Finite Group Databasebeta

← C11×#23594 #14600787

Subgroups — C11×#23594 #14600787

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3461C211yesmaximal, characteristic
2C4×C11×#137C212yesmaximal, complemented
3C11×#2327C211yesmaximal, characteristic, complemented
4C11×#2061C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic
6C11×#2038C212yesmaximal, complemented
7C11×#2028C211yesmaximal, characteristic, complemented
8C11×#2007C211yesmaximal, characteristic
9C11×#2005C212yesmaximal, complemented
10C11×#1759C212yesmaximal, complemented
11C4×C11×#101C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C11×#544C2211yescharacteristic
14C11×#542—22no—
15C11×#541—22no—
16C11×#539—22no—
17C11×#537C2211yescharacteristic
18C11×#536C2212yes—
19C11×#533—22no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C11×#529—22no—
22C11×#529—22no—
23C4×C11×#41C2212yes—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C11×#441—22no—
27C11×#440—22no—
28C4×C11×Q16—22no—
29C4×C11×SD16—22no—
30C11×#428C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#419C2212yes—
34C11×#417C2212yes—
35C2×C11×#101C2212yes—
36C4×C11×M16C2212yes—
37C11×#391C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#387—22no—
40C11×#387—22no—
41C11×#382C2211yescharacteristic
42C11×#376C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C11×#137—24no—
51C11×#137—24no—
52C2×C11×Q16—22no—
53C2×C11×SD16—22no—
54C2×C11×M16C2312yes—
55C2×C11×M16C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×#126—24no—
61C11×#126—24no—
62C11×#125—22no—
63C11×#125—24no—
64C11×#125—22no—
65C11×#124—22no—
66C11×#124—22no—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×#121—22no—
75C11×#121—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11D412yes—
82C4×Q8×C11D412yes—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D412yes—
87C4×D4×C11D412yes—
88C11×#117—24no—
89C11×#117—22no—
90C11×#117C2312yes—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D412yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C42×C11—22no—
97C2×C42×C11—21no—
98C2×C42×C11D412yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107—22no—
103C11×#106—22no—
104C11×#104—24no—
105C11×#104—24no—
106C11×#103—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#102—22no—
110C11×#101—24no—
111C11×#97—22no—
112C4×C8×C11—22no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118#23594C1111yesmaximal, characteristic, direct product factor, Sylow
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11#4112yes—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×Q16—28no—
149C11×SD16—28no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16#4114yes—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—21no—
183C42×C11—22no—
184C42×C11—42no—
185C42×C11C2×D412yes—
186C42×C11C2×D412yes—
187C42×C11#4112yes—
188#3461C2×C1111yescharacteristic
189C4×#137C2×C1112yescomplemented
190#2327C2×C1111yescharacteristic, complemented
191#2061C2×C1111yescharacteristic, complemented
192#2040C2×C1111yescharacteristic
193#2038C2×C1112yescomplemented
194#2028C2×C1111yescharacteristic, complemented
195#2007C2×C1111yescharacteristic
196#2005C2×C1112yescomplemented
197#1759C2×C1112yescomplemented
198C4×#101C2×C1111yescharacteristic, complemented
199C23×C11—22no—
200C23×C11C22×D411yescharacteristic
201Q8×C11—24no—
202Q8×C11—22no—
203Q8×C11—22no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—42no—
207Q8×C11—82no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—82no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—44no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—82no—
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12012yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4112yes—
244C2×C4×C11C2×#4111yescharacteristic
245C8×C11—24no—
246C8×C11—42no—
247C2×#137C22×C1112yes—
248#544C22×C1111yescharacteristic
249#542—22no—
250#541—22no—
251#539—22no—
252#537C22×C1111yescharacteristic
253#536C22×C1112yes—
254#533—22no—
255C2×C4⋊Q8C22×C1111yescharacteristic
256#529—22no—
257#529—22no—
258C4×#41C22×C1112yes—
259C2×C4×Q8C22×C1111yescharacteristic
260C2×C4×Q8C22×C1111yescharacteristic
261#441—22no—
262#440—22no—
263C4×Q16—22no—
264C4×SD16—22no—
265#428C22×C1112yes—
266C2×#104C22×C1112yes—
267C2×#104C22×C1112yes—
268#419C22×C1112yes—
269#417C22×C1112yes—
270C2×#101C22×C1112yes—
271C4×M16C22×C1112yes—
272#391C22×C1111yescharacteristic
273#391C22×C1111yescharacteristic
274#387—22no—
275#387—22no—
276#382C22×C1111yescharacteristic
277#376C22×C1111yescharacteristic
278#343C22×C1111yescharacteristic
279#343C22×C1111yescharacteristic
280#339C22×C1112yes—
281#339C22×C1112yes—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11C2×#12011yescharacteristic
288C22×C11#52511yescharacteristic
289C22×C11#53211yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11#52512yes—
303C4×C11#53212yes—
304C2×#41C23×C1112yes—
305C22×Q8C23×C1111yescharacteristic
306C22×Q8C23×C1111yescharacteristic
307#137—24no—
308#137—24no—
309C2×Q16—22no—
310C2×SD16—22no—
311C2×M16C23×C1112yes—
312C2×M16C23×C1112yes—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317#126—24no—
318#126—24no—
319#125—22no—
320#125—24no—
321#125—22no—
322#124—22no—
323#124—22no—
324#123—24no—
325#123—24no—
326C22⋊Q8—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331#121—22no—
332#121—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8D4×C1112yes—
339C4×Q8D4×C1112yes—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4D4×C1112yes—
344C4×D4D4×C1112yes—
345#117—24no—
346#117—22no—
347#117C23×C1112yes—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4D4×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C42—22no—
354C2×C42—21no—
355C2×C42D4×C1112yes—
356C2×C42C23×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358C2×C42C23×C1111yescharacteristic
359#107—22no—
360#106—22no—
361#104—24no—
362#104—24no—
363#103—22no—
364#103—22no—
365#103—22no—
366#102—22no—
367#101—24no—
368#97—22no—
369C4×C8—22no—
370#95—21no—
371#95—21no—
372#95—22no—
373#95—22no—
374#95—22no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—82no—
378C2×C11#238811yescharacteristic
379C2×C11#302011yescharacteristic
380C2×C11#302211yescharacteristic
381#41—22no—
382#41—22no—
383#41—22no—
384#41—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8C2×D4×C1112yes—
394C2×Q8C11×#4112yes—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4C2×D4×C1112yes—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4C2×D4×C1112yes—
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C24×C1111yescharacteristic
410Q16—28no—
411SD16—28no—
412M16—22no—
413M16—22no—
414M16—22no—
415M16C11×#4114yes—
416C2×C8—22no—
417C2×C8—22no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4C2×D4×C1112yes—
432C4⋊C4C2×D4×C1112yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C42—22no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—21no—
445C42—22no—
446C42—42no—
447C42C2×D4×C1112yes—
448C42C2×D4×C1112yes—
449C42C11×#4112yes—
450C11#2359411yescharacteristic, direct product factor, Sylow
451C23—22no—
452C23C22×D4×C1111yescharacteristic
453Q8—24no—
454Q8—22no—
455Q8—22no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—82no—
460D4—22no—
461D4—22no—
462D4—42no—
463D4—42no—
464D4—82no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4C11×#12011yescharacteristic
491C2×C4C11×#12011yescharacteristic
492C2×C4C11×#12012yes—
493C2×C4C22×D4×C1112yes—
494C2×C4C2×C11×#4111yescharacteristic
495C2×C4C2×C11×#4112yes—
496C2×C4C2×C11×#4111yescharacteristic
497C8—24no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22C2×C11×#12011yescharacteristic
505C22C11×#52511yescharacteristic
506C22C11×#53211yescharacteristic
507C4—21no—
508C4—21no—
509C4—22no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4C11×#52512yes—
520C4C11×#53212yes—
521C2—21no—
522C2—21no—
523C2—82no—
524C2C11×#238811yescharacteristic
525C2C11×#302011yescharacteristic
526C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#537C22
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. C4×C11×#137C2semidirect
3. C11×#2327C2semidirect
4. C11×#2061C2semidirect
6. C11×#2038C2semidirect
7. C11×#2028C2semidirect
9. C11×#2005C2semidirect
10. C11×#1759C2semidirect
11. C4×C11×#101C2semidirect
118. #23594C11direct (N × H)
189. C4×#137C2×C11semidirect
190. #2327C2×C11semidirect
191. #2061C2×C11semidirect
193. #2038C2×C11semidirect
194. #2028C2×C11semidirect
196. #2005C2×C11semidirect
197. #1759C2×C11semidirect
198. C4×#101C2×C11semidirect
450. C11#23594direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34612
C4×C11×#1372
C11×#23272
C11×#20612
C11×#20402
C11×#20382
C11×#20282
C11×#20072
C11×#20052
C11×#17592
C4×C11×#1012
#2359411