245112yes—
510C2C11×#255511yescharacteristic
511C2C11×#255612yes—
512C2C11×#256512yes—
513C2C11×#261211yescharacteristic
514C2C11×#267711yescharacteristic
515C2C11×#268712yes—
516C2C11×#276411yescharacteristic
517C2C11×#280611yescharacteristic
518C2C11×#280911yescharacteristic
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
77. C11×#95Q8semidirect
78. #15511C11direct (N × H)
325. #95Q8×C11semidirect
406. C11#15511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C2×C11×#3912
C11×#14462
C11×#14452
C11×#14442
C11×#14422
C11×#14412
C11×#14362
C11×#14342
#1551111