Finite Group Databasebeta

← C11×#22522 #14599715

Subgroups — C11×#22522 #14599715

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#446C211yesmaximal, characteristic, complemented
3Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C11×#1992C212yesmaximal, complemented
5C11×#1990C211yesmaximal, characteristic, complemented
6C11×#1989C212yesmaximal, complemented
7C11×#1987C211yesmaximal, characteristic, complemented
8C11×#1802C212yesmaximal
9C11×#1802C211yesmaximal, characteristic
10C11×#1762C212yesmaximal
11C4×C11×#102C211yesmaximal, characteristic
12C11×#554—24no—
13C11×#554C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C22×C11×C4⋊C4—21no—
23C11×#446—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#389—21no—
32C11×#389—22no—
33C11×#384C2211yescharacteristic
34C11×#384C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2212yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yes—
54C11×#125—24no—
55C11×#125C2×C418yes—
56C11×C22⋊Q8—28no—
57C11×C22⋊Q8—216no—
58C4×Q8×C11—44no—
59C4×Q8×C11C2×C414yes—
60C4×Q8×C11D414yes—
61C4×D4×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11C2×C418yes—
64C4×D4×C11C2×C414yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—28no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—22no—
83C2×C42×C11—21no—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C11×C4⋊C8—22no—
87C11×C4⋊C8—24no—
88C11×#102—22no—
89C11×#102—24no—
90C11×#102Q814yescomplemented
91C11×#97—24no—
92C4×C8×C11—22no—
93C11×#95—21no—
94C11×#95—22no—
95#22522C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C2×Q8×C11—24no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—81no—
101C2×Q8×C11—81no—
102C2×Q8×C11C22⋊C414yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C22×C412yes—
107C2×D4×C11C2×Q812yes—
108C2×D4×C11#4112yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—28no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—82no—
119C22×C4×C11—82no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11C2×Q812yes—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—28no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—82no—
147C11×C4⋊C4—81no—
148C11×C4⋊C4C22⋊C414yes—
149C11×C4⋊C4C22⋊C418yes—
150C11×C4⋊C4C22×C412yes—
151C11×C4⋊C4C22×C414yes—
152C11×C4⋊C4C2×Q812yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—28no—
155C42×C11—44no—
156C42×C11—42no—
157C42×C11C22×C414yes—
158C42×C11C22×C412yes—
159C42×C11C2×D412yes—
160C42×C11C2×D414yes—
161C2×#554C2×C1111yescharacteristic
162C2×#446C2×C1111yescharacteristic, complemented
163Q8×C4⋊C4C2×C1111yescharacteristic, complemented
164#1992C2×C1112yescomplemented
165#1990C2×C1111yescharacteristic, complemented
166#1989C2×C1112yescomplemented
167#1987C2×C1111yescharacteristic, complemented
168#1802C2×C1111yescharacteristic
169#1802C2×C1112yes—
170#1762C2×C1112yes—
171C4×#102C2×C1111yescharacteristic
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—28no—
181Q8×C11—84no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11C4×Q814yescomplemented
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—48no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—88no—
209C2×C4×C11C2×C22⋊C414yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C2×C22⋊C414yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C8×C11—22no—
222C8×C11—41no—
223C8×C11—42no—
224#554—24no—
225#554C4×C1118yescomplemented
226C2×C4⋊Q8C22×C1111yescharacteristic
227C2×#125C22×C1112yes—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—22no—
230C2×C4×Q8—21no—
231C2×C4×Q8C22×C1111yescharacteristic
232C2×C4×D4C22×C1111yescharacteristic
233C2×C4×D4C22×C1112yes—
234C22×C4⋊C4—21no—
235#446—24no—
236C2×C4⋊C8C22×C1111yescharacteristic
237C2×C4⋊C8C22×C1112yes—
238C2×#102C22×C1111yescharacteristic
239C2×#102C22×C1112yes—
240C2×#102C22×C1111yescharacteristic
241C2×#97C22×C1112yes—
242C2×C4×C8C22×C1111yescharacteristic
243#389—21no—
244#389—22no—
245#384C22×C1111yescharacteristic
246#384C22×C1112yes—
247C4×C4⋊C4C22×C1111yescharacteristic
248C4×C4⋊C4C22×C1112yes—
249#340C22×C1112yes—
250#340C22×C1112yes—
251#340C22×C1112yes—
252#340C22×C1112yes—
253#340C22×C1111yescharacteristic
254#340C22×C1112yes—
255#340C22×C1111yescharacteristic
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11C22×C22⋊C411yescharacteristic
264C22×C11#54811yescharacteristic
265C22×C11D4×Q811yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C22×C11#57611yescharacteristic
269C22×C11#57711yescharacteristic
270C4×C11—24no—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—44no—
276C4×C11—82no—
277C4×C11—81no—
278C4×C11#41714yes—
279C4×C11C2×C4×Q811yescharacteristic
280C4×C11#51911yescharacteristic
281C4×C11#54811yescharacteristic
282C4×C11D4×Q811yescharacteristic
283C22×Q8—21no—
284C22×Q8D4×C1111yescharacteristic
285C22×D4C23×C1111yescharacteristic
286C23×C4—21no—
287C23×C4—22no—
288C22×C8C23×C1111yescharacteristic
289C22×C8C23×C1112yes—
290C22×C8C23×C1111yescharacteristic
291C4⋊Q8—22no—
292C4⋊Q8C2×C4×C1114yes—
293#125—24no—
294#125C2×C4×C1118yes—
295C22⋊Q8—28no—
296C22⋊Q8—216no—
297C4×Q8—44no—
298C4×Q8C2×C4×C1114yes—
299C4×Q8D4×C1114yes—
300C4×D4—22no—
301C4×D4—24no—
302C4×D4C2×C4×C1118yes—
303C4×D4C2×C4×C1114yes—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C4⋊C4D4×C1112yes—
314C2×C4⋊C4C23×C1111yescharacteristic
315C2×C4⋊C4C23×C1112yes—
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C42—22no—
322C2×C42—21no—
323C2×C42C23×C1112yes—
324C2×C42C23×C1111yescharacteristic
325C4⋊C8—22no—
326C4⋊C8—24no—
327#102—22no—
328#102—24no—
329#102Q8×C1114yescomplemented
330#97—24no—
331C4×C8—22no—
332#95—21no—
333#95—22no—
334C2×C11—44no—
335C2×C11Q8×C22⋊C411yescharacteristic
336C2×C11C2×#41711yescharacteristic
337C2×C11#289711yescharacteristic
338C2×C11#336611yescharacteristic
339C2×C11#337211yescharacteristic
340C2×C11#338411yescharacteristic
341C2×C11#338511yescharacteristic
342C24—21no—
343C2×Q8—24no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—81no—
347C2×Q8—81no—
348C2×Q8C11×C22⋊C414yes—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4C22×C4×C1112yes—
353C2×D4C2×Q8×C1112yes—
354C2×D4C11×#4112yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—28no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—82no—
365C22×C4—82no—
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C2×D4×C1112yes—
368C22×C4C2×D4×C1112yes—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C24×C1111yescharacteristic
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8C2×Q8×C1112yes—
380C4⋊C4—28no—
381C4⋊C4—24no—
382C4⋊C4—28no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—44no—
391C4⋊C4—42no—
392C4⋊C4—82no—
393C4⋊C4—81no—
394C4⋊C4C11×C22⋊C414yes—
395C4⋊C4C11×C22⋊C418yes—
396C4⋊C4C22×C4×C1112yes—
397C4⋊C4C22×C4×C1114yes—
398C4⋊C4C2×Q8×C1112yes—
399C22⋊C4—24no—
400C22⋊C4—28no—
401C42—44no—
402C42—42no—
403C42C22×C4×C1114yes—
404C42C22×C4×C1112yes—
405C42C2×D4×C1112yes—
406C42C2×D4×C1114yes—
407C11#2252211yescharacteristic, direct product factor, Sylow
408C23—22no—
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23C22×D4×C1111yescharacteristic
416Q8—28no—
417Q8—84no—
418D4—22no—
419D4—22no—
420D4—22no—
421D4C4×Q8×C1114yescomplemented
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—48no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—88no—
445C2×C4C2×C11×C22⋊C414yes—
446C2×C4C2×C11×C22⋊C412yes—
447C2×C4C2×C11×C22⋊C414yes—
448C2×C4C2×C11×C22⋊C412yes—
449C2×C4C11×AGL(1,ℤ/8)12yes—
450C2×C4C11×#13712yes—
451C2×C4C23×C4×C1111yescharacteristic
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×Q8×C1111yescharacteristic
454C2×C4C2×C11×#4111yescharacteristic
455C2×C4C11×2−1+411yescharacteristic
456C2×C4C11×2−1+411yescharacteristic
457C8—22no—
458C8—41no—
459C8—42no—
460C22—24no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C22×C11×C22⋊C411yescharacteristic
468C22C11×#54811yescharacteristic
469C22D4×Q8×C1111yescharacteristic
470C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
471C22C2×C11×#13711yescharacteristic
472C22C11×#57611yescharacteristic
473C22C11×#57711yescharacteristic
474C4—24no—
475C4—24no—
476C4—22no—
477C4—42no—
478C4—44no—
479C4—42no—
480C4—82no—
481C4—81no—
482C4C11×#41714yes—
483C4C2×C4×Q8×C1111yescharacteristic
484C4C11×#51911yescharacteristic
485C4C11×#54811yescharacteristic
486C4D4×Q8×C1111yescharacteristic
487C2—44no—
488C2Q8×C11×C22⋊C411yescharacteristic
489C2C2×C11×#41711yescharacteristic
490C2C11×#289711yescharacteristic
491C2C11×#336611yescharacteristic
492C2C11×#337211yescharacteristic
493C2C11×#338411yescharacteristic
494C2C11×#338511yescharacteristic
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 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#446C2semidirect
3. Q8×C11×C4⋊C4C2semidirect
4. C11×#1992C2semidirect
5. C11×#1990C2semidirect
6. C11×#1989C2semidirect
7. C11×#1987C2semidirect
13. C11×#554C4semidirect
90. C11×#102Q8semidirect
95. #22522C11direct (N × H)
162. C2×#446C2×C11semidirect
163. Q8×C4⋊C4C2×C11semidirect
164. #1992C2×C11semidirect
165. #1990C2×C11semidirect
166. #1989C2×C11semidirect
167. #1987C2×C11semidirect
185. D4×C11C4×Q8semidirect
225. #554C4×C11semidirect
329. #102Q8×C11semidirect
407. C11#22522direct (N × H)
421. D4C4×Q8×C11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4462
Q8×C11×C4⋊C42
C11×#19922
C11×#19902
C11×#19892
C11×#19872
C11×#18022
C11×#17622
C4×C11×#1022
#2252211