Finite Group Databasebeta

← C11×#32922 #14610115

Subgroups — C11×#32922 #14610115

Order 2816.

1418 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
1C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
2C11×#3039C212yesmaximal, complemented
3C2×C11×#455C212yesmaximal
4C11×#2547C211yesmaximal, characteristic, complemented
5C11×#1885C212yesmaximal, complemented
6C11×#1882C214yesmaximal, complemented
7C11×#1806C212yesmaximal, complemented
8C11×#1800C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C2×C11×#137C2214yes—
11C2×C11×C4⋊Q8C2211yescharacteristic, complemented
12C2×C11×#124C2212yes—
13C11×#520—22no—
14C11×#520C2212yes—
15C11×#518—22no—
16C11×#518—22no—
17C11×#518C2211yescharacteristic
18C4×C11×#41—22no—
19C4×C11×#41C2212yes—
20C2×C4×D4×C11—22no—
21C2×C4×D4×C11—22no—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#462—22no—
24C11×#462—22no—
25C11×#461—22no—
26C11×#461—22no—
27C11×#455—28no—
28C11×#423C2212yescomplemented
29C2×C11×#104C2214yes—
30C11×#419C2214yescomplemented
31C2×C11×#100C2212yes—
32C11×#397—22no—
33C11×#391C2212yescomplemented
34C11×#380—22no—
35C4×C11×C4⋊C4C2211yescharacteristic, complemented
36C11×#343C2212yescomplemented
37C11×#339C2214yescomplemented
38C11×H(5,𝔽2)—24no—
39C11×H(5,𝔽2)—22no—
40C11×H(5,𝔽2)D414yes—
41C2×C11×#41—22no—
42C2×C11×#41C2312yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11D412yes—
49C11×#137—28no—
50C11×#137—28no—
51C2×C11×Q16—24no—
52C2×C11×SD16—24no—
53C2×C11×M16C2314yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×#124—24no—
57C11×#124—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11D412yes—
60C4×Q8×C11D412yes—
61C4×D4×C11—24no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11D412yes—
74C4×D4×C11D412yes—
75C11×#117—24no—
76C11×#117—22no—
77C11×#117—22no—
78C11×#117C2312yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11C2312yes—
93C2×C42×C11C2311yescharacteristic
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#104—28no—
97C11×#103—24no—
98C11×#103—24no—
99C11×#100—24no—
100C11×#95—21no—
101C11×#95—24no—
102#32922C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C24×C11C2×D412yes—
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41C2×D414yes—
110C11×#41#4114yes—
111C2×Q8×C11—24no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—24no—
117C2×D4×C11—28no—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—22no—
121C2×D4×C11—28no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11C2×D412yes—
125C2×D4×C11C2×D412yes—
126C2×D4×C11#4112yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
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—44no—
139C22×C4×C11—84no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C11×Q16—48no—
145C11×SD16—48no—
146C11×M16—24no—
147C11×M16—24no—
148C2×C8×C11—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—48no—
166C42×C11—24no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C4×H(5,𝔽2)C2×C1111yescharacteristic
175#3039C2×C1112yescomplemented
176C2×#455C2×C1112yes—
177#2547C2×C1111yescharacteristic, complemented
178#1885C2×C1112yescomplemented
179#1882C2×C1114yescomplemented
180#1806C2×C1112yescomplemented
181#1800C2×C1111yescharacteristic, complemented
182C23×C11—28no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—82no—
189C23×C11—82no—
190C23×C11#12114yes—
191C23×C11C22×D411yescharacteristic
192Q8×C11—22no—
193Q8×C11—44no—
194Q8×C11—44no—
195Q8×C11#12114yes—
196D4×C11—216no—
197D4×C11—24no—
198D4×C11—24no—
199D4×C11—24no—
200D4×C11—22no—
201D4×C11—24no—
202D4×C11#12114yes—
203C2×C4×C11—28no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11—82no—
224C2×C4×C11—84no—
225C2×C4×C11—82no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11C2×#4111yescharacteristic
233C8×C11—44no—
234C2×H(5,𝔽2)C22×C1111yescharacteristic
235C2×#137C22×C1114yes—
236C2×C4⋊Q8C22×C1111yescharacteristic, complemented
237C2×#124C22×C1112yes—
238#520—22no—
239#520C22×C1112yes—
240#518—22no—
241#518—22no—
242#518C22×C1111yescharacteristic
243C4×#41—22no—
244C4×#41C22×C1112yes—
245C2×C4×D4—22no—
246C2×C4×D4—22no—
247C2×C4×D4C22×C1111yescharacteristic
248#462—22no—
249#462—22no—
250#461—22no—
251#461—22no—
252#455—28no—
253#423C22×C1112yescomplemented
254C2×#104C22×C1114yes—
255#419C22×C1114yescomplemented
256C2×#100C22×C1112yes—
257#397—22no—
258#391C22×C1112yescomplemented
259#380—22no—
260C4×C4⋊C4C22×C1111yescharacteristic, complemented
261#343C22×C1112yescomplemented
262#339C22×C1114yescomplemented
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11—88no—
274C22×C11C2×#12011yescharacteristic
275C22×C11C2×#12111yescharacteristic
276C22×C11#52511yescharacteristic
277C4×C11—24no—
278C4×C11—21no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—82no—
284C4×C11—82no—
285C4×C11#45512yescomplemented
286C4×C11C2×#12112yes—
287C4×C11#52512yes—
288H(5,𝔽2)—24no—
289H(5,𝔽2)—22no—
290H(5,𝔽2)D4×C1114yes—
291C2×#41—22no—
292C2×#41C23×C1112yes—
293C22×Q8C23×C1112yes—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4C23×C1111yescharacteristic
297C23×C4—22no—
298C23×C4D4×C1112yes—
299#137—28no—
300#137—28no—
301C2×Q16—24no—
302C2×SD16—24no—
303C2×M16C23×C1114yes—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#124—24no—
307#124—24no—
308C4×Q8—22no—
309C4×Q8D4×C1112yes—
310C4×Q8D4×C1112yes—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—24no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—24no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4D4×C1112yes—
324C4×D4D4×C1112yes—
325#117—24no—
326#117—22no—
327#117—22no—
328#117C23×C1112yes—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4D4×C1112yes—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42C23×C1112yes—
343C2×C42C23×C1111yescharacteristic
344C4⋊C8—22no—
345C4⋊C8—22no—
346#104—28no—
347#103—24no—
348#103—24no—
349#100—24no—
350#95—21no—
351#95—24no—
352C2×C11—21no—
353C2×C11—21no—
354C2×C11—44no—
355C2×C11—44no—
356C2×C11#284711yescharacteristic
357C2×C11C2×#45511yescharacteristic
358C2×C11#302211yescharacteristic
359C24—22no—
360C24C2×D4×C1112yes—
361#41—28no—
362#41—28no—
363#41—22no—
364#41—22no—
365#41C2×D4×C1114yes—
366#41C11×#4114yes—
367C2×Q8—24no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—24no—
371C2×Q8C2×D4×C1112yes—
372C2×D4—24no—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—28no—
376C2×D4—22no—
377C2×D4—28no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4C2×D4×C1112yes—
381C2×D4C2×D4×C1112yes—
382C2×D4C11×#4112yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—44no—
395C22×C4—84no—
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C24×C1111yescharacteristic
400Q16—48no—
401SD16—48no—
402M16—24no—
403M16—24no—
404C2×C8—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C2×D4×C1112yes—
414C4⋊C4C2×D4×C1112yes—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—24no—
421C22⋊C4—48no—
422C42—24no—
423C42—22no—
424C42—22no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42C2×D4×C1112yes—
429C42C2×D4×C1112yes—
430C11#3292211yescharacteristic, direct product factor, Sylow
431C23—28no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—42no—
436C23—42no—
437C23—82no—
438C23—82no—
439C23C11×#12114yes—
440C23C22×D4×C1111yescharacteristic
441Q8—22no—
442Q8—44no—
443Q8—44no—
444Q8C11×#12114yes—
445D4—216no—
446D4—24no—
447D4—24no—
448D4—24no—
449D4—22no—
450D4—24no—
451D4C11×#12114yes—
452C2×C4—28no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—84no—
474C2×C4—82no—
475C2×C4C11×#12012yes—
476C2×C4C11×#12011yescharacteristic
477C2×C4C11×#12011yescharacteristic
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C22×D4×C1112yes—
480C2×C4C2×C11×#4112yes—
481C2×C4C2×C11×#4111yescharacteristic
482C8—44no—
483C22—21no—
484C22—21no—
485C22—24no—
486C22—24no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—82no—
493C22—88no—
494C22C2×C11×#12011yescharacteristic
495C22C2×C11×#12111yescharacteristic
496C22C11×#52511yescharacteristic
497C4—21no—
498C4—22no—
499C4—24no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—82no—
505C4C11×#45512yescomplemented
506C4C2×C11×#12112yes—
507C4C11×#52512yes—
508C2—21no—
509C2—21no—
510C2—44no—
511C2—44no—
512C2C11×#284711yescharacteristic
513C2C2×C11×#45511yescharacteristic
514C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×H(5,𝔽2)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3039C2semidirect
4. C11×#2547C2semidirect
5. C11×#1885C2semidirect
6. C11×#1882C2semidirect
7. C11×#1806C2semidirect
8. C11×#1800C2semidirect
11. C2×C11×C4⋊Q8C22semidirect
28. C11×#423C22semidirect
30. C11×#419C22semidirect
33. C11×#391C22semidirect
35. C4×C11×C4⋊C4C22semidirect
36. C11×#343C22semidirect
37. C11×#339C22semidirect
102. #32922C11direct (N × H)
175. #3039C2×C11semidirect
177. #2547C2×C11semidirect
178. #1885C2×C11semidirect
179. #1882C2×C11semidirect
180. #1806C2×C11semidirect
181. #1800C2×C11semidirect
236. C2×C4⋊Q8C22×C11semidirect
253. #423C22×C11semidirect
255. #419C22×C11semidirect
258. #391C22×C11semidirect
260. C4×C4⋊C4C22×C11semidirect
261. #343C22×C11semidirect
262. #339C22×C11semidirect
285. C4×C11#455semidirect
430. C11#32922direct (N × H)
505. C4C11×#455semidirect

Maximal subgroups

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

subgroupindex
C4×C11×H(5,𝔽2)2
C11×#30392
C2×C11×#4552
C11×#25472
C11×#18852
C11×#18822
C11×#18062
C11×#18002
#3292211