Finite Group Databasebeta

← C11×#18383 #14595576

Subgroups — C11×#18383 #14595576

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3189C212yesmaximal, complemented
3C11×#2564C211yesmaximal, characteristic
4C11×#1617C212yesmaximal, complemented
5C11×#1614C212yesmaximal, complemented
6C11×#1605C212yesmaximal, complemented
7C11×#1602C212yesmaximal, complemented
8C2×C11×#328C212yesmaximal, complemented
9C11×#1459C211yesmaximal, characteristic
10C11×#554—24no—
11C11×#554—22no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C11×#518—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C11×#484—22no—
23C11×#484C2214yes—
24C11×#467—24no—
25C11×#451—22no—
26C11×#451C2214yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#400C2211yescharacteristic
29C11×#399C2211yescharacteristic
30C11×#395C2211yescharacteristic
31C11×#393C2211yescharacteristic
32C11×#387—21no—
33C11×#386—21no—
34C11×#385—21no—
35C11×#380—21no—
36C2×C11×#95C2211yescharacteristic
37C11×#328C2214yes—
38C11×#328C2214yes—
39C11×#324C2212yes—
40C11×#323C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11D412yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C2×C11×Q16—24no—
49C22×C8×C11—22no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—24no—
53C11×#125—22no—
54C11×#125—24no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D414yes—
68C11×C22⋊Q8C2314yes—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4C2311yescharacteristic
92C2×C42×C11D411yescharacteristic
93C11×#107—24no—
94C11×#103—24no—
95C11×#103—24no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8C2314yes—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95C2311yescharacteristic
104C11×#95C2311yescharacteristic
105#18383C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—81no—
113C2×Q8×C11—82no—
114C2×Q8×C11—82no—
115C2×Q8×C11C2×D414yes—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11Q1614yescomplemented
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—81no—
132C22×C4×C11—81no—
133C22×C4×C11—81no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2411yescharacteristic
141C11×Q16—84no—
142C2×C8×C11—24no—
143C2×C8×C11—82no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4C2×D414yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—81no—
168C42×C11—24no—
169C42×C11—21no—
170C42×C11—21no—
171#3501C2×C1111yescharacteristic
172#3189C2×C1112yescomplemented
173#2564C2×C1111yescharacteristic
174#1617C2×C1112yescomplemented
175#1614C2×C1112yescomplemented
176#1605C2×C1112yescomplemented
177#1602C2×C1112yescomplemented
178C2×#328C2×C1112yescomplemented
179#1459C2×C1111yescharacteristic
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11#12012yes—
187C23×C11C2×Q1612yes—
188C23×C11C2×Q1612yes—
189C23×C11#13712yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—44no—
192Q8×C11—44no—
193Q8×C11—44no—
194Q8×C11—82no—
195Q8×C11—82no—
196D4×C11—28no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—21no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—81no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11—84no—
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11C2×Q1612yes—
231C2×C4×C11C22×D412yes—
232C8×C11—44no—
233#554—24no—
234#554—22no—
235D4×Q8—22no—
236#544C22×C1112yes—
237#543—21no—
238#543C22×C1112yes—
239#533—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8C22×C1112yes—
242C2×C22⋊Q8C22×C1111yescharacteristic
243#518—21no—
244C2×C4×D4C22×C1111yescharacteristic
245#484—22no—
246#484C22×C1114yes—
247#467—24no—
248#451—22no—
249#451C22×C1114yes—
250C2×C22⋊C8C22×C1112yes—
251#400C22×C1111yescharacteristic
252#399C22×C1111yescharacteristic
253#395C22×C1111yescharacteristic
254#393C22×C1111yescharacteristic
255#387—21no—
256#386—21no—
257#385—21no—
258#380—21no—
259C2×#95C22×C1111yescharacteristic
260#328C22×C1114yes—
261#328C22×C1114yes—
262#324C22×C1112yes—
263#323C22×C1112yes—
264C22×C11—21no—
265C22×C11—22no—
266C22×C11—21no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—81no—
275C22×C11#45114yes—
276C22×C11C2×#12011yescharacteristic
277C22×C11C22×Q1611yescharacteristic
278C22×C11C2×#13711yescharacteristic
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—41no—
285C4×C11—44no—
286C4×C11—41no—
287C4×C11—44no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11—81no—
291C22×Q8—21no—
292C22×Q8D4×C1112yes—
293C22×Q8C23×C1111yescharacteristic
294C22×D4D4×C1111yescharacteristic
295C23×C4—21no—
296C23×C4D4×C1111yescharacteristic
297C23×C4C23×C1111yescharacteristic
298C2×Q16—24no—
299C22×C8—22no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—24no—
303#125—22no—
304#125—24no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—24no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8D4×C1114yes—
318C22⋊Q8C23×C1114yes—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—22no—
324C4×D4—22no—
325#117—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4D4×C1112yes—
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4D4×C1111yescharacteristic
341C2×C22⋊C4C23×C1111yescharacteristic
342C2×C42D4×C1111yescharacteristic
343#107—24no—
344#103—24no—
345#103—24no—
346C22⋊C8—22no—
347C22⋊C8C23×C1114yes—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95C23×C1111yescharacteristic
354#95C23×C1111yescharacteristic
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—24no—
358C2×C11—42no—
359C2×C11C2×#45111yescharacteristic
360C2×C11#301811yescharacteristic
361C2×C11#302611yescharacteristic
362C24C2×D4×C1111yescharacteristic
363C24C2×D4×C1111yescharacteristic
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—81no—
369C2×Q8—82no—
370C2×Q8—82no—
371C2×Q8C2×D4×C1114yes—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4C11×Q1614yescomplemented
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—81no—
388C22×C4—81no—
389C22×C4—81no—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1112yes—
396C22×C4C24×C1111yescharacteristic
397Q16—84no—
398C2×C8—24no—
399C2×C8—82no—
400C4⋊C4—22no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—81no—
415C4⋊C4C2×D4×C1114yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—22no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—81no—
424C42—24no—
425C42—21no—
426C42—21no—
427C11#1838311yescharacteristic, direct product factor, Sylow
428C23—21no—
429C23—21no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23C11×#12012yes—
435C23C2×C11×Q1612yes—
436C23C2×C11×Q1612yes—
437C23C11×#13712yes—
438C23C22×D4×C1111yescharacteristic
439Q8—44no—
440Q8—44no—
441Q8—44no—
442Q8—82no—
443Q8—82no—
444D4—28no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—21no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—84no—
476C2×C4C11×#12011yescharacteristic
477C2×C4C11×#12011yescharacteristic
478C2×C4C2×C11×Q1612yes—
479C2×C4C22×D4×C1112yes—
480C8—44no—
481C22—21no—
482C22—22no—
483C22—21no—
484C22—22no—
485C22—22no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—81no—
492C22C11×#45114yes—
493C22C2×C11×#12011yescharacteristic
494C22C22×C11×Q1611yescharacteristic
495C22C2×C11×#13711yescharacteristic
496C4—22no—
497C4—22no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—41no—
502C4—44no—
503C4—41no—
504C4—44no—
505C4—81no—
506C4—81no—
507C4—81no—
508C2—21no—
509C2—21no—
510C2—24no—
511C2—42no—
512C2C2×C11×#45111yescharacteristic
513C2C11×#301811yescharacteristic
514C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3189C2semidirect
4. C11×#1617C2semidirect
5. C11×#1614C2semidirect
6. C11×#1605C2semidirect
7. C11×#1602C2semidirect
8. C2×C11×#328C2semidirect
105. #18383C11direct (N × H)
118. C2×D4×C11Q16semidirect
172. #3189C2×C11semidirect
174. #1617C2×C11semidirect
175. #1614C2×C11semidirect
176. #1605C2×C11semidirect
177. #1602C2×C11semidirect
178. C2×#328C2×C11semidirect
374. C2×D4C11×Q16semidirect
427. C11#18383direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#31892
C11×#25642
C11×#16172
C11×#16142
C11×#16052
C11×#16022
C2×C11×#3282
C11×#14592
#1838311