Finite Group Databasebeta

← C11×#21422 #14598615

Subgroups — C11×#21422 #14598615

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#538C211yesmaximal, characteristic
2C11×#2312C211yesmaximal, characteristic, complemented
3C11×#2273C211yesmaximal, characteristic, complemented
4C11×#1996C212yesmaximal, complemented
5C11×#1964C212yesmaximal, complemented
6C11×#1898C214yesmaximal, complemented
7C4×C11×#99C214yesmaximal, complemented
8C11×#538—24no—
9C11×#538—24no—
10C2×C11×#126C412yescomplemented
11C2×C11×#124C412yescomplemented
12C2×C11×#123C412yescomplemented
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#121C412yescomplemented
15C2×C11×#121C2211yescharacteristic
16C2×C11×#120C2212yes—
17C2×C4×D4×C11C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C2×C11×#99C2218yes—
21C11×#388—24no—
22C11×#380C2212yes—
23C11×#379C2212yes—
24C4×C11×C22⋊C4—24no—
25C4×C11×C22⋊C4C2212yes—
26C4×C11×C22⋊C4C2212yes—
27C4×C11×C22⋊C4C2212yes—
28C11×#342C2218yes—
29C25×C11C2311yescharacteristic
30C22×Q8×C11C2×C411yescharacteristic, complemented
31C22×D4×C11C2×C412yes—
32C22×D4×C11C2×C412yes—
33C22×D4×C11C2×C411yescharacteristic, complemented
34C22×D4×C11C2312yes—
35C23×C4×C11—22no—
36C23×C4×C11C2×C412yescomplemented
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C11×#126—28no—
40C11×#124—28no—
41C11×#123—28no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C11×#121—22no—
45C11×#121—22no—
46C11×#121—28no—
47C11×#120—24no—
48C11×#120—24no—
49C4×D4×C11—24no—
50C4×D4×C11—24no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4C2×C412yescomplemented
53C2×C11×C4⋊C4C2×C412yescomplemented
54C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
55C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—28no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4C2×C412yes—
61C2×C11×C22⋊C4C2×C412yes—
62C2×C11×C22⋊C4C2×C412yes—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2×C412yescomplemented
65C2×C11×C22⋊C4C2×C412yescomplemented
66C2×C11×C22⋊C4D414yes—
67C2×C11×C22⋊C4D414yes—
68C2×C11×C22⋊C4C2314yes—
69C2×C11×C22⋊C4C2312yes—
70C2×C11×C22⋊C4C2314yes—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11C2×C412yescomplemented
75C11×#99—216no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80#21422C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—24no—
82C24×C11—81no—
83C24×C11—81no—
84C24×C11C22×C412yes—
85C24×C11C22×C412yes—
86C24×C11C2×D412yes—
87C24×C11C2×D412yes—
88C24×C11C2411yescharacteristic
89C2×Q8×C11—22no—
90C2×Q8×C11—81no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—28no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C2×D4×C11—81no—
100C22×C4×C11—24no—
101C22×C4×C11—28no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—81no—
105C22×C4×C11—81no—
106C22×C4×C11—82no—
107C22×C4×C11—82no—
108C22×C4×C11—82no—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—82no—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—28no—
133C11×C22⋊C4—82no—
134C11×C22⋊C4—82no—
135C11×C22⋊C4C22⋊C418yes—
136C11×C22⋊C4C22⋊C418yes—
137C11×C22⋊C4#4118yes—
138C42×C11—24no—
139C42×C11—82no—
140C42×C11—82no—
141C42×C11—82no—
142C2×#538C2×C1111yescharacteristic
143#2312C2×C1111yescharacteristic, complemented
144#2273C2×C1111yescharacteristic, complemented
145#1996C2×C1112yescomplemented
146#1964C2×C1112yescomplemented
147#1898C2×C1114yescomplemented
148C4×#99C2×C1114yescomplemented
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—22no—
154C23×C11—24no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—88no—
166C23×C11C2×C22⋊C414yes—
167C23×C11C23×C411yescharacteristic
168C23×C11C22×D411yescharacteristic
169C23×C11C22×D411yescharacteristic
170C23×C11C2×#4114yes—
171Q8×C11—82no—
172D4×C11—44no—
173D4×C11—44no—
174D4×C11—82no—
175D4×C11—84no—
176D4×C11—84no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—28no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—44no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—84no—
197C2×C4×C11—88no—
198C2×C4×C11C2×C22⋊C414yes—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11C2×C22⋊C412yes—
201#538—24no—
202#538—24no—
203C2×#126C4×C1112yescomplemented
204C2×#124C4×C1112yescomplemented
205C2×#123C4×C1112yescomplemented
206C2×C22⋊Q8C22×C1111yescharacteristic
207C2×#121C4×C1112yescomplemented
208C2×#121C22×C1111yescharacteristic
209C2×#120C22×C1112yes—
210C2×C4×D4C22×C1112yes—
211C22×C22⋊C4C22×C1112yes—
212C22×C22⋊C4C22×C1111yescharacteristic
213C2×#99C22×C1118yes—
214#388—24no—
215#380C22×C1112yes—
216#379C22×C1112yes—
217C4×C22⋊C4—24no—
218C4×C22⋊C4C22×C1112yes—
219C4×C22⋊C4C22×C1112yes—
220C4×C22⋊C4C22×C1112yes—
221#342C22×C1118yes—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—24no—
229C22×C11—24no—
230C22×C11—24no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—84no—
238C22×C11—84no—
239C22×C11—84no—
240C22×C11C22×C22⋊C411yescharacteristic
241C22×C11C4×#4112yes—
242C22×C11#52512yes—
243C22×C11#53212yes—
244C4×C11—24no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—48no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—84no—
252C25C23×C1111yescharacteristic
253C22×Q8C2×C4×C1111yescharacteristic, complemented
254C22×D4C2×C4×C1112yes—
255C22×D4C2×C4×C1112yes—
256C22×D4C2×C4×C1111yescharacteristic, complemented
257C22×D4C23×C1112yes—
258C23×C4—22no—
259C23×C4C2×C4×C1112yescomplemented
260C23×C4C23×C1111yescharacteristic
261C23×C4C23×C1111yescharacteristic
262#126—28no—
263#124—28no—
264#123—28no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267#121—22no—
268#121—22no—
269#121—28no—
270#120—24no—
271#120—24no—
272C4×D4—24no—
273C4×D4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4C2×C4×C1112yescomplemented
276C2×C4⋊C4C2×C4×C1112yescomplemented
277C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
278C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
279C2×C22⋊C4—22no—
280C2×C22⋊C4—28no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4C2×C4×C1112yes—
284C2×C22⋊C4C2×C4×C1112yes—
285C2×C22⋊C4C2×C4×C1112yes—
286C2×C22⋊C4C2×C4×C1112yes—
287C2×C22⋊C4C2×C4×C1112yescomplemented
288C2×C22⋊C4C2×C4×C1112yescomplemented
289C2×C22⋊C4D4×C1114yes—
290C2×C22⋊C4D4×C1114yes—
291C2×C22⋊C4C23×C1114yes—
292C2×C22⋊C4C23×C1112yes—
293C2×C22⋊C4C23×C1114yes—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42C2×C4×C1112yescomplemented
298#99—216no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—22no—
303C2×C11—22no—
304C2×C11—22no—
305C2×C11—22no—
306C2×C11—44no—
307C2×C11—82no—
308C2×C11#229711yescharacteristic
309C2×C11#288311yescharacteristic
310C2×C11#288311yescharacteristic
311C24—24no—
312C24—81no—
313C24—81no—
314C24C22×C4×C1112yes—
315C24C22×C4×C1112yes—
316C24C2×D4×C1112yes—
317C24C2×D4×C1112yes—
318C24C24×C1111yescharacteristic
319C2×Q8—22no—
320C2×Q8—81no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—28no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—22no—
327C2×D4—82no—
328C2×D4—82no—
329C2×D4—81no—
330C22×C4—24no—
331C22×C4—28no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—81no—
335C22×C4—81no—
336C22×C4—82no—
337C22×C4—82no—
338C22×C4—82no—
339C22×C4C22×C4×C1112yes—
340C22×C4C22×C4×C1112yes—
341C22×C4C22×C4×C1112yes—
342C22×C4C22×C4×C1112yes—
343C22×C4C22×C4×C1111yescharacteristic
344C22×C4C22×C4×C1111yescharacteristic
345C22×C4C2×D4×C1112yes—
346C22×C4C2×D4×C1112yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1112yes—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—82no—
354C22⋊C4—28no—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—28no—
363C22⋊C4—82no—
364C22⋊C4—82no—
365C22⋊C4C11×C22⋊C418yes—
366C22⋊C4C11×C22⋊C418yes—
367C22⋊C4C11×#4118yes—
368C42—24no—
369C42—82no—
370C42—82no—
371C42—82no—
372C11#2142211yescharacteristic, direct product factor, Sylow
373C23—22no—
374C23—22no—
375C23—24no—
376C23—24no—
377C23—22no—
378C23—24no—
379C23—42no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—88no—
390C23C2×C11×C22⋊C414yes—
391C23C23×C4×C1111yescharacteristic
392C23C22×D4×C1111yescharacteristic
393C23C22×D4×C1111yescharacteristic
394C23C2×C11×#4114yes—
395Q8—82no—
396D4—44no—
397D4—44no—
398D4—82no—
399D4—84no—
400D4—84no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—28no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—84no—
421C2×C4—88no—
422C2×C4C2×C11×C22⋊C414yes—
423C2×C4C2×C11×C22⋊C412yes—
424C2×C4C2×C11×C22⋊C412yes—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—24no—
432C22—24no—
433C22—24no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—84no—
441C22—84no—
442C22—84no—
443C22C22×C11×C22⋊C411yescharacteristic
444C22C4×C11×#4112yes—
445C22C11×#52512yes—
446C22C11×#53212yes—
447C4—24no—
448C4—22no—
449C4—22no—
450C4—48no—
451C4—42no—
452C4—42no—
453C4—42no—
454C4—84no—
455C2—22no—
456C2—22no—
457C2—22no—
458C2—44no—
459C2—82no—
460C2C11×#229711yescharacteristic
461C2C11×#288311yescharacteristic
462C2C11×#288311yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#538C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2312C2semidirect
3. C11×#2273C2semidirect
4. C11×#1996C2semidirect
5. C11×#1964C2semidirect
6. C11×#1898C2semidirect
7. C4×C11×#99C2semidirect
10. C2×C11×#126C4semidirect
11. C2×C11×#124C4semidirect
12. C2×C11×#123C4semidirect
14. C2×C11×#121C4semidirect
30. C22×Q8×C11C2×C4semidirect
33. C22×D4×C11C2×C4semidirect
36. C23×C4×C11C2×C4semidirect
52. C2×C11×C4⋊C4C2×C4semidirect
53. C2×C11×C4⋊C4C2×C4semidirect
54. C2×C11×C4⋊C4C2×C4semidirect
55. C2×C11×C4⋊C4C2×C4semidirect
64. C2×C11×C22⋊C4C2×C4semidirect
65. C2×C11×C22⋊C4C2×C4semidirect
74. C2×C42×C11C2×C4semidirect
80. #21422C11direct (N × H)
143. #2312C2×C11semidirect
144. #2273C2×C11semidirect
145. #1996C2×C11semidirect
146. #1964C2×C11semidirect
147. #1898C2×C11semidirect
148. C4×#99C2×C11semidirect
203. C2×#126C4×C11semidirect
204. C2×#124C4×C11semidirect
205. C2×#123C4×C11semidirect
207. C2×#121C4×C11semidirect
253. C22×Q8C2×C4×C11semidirect
256. C22×D4C2×C4×C11semidirect
259. C23×C4C2×C4×C11semidirect
275. C2×C4⋊C4C2×C4×C11semidirect
276. C2×C4⋊C4C2×C4×C11semidirect
277. C2×C4⋊C4C2×C4×C11semidirect
278. C2×C4⋊C4C2×C4×C11semidirect
287. C2×C22⋊C4C2×C4×C11semidirect
288. C2×C22⋊C4C2×C4×C11semidirect
297. C2×C42C2×C4×C11semidirect
372. C11#21422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5382
C11×#23122
C11×#22732
C11×#19962
C11×#19642
C11×#18982
C4×C11×#992
#2142211