Finite Group Databasebeta

← C11×#2685 #13065523

Subgroups — C11×#2685 #13065523

Order 1408.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#126C211yesmaximal, characteristic, complemented
2C2×C11×#120C211yesmaximal, characteristic
3C11×#399C211yesmaximal, characteristic, complemented
4C11×#396C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#394C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8C11×#394C211yesmaximal, characteristic, complemented
9C11×#390C211yesmaximal, characteristic, complemented
10C11×#390C211yesmaximal, characteristic, complemented
11C11×#388C211yesmaximal, characteristic, complemented
12C11×#388C211yesmaximal, characteristic, complemented
13C11×#388C211yesmaximal, characteristic, complemented
14C11×#379C211yesmaximal, characteristic, complemented
15C11×#379C211yesmaximal, characteristic, complemented
16C25×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C11×#126—24no—
21C11×#120—24no—
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C4⋊C4C2211yescharacteristic, complemented
24C2×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×C11×C4⋊C4C2211yescharacteristic, complemented
26C2×C11×C4⋊C4C2211yescharacteristic, complemented
27C2×C11×C4⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C11×C22⋊C4C2211yescharacteristic
41C2×C11×C22⋊C4C2211yescharacteristic
42C2×C11×C22⋊C4C2211yescharacteristic
43C2×C11×C22⋊C4C2211yescharacteristic, complemented
44C2×C11×C22⋊C4C2211yescharacteristic, complemented
45C2×C11×C22⋊C4C2211yescharacteristic, complemented
46C2×C11×C22⋊C4C2211yescharacteristic, complemented
47C2×C42×C11C2211yescharacteristic, complemented
48C2×C42×C11C2211yescharacteristic, complemented
49C11×#95C2211yescharacteristic, complemented
50C11×#95C2211yescharacteristic, complemented
51C11×#95C2211yescharacteristic, complemented
52C11×#95C2211yescharacteristic, complemented
53C24×C11—22no—
54C24×C11—22no—
55C24×C11—22no—
56C24×C11—41no—
57C24×C11—41no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11C2311yescharacteristic
61C24×C11C2311yescharacteristic
62C24×C11C2311yescharacteristic
63C24×C11C2311yescharacteristic
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C22×C4×C11C2311yescharacteristic
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4D414yes—
109C42×C11—22no—
110C42×C11—41no—
111#2685C1111yesmaximal, characteristic, direct product factor, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—44no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11C2×D412yes—
145C23×C11#4112yes—
146C23×C11#4112yes—
147C23×C11C2411yescharacteristic
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—44no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11C2×D412yes—
183C2×C4×C11C2×D412yes—
184C2×#126C2×C1111yescharacteristic, complemented
185C2×#120C2×C1111yescharacteristic
186#399C2×C1111yescharacteristic, complemented
187#396C2×C1111yescharacteristic, complemented
188#394C2×C1111yescharacteristic, complemented
189#394C2×C1111yescharacteristic, complemented
190#394C2×C1111yescharacteristic, complemented
191#394C2×C1111yescharacteristic, complemented
192#390C2×C1111yescharacteristic, complemented
193#390C2×C1111yescharacteristic, complemented
194#388C2×C1111yescharacteristic, complemented
195#388C2×C1111yescharacteristic, complemented
196#388C2×C1111yescharacteristic, complemented
197#379C2×C1111yescharacteristic, complemented
198#379C2×C1111yescharacteristic, complemented
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—416no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11C22×D411yescharacteristic
229C22×C11C2×#4111yescharacteristic
230C22×C11C2×#4111yescharacteristic
231C22×C11H(5,𝔽2)11yescharacteristic
232C22×C11H(5,𝔽2)11yescharacteristic
233C22×C11H(5,𝔽2)11yescharacteristic
234C22×C11H(5,𝔽2)11yescharacteristic
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—41no—
246C25C22×C1111yescharacteristic
247C22×D4C22×C1111yescharacteristic
248C22×D4C22×C1111yescharacteristic
249C22×D4C22×C1111yescharacteristic
250#126—24no—
251#120—24no—
252C2×C4⋊C4C22×C1111yescharacteristic, complemented
253C2×C4⋊C4C22×C1111yescharacteristic, complemented
254C2×C4⋊C4C22×C1111yescharacteristic, complemented
255C2×C4⋊C4C22×C1111yescharacteristic, complemented
256C2×C4⋊C4C22×C1111yescharacteristic, complemented
257C2×C4⋊C4C22×C1111yescharacteristic, complemented
258C2×C22⋊C4C22×C1111yescharacteristic
259C2×C22⋊C4C22×C1111yescharacteristic
260C2×C22⋊C4C22×C1111yescharacteristic
261C2×C22⋊C4C22×C1111yescharacteristic
262C2×C22⋊C4C22×C1111yescharacteristic
263C2×C22⋊C4C22×C1111yescharacteristic
264C2×C22⋊C4C22×C1111yescharacteristic
265C2×C22⋊C4C22×C1111yescharacteristic
266C2×C22⋊C4C22×C1111yescharacteristic
267C2×C22⋊C4C22×C1111yescharacteristic
268C2×C22⋊C4C22×C1111yescharacteristic
269C2×C22⋊C4C22×C1111yescharacteristic
270C2×C22⋊C4C22×C1111yescharacteristic
271C2×C22⋊C4C22×C1111yescharacteristic
272C2×C22⋊C4C22×C1111yescharacteristic
273C2×C22⋊C4C22×C1111yescharacteristic, complemented
274C2×C22⋊C4C22×C1111yescharacteristic, complemented
275C2×C22⋊C4C22×C1111yescharacteristic, complemented
276C2×C22⋊C4C22×C1111yescharacteristic, complemented
277C2×C42C22×C1111yescharacteristic, complemented
278C2×C42C22×C1111yescharacteristic, complemented
279#95C22×C1111yescharacteristic, complemented
280#95C22×C1111yescharacteristic, complemented
281#95C22×C1111yescharacteristic, complemented
282#95C22×C1111yescharacteristic, complemented
283C2×C11—42no—
284C2×C11—42no—
285C2×C11—42no—
286C2×C11—81no—
287C2×C11#53511yescharacteristic
288C2×C11#53811yescharacteristic
289C2×C11#53811yescharacteristic
290C2×C11#54611yescharacteristic
291C2×C11#54611yescharacteristic
292C2×C11#55111yescharacteristic
293C2×C11#56011yescharacteristic
294C24—22no—
295C24—22no—
296C24—22no—
297C24—41no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24C23×C1111yescharacteristic
302C24C23×C1111yescharacteristic
303C24C23×C1111yescharacteristic
304C24C23×C1111yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C22×C4C23×C1111yescharacteristic
315C22×C4C23×C1111yescharacteristic
316C22×C4C23×C1111yescharacteristic
317C22×C4C23×C1111yescharacteristic
318C22×C4C23×C1111yescharacteristic
319C22×C4C23×C1111yescharacteristic
320C22×C4C23×C1111yescharacteristic
321C22×C4C23×C1111yescharacteristic
322C22×C4C23×C1111yescharacteristic
323C22×C4C23×C1111yescharacteristic
324C22×C4C23×C1111yescharacteristic
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4D4×C1114yes—
350C42—22no—
351C42—41no—
352C11#268511yescharacteristic, direct product factor, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—44no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—44no—
383C23—44no—
384C23—44no—
385C23C2×D4×C1112yes—
386C23C11×#4112yes—
387C23C11×#4112yes—
388C23C24×C1111yescharacteristic
389D4—44no—
390D4—44no—
391D4—44no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4C2×D4×C1112yes—
424C2×C4C2×D4×C1112yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—416no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22C22×D4×C1111yescharacteristic
455C22C2×C11×#4111yescharacteristic
456C22C2×C11×#4111yescharacteristic
457C22C11×H(5,𝔽2)11yescharacteristic
458C22C11×H(5,𝔽2)11yescharacteristic
459C22C11×H(5,𝔽2)11yescharacteristic
460C22C11×H(5,𝔽2)11yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—41no—
472C2—42no—
473C2—42no—
474C2—42no—
475C2—81no—
476C2C11×#53511yescharacteristic
477C2C11×#53811yescharacteristic
478C2C11×#53811yescharacteristic
479C2C11×#54611yescharacteristic
480C2C11×#54611yescharacteristic
481C2C11×#55111yescharacteristic
482C2C11×#56011yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC2×C11×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#126C2semidirect
3. C11×#399C2semidirect
4. C11×#396C2semidirect
5. C11×#394C2semidirect
6. C11×#394C2semidirect
7. C11×#394C2semidirect
8. C11×#394C2semidirect
9. C11×#390C2semidirect
10. C11×#390C2semidirect
11. C11×#388C2semidirect
12. C11×#388C2semidirect
13. C11×#388C2semidirect
14. C11×#379C2semidirect
15. C11×#379C2semidirect
22. C2×C11×C4⋊C4C22semidirect
23. C2×C11×C4⋊C4C22semidirect
24. C2×C11×C4⋊C4C22semidirect
25. C2×C11×C4⋊C4C22semidirect
26. C2×C11×C4⋊C4C22semidirect
27. C2×C11×C4⋊C4C22semidirect
43. C2×C11×C22⋊C4C22semidirect
44. C2×C11×C22⋊C4C22semidirect
45. C2×C11×C22⋊C4C22semidirect
46. C2×C11×C22⋊C4C22semidirect
47. C2×C42×C11C22semidirect
48. C2×C42×C11C22semidirect
49. C11×#95C22semidirect
50. C11×#95C22semidirect
51. C11×#95C22semidirect
52. C11×#95C22semidirect
111. #2685C11direct (N × H)
184. C2×#126C2×C11semidirect
186. #399C2×C11semidirect
187. #396C2×C11semidirect
188. #394C2×C11semidirect
189. #394C2×C11semidirect
190. #394C2×C11semidirect
191. #394C2×C11semidirect
192. #390C2×C11semidirect
193. #390C2×C11semidirect
194. #388C2×C11semidirect
195. #388C2×C11semidirect
196. #388C2×C11semidirect
197. #379C2×C11semidirect
198. #379C2×C11semidirect
252. C2×C4⋊C4C22×C11semidirect
253. C2×C4⋊C4C22×C11semidirect
254. C2×C4⋊C4C22×C11semidirect
255. C2×C4⋊C4C22×C11semidirect
256. C2×C4⋊C4C22×C11semidirect
257. C2×C4⋊C4C22×C11semidirect
273. C2×C22⋊C4C22×C11semidirect
274. C2×C22⋊C4C22×C11semidirect
275. C2×C22⋊C4C22×C11semidirect
276. C2×C22⋊C4C22×C11semidirect
277. C2×C42C22×C11semidirect
278. C2×C42C22×C11semidirect
279. #95C22×C11semidirect
280. #95C22×C11semidirect
281. #95C22×C11semidirect
282. #95C22×C11semidirect
352. C11#2685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C11×#1202
C11×#3992
C11×#3962
C11×#3942
C11×#3902
C11×#3882
C11×#3792
#268511