Finite Group Databasebeta

← C11×#23933 #14601126

Subgroups — C11×#23933 #14601126

Order 2816.

1488 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#450C212yesmaximal
3C2×C11×#390C211yesmaximal, characteristic
4C11×#2023C212yesmaximal, complemented
5C11×#2013C212yesmaximal, complemented
6C11×#1880C214yesmaximal, complemented
7C11×#1872C212yesmaximal, complemented
8C11×#1817C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C22×C11×SD16C2214yes—
11C11×#533—28no—
12C2×C11×C4⋊Q8C2211yescharacteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic, complemented
14C2×C11×#125—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2212yescomplemented
19C2×C11×#117—21no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4—21no—
22C22×C11×C22⋊C4—21no—
23C22×C42×C11C2211yescharacteristic
24C11×#450—28no—
25C2×C11×#103C2214yescomplemented
26C2×C11×#102C2214yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#390—21no—
29C11×#390—21no—
30C11×#390C2212yes—
31C11×#390C2212yes—
32C11×#340C2214yescomplemented
33C11×#336C2212yescomplemented
34C11×#336C2212yescomplemented
35C25×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11C2312yes—
38C22×D4×C11—24no—
39C22×D4×C11—21no—
40C22×D4×C11—24no—
41C22×D4×C11—42no—
42C22×D4×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C2×C11×SD16—28no—
48C2×C11×SD16—28no—
49C2×C11×SD16—44no—
50C22×C8×C11C2314yes—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—24no—
53C11×#125—28no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8D418yes—
57C4×Q8×C11—28no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C11×#117—28no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4—44no—
77C2×C42×C11—24no—
78C2×C42×C11—22no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C11×#103—44no—
84C11×#102—28no—
85C11×C22⋊C8—24no—
86#23933C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—24no—
88C24×C11—22no—
89C24×C11—42no—
90C24×C11—42no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11C2×D411yescharacteristic
96C2×Q8×C11—24no—
97C2×Q8×C11—22no—
98C2×Q8×C11—24no—
99C2×Q8×C11—24no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11C2×D414yes—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—24no—
107C2×D4×C11—416no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11#4114yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—41no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11SD1614yescomplemented
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C11×SD16—416no—
133C2×C8×C11—24no—
134C2×C8×C11—24no—
135C2×C8×C11—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4C2×D414yes—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—44no—
150C42×C11—28no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11—22no—
155C2×#533C2×C1111yescharacteristic, complemented
156C2×#450C2×C1112yes—
157C2×#390C2×C1111yescharacteristic
158#2023C2×C1112yescomplemented
159#2013C2×C1112yescomplemented
160#1880C2×C1114yescomplemented
161#1872C2×C1112yescomplemented
162#1817C2×C1111yescharacteristic, complemented
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—24no—
168C23×C11—48no—
169C23×C11—48no—
170C23×C11—48no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—84no—
178C23×C11—84no—
179C23×C11—84no—
180C23×C11—84no—
181C23×C11#12012yes—
182C23×C11C2×SD1612yes—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—28no—
186Q8×C11—48no—
187Q8×C11—44no—
188D4×C11—28no—
189D4×C11—48no—
190D4×C11—44no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—28no—
200C2×C4×C11—28no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—84no—
215C2×C4×C11#12012yes—
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11C2×SD1612yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D412yes—
220C2×C4×C11C2×#4112yes—
221C2×C4×C11H(5,𝔽2)12yes—
222C8×C11—44no—
223C23×D4C22×C1111yescharacteristic
224C22×SD16C22×C1114yes—
225#533—28no—
226C2×C4⋊Q8C22×C1111yescharacteristic, complemented
227C2×C4⋊Q8C22×C1111yescharacteristic, complemented
228C2×#125—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C22×C1112yes—
231C2×C4×Q8—21no—
232C2×C4×Q8C22×C1112yescomplemented
233C2×#117—21no—
234C22×C4⋊C4C22×C1111yescharacteristic
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C42C22×C1111yescharacteristic
238#450—28no—
239C2×#103C22×C1114yescomplemented
240C2×#102C22×C1114yes—
241C2×C22⋊C8C22×C1112yes—
242#390—21no—
243#390—21no—
244#390C22×C1112yes—
245#390C22×C1112yes—
246#340C22×C1114yescomplemented
247#336C22×C1112yescomplemented
248#336C22×C1112yescomplemented
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—44no—
258C22×C11—816no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11#44814yes—
264C22×C11C2×#12011yescharacteristic
265C22×C11#52511yescharacteristic
266C22×C11#53511yescharacteristic
267C22×C11C22×SD1611yescharacteristic
268C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11#57511yescharacteristic
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—22no—
275C4×C11—44no—
276C4×C11—41no—
277C4×C11—44no—
278C4×C11—82no—
279C4×C11#54614yes—
280C25—21no—
281C22×Q8—21no—
282C22×Q8C23×C1112yes—
283C22×D4—24no—
284C22×D4—21no—
285C22×D4—24no—
286C22×D4—42no—
287C22×D4C23×C1112yes—
288C23×C4—21no—
289C23×C4D4×C1111yescharacteristic
290C23×C4D4×C1111yescharacteristic
291C23×C4C23×C1111yescharacteristic
292C2×SD16—28no—
293C2×SD16—28no—
294C2×SD16—44no—
295C22×C8C23×C1114yes—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298#125—28no—
299C22⋊Q8—28no—
300C22⋊Q8—24no—
301C22⋊Q8D4×C1118yes—
302C4×Q8—28no—
303C4×Q8—24no—
304C4×Q8—24no—
305#117—28no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4C23×C1112yes—
314C2×C4⋊C4C23×C1112yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C42—22no—
323C2×C42—24no—
324C2×C42D4×C1111yescharacteristic
325C2×C42D4×C1111yescharacteristic
326C2×C42C23×C1111yescharacteristic
327C2×C42C23×C1111yescharacteristic
328#103—44no—
329#102—28no—
330C22⋊C8—24no—
331C2×C11—24no—
332C2×C11—84no—
333C2×C11#240411yescharacteristic
334C2×C11C2×#44811yescharacteristic
335C2×C11#300611yescharacteristic
336C2×C11#310111yescharacteristic
337C2×C11#311011yescharacteristic
338C2×C11#320811yescharacteristic
339C2×C11#321511yescharacteristic
340C24—24no—
341C24—22no—
342C24—42no—
343C24—42no—
344C24—42no—
345C24—42no—
346C24—42no—
347C24—42no—
348C24C2×D4×C1111yescharacteristic
349C2×Q8—24no—
350C2×Q8—22no—
351C2×Q8—24no—
352C2×Q8—24no—
353C2×Q8—42no—
354C2×Q8—42no—
355C2×Q8C2×D4×C1114yes—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—22no—
359C2×D4—24no—
360C2×D4—416no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4C11×#4114yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4C11×SD1614yescomplemented
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1114yes—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C24×C1111yescharacteristic
385SD16—416no—
386C2×C8—24no—
387C2×C8—24no—
388C2×C8—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—28no—
394C4⋊C4—22no—
395C4⋊C4—24no—
396C4⋊C4—42no—
397C4⋊C4C2×D4×C1114yes—
398C22⋊C4—28no—
399C22⋊C4—44no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C42—28no—
404C42—22no—
405C42—22no—
406C42—22no—
407C42—22no—
408C11#2393311yescharacteristic, direct product factor, Sylow
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—24no—
414C23—48no—
415C23—48no—
416C23—48no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—84no—
424C23—84no—
425C23—84no—
426C23—84no—
427C23C11×#12012yes—
428C23C2×C11×SD1612yes—
429C23C11×#13712yes—
430C23C22×D4×C1111yescharacteristic
431Q8—28no—
432Q8—48no—
433Q8—44no—
434D4—28no—
435D4—48no—
436D4—44no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—28no—
446C2×C4—28no—
447C2×C4—21no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—84no—
461C2×C4C11×#12012yes—
462C2×C4C2×C11×SD1612yes—
463C2×C4C2×C11×SD1612yes—
464C2×C4C11×AGL(1,ℤ/8)12yes—
465C2×C4C22×D4×C1112yes—
466C2×C4C2×C11×#4112yes—
467C2×C4C11×H(5,𝔽2)12yes—
468C8—44no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—44no—
476C22—44no—
477C22—44no—
478C22—816no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22C11×#44814yes—
484C22C2×C11×#12011yescharacteristic
485C22C11×#52511yescharacteristic
486C22C11×#53511yescharacteristic
487C22C22×C11×SD1611yescharacteristic
488C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
489C22C2×C11×#13711yescharacteristic
490C22C11×#57511yescharacteristic
491C4—22no—
492C4—22no—
493C4—22no—
494C4—22no—
495C4—44no—
496C4—41no—
497C4—44no—
498C4—82no—
499C4C11×#54614yes—
500C2—24no—
501C2—84no—
502C2C11×#240411yescharacteristic
503C2C2×C11×#44811yescharacteristic
504C2C11×#300611yescharacteristic
505C2C11×#310111yescharacteristic
506C2C11×#311011yescharacteristic
507C2C11×#320811yescharacteristic
508C2C11×#321511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#533C2semidirect
4. C11×#2023C2semidirect
5. C11×#2013C2semidirect
6. C11×#1880C2semidirect
7. C11×#1872C2semidirect
8. C11×#1817C2semidirect
12. C2×C11×C4⋊Q8C22semidirect
13. C2×C11×C4⋊Q8C22semidirect
18. C2×C4×Q8×C11C22semidirect
25. C2×C11×#103C22semidirect
32. C11×#340C22semidirect
33. C11×#336C22semidirect
34. C11×#336C22semidirect
86. #23933C11direct (N × H)
124. C22×C4×C11SD16semidirect
155. C2×#533C2×C11semidirect
158. #2023C2×C11semidirect
159. #2013C2×C11semidirect
160. #1880C2×C11semidirect
161. #1872C2×C11semidirect
162. #1817C2×C11semidirect
226. C2×C4⋊Q8C22×C11semidirect
227. C2×C4⋊Q8C22×C11semidirect
232. C2×C4×Q8C22×C11semidirect
239. C2×#103C22×C11semidirect
246. #340C22×C11semidirect
247. #336C22×C11semidirect
248. #336C22×C11semidirect
377. C22×C4C11×SD16semidirect
408. C11#23933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4502
C2×C11×#3902
C11×#20232
C11×#20132
C11×#18802
C11×#18722
C11×#18172
#2393311