Finite Group Databasebeta

← C11×#22671 #14599864

Subgroups — C11×#22671 #14599864

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#440C212yesmaximal
2C2×C4×C11×SD16C211yesmaximal, characteristic
3Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#1944C212yesmaximal, complemented
6C11×#1863C212yesmaximal, complemented
7C11×#1862C212yesmaximal
8C11×#1845C211yesmaximal, characteristic, complemented
9C11×#1803C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic
11C11×#1770C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4—21no—
18C11×#440—28no—
19C4×C11×SD16C418yescomplemented
20C2×C11×#107C2212yes—
21C2×C11×#107C2212yes—
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#97C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#389—22no—
31C11×#389C2212yes—
32C11×#389C2212yes—
33C11×#385—22no—
34C11×#384—21no—
35C11×#384C2211yescharacteristic
36C11×#384C2211yescharacteristic
37C11×#380—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—22no—
47C2×C11×SD16C2×C414yes—
48C2×C11×SD16D414yes—
49C2×C11×SD16Q814yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C4×Q8×C11—22no—
54C4×Q8×C11—24no—
55C4×Q8×C11—42no—
56C4×Q8×C11C2×C414yescomplemented
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—42no—
60C4×D4×C11C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—44no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11C2312yes—
81C2×C42×C11C2311yescharacteristic
82C11×#107—24no—
83C11×#107—42no—
84C11×#106C2×C414yescomplemented
85C11×C4⋊C8—22no—
86C11×#103—24no—
87C11×#103C2×C414yescomplemented
88C11×#102—24no—
89C11×#102C2×C414yes—
90C11×#97—24no—
91C4×C8×C11C2×C414yescomplemented
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D412yes—
95#22671C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11C22×C412yes—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C22×C412yes—
107C2×D4×C11C2×D412yes—
108C2×D4×C11C2×Q812yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—82no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C11×SD16C4⋊C4116yescomplemented
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11C22×C412yes—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C2×D412yes—
134C2×C8×C11C2×Q812yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—81no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4—82no—
151C11×C4⋊C4C22×C412yes—
152C11×C4⋊C4C22×C412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—44no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—44no—
159C42×C11C22×C412yes—
160C42×C11#4112yes—
161C2×#440C2×C1112yes—
162C2×C4×SD16C2×C1111yescharacteristic
163Q8×C4⋊C4C2×C1111yescharacteristic, complemented
164D4×C4⋊C4C2×C1111yescharacteristic
165#1944C2×C1112yescomplemented
166#1863C2×C1112yescomplemented
167#1862C2×C1112yes—
168#1845C2×C1111yescharacteristic, complemented
169#1803C2×C1111yescharacteristic, complemented
170#1802C2×C1111yescharacteristic
171#1770C2×C1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11C22×D411yescharacteristic
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11C2×C4⋊C414yescomplemented
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11C2×C4⋊C414yes—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—48no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—88no—
213C2×C4×C11C4×D412yes—
214C2×C4×C11C4×D412yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11#13712yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×Q811yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C112−1+411yescharacteristic
223C8×C11—22no—
224C8×C11—42no—
225C8×C11C2×C4⋊C414yescomplemented
226C22×SD16C22×C1111yescharacteristic
227C2×C4×Q8C22×C1112yes—
228C2×C4×Q8C22×C1111yescharacteristic
229C2×C4×D4C22×C1112yes—
230C2×C4×D4C22×C1111yescharacteristic
231C22×C4⋊C4—21no—
232#440—28no—
233C4×SD16C4×C1118yescomplemented
234C2×#107C22×C1112yes—
235C2×#107C22×C1112yes—
236C2×#106C22×C1111yescharacteristic
237C2×C4⋊C8C22×C1111yescharacteristic
238C2×#103C22×C1112yes—
239C2×#103C22×C1111yescharacteristic
240C2×#102C22×C1112yes—
241C2×#102C22×C1111yescharacteristic
242C2×#97C22×C1112yes—
243C2×C4×C8C22×C1111yescharacteristic
244#389—22no—
245#389C22×C1112yes—
246#389C22×C1112yes—
247#385—22no—
248#384—21no—
249#384C22×C1111yescharacteristic
250#384C22×C1111yescharacteristic
251#380—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4C22×C1111yescharacteristic
254#340C22×C1112yes—
255#340C22×C1112yes—
256#336C22×C1112yes—
257C22×C11—24no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11C2×C4×D411yescharacteristic
265C22×C11D4211yescharacteristic
266C22×C11D4×Q811yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C11C2×#13711yescharacteristic
269C22×C11#57611yescharacteristic
270C22×C11#57811yescharacteristic
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11—82no—
279C4×C11#44014yescomplemented
280C4×C11C22×C4⋊C411yescharacteristic
281C4×C11#52011yescharacteristic
282C4×C11#54711yescharacteristic
283C4×C11#55411yescharacteristic
284C22×Q8C23×C1111yescharacteristic
285C22×D4C23×C1111yescharacteristic
286C23×C4—21no—
287C23×C4—22no—
288C2×SD16C2×C4×C1114yes—
289C2×SD16D4×C1114yes—
290C2×SD16Q8×C1114yes—
291C22×C8C23×C1112yes—
292C22×C8C23×C1111yescharacteristic
293C22×C8C23×C1111yescharacteristic
294C4×Q8—22no—
295C4×Q8—24no—
296C4×Q8—42no—
297C4×Q8C2×C4×C1114yescomplemented
298C4×D4—24no—
299C4×D4—22no—
300C4×D4—42no—
301C4×D4C2×C4×C1114yes—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4D4×C1111yescharacteristic
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4C23×C1112yes—
314C2×C4⋊C4C23×C1112yes—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—22no—
319C2×C42—21no—
320C2×C42—22no—
321C2×C42C23×C1112yes—
322C2×C42C23×C1111yescharacteristic
323#107—24no—
324#107—42no—
325#106C2×C4×C1114yescomplemented
326C4⋊C8—22no—
327#103—24no—
328#103C2×C4×C1114yescomplemented
329#102—24no—
330#102C2×C4×C1114yes—
331#97—24no—
332C4×C8C2×C4×C1114yescomplemented
333#95—22no—
334#95—22no—
335#95D4×C1112yes—
336C2×C11—44no—
337C2×C11D4×C4⋊C411yescharacteristic
338C2×C11C2×#44011yescharacteristic
339C2×C11#295111yescharacteristic
340C2×C11#327411yescharacteristic
341C2×C11#327611yescharacteristic
342C2×C11#338511yescharacteristic
343C2×C11#338611yescharacteristic
344C24—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8C22×C4×C1112yes—
349C2×Q8C2×D4×C1112yes—
350C2×Q8C2×Q8×C1112yes—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C22×C4×C1112yes—
355C2×D4C2×D4×C1112yes—
356C2×D4C2×Q8×C1112yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—82no—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C24×C1111yescharacteristic
373SD16C11×C4⋊C4116yescomplemented
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8C22×C4×C1112yes—
380C2×C8C22×C4×C1112yes—
381C2×C8C2×D4×C1112yes—
382C2×C8C2×Q8×C1112yes—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—81no—
397C4⋊C4—81no—
398C4⋊C4—82no—
399C4⋊C4C22×C4×C1112yes—
400C4⋊C4C22×C4×C1112yes—
401C22⋊C4—24no—
402C22⋊C4—44no—
403C42—24no—
404C42—22no—
405C42—22no—
406C42—44no—
407C42C22×C4×C1112yes—
408C42C11×#4112yes—
409C11#2267111yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23C22×D4×C1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—22no—
421Q8C2×C11×C4⋊C414yescomplemented
422D4—22no—
423D4—22no—
424D4—22no—
425D4C2×C11×C4⋊C414yes—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—48no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—88no—
451C2×C4C4×D4×C1112yes—
452C2×C4C4×D4×C1112yes—
453C2×C4C11×AGL(1,ℤ/8)12yes—
454C2×C4C11×#13712yes—
455C2×C4C23×C4×C1111yescharacteristic
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C22×Q8×C1111yescharacteristic
458C2×C4C2×C11×#4111yescharacteristic
459C2×C4C11×H(5,𝔽2)11yescharacteristic
460C2×C4C11×2−1+411yescharacteristic
461C8—22no—
462C8—42no—
463C8C2×C11×C4⋊C414yescomplemented
464C22—24no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22C2×C4×D4×C1111yescharacteristic
472C22D42×C1111yescharacteristic
473C22D4×Q8×C1111yescharacteristic
474C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
475C22C2×C11×#13711yescharacteristic
476C22C11×#57611yescharacteristic
477C22C11×#57811yescharacteristic
478C4—22no—
479C4—24no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—82no—
485C4—82no—
486C4C11×#44014yescomplemented
487C4C22×C11×C4⋊C411yescharacteristic
488C4C11×#52011yescharacteristic
489C4C11×#54711yescharacteristic
490C4C11×#55411yescharacteristic
491C2—44no—
492C2D4×C11×C4⋊C411yescharacteristic
493C2C2×C11×#44011yescharacteristic
494C2C11×#295111yescharacteristic
495C2C11×#327411yescharacteristic
496C2C11×#327611yescharacteristic
497C2C11×#338511yescharacteristic
498C2C11×#338611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. Q8×C11×C4⋊C4C2semidirect
5. C11×#1944C2semidirect
6. C11×#1863C2semidirect
8. C11×#1845C2semidirect
9. C11×#1803C2semidirect
11. C11×#1770C2semidirect
19. C4×C11×SD16C4semidirect
56. C4×Q8×C11C2×C4semidirect
84. C11×#106C2×C4semidirect
87. C11×#103C2×C4semidirect
91. C4×C8×C11C2×C4semidirect
95. #22671C11direct (N × H)
125. C11×SD16C4⋊C4semidirect
163. Q8×C4⋊C4C2×C11semidirect
165. #1944C2×C11semidirect
166. #1863C2×C11semidirect
168. #1845C2×C11semidirect
169. #1803C2×C11semidirect
171. #1770C2×C11semidirect
183. Q8×C11C2×C4⋊C4semidirect
225. C8×C11C2×C4⋊C4semidirect
233. C4×SD16C4×C11semidirect
279. C4×C11#440semidirect
297. C4×Q8C2×C4×C11semidirect
325. #106C2×C4×C11semidirect
328. #103C2×C4×C11semidirect
332. C4×C8C2×C4×C11semidirect
373. SD16C11×C4⋊C4semidirect
409. C11#22671direct (N × H)
421. Q8C2×C11×C4⋊C4semidirect
463. C8C2×C11×C4⋊C4semidirect
486. C4C11×#440semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4402
C2×C4×C11×SD162
Q8×C11×C4⋊C42
D4×C11×C4⋊C42
C11×#19442
C11×#18632
C11×#18622
C11×#18452
C11×#18032
C11×#18022
C11×#17702
#2267111