Finite Group Databasebeta

← C11×#23456 #14600649

Subgroups — C11×#23456 #14600649

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C22×C11×#102C211yesmaximal, characteristic
4C11×#2309C211yesmaximal, characteristic
5C11×#2025C214yesmaximal, complemented
6C11×#2023C214yesmaximal, complemented
7C11×#1736C211yesmaximal, characteristic, complemented
8C11×#1735C211yesmaximal, characteristic, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C11×#544—24no—
14C11×#544—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2212yescomplemented
17C2×C11×#125—21no—
18C2×C11×#125C2212yescomplemented
19C2×C11×C22⋊Q8—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#418—24no—
25C2×C11×#102—24no—
26C2×C11×#102C2214yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C11×#390—21no—
30C11×#390—21no—
31C11×#390C2214yes—
32C11×#379—22no—
33C11×#340C2212yescomplemented
34C11×#340C2212yescomplemented
35C11×#340C2214yescomplemented
36C11×#336C2214yescomplemented
37C25×C11—21no—
38C22×Q8×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—21no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11Q814yescomplemented
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—28no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×#125—28no—
61C11×#125—24no—
62C11×#125—24no—
63C11×C22⋊Q8—216no—
64C11×#117—22no—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117D414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D414yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2312yes—
90C11×#102—28no—
91C11×#102—24no—
92C11×#102—24no—
93#23456C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—22no—
95C24×C11—24no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—82no—
99C24×C11—82no—
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—28no—
102C2×Q8×C11—84no—
103C2×D4×C11—28no—
104C2×D4×C11—28no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—42no—
115C2×D4×C11C2×Q814yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—82no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×Q812yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C11×M16—44no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—44no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2×D414yes—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—84no—
158C11×C22⋊C4—84no—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—42no—
163C2×#544C2×C1111yescharacteristic, complemented
164C2×#418C2×C1111yescharacteristic
165C22×#102C2×C1111yescharacteristic
166#2309C2×C1111yescharacteristic
167#2025C2×C1114yescomplemented
168#2023C2×C1114yescomplemented
169#1736C2×C1111yescharacteristic, complemented
170#1735C2×C1111yescharacteristic, complemented
171#1729C2×C1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—24no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—44no—
178C23×C11—44no—
179C23×C11—48no—
180C23×C11—88no—
181C23×C11—88no—
182C23×C11—84no—
183C23×C11—84no—
184C23×C11#12012yes—
185C23×C11C22⋊Q812yes—
186C23×C11#12412yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—88no—
189D4×C11—24no—
190D4×C11—24no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—48no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—84no—
208C2×C4×C11#12012yes—
209C2×C4×C11C22⋊Q814yes—
210C2×C4×C11C22⋊Q814yes—
211C2×C4×C11C22⋊Q812yes—
212C2×C4×C11#12414yes—
213C2×C4×C11#12414yes—
214C2×C4×C11#12412yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C8×C11—42no—
222C8×C11—42no—
223C23×D4C22×C1111yescharacteristic
224C22×M16C22×C1111yescharacteristic
225C23×C8C22×C1111yescharacteristic
226#544—24no—
227#544—24no—
228C2×C4⋊Q8—21no—
229C2×C4⋊Q8C22×C1112yescomplemented
230C2×#125—21no—
231C2×#125C22×C1112yescomplemented
232C2×C22⋊Q8—22no—
233C2×#117C22×C1111yescharacteristic
234C2×#117C22×C1111yescharacteristic
235C2×#117C22×C1111yescharacteristic
236C22×C4⋊C4C22×C1111yescharacteristic
237#418—24no—
238C2×#102—24no—
239C2×#102C22×C1114yes—
240C2×#102C22×C1112yes—
241C2×#102C22×C1112yes—
242#390—21no—
243#390—21no—
244#390C22×C1114yes—
245#379—22no—
246#340C22×C1112yescomplemented
247#340C22×C1112yescomplemented
248#340C22×C1114yescomplemented
249#336C22×C1114yescomplemented
250C22×C11—24no—
251C22×C11—24no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—48no—
255C22×C11—44no—
256C22×C11—816no—
257C22×C11—84no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11#39314yes—
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×C22⋊Q811yescharacteristic
263C22×C11C2×#12411yescharacteristic
264C22×C11#57612yes—
265C22×C11#57712yes—
266C4×C11—42no—
267C4×C11—44no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—82no—
272C4×C11#39314yes—
273C4×C11C2×C22⋊Q811yescharacteristic
274C4×C11C2×C22⋊Q811yescharacteristic
275C4×C11C2×#12411yescharacteristic
276C4×C11C2×#12411yescharacteristic
277C25—21no—
278C22×Q8—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4Q8×C1114yescomplemented
286C22×D4C23×C1112yes—
287C23×C4—21no—
288C23×C4C23×C1111yescharacteristic
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8C23×C1112yes—
296C22×C8C23×C1112yes—
297C4⋊Q8—28no—
298C4⋊Q8—24no—
299C4⋊Q8—24no—
300#125—28no—
301#125—24no—
302#125—24no—
303C22⋊Q8—216no—
304#117—22no—
305#117—22no—
306#117—22no—
307#117—22no—
308#117—22no—
309#117D4×C1114yes—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4D4×C1111yescharacteristic
316C2×C4⋊C4D4×C1111yescharacteristic
317C2×C4⋊C4D4×C1114yes—
318C2×C4⋊C4C23×C1112yes—
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4D4×C1112yes—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42C23×C1112yes—
330#102—28no—
331#102—24no—
332#102—24no—
333C2×C11—24no—
334C2×C11—84no—
335C2×C11C2×#39311yescharacteristic
336C2×C11#300811yescharacteristic
337C2×C11#301011yescharacteristic
338C2×C11#308112yes—
339C2×C11#313612yes—
340C24—22no—
341C24—24no—
342C24—42no—
343C24—42no—
344C24—82no—
345C24—82no—
346C24C2×D4×C1111yescharacteristic
347C2×Q8—28no—
348C2×Q8—84no—
349C2×D4—28no—
350C2×D4—28no—
351C2×D4—24no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—42no—
358C2×D4—44no—
359C2×D4—44no—
360C2×D4—42no—
361C2×D4C2×Q8×C1114yes—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—82no—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1112yes—
373C22×C4C2×Q8×C1112yes—
374C22×C4C11×#4112yes—
375C22×C4C11×#4112yes—
376C22×C4C11×#4112yes—
377C22×C4C24×C1111yescharacteristic
378M16—44no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—44no—
386C4⋊C4—28no—
387C4⋊C4—28no—
388C4⋊C4—28no—
389C4⋊C4—24no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4C2×D4×C1114yes—
398C4⋊C4C2×D4×C1112yes—
399C4⋊C4C2×D4×C1112yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—42no—
403C22⋊C4—84no—
404C22⋊C4—84no—
405C42—24no—
406C42—22no—
407C42—22no—
408C42—42no—
409C11#2345611yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23—22no—
412C23—24no—
413C23—42no—
414C23—42no—
415C23—48no—
416C23—44no—
417C23—44no—
418C23—88no—
419C23—84no—
420C23—84no—
421C23—88no—
422C23C11×#12012yes—
423C23C11×C22⋊Q812yes—
424C23C11×#12412yes—
425C23C22×D4×C1111yescharacteristic
426Q8—88no—
427D4—24no—
428D4—24no—
429D4—42no—
430D4—42no—
431D4—48no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—84no—
446C2×C4C11×#12012yes—
447C2×C4C11×C22⋊Q814yes—
448C2×C4C11×C22⋊Q814yes—
449C2×C4C11×C22⋊Q812yes—
450C2×C4C11×#12414yes—
451C2×C4C11×#12414yes—
452C2×C4C11×#12412yes—
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C22×Q8×C1111yescharacteristic
456C2×C4C2×C11×#4111yescharacteristic
457C2×C4C2×C11×#4111yescharacteristic
458C2×C4C2×C11×#4111yescharacteristic
459C8—42no—
460C8—42no—
461C22—22no—
462C22—22no—
463C22—24no—
464C22—24no—
465C22—44no—
466C22—48no—
467C22—816no—
468C22—82no—
469C22—82no—
470C22—84no—
471C22C11×#39314yes—
472C22C2×C11×#12011yescharacteristic
473C22C2×C11×C22⋊Q811yescharacteristic
474C22C2×C11×#12411yescharacteristic
475C22C11×#57612yes—
476C22C11×#57712yes—
477C4—42no—
478C4—44no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—82no—
483C4C11×#39314yes—
484C4C2×C11×C22⋊Q811yescharacteristic
485C4C2×C11×C22⋊Q811yescharacteristic
486C4C2×C11×#12411yescharacteristic
487C4C2×C11×#12411yescharacteristic
488C2—24no—
489C2—84no—
490C2C2×C11×#39311yescharacteristic
491C2C11×#300811yescharacteristic
492C2C11×#301011yescharacteristic
493C2C11×#308112yes—
494C2C11×#313612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#544C2semidirect
5. C11×#2025C2semidirect
6. C11×#2023C2semidirect
7. C11×#1736C2semidirect
8. C11×#1735C2semidirect
9. C11×#1729C2semidirect
16. C2×C11×C4⋊Q8C22semidirect
18. C2×C11×#125C22semidirect
33. C11×#340C22semidirect
34. C11×#340C22semidirect
35. C11×#340C22semidirect
36. C11×#336C22semidirect
45. C22×D4×C11Q8semidirect
93. #23456C11direct (N × H)
163. C2×#544C2×C11semidirect
167. #2025C2×C11semidirect
168. #2023C2×C11semidirect
169. #1736C2×C11semidirect
170. #1735C2×C11semidirect
171. #1729C2×C11semidirect
229. C2×C4⋊Q8C22×C11semidirect
231. C2×#125C22×C11semidirect
246. #340C22×C11semidirect
247. #340C22×C11semidirect
248. #340C22×C11semidirect
249. #336C22×C11semidirect
285. C22×D4Q8×C11semidirect
409. C11#23456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4182
C22×C11×#1022
C11×#23092
C11×#20252
C11×#20232
C11×#17362
C11×#17352
C11×#17292
#2345611