Finite Group Databasebeta

← C11×#60027 #14637220

Subgroups — C11×#60027 #14637220

Order 2816.

1674 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2787C213yesmaximal, complemented
2C11×#2736C211yesmaximal, characteristic
3C11×#2574C213yesmaximal, complemented
4C11×#2527C213yesmaximal, complemented
5C11×#2515C213yesmaximal, complemented
6C11×#2494C213yesmaximal, complemented
7C11×#2480C213yesmaximal
8C11×#2478C213yesmaximal, complemented
9C11×#2373C213yesmaximal, complemented
10C11×#2342C213yesmaximal
11C11×#2298C213yesmaximal, complemented
12C2×C11×#126C2213yes—
13C2×C11×#117C2213yes—
14C22×C11×C22⋊C4C2213yes—
15C11×#401C2211yescharacteristic, complemented
16C11×#401C2213yescomplemented
17C11×#400C2213yescomplemented
18C11×#398C2213yescomplemented
19C11×#398C2213yescomplemented
20C11×#397C2213yes—
21C11×#397C2213yes—
22C11×#397C2213yes—
23C11×#397C2213yes—
24C11×#396C2213yes—
25C11×#395C2211yescharacteristic, complemented
26C11×#393C2213yes—
27C11×#391C2213yescomplemented
28C11×#389C2213yescomplemented
29C11×#389C2213yescomplemented
30C11×#388C2213yes—
31C11×#388C2213yes—
32C11×#388C2213yes—
33C11×#388C2213yes—
34C11×#388C2213yes—
35C11×#388C2213yes—
36C11×#388C2213yes—
37C11×#388C2213yes—
38C11×#388C2213yes—
39C11×#387C2213yescomplemented
40C11×#387C2213yescomplemented
41C11×#387C2213yescomplemented
42C11×#387C2213yescomplemented
43C11×#387C2213yescomplemented
44C11×#387C2213yescomplemented
45C11×#387C2213yescomplemented
46C11×#387C2213yescomplemented
47C11×#385C2213yes—
48C11×#385C2213yes—
49C11×#385C2213yes—
50C11×#385C2213yes—
51C11×#383C2211yescharacteristic, complemented
52C11×#382C2213yescomplemented
53C11×#381C2213yes—
54C11×#380C2213yes—
55C11×#380C2213yes—
56C11×#379C2211yescharacteristic
57C11×#379C2213yes—
58C4×C11×C4⋊C4C2213yescomplemented
59C4×C11×C4⋊C4C2213yescomplemented
60C4×C11×C4⋊C4C2213yescomplemented
61C4×C11×C22⋊C4C2213yes—
62C4×C11×C22⋊C4C2213yes—
63C4×C11×C22⋊C4C2213yes—
64C4×C11×C22⋊C4C2213yes—
65C11×#376C2213yescomplemented
66C43×C11C2211yescharacteristic, complemented
67C25×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C23×C4×C11C2313yes—
70C23×C4×C11C2313yes—
71C11×#126—212no—
72C11×#117—212no—
73C2×C11×C4⋊C4C2313yes—
74C2×C11×C4⋊C4C2313yes—
75C2×C11×C4⋊C4C2313yes—
76C2×C11×C4⋊C4C2313yes—
77C2×C11×C4⋊C4C2313yes—
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2313yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C4⋊C4C2313yes—
84C2×C11×C22⋊C4—212no—
85C2×C11×C22⋊C4C2313yes—
86C2×C11×C22⋊C4C2313yes—
87C2×C11×C22⋊C4C2313yes—
88C2×C11×C22⋊C4C2313yes—
89C2×C11×C22⋊C4C2313yes—
90C2×C11×C22⋊C4C2313yes—
91C2×C11×C22⋊C4C2313yes—
92C2×C11×C22⋊C4C2313yes—
93C2×C11×C22⋊C4C2313yes—
94C2×C11×C22⋊C4C2313yes—
95C2×C11×C22⋊C4C2313yes—
96C2×C11×C22⋊C4C2313yes—
97C2×C42×C11C2313yes—
98C2×C42×C11C2313yes—
99C2×C42×C11C2313yes—
100C2×C42×C11C2313yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2313yes—
103C2×C42×C11C2313yes—
104C2×C42×C11C2311yescharacteristic
105C11×#95C2313yes—
106C11×#95C2313yes—
107C11×#95C2313yes—
108C11×#95C2313yes—
109C11×#95C2313yes—
110C11×#95C2313yes—
111C11×#95C2313yes—
112C11×#95C2313yes—
113C11×#95C2313yes—
114C11×#95C2313yes—
115C11×#95C2313yes—
116C11×#95C2313yes—
117C11×#95C2313yes—
118C11×#95C2313yes—
119C11×#95C2313yes—
120C11×#95C2313yes—
121C11×#95C2313yes—
122C11×#95C2313yes—
123C11×#95C2313yes—
124C11×#95C2311yescharacteristic
125#60027C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—26no—
127C24×C11—43no—
128C24×C11—41no—
129C24×C11C2413yes—
130C2×Q8×C11—43no—
131C22×C4×C11—26no—
132C22×C4×C11—26no—
133C22×C4×C11—26no—
134C22×C4×C11—43no—
135C22×C4×C11—43no—
136C22×C4×C11—43no—
137C22×C4×C11C2413yes—
138C22×C4×C11C2413yes—
139C22×C4×C11C2413yes—
140C22×C4×C11C2413yes—
141C22×C4×C11C2413yes—
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2413yes—
144C22×C4×C11C2413yes—
145C22×C4×C11C2413yes—
146C22×C4×C11C2413yes—
147C11×C4⋊C4—26no—
148C11×C4⋊C4—26no—
149C11×C4⋊C4—26no—
150C11×C4⋊C4—26no—
151C11×C4⋊C4—26no—
152C11×C4⋊C4—43no—
153C11×C4⋊C4—43no—
154C11×C4⋊C4—43no—
155C11×C4⋊C4—43no—
156C11×C4⋊C4—43no—
157C11×C4⋊C4—43no—
158C11×C22⋊C4—26no—
159C11×C22⋊C4—26no—
160C11×C22⋊C4—26no—
161C11×C22⋊C4—26no—
162C11×C22⋊C4—26no—
163C11×C22⋊C4—26no—
164C11×C22⋊C4—43no—
165C11×C22⋊C4—43no—
166C11×C22⋊C4—43no—
167C11×C22⋊C4—43no—
168C11×C22⋊C4—43no—
169C11×C22⋊C4#41112yes—
170C42×C11—26no—
171C42×C11—26no—
172C42×C11—26no—
173C42×C11—43no—
174C42×C11—43no—
175C42×C11—43no—
176C42×C11—41no—
177C42×C11—41no—
178#2787C2×C1113yescomplemented
179#2736C2×C1111yescharacteristic
180#2574C2×C1113yescomplemented
181#2527C2×C1113yescomplemented
182#2515C2×C1113yescomplemented
183#2494C2×C1113yescomplemented
184#2480C2×C1113yes—
185#2478C2×C1113yescomplemented
186#2373C2×C1113yescomplemented
187#2342C2×C1113yes—
188#2298C2×C1113yescomplemented
189C23×C11—23no—
190C23×C11—23no—
191C23×C11—23no—
192C23×C11—23no—
193C23×C11—23no—
194C23×C11—23no—
195C23×C11—412no—
196C23×C11—86no—
197C23×C11—82no—
198C23×C11C2×#4116yes—
199C23×C11C2511yescharacteristic
200Q8×C11—82no—
201C2×C4×C11—23no—
202C2×C4×C11—23no—
203C2×C4×C11—23no—
204C2×C4×C11—23no—
205C2×C4×C11—23no—
206C2×C4×C11—23no—
207C2×C4×C11—23no—
208C2×C4×C11—23no—
209C2×C4×C11—23no—
210C2×C4×C11—23no—
211C2×C4×C11—23no—
212C2×C4×C11—23no—
213C2×C4×C11—23no—
214C2×C4×C11—23no—
215C2×C4×C11—23no—
216C2×C4×C11—23no—
217C2×C4×C11—23no—
218C2×C4×C11—23no—
219C2×C4×C11—23no—
220C2×C4×C11—23no—
221C2×C4×C11—23no—
222C2×C4×C11—23no—
223C2×C4×C11—23no—
224C2×C4×C11—23no—
225C2×C4×C11—23no—
226C2×C4×C11—23no—
227C2×C4×C11—412no—
228C2×C4×C11—86no—
229C2×C4×C11C2×#4116yes—
230C2×C4×C11C2×#4116yes—
231C2×#126C22×C1113yes—
232C2×#117C22×C1113yes—
233C22×C22⋊C4C22×C1113yes—
234#401C22×C1111yescharacteristic, complemented
235#401C22×C1113yescomplemented
236#400C22×C1113yescomplemented
237#398C22×C1113yescomplemented
238#398C22×C1113yescomplemented
239#397C22×C1113yes—
240#397C22×C1113yes—
241#397C22×C1113yes—
242#397C22×C1113yes—
243#396C22×C1113yes—
244#395C22×C1111yescharacteristic, complemented
245#393C22×C1113yes—
246#391C22×C1113yescomplemented
247#389C22×C1113yescomplemented
248#389C22×C1113yescomplemented
249#388C22×C1113yes—
250#388C22×C1113yes—
251#388C22×C1113yes—
252#388C22×C1113yes—
253#388C22×C1113yes—
254#388C22×C1113yes—
255#388C22×C1113yes—
256#388C22×C1113yes—
257#388C22×C1113yes—
258#387C22×C1113yescomplemented
259#387C22×C1113yescomplemented
260#387C22×C1113yescomplemented
261#387C22×C1113yescomplemented
262#387C22×C1113yescomplemented
263#387C22×C1113yescomplemented
264#387C22×C1113yescomplemented
265#387C22×C1113yescomplemented
266#385C22×C1113yes—
267#385C22×C1113yes—
268#385C22×C1113yes—
269#385C22×C1113yes—
270#383C22×C1111yescharacteristic, complemented
271#382C22×C1113yescomplemented
272#381C22×C1113yes—
273#380C22×C1113yes—
274#380C22×C1113yes—
275#379C22×C1113yes—
276#379C22×C1111yescharacteristic
277C4×C4⋊C4C22×C1113yescomplemented
278C4×C4⋊C4C22×C1113yescomplemented
279C4×C4⋊C4C22×C1113yescomplemented
280C4×C22⋊C4C22×C1113yes—
281C4×C22⋊C4C22×C1113yes—
282C4×C22⋊C4C22×C1113yes—
283C4×C22⋊C4C22×C1113yes—
284#376C22×C1113yescomplemented
285C43C22×C1111yescharacteristic, complemented
286C22×C11—26no—
287C22×C11—26no—
288C22×C11—26no—
289C22×C11—43no—
290C22×C11—43no—
291C22×C11—43no—
292C22×C11—43no—
293C22×C11—88no—
294C22×C11C22×#4113yes—
295C22×C11#58513yes—
296C22×C11#58511yescharacteristic
297C4×C11—26no—
298C4×C11—26no—
299C4×C11—43no—
300C4×C11—43no—
301C4×C11—43no—
302C4×C11—43no—
303C4×C11—43no—
304C4×C11—43no—
305C4×C11—41no—
306C4×C11—43no—
307C25C23×C1111yescharacteristic
308C22×Q8C23×C1111yescharacteristic
309C23×C4C23×C1113yes—
310C23×C4C23×C1113yes—
311#126—212no—
312#117—212no—
313C2×C4⋊C4C23×C1113yes—
314C2×C4⋊C4C23×C1113yes—
315C2×C4⋊C4C23×C1113yes—
316C2×C4⋊C4C23×C1113yes—
317C2×C4⋊C4C23×C1113yes—
318C2×C4⋊C4C23×C1113yes—
319C2×C4⋊C4C23×C1113yes—
320C2×C4⋊C4C23×C1113yes—
321C2×C4⋊C4C23×C1113yes—
322C2×C4⋊C4C23×C1113yes—
323C2×C4⋊C4C23×C1113yes—
324C2×C22⋊C4—212no—
325C2×C22⋊C4C23×C1113yes—
326C2×C22⋊C4C23×C1113yes—
327C2×C22⋊C4C23×C1113yes—
328C2×C22⋊C4C23×C1113yes—
329C2×C22⋊C4C23×C1113yes—
330C2×C22⋊C4C23×C1113yes—
331C2×C22⋊C4C23×C1113yes—
332C2×C22⋊C4C23×C1113yes—
333C2×C22⋊C4C23×C1113yes—
334C2×C22⋊C4C23×C1113yes—
335C2×C22⋊C4C23×C1113yes—
336C2×C22⋊C4C23×C1113yes—
337C2×C42C23×C1113yes—
338C2×C42C23×C1113yes—
339C2×C42C23×C1113yes—
340C2×C42C23×C1113yes—
341C2×C42C23×C1111yescharacteristic
342C2×C42C23×C1113yes—
343C2×C42C23×C1113yes—
344C2×C42C23×C1111yescharacteristic
345#95C23×C1113yes—
346#95C23×C1113yes—
347#95C23×C1113yes—
348#95C23×C1113yes—
349#95C23×C1113yes—
350#95C23×C1113yes—
351#95C23×C1113yes—
352#95C23×C1113yes—
353#95C23×C1113yes—
354#95C23×C1113yes—
355#95C23×C1113yes—
356#95C23×C1113yes—
357#95C23×C1113yes—
358#95C23×C1113yes—
359#95C23×C1113yes—
360#95C23×C1113yes—
361#95C23×C1113yes—
362#95C23×C1113yes—
363#95C23×C1113yes—
364#95C23×C1111yescharacteristic
365C2×C11—46no—
366C2×C11#347513yes—
367C2×C11#352113yes—
368C2×C11#356811yescharacteristic
369C24—26no—
370C24—43no—
371C24—41no—
372C24C24×C1113yes—
373C2×Q8—43no—
374C22×C4—26no—
375C22×C4—26no—
376C22×C4—26no—
377C22×C4—43no—
378C22×C4—43no—
379C22×C4—43no—
380C22×C4C24×C1113yes—
381C22×C4C24×C1113yes—
382C22×C4C24×C1113yes—
383C22×C4C24×C1113yes—
384C22×C4C24×C1113yes—
385C22×C4C24×C1111yescharacteristic
386C22×C4C24×C1113yes—
387C22×C4C24×C1113yes—
388C22×C4C24×C1113yes—
389C22×C4C24×C1113yes—
390C4⋊C4—26no—
391C4⋊C4—26no—
392C4⋊C4—26no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—43no—
396C4⋊C4—43no—
397C4⋊C4—43no—
398C4⋊C4—43no—
399C4⋊C4—43no—
400C4⋊C4—43no—
401C22⋊C4—26no—
402C22⋊C4—26no—
403C22⋊C4—26no—
404C22⋊C4—26no—
405C22⋊C4—26no—
406C22⋊C4—26no—
407C22⋊C4—43no—
408C22⋊C4—43no—
409C22⋊C4—43no—
410C22⋊C4—43no—
411C22⋊C4—43no—
412C22⋊C4C11×#41112yes—
413C42—26no—
414C42—26no—
415C42—26no—
416C42—43no—
417C42—43no—
418C42—43no—
419C42—41no—
420C42—41no—
421C11#6002711yescharacteristic, direct product factor, Sylow
422C23—23no—
423C23—23no—
424C23—23no—
425C23—23no—
426C23—23no—
427C23—23no—
428C23—412no—
429C23—86no—
430C23—82no—
431C23C2×C11×#4116yes—
432C23C25×C1111yescharacteristic
433Q8—82no—
434C2×C4—23no—
435C2×C4—23no—
436C2×C4—23no—
437C2×C4—23no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—23no—
441C2×C4—23no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—23no—
445C2×C4—23no—
446C2×C4—23no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—23no—
450C2×C4—23no—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—23no—
457C2×C4—23no—
458C2×C4—23no—
459C2×C4—23no—
460C2×C4—412no—
461C2×C4—86no—
462C2×C4C2×C11×#4116yes—
463C2×C4C2×C11×#4116yes—
464C22—26no—
465C22—26no—
466C22—26no—
467C22—43no—
468C22—43no—
469C22—43no—
470C22—43no—
471C22—88no—
472C22C22×C11×#4113yes—
473C22C11×#58513yes—
474C22C11×#58511yescharacteristic
475C4—26no—
476C4—26no—
477C4—43no—
478C4—43no—
479C4—43no—
480C4—43no—
481C4—43no—
482C4—43no—
483C4—43no—
484C4—41no—
485C2—46no—
486C2C11×#347513yes—
487C2C11×#352113yes—
488C2C11×#356811yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2787C2semidirect
3. C11×#2574C2semidirect
4. C11×#2527C2semidirect
5. C11×#2515C2semidirect
6. C11×#2494C2semidirect
8. C11×#2478C2semidirect
9. C11×#2373C2semidirect
11. C11×#2298C2semidirect
15. C11×#401C22semidirect
16. C11×#401C22semidirect
17. C11×#400C22semidirect
18. C11×#398C22semidirect
19. C11×#398C22semidirect
25. C11×#395C22semidirect
27. C11×#391C22semidirect
28. C11×#389C22semidirect
29. C11×#389C22semidirect
39. C11×#387C22semidirect
40. C11×#387C22semidirect
41. C11×#387C22semidirect
42. C11×#387C22semidirect
43. C11×#387C22semidirect
44. C11×#387C22semidirect
45. C11×#387C22semidirect
46. C11×#387C22semidirect
51. C11×#383C22semidirect
52. C11×#382C22semidirect
58. C4×C11×C4⋊C4C22semidirect
59. C4×C11×C4⋊C4C22semidirect
60. C4×C11×C4⋊C4C22semidirect
65. C11×#376C22semidirect
66. C43×C11C22semidirect
125. #60027C11direct (N × H)
178. #2787C2×C11semidirect
180. #2574C2×C11semidirect
181. #2527C2×C11semidirect
182. #2515C2×C11semidirect
183. #2494C2×C11semidirect
185. #2478C2×C11semidirect
186. #2373C2×C11semidirect
188. #2298C2×C11semidirect
234. #401C22×C11semidirect
235. #401C22×C11semidirect
236. #400C22×C11semidirect
237. #398C22×C11semidirect
238. #398C22×C11semidirect
244. #395C22×C11semidirect
246. #391C22×C11semidirect
247. #389C22×C11semidirect
248. #389C22×C11semidirect
258. #387C22×C11semidirect
259. #387C22×C11semidirect
260. #387C22×C11semidirect
261. #387C22×C11semidirect
262. #387C22×C11semidirect
263. #387C22×C11semidirect
264. #387C22×C11semidirect
265. #387C22×C11semidirect
270. #383C22×C11semidirect
271. #382C22×C11semidirect
277. C4×C4⋊C4C22×C11semidirect
278. C4×C4⋊C4C22×C11semidirect
279. C4×C4⋊C4C22×C11semidirect
284. #376C22×C11semidirect
285. C43C22×C11semidirect
421. C11#60027direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27872
C11×#27362
C11×#25742
C11×#25272
C11×#25152
C11×#24942
C11×#24802
C11×#24782
C11×#23732
C11×#23422
C11×#22982
#6002711