Finite Group Databasebeta

← C11×#23926 #14601119

Subgroups — C11×#23926 #14601119

Order 2816.

1888 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic
3C2×C11×#448C212yesmaximal, complemented
4C2×C11×#450C212yesmaximal, complemented
5C11×#2000C214yesmaximal, complemented
6C11×#1875C212yesmaximal, complemented
7C11×#1873C212yesmaximal, complemented
8C11×#1780C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic, complemented
11C23×D4×C11C2211yescharacteristic
12C22×C11×SD16C2214yes—
13C11×#536—28no—
14C11×#535—28no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×#127—21no—
17C2×C11×#124—21no—
18C2×C11×#124—21no—
19C2×C11×#123—21no—
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2212yescomplemented
23C2×C11×#121C2212yes—
24C2×C11×#121C2212yes—
25C2×C11×#120—21no—
26C2×C11×#120—21no—
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C11×#450—28no—
30C11×#448—28no—
31C2×C11×#103C2214yescomplemented
32C2×C11×#102C2214yes—
33C2×C11×C22⋊C8C2212yes—
34C2×C11×C22⋊C8C2212yescomplemented
35C2×C11×C22⋊C8C2212yescomplemented
36C11×#340C2214yescomplemented
37C25×C11—21no—
38C2×C11×#41—24no—
39C2×C11×#41—24no—
40C2×C11×#41—42no—
41C22×Q8×C11—24no—
42C22×Q8×C11—21no—
43C22×Q8×C11—24no—
44C22×Q8×C11—42no—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—24no—
50C22×D4×C11—21no—
51C22×D4×C11—24no—
52C22×D4×C11—42no—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11D411yescharacteristic
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2312yes—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C2×C11×SD16—28no—
62C2×C11×SD16—28no—
63C2×C11×SD16—44no—
64C22×C8×C11C2314yes—
65C11×C4⋊Q8—28no—
66C11×#127—28no—
67C11×#124—28no—
68C11×#124—28no—
69C11×#123—28no—
70C11×#123—28no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8D418yescomplemented
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121D418yes—
79C11×#120—28no—
80C11×#120—28no—
81C11×#117—24no—
82C11×#117—24no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C11×#103—28no—
96C11×#102—28no—
97C11×C22⋊C8—24no—
98C11×C22⋊C8—24no—
99C11×C22⋊C8—42no—
100#23926C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—84no—
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C24×C11C2×D411yescharacteristic
109C11×#41—416no—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C2×Q8×C11—41no—
117C2×Q8×C11—416no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D414yes—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—416no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—84no—
140C2×D4×C11—84no—
141C2×D4×C11C2×D414yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
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—22no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2411yescharacteristic
161C11×SD16—416no—
162C2×C8×C11—24no—
163C2×C8×C11—24no—
164C2×C8×C11—24no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D414yes—
170C11×C4⋊C4C2×D414yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—28no—
177C42×C11—24no—
178C42×C11—24no—
179C2×#536C2×C1111yescharacteristic, complemented
180C2×#535C2×C1111yescharacteristic
181C2×#448C2×C1112yescomplemented
182C2×#450C2×C1112yescomplemented
183#2000C2×C1114yescomplemented
184#1875C2×C1112yescomplemented
185#1873C2×C1112yescomplemented
186#1780C2×C1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—21no—
194C23×C11—24no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—24no—
198C23×C11—48no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—88no—
204C23×C11—88no—
205C23×C11—88no—
206C23×C11#12012yes—
207C23×C11#12012yes—
208C23×C11C22×D411yescharacteristic
209Q8×C11—28no—
210Q8×C11—44no—
211Q8×C11—48no—
212Q8×C11—44no—
213D4×C11—28no—
214D4×C11—44no—
215D4×C11—44no—
216D4×C11—48no—
217D4×C11—44no—
218D4×C11—44no—
219D4×C11—88no—
220D4×C11—88no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—28no—
226C2×C4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11#12012yes—
240C2×C4×C11#12012yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11H(5,𝔽2)12yes—
244C8×C11—44no—
245C22×#41C22×C1111yescharacteristic
246C23×Q8C22×C1111yescharacteristic, complemented
247C23×D4C22×C1111yescharacteristic
248C22×SD16C22×C1114yes—
249#536—28no—
250#535—28no—
251C2×C4⋊Q8—21no—
252C2×#127—21no—
253C2×#124—21no—
254C2×#124—21no—
255C2×#123—21no—
256C2×#123—21no—
257C2×C22⋊Q8C22×C1112yes—
258C2×C22⋊Q8C22×C1112yescomplemented
259C2×#121C22×C1112yes—
260C2×#121C22×C1112yes—
261C2×#120—21no—
262C2×#120—21no—
263C2×#117C22×C1111yescharacteristic
264C2×#117C22×C1111yescharacteristic, complemented
265#450—28no—
266#448—28no—
267C2×#103C22×C1114yescomplemented
268C2×#102C22×C1114yes—
269C2×C22⋊C8C22×C1112yes—
270C2×C22⋊C8C22×C1112yescomplemented
271C2×C22⋊C8C22×C1112yescomplemented
272#340C22×C1114yescomplemented
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—24no—
276C22×C11—24no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—41no—
282C22×C11—44no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11—42no—
288C22×C11—816no—
289C22×C11—84no—
290C22×C11—84no—
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×#12011yescharacteristic
293C22×C11#53411yescharacteristic
294C22×C11#57714yes—
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—41no—
298C4×C11—44no—
299C4×C11—44no—
300C4×C11—44no—
301C4×C11D4214yes—
302C25—21no—
303C2×#41—24no—
304C2×#41—24no—
305C2×#41—42no—
306C22×Q8—24no—
307C22×Q8—21no—
308C22×Q8—24no—
309C22×Q8—42no—
310C22×Q8D4×C1111yescharacteristic
311C22×Q8C23×C1112yes—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—24no—
315C22×D4—21no—
316C22×D4—24no—
317C22×D4—42no—
318C22×D4D4×C1111yescharacteristic
319C22×D4D4×C1111yescharacteristic
320C22×D4D4×C1111yescharacteristic
321C22×D4C23×C1112yes—
322C23×C4—21no—
323C23×C4C23×C1111yescharacteristic
324C23×C4C23×C1111yescharacteristic
325C23×C4C23×C1111yescharacteristic
326C2×SD16—28no—
327C2×SD16—28no—
328C2×SD16—44no—
329C22×C8C23×C1114yes—
330C4⋊Q8—28no—
331#127—28no—
332#124—28no—
333#124—28no—
334#123—28no—
335#123—28no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8D4×C1118yescomplemented
340#121—24no—
341#121—24no—
342#121—24no—
343#121D4×C1118yes—
344#120—28no—
345#120—28no—
346#117—24no—
347#117—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1112yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C42—21no—
359C2×C42—21no—
360#103—28no—
361#102—28no—
362C22⋊C8—24no—
363C22⋊C8—24no—
364C22⋊C8—42no—
365C2×C11—42no—
366C2×C11—42no—
367C2×C11—81no—
368C2×C11—84no—
369C2×C11#240311yescharacteristic
370C2×C11#300912yes—
371C2×C11#301012yes—
372C2×C11#320012yes—
373C24—24no—
374C24—22no—
375C24—42no—
376C24—42no—
377C24—84no—
378C24C2×D4×C1111yescharacteristic
379C24C2×D4×C1111yescharacteristic
380C24C2×D4×C1111yescharacteristic
381#41—416no—
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—24no—
387C2×Q8—24no—
388C2×Q8—41no—
389C2×Q8—416no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8C2×D4×C1114yes—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—416no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—84no—
412C2×D4—84no—
413C2×D4C2×D4×C1114yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1114yes—
431C22×C4C2×D4×C1114yes—
432C22×C4C24×C1111yescharacteristic
433SD16—416no—
434C2×C8—24no—
435C2×C8—24no—
436C2×C8—24no—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4C2×D4×C1114yes—
442C4⋊C4C2×D4×C1114yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C22⋊C4—28no—
448C22⋊C4—28no—
449C42—24no—
450C42—24no—
451C11#2392611yescharacteristic, direct product factor, Sylow
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—24no—
457C23—24no—
458C23—21no—
459C23—24no—
460C23—21no—
461C23—21no—
462C23—24no—
463C23—48no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—88no—
469C23—88no—
470C23—88no—
471C23C11×#12012yes—
472C23C11×#12012yes—
473C23C22×D4×C1111yescharacteristic
474Q8—28no—
475Q8—44no—
476Q8—48no—
477Q8—44no—
478D4—28no—
479D4—44no—
480D4—44no—
481D4—48no—
482D4—44no—
483D4—44no—
484D4—88no—
485D4—88no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—28no—
491C2×C4—28no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—24no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—48no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4C11×#12012yes—
505C2×C4C11×#12012yes—
506C2×C4C22×D4×C1112yes—
507C2×C4C22×D4×C1112yes—
508C2×C4C11×H(5,𝔽2)12yes—
509C8—44no—
510C22—22no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—41no—
519C22—44no—
520C22—42no—
521C22—42no—
522C22—44no—
523C22—44no—
524C22—42no—
525C22—816no—
526C22—84no—
527C22—84no—
528C22C2×C11×#12011yescharacteristic
529C22C2×C11×#12011yescharacteristic
530C22C11×#53411yescharacteristic
531C22C11×#57714yes—
532C4—22no—
533C4—22no—
534C4—41no—
535C4—44no—
536C4—44no—
537C4—44no—
538C4D42×C1114yes—
539C2—42no—
540C2—42no—
541C2—81no—
542C2—84no—
543C2C11×#240311yescharacteristic
544C2C11×#300912yes—
545C2C11×#301012yes—
546C2C11×#320012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#536C2semidirect
3. C2×C11×#448C2semidirect
4. C2×C11×#450C2semidirect
5. C11×#2000C2semidirect
6. C11×#1875C2semidirect
7. C11×#1873C2semidirect
8. C11×#1780C2semidirect
10. C23×Q8×C11C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
28. C2×C11×#117C22semidirect
31. C2×C11×#103C22semidirect
34. C2×C11×C22⋊C8C22semidirect
35. C2×C11×C22⋊C8C22semidirect
36. C11×#340C22semidirect
74. C11×C22⋊Q8D4semidirect
100. #23926C11direct (N × H)
179. C2×#536C2×C11semidirect
181. C2×#448C2×C11semidirect
182. C2×#450C2×C11semidirect
183. #2000C2×C11semidirect
184. #1875C2×C11semidirect
185. #1873C2×C11semidirect
186. #1780C2×C11semidirect
246. C23×Q8C22×C11semidirect
258. C2×C22⋊Q8C22×C11semidirect
264. C2×#117C22×C11semidirect
267. C2×#103C22×C11semidirect
270. C2×C22⋊C8C22×C11semidirect
271. C2×C22⋊C8C22×C11semidirect
272. #340C22×C11semidirect
339. C22⋊Q8D4×C11semidirect
451. C11#23926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#5352
C2×C11×#4482
C2×C11×#4502
C11×#20002
C11×#18752
C11×#18732
C11×#17802
#2392611