Finite Group Databasebeta

← C11×#23898 #14601091

Subgroups — C11×#23898 #14601091

Order 2816.

1718 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×#3487C211yesmaximal, characteristic, complemented
2C11×#3485C211yesmaximal, characteristic, complemented
3C11×#3020C212yesmaximal, complemented
4C11×#3019C212yesmaximal, complemented
5C11×#2010C214yesmaximal, complemented
6C11×#1912C212yesmaximal, complemented
7C11×#1911C212yesmaximal, complemented
8C11×#1785C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic, complemented
10C2×C11×H(5,𝔽2)C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C11×#575C2214yes—
13C11×#550—24no—
14C11×#548—24no—
15C11×#547—24no—
16C11×#546—24no—
17C11×#536C2212yes—
18C11×#535—22no—
19C11×#535C2212yes—
20C11×#534—22no—
21C11×#525—22no—
22C11×#525C2212yes—
23C11×#525C2212yescomplemented
24C2×C11×#123—22no—
25C11×#519C2211yescharacteristic, complemented
26C11×#518C2211yescharacteristic
27C11×#456—24no—
28C11×#455—24no—
29C11×#454—24no—
30C11×#453—24no—
31C11×#421C2214yes—
32C11×#421C2214yescomplemented
33C2×C11×#101C2212yescomplemented
34C2×C11×#100C2212yes—
35C11×#407C2212yescomplemented
36C11×H(3,ℤ/4)C2214yescomplemented
37C11×2−1+4—24no—
38C11×2−1+4—42no—
39C11×H(5,𝔽2)—24no—
40C11×H(5,𝔽2)—42no—
41C2×C11×#41—24no—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—42no—
47C2×C11×#41C2312yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11—22no—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11D412yes—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11D412yes—
56C23×C4×C11C2311yescharacteristic
57C11×#137—24no—
58C11×#137—24no—
59C11×AGL(1,ℤ/8)—24no—
60C11×AGL(1,ℤ/8)—24no—
61C11×#135—44no—
62C2×C11×M16C2314yes—
63C11×C4⋊Q8D414yescomplemented
64C11×#127—24no—
65C11×#127D414yescomplemented
66C11×#124—24no—
67C11×#124D414yescomplemented
68C11×#124D414yescomplemented
69C11×#123—28no—
70C11×#123—24no—
71C11×#123—22no—
72C11×#123—24no—
73C11×#123—22no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×#121—24no—
79C11×#121—28no—
80C11×#121—28no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—24no—
84C11×#120—24no—
85C11×#120—24no—
86C11×#120—22no—
87C11×#120—22no—
88C4×Q8×C11—24no—
89C4×D4×C11—28no—
90C4×D4×C11—24no—
91C4×D4×C11—24no—
92C4×D4×C11—24no—
93C11×#117—22no—
94C11×#117C2312yes—
95C11×#117C2312yes—
96C2×C11×C4⋊C4—24no—
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4—22no—
99C11×#104—28no—
100C11×#104—28no—
101C11×#101—24no—
102C11×#100—24no—
103C11×C22⋊C8—42no—
104#23898C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—22no—
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D412yes—
108C11×#41—24no—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—44no—
113C11×#41—416no—
114C11×#41—48no—
115C11×#41—48no—
116C11×#41—44no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—48no—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11C2×D412yes—
123C2×Q8×C11C2×D414yes—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—24no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—28no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—42no—
136C2×D4×C11—48no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C2×D4×C11C2×D412yes—
140C2×D4×C11C2×D412yes—
141C2×D4×C11C2×D414yes—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—42no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2411yescharacteristic
156C11×Q16—44no—
157C11×SD16—44no—
158C11×SD16—44no—
159C11×D8—44no—
160C11×M16—24no—
161C11×M16—24no—
162C2×C8×C11—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—28no—
178C42×C11—24no—
179C42×C11C2×D414yes—
180C42×C11C2×D414yes—
181#3487C2×C1111yescharacteristic, complemented
182#3485C2×C1111yescharacteristic, complemented
183#3020C2×C1112yescomplemented
184#3019C2×C1112yescomplemented
185#2010C2×C1114yescomplemented
186#1912C2×C1112yescomplemented
187#1911C2×C1112yescomplemented
188#1785C2×C1111yescharacteristic, complemented
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—21no—
196C23×C11—44no—
197C23×C11—81no—
198C23×C11—82no—
199C23×C11—84no—
200C23×C11#12014yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—28no—
203Q8×C11—24no—
204Q8×C11—24no—
205Q8×C11—44no—
206D4×C11—28no—
207D4×C11—24no—
208D4×C11—24no—
209D4×C11—48no—
210D4×C11—44no—
211D4×C11—48no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—84no—
217D4×C11—88no—
218D4×C11—84no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—48no—
229C2×C4×C11—48no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—84no—
235C2×C4×C11#12014yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11H(5,𝔽2)12yes—
239C8×C11—44no—
240C2×2−1+4C22×C1111yescharacteristic, complemented
241C2×H(5,𝔽2)C22×C1111yescharacteristic
242C22×#41C22×C1111yescharacteristic
243#575C22×C1114yes—
244#550—24no—
245#548—24no—
246#547—24no—
247#546—24no—
248#536C22×C1112yes—
249#535—22no—
250#535C22×C1112yes—
251#534—22no—
252#525—22no—
253#525C22×C1112yes—
254#525C22×C1112yescomplemented
255C2×#123—22no—
256#519C22×C1111yescharacteristic, complemented
257#518C22×C1111yescharacteristic
258#456—24no—
259#455—24no—
260#454—24no—
261#453—24no—
262#421C22×C1114yes—
263#421C22×C1114yescomplemented
264C2×#101C22×C1112yescomplemented
265C2×#100C22×C1112yes—
266#407C22×C1112yescomplemented
267H(3,ℤ/4)C22×C1114yescomplemented
268C22×C11—24no—
269C22×C11—41no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—42no—
280C22×C11—82no—
281C22×C11—164no—
282C22×C11C2×#12011yescharacteristic
283C22×C11C2×#12011yescharacteristic
284C22×C11#53411yescharacteristic
285C4×C11—24no—
286C4×C11—44no—
287C4×C11—44no—
288C4×C11—41no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11D4214yes—
2922−1+4—24no—
2932−1+4—42no—
294H(5,𝔽2)—24no—
295H(5,𝔽2)—42no—
296C2×#41—24no—
297C2×#41—22no—
298C2×#41—24no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—42no—
302C2×#41C23×C1112yes—
303C2×#41C23×C1112yes—
304C22×Q8—22no—
305C22×Q8C23×C1111yescharacteristic
306C22×D4—22no—
307C22×D4—22no—
308C22×D4D4×C1112yes—
309C22×D4C23×C1111yescharacteristic
310C23×C4D4×C1112yes—
311C23×C4C23×C1111yescharacteristic
312#137—24no—
313#137—24no—
314AGL(1,ℤ/8)—24no—
315AGL(1,ℤ/8)—24no—
316#135—44no—
317C2×M16C23×C1114yes—
318C4⋊Q8D4×C1114yescomplemented
319#127—24no—
320#127D4×C1114yescomplemented
321#124—24no—
322#124D4×C1114yescomplemented
323#124D4×C1114yescomplemented
324#123—28no—
325#123—24no—
326#123—22no—
327#123—24no—
328#123—22no—
329C22⋊Q8—24no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—24no—
333#121—24no—
334#121—28no—
335#121—28no—
336#121—22no—
337#121—22no—
338#121—24no—
339#120—24no—
340#120—24no—
341#120—22no—
342#120—22no—
343C4×Q8—24no—
344C4×D4—28no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—24no—
348#117—22no—
349#117C23×C1112yes—
350#117C23×C1112yes—
351C2×C4⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—22no—
354#104—28no—
355#104—28no—
356#101—24no—
357#100—24no—
358C22⋊C8—42no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—44no—
363C2×C11—82no—
364C2×C11—81no—
365C2×C11—82no—
366C2×C11#240311yescharacteristic
367C24—22no—
368C24C2×D4×C1111yescharacteristic
369C24C2×D4×C1112yes—
370#41—24no—
371#41—24no—
372#41—24no—
373#41—24no—
374#41—44no—
375#41—416no—
376#41—48no—
377#41—48no—
378#41—44no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—48no—
383C2×Q8C2×D4×C1112yes—
384C2×Q8C2×D4×C1112yes—
385C2×Q8C2×D4×C1114yes—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—24no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—28no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—42no—
398C2×D4—48no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4C2×D4×C1112yes—
402C2×D4C2×D4×C1112yes—
403C2×D4C2×D4×C1114yes—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—42no—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1112yes—
417C22×C4C24×C1111yescharacteristic
418Q16—44no—
419SD16—44no—
420SD16—44no—
421D8—44no—
422M16—24no—
423M16—24no—
424C2×C8—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—28no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—28no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—28no—
440C42—24no—
441C42C2×D4×C1114yes—
442C42C2×D4×C1114yes—
443C11#2389811yescharacteristic, direct product factor, Sylow
444C23—22no—
445C23—22no—
446C23—22no—
447C23—21no—
448C23—21no—
449C23—22no—
450C23—21no—
451C23—44no—
452C23—81no—
453C23—82no—
454C23—84no—
455C23C11×#12014yes—
456C23C22×D4×C1111yescharacteristic
457Q8—28no—
458Q8—24no—
459Q8—24no—
460Q8—44no—
461D4—28no—
462D4—24no—
463D4—24no—
464D4—48no—
465D4—44no—
466D4—48no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—84no—
472D4—88no—
473D4—84no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—48no—
484C2×C4—48no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—84no—
490C2×C4C11×#12014yes—
491C2×C4C22×D4×C1112yes—
492C2×C4C22×D4×C1112yes—
493C2×C4C11×H(5,𝔽2)12yes—
494C8—44no—
495C22—24no—
496C22—41no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—42no—
501C22—42no—
502C22—44no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—42no—
507C22—82no—
508C22—164no—
509C22C2×C11×#12011yescharacteristic
510C22C2×C11×#12011yescharacteristic
511C22C11×#53411yescharacteristic
512C4—24no—
513C4—44no—
514C4—44no—
515C4—41no—
516C4—42no—
517C4—42no—
518C4D42×C1114yes—
519C2—21no—
520C2—21no—
521C2—21no—
522C2—44no—
523C2—81no—
524C2—82no—
525C2—82no—
526C2C11×#240311yescharacteristic
subgroupG/H
center, socleC2×C11#2403
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3487C2semidirect
2. C11×#3485C2semidirect
3. C11×#3020C2semidirect
4. C11×#3019C2semidirect
5. C11×#2010C2semidirect
6. C11×#1912C2semidirect
7. C11×#1911C2semidirect
8. C11×#1785C2semidirect
9. C2×C11×2−1+4C22semidirect
23. C11×#525C22semidirect
25. C11×#519C22semidirect
32. C11×#421C22semidirect
33. C2×C11×#101C22semidirect
35. C11×#407C22semidirect
36. C11×H(3,ℤ/4)C22semidirect
63. C11×C4⋊Q8D4semidirect
65. C11×#127D4semidirect
67. C11×#124D4semidirect
68. C11×#124D4semidirect
104. #23898C11direct (N × H)
181. #3487C2×C11semidirect
182. #3485C2×C11semidirect
183. #3020C2×C11semidirect
184. #3019C2×C11semidirect
185. #2010C2×C11semidirect
186. #1912C2×C11semidirect
187. #1911C2×C11semidirect
188. #1785C2×C11semidirect
240. C2×2−1+4C22×C11semidirect
254. #525C22×C11semidirect
256. #519C22×C11semidirect
263. #421C22×C11semidirect
264. C2×#101C22×C11semidirect
266. #407C22×C11semidirect
267. H(3,ℤ/4)C22×C11semidirect
318. C4⋊Q8D4×C11semidirect
320. #127D4×C11semidirect
322. #124D4×C11semidirect
323. #124D4×C11semidirect
443. C11#23898direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34872
C11×#34852
C11×#30202
C11×#30192
C11×#20102
C11×#19122
C11×#19112
C11×#17852
#2389811