Finite Group Databasebeta

← C11×#11222 #14588415

Subgroups — C11×#11222 #14588415

Order 2816.

1190 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
1C11×#2315C211yesmaximal, characteristic
2C2×C11×#385C211yesmaximal, characteristic
3C2×C11×#342C212yesmaximal
4C2×C11×#342C211yesmaximal, characteristic
5C11×C22⋊#95C212yesmaximal
6C24×C4×C11C2211yescharacteristic
7C22×C11×C4⋊C4—21no—
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2212yes—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C11×#385—24no—
13C11×#385—22no—
14C11×#385C414yescomplemented
15C11×#380—21no—
16C11×#380—21no—
17C2×C11×#95—21no—
18C2×C11×#95—24no—
19C11×#342—22no—
20C11×#342—24no—
21C25×C11C2311yescharacteristic
22C23×C4×C11—21no—
23C23×C4×C11—22no—
24C23×C4×C11—21no—
25C23×C4×C11—22no—
26C23×C4×C11—21no—
27C23×C4×C11—22no—
28C23×C4×C11—44no—
29C23×C4×C11C2×C412yes—
30C23×C4×C11D414yes—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C2×C11×C4⋊C4—24no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—44no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4D412yes—
56C2×C11×C22⋊C4D412yes—
57C2×C11×C22⋊C4Q814yes—
58C2×C11×C22⋊C4Q812yes—
59C11×#95—22no—
60C11×#95—22no—
61C11×#95—24no—
62C11×#95—48no—
63#11222C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—42no—
65C24×C11—42no—
66C24×C11C22×C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C24×C11C2×D412yes—
69C24×C11C2×D411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C24×C11C2×Q811yescharacteristic
72C24×C11C2×Q812yes—
73C24×C11#4111yescharacteristic
74C24×C11#4111yescharacteristic
75C24×C11#4112yes—
76C24×C11#4112yes—
77C22×C4×C11—28no—
78C22×C4×C11—24no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—24no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11—48no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—44no—
98C22×C4×C11—42no—
99C22×C4×C11—41no—
100C22×C4×C11—42no—
101C22×C4×C11—41no—
102C22×C4×C11—44no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—44no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C22⋊C412yes—
111C22×C4×C11C22⋊C412yes—
112C11×C4⋊C4—48no—
113C11×C4⋊C4—82no—
114C11×C4⋊C4—82no—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4C4⋊C414yescomplemented
129#2315C2×C1111yescharacteristic
130C2×#385C2×C1111yescharacteristic
131C2×#342C2×C1112yes—
132C2×#342C2×C1111yescharacteristic
133C22⋊#95C2×C1112yes—
134C23×C11—22no—
135C23×C11—24no—
136C23×C11—22no—
137C23×C11—24no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—44no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—44no—
150C23×C11C2×C22⋊C411yescharacteristic
151C23×C11C2×C4⋊C411yescharacteristic
152C23×C11#11711yescharacteristic
153C23×C11C4×D412yes—
154C23×C11C4×Q812yes—
155C23×C11#12011yescharacteristic
156C23×C11#12111yescharacteristic
157C23×C11#12112yes—
158C23×C11#12112yes—
159C23×C11#12111yescharacteristic
160C23×C11C22⋊Q811yescharacteristic
161C23×C11C22⋊Q812yes—
162C23×C11C22⋊Q811yescharacteristic
163C23×C11C22⋊Q812yes—
164C23×C11C22⋊Q812yes—
165C23×C11#12311yescharacteristic
166C23×C11#12312yes—
167C23×C11#12411yescharacteristic
168C23×C11#12512yes—
169C23×C11#12512yes—
170C23×C11#12612yes—
171C23×C11C4⋊Q812yes—
172C23×C11C4⋊Q811yescharacteristic
173C2×C4×C11—24no—
174C2×C4×C11—28no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—42no—
179C2×C4×C11—44no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—48no—
185C2×C4×C11—44no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—44no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—48no—
193C2×C4×C11—48no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—81no—
199C2×C4×C11—81no—
200C2×C4×C11—82no—
201C2×C4×C11—82no—
202C2×C4×C11—84no—
203C2×C4×C11—84no—
204C24×C4C22×C1111yescharacteristic
205C22×C4⋊C4—21no—
206C22×C22⋊C4C22×C1112yes—
207C22×C22⋊C4C22×C1112yes—
208C22×C22⋊C4C22×C1111yescharacteristic
209C22×C22⋊C4C22×C1111yescharacteristic
210#385—24no—
211#385—22no—
212#385C4×C1114yescomplemented
213#380—21no—
214#380—21no—
215C2×#95—21no—
216C2×#95—24no—
217#342—22no—
218#342—24no—
219C22×C11—22no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—22no—
223C22×C11—21no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—22no—
229C22×C11—21no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—22no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—42no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11#38011yescharacteristic
246C22×C11#38611yescharacteristic
247C22×C11#38712yes—
248C22×C11#38912yes—
249C22×C11#39111yescharacteristic
250C22×C11#39411yescharacteristic
251C22×C11#39511yescharacteristic
252C22×C11#39612yes—
253C22×C11#39811yescharacteristic
254C22×C11#39812yes—
255C22×C11#40011yescharacteristic
256C22×C11B(4,𝔽2)12yes—
257C22×C11#45812yes—
258C4×C11—44no—
259C4×C11—44no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—84no—
263C4×C11—84no—
264C25C23×C1111yescharacteristic
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—44no—
272C23×C4C2×C4×C1112yes—
273C23×C4D4×C1114yes—
274C23×C4D4×C1111yescharacteristic
275C23×C4D4×C1111yescharacteristic
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—44no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4C2×C4×C1112yes—
297C2×C22⋊C4C2×C4×C1112yes—
298C2×C22⋊C4D4×C1112yes—
299C2×C22⋊C4D4×C1112yes—
300C2×C22⋊C4Q8×C1114yes—
301C2×C22⋊C4Q8×C1112yes—
302#95—22no—
303#95—22no—
304#95—24no—
305#95—48no—
306C2×C11—21no—
307C2×C11—22no—
308C2×C11—22no—
309C2×C11—22no—
310C2×C11—21no—
311C2×C11—22no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11#144111yescharacteristic
315C2×C11#188911yescharacteristic
316C2×C11#189011yescharacteristic
317C2×C11#204412yes—
318C2×C11#206212yes—
319C24—42no—
320C24—42no—
321C24C22×C4×C1111yescharacteristic
322C24C2×D4×C1111yescharacteristic
323C24C2×D4×C1112yes—
324C24C2×D4×C1111yescharacteristic
325C24C2×D4×C1111yescharacteristic
326C24C2×Q8×C1111yescharacteristic
327C24C2×Q8×C1112yes—
328C24C11×#4111yescharacteristic
329C24C11×#4111yescharacteristic
330C24C11×#4112yes—
331C24C11×#4112yes—
332C22×C4—28no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—48no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—44no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—44no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C11×C22⋊C412yes—
366C22×C4C11×C22⋊C412yes—
367C4⋊C4—48no—
368C4⋊C4—82no—
369C4⋊C4—82no—
370C22⋊C4—22no—
371C22⋊C4—24no—
372C22⋊C4—22no—
373C22⋊C4—24no—
374C22⋊C4—22no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—42no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4C11×C4⋊C414yescomplemented
384C11#1122211yescharacteristic, direct product factor, Sylow
385C23—22no—
386C23—24no—
387C23—22no—
388C23—24no—
389C23—41no—
390C23—41no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—44no—
397C23—42no—
398C23—42no—
399C23—44no—
400C23—42no—
401C23C2×C11×C22⋊C411yescharacteristic
402C23C2×C11×C4⋊C411yescharacteristic
403C23C11×#11711yescharacteristic
404C23C4×D4×C1112yes—
405C23C4×Q8×C1112yes—
406C23C11×#12011yescharacteristic
407C23C11×#12111yescharacteristic
408C23C11×#12112yes—
409C23C11×#12112yes—
410C23C11×#12111yescharacteristic
411C23C11×C22⋊Q811yescharacteristic
412C23C11×C22⋊Q812yes—
413C23C11×C22⋊Q811yescharacteristic
414C23C11×C22⋊Q812yes—
415C23C11×C22⋊Q812yes—
416C23C11×#12311yescharacteristic
417C23C11×#12312yes—
418C23C11×#12411yescharacteristic
419C23C11×#12512yes—
420C23C11×#12512yes—
421C23C11×#12612yes—
422C23C11×C4⋊Q812yes—
423C23C11×C4⋊Q811yescharacteristic
424C2×C4—24no—
425C2×C4—28no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—48no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—48no—
444C2×C4—48no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—84no—
454C2×C4—84no—
455C22—21no—
456C22—22no—
457C22—22no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—24no—
465C22—24no—
466C22—22no—
467C22—22no—
468C22—24no—
469C22—24no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22C11×#38011yescharacteristic
482C22C11×#38611yescharacteristic
483C22C11×#38712yes—
484C22C11×#38912yes—
485C22C11×#39111yescharacteristic
486C22C11×#39411yescharacteristic
487C22C11×#39511yescharacteristic
488C22C11×#39612yes—
489C22C11×#39811yescharacteristic
490C22C11×#39812yes—
491C22C11×#40011yescharacteristic
492C22C11×B(4,𝔽2)12yes—
493C22C11×#45812yes—
494C4—44no—
495C4—44no—
496C4—42no—
497C4—42no—
498C4—84no—
499C4—84no—
500C2—21no—
501C2—22no—
502C2—22no—
503C2—22no—
504C2—21no—
505C2—22no—
506C2—21no—
507C2—21no—
508C2C11×#144111yescharacteristic
509C2C11×#188911yescharacteristic
510C2C11×#189011yescharacteristic
511C2C11×#204412yes—
512C2C11×#206212yes—
subgroupG/H
center, socleC23×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
14. C11×#385C4semidirect
63. #11222C11direct (N × H)
128. C11×C22⋊C4C4⋊C4semidirect
212. #385C4×C11semidirect
383. C22⋊C4C11×C4⋊C4semidirect
384. C11#11222direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23152
C2×C11×#3852
C2×C11×#3422
C11×C22⋊#952
#1122211