Finite Group Databasebeta

← C11×#2676 #13065514

Subgroups — C11×#2676 #13065514

Order 1408.

676 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C11×#121C211yesmaximal, characteristic, complemented
4C2×C11×#121C211yesmaximal, characteristic, complemented
5C11×#396C211yesmaximal, characteristic, complemented
6C11×#394C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8C11×#393C211yesmaximal, characteristic, complemented
9C11×#392C211yesmaximal, characteristic, complemented
10C11×#392C211yesmaximal, characteristic, complemented
11C11×#390C211yesmaximal, characteristic, complemented
12C11×#387C211yesmaximal, characteristic, complemented
13C11×#386C211yesmaximal, characteristic, complemented
14C11×#386C211yesmaximal, characteristic, complemented
15C11×#385C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C22×D4×C11C2211yescharacteristic
21C22×D4×C11C2211yescharacteristic
22C22×D4×C11C2211yescharacteristic
23C23×C4×C11C2211yescharacteristic
24C23×C4×C11C2211yescharacteristic
25C11×#124—24no—
26C11×C22⋊Q8—24no—
27C11×#121—24no—
28C11×#121—24no—
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C4⋊C4C2211yescharacteristic
32C2×C11×C4⋊C4C2211yescharacteristic
33C2×C11×C4⋊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
44C2×C11×C22⋊C4C2211yescharacteristic
45C2×C11×C22⋊C4C2211yescharacteristic
46C2×C11×C22⋊C4C2211yescharacteristic
47C2×C11×C22⋊C4C2211yescharacteristic
48C2×C42×C11C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C11×#95C2211yescharacteristic
54C11×#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C2×Q8×C11—22no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2311yescharacteristic
87C22×C4×C11C2311yescharacteristic
88C22×C4×C11C2311yescharacteristic
89C22×C4×C11C2311yescharacteristic
90C22×C4×C11C2311yescharacteristic
91C22×C4×C11C2311yescharacteristic
92C22×C4×C11C2311yescharacteristic
93C22×C4×C11C2311yescharacteristic
94C22×C4×C11C2311yescharacteristic
95C22×C4×C11C2311yescharacteristic
96C22×C4×C11C2311yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4D414yescomplemented
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4D414yescomplemented
116C42×C11—22no—
117#2676C1111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11C2×D412yes—
145C23×C11#4112yes—
146C23×C11C2411yescharacteristic
147Q8×C11—44no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—44no—
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×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11C2×D412yes—
185C2×C4×C11C2×D412yes—
186C2×C4×C11C2×D412yes—
187C2×C4×C11C2×D412yes—
188C2×C4×C11C2×D412yes—
189C2×#124C2×C1111yescharacteristic, complemented
190C2×C22⋊Q8C2×C1111yescharacteristic, complemented
191C2×#121C2×C1111yescharacteristic, complemented
192C2×#121C2×C1111yescharacteristic, complemented
193#396C2×C1111yescharacteristic, complemented
194#394C2×C1111yescharacteristic, complemented
195#394C2×C1111yescharacteristic, complemented
196#393C2×C1111yescharacteristic, complemented
197#392C2×C1111yescharacteristic, complemented
198#392C2×C1111yescharacteristic, complemented
199#390C2×C1111yescharacteristic, complemented
200#387C2×C1111yescharacteristic, complemented
201#386C2×C1111yescharacteristic, complemented
202#386C2×C1111yescharacteristic, complemented
203#385C2×C1111yescharacteristic, complemented
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
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×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11C22×D411yescharacteristic
233C22×C11C22×D411yescharacteristic
234C22×C11C2×#4111yescharacteristic
235C22×C11H(5,𝔽2)11yescharacteristic
236C22×C11H(5,𝔽2)11yescharacteristic
237C22×C11H(5,𝔽2)11yescharacteristic
238C22×C112−1+411yescharacteristic
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—22no—
242C4×C11—22no—
243C4×C11—22no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11—41no—
249C4×C11—41no—
250C22×Q8C22×C1111yescharacteristic
251C22×D4C22×C1111yescharacteristic
252C22×D4C22×C1111yescharacteristic
253C22×D4C22×C1111yescharacteristic
254C22×D4C22×C1111yescharacteristic
255C22×D4C22×C1111yescharacteristic
256C22×D4C22×C1111yescharacteristic
257C23×C4C22×C1111yescharacteristic
258C23×C4C22×C1111yescharacteristic
259#124—24no—
260C22⋊Q8—24no—
261#121—24no—
262#121—24no—
263C2×C4⋊C4C22×C1111yescharacteristic
264C2×C4⋊C4C22×C1111yescharacteristic
265C2×C4⋊C4C22×C1111yescharacteristic
266C2×C4⋊C4C22×C1111yescharacteristic
267C2×C4⋊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
274C2×C22⋊C4C22×C1111yescharacteristic
275C2×C22⋊C4C22×C1111yescharacteristic
276C2×C22⋊C4C22×C1111yescharacteristic
277C2×C22⋊C4C22×C1111yescharacteristic
278C2×C22⋊C4C22×C1111yescharacteristic
279C2×C22⋊C4C22×C1111yescharacteristic
280C2×C22⋊C4C22×C1111yescharacteristic
281C2×C22⋊C4C22×C1111yescharacteristic
282C2×C42C22×C1111yescharacteristic
283#95C22×C1111yescharacteristic
284#95C22×C1111yescharacteristic
285#95C22×C1111yescharacteristic
286#95C22×C1111yescharacteristic
287#95C22×C1111yescharacteristic
288#95C22×C1111yescharacteristic
289C2×C11—42no—
290C2×C11—42no—
291C2×C11—81no—
292C2×C11—81no—
293C2×C11#53511yescharacteristic
294C2×C11#53711yescharacteristic
295C2×C11#53811yescharacteristic
296C2×C11D4211yescharacteristic
297C2×C11#54611yescharacteristic
298C2×C11#54811yescharacteristic
299C2×C11#56211yescharacteristic
300C24C23×C1111yescharacteristic
301C24C23×C1111yescharacteristic
302C24C23×C1111yescharacteristic
303C24C23×C1111yescharacteristic
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—41no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C23×C1111yescharacteristic
332C22×C4C23×C1111yescharacteristic
333C22×C4C23×C1111yescharacteristic
334C22×C4C23×C1111yescharacteristic
335C22×C4C23×C1111yescharacteristic
336C22×C4C23×C1111yescharacteristic
337C22×C4C23×C1111yescharacteristic
338C22×C4C23×C1111yescharacteristic
339C22×C4C23×C1111yescharacteristic
340C22×C4C23×C1111yescharacteristic
341C22×C4C23×C1111yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—41no—
346C4⋊C4D4×C1114yescomplemented
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4D4×C1114yescomplemented
361C42—22no—
362C11#267611yescharacteristic, direct product factor, Sylow
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—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23C2×D4×C1112yes—
390C23C11×#4112yes—
391C23C24×C1111yescharacteristic
392Q8—44no—
393D4—44no—
394D4—44no—
395D4—44no—
396D4—44no—
397D4—44no—
398D4—44no—
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×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4C2×D4×C1112yes—
430C2×C4C2×D4×C1112yes—
431C2×C4C2×D4×C1112yes—
432C2×C4C2×D4×C1112yes—
433C2×C4C2×D4×C1112yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
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—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22C22×D4×C1111yescharacteristic
463C22C22×D4×C1111yescharacteristic
464C22C2×C11×#4111yescharacteristic
465C22C11×H(5,𝔽2)11yescharacteristic
466C22C11×H(5,𝔽2)11yescharacteristic
467C22C11×H(5,𝔽2)11yescharacteristic
468C22C11×2−1+411yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—41no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—81no—
484C2C11×#53511yescharacteristic
485C2C11×#53711yescharacteristic
486C2C11×#53811yescharacteristic
487C2D42×C1111yescharacteristic
488C2C11×#54611yescharacteristic
489C2C11×#54811yescharacteristic
490C2C11×#56211yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#124C2semidirect
2. C2×C11×C22⋊Q8C2semidirect
3. C2×C11×#121C2semidirect
4. C2×C11×#121C2semidirect
5. C11×#396C2semidirect
6. C11×#394C2semidirect
7. C11×#394C2semidirect
8. C11×#393C2semidirect
9. C11×#392C2semidirect
10. C11×#392C2semidirect
11. C11×#390C2semidirect
12. C11×#387C2semidirect
13. C11×#386C2semidirect
14. C11×#386C2semidirect
15. C11×#385C2semidirect
101. C11×C4⋊C4D4semidirect
115. C11×C22⋊C4D4semidirect
117. #2676C11direct (N × H)
189. C2×#124C2×C11semidirect
190. C2×C22⋊Q8C2×C11semidirect
191. C2×#121C2×C11semidirect
192. C2×#121C2×C11semidirect
193. #396C2×C11semidirect
194. #394C2×C11semidirect
195. #394C2×C11semidirect
196. #393C2×C11semidirect
197. #392C2×C11semidirect
198. #392C2×C11semidirect
199. #390C2×C11semidirect
200. #387C2×C11semidirect
201. #386C2×C11semidirect
202. #386C2×C11semidirect
203. #385C2×C11semidirect
346. C4⋊C4D4×C11semidirect
360. C22⋊C4D4×C11semidirect
362. C11#2676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×C11×C22⋊Q82
C2×C11×#1212
C11×#3962
C11×#3942
C11×#3932
C11×#3922
C11×#3902
C11×#3872
C11×#3862
C11×#3852
#267611