Finite Group Databasebeta

← C11×#22152 #14599345

Subgroups — C11×#22152 #14599345

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C11×#2293C211yesmaximal, characteristic
4C11×#1981C211yesmaximal, characteristic, complemented
5C11×#1973C212yesmaximal
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1935C212yesmaximal, complemented
8C11×#1880C212yesmaximal
9C11×#1863C212yesmaximal, complemented
10C11×#1802C211yesmaximal, characteristic
11C11×#1767C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#117—21no—
17C11×#461C418yescomplemented
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#97C2212yes—
26C11×#391C2212yes—
27C11×#390C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#389—21no—
30C11×#389—21no—
31C11×#389C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#388—21no—
34C11×#388—21no—
35C11×#384C2211yescharacteristic
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C4×C11×C22⋊C4—21no—
40C43×C11C2211yescharacteristic
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—42no—
48C2×C11×SD16—42no—
49C2×C11×SD16C2×C418yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yes—
54C4×Q8×C11—42no—
55C4×Q8×C11—42no—
56C4×D4×C11—22no—
57C4×D4×C11C2×C414yes—
58C11×#117—44no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C42×C11D411yescharacteristic
80C2×C42×C11D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C11×#107—42no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8C2×C414yes—
87C11×#103—42no—
88C11×#103—42no—
89C11×#103C2×C418yes—
90C11×#102—42no—
91C11×#97—42no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—21no—
97#22152C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11C22×C414yes—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11C22×C412yes—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C11×SD16—48no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11C22×C414yes—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4C22×C412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—42no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—41no—
161C42×C11—44no—
162C42×C11—42no—
163C42×C11C22×C412yes—
164C42×C11#4112yes—
165C2×#461C2×C1111yescharacteristic
166C4×C4⋊Q8C2×C1111yescharacteristic, complemented
167#2293C2×C1111yescharacteristic
168#1981C2×C1111yescharacteristic, complemented
169#1973C2×C1112yes—
170#1947C2×C1111yescharacteristic, complemented
171#1935C2×C1112yescomplemented
172#1880C2×C1112yes—
173#1863C2×C1112yescomplemented
174#1802C2×C1111yescharacteristic
175#1767C2×C1111yescharacteristic, complemented
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11C22×D411yescharacteristic
184Q8×C11—24no—
185Q8×C11—24no—
186Q8×C11—42no—
187Q8×C11—42no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—41no—
191D4×C11—41no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—48no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C4×D412yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11#13712yes—
225C2×C4×C11#13712yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C8×C11—24no—
233C8×C11—42no—
234C22×SD16C22×C1112yes—
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×C4×Q8C22×C1112yes—
237C2×C4×D4C22×C1111yescharacteristic
238C2×#117—21no—
239#461C4×C1118yescomplemented
240C2×#107C22×C1112yes—
241C2×C4⋊C8C22×C1111yescharacteristic
242C2×C4⋊C8C22×C1111yescharacteristic
243C2×#103C22×C1112yes—
244C2×#103C22×C1112yes—
245C2×#103C22×C1112yes—
246C2×#102C22×C1112yes—
247C2×#97C22×C1112yes—
248#391C22×C1112yes—
249#390C22×C1111yescharacteristic
250#390C22×C1111yescharacteristic
251#389—21no—
252#389—21no—
253#389C22×C1111yescharacteristic
254#389C22×C1111yescharacteristic
255#388—21no—
256#388—21no—
257#384C22×C1111yescharacteristic
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4C22×C1111yescharacteristic
261C4×C22⋊C4—21no—
262C43C22×C1111yescharacteristic
263#340C22×C1112yes—
264#340C22×C1112yes—
265#336C22×C1112yes—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11C2×C4×D411yescharacteristic
274C22×C11#53511yescharacteristic
275C22×C11#53711yescharacteristic
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11C2×#13711yescharacteristic
278C22×C11C2×#13711yescharacteristic
279C22×C11#57511yescharacteristic
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—44no—
283C4×C11—42no—
284C4×C11—41no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11#44014yes—
291C4×C11#51811yescharacteristic
292C4×C11#52011yescharacteristic
293C4×C11#54011yescharacteristic
294C4×C11#54211yescharacteristic
295C22×Q8C23×C1112yes—
296C22×D4C23×C1111yescharacteristic
297C23×C4—21no—
298C2×SD16—42no—
299C2×SD16—42no—
300C2×SD16C2×C4×C1118yes—
301C22×C8C23×C1112yes—
302C22×C8C23×C1112yes—
303C4⋊Q8—22no—
304C4⋊Q8C2×C4×C1114yes—
305C4×Q8—42no—
306C4×Q8—42no—
307C4×D4—22no—
308C4×D4C2×C4×C1114yes—
309#117—44no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C42—21no—
327C2×C42—22no—
328C2×C42D4×C1111yescharacteristic
329C2×C42D4×C1111yescharacteristic
330C2×C42D4×C1111yescharacteristic
331C2×C42D4×C1111yescharacteristic
332C2×C42C23×C1111yescharacteristic
333C2×C42C23×C1111yescharacteristic
334C2×C42C23×C1111yescharacteristic
335#107—42no—
336C4⋊C8—22no—
337C4⋊C8C2×C4×C1114yes—
338#103—42no—
339#103—42no—
340#103C2×C4×C1118yes—
341#102—42no—
342#97—42no—
343#95—21no—
344#95—21no—
345#95—22no—
346#95—22no—
347#95—21no—
348C2×C11—82no—
349C2×C11#232411yescharacteristic
350C2×C11C2×#44011yescharacteristic
351C2×C11C4×#13711yescharacteristic
352C2×C11#321411yescharacteristic
353C2×C11#321811yescharacteristic
354C2×C11#325211yescharacteristic
355C2×C11#325411yescharacteristic
356C24—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8C22×C4×C1114yes—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C22×C4×C1112yes—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C24×C1111yescharacteristic
384SD16—48no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8C22×C4×C1114yes—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—44no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4C22×C4×C1112yes—
406C22⋊C4—24no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C42—22no—
412C42—22no—
413C42—22no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—41no—
419C42—44no—
420C42—42no—
421C42C22×C4×C1112yes—
422C42C11×#4112yes—
423C11#2215211yescharacteristic, direct product factor, Sylow
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23C22×D4×C1111yescharacteristic
432Q8—24no—
433Q8—24no—
434Q8—42no—
435Q8—42no—
436D4—22no—
437D4—22no—
438D4—41no—
439D4—41no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—48no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4C4×D4×C1112yes—
470C2×C4C4×D4×C1112yes—
471C2×C4C11×AGL(1,ℤ/8)12yes—
472C2×C4C11×#13712yes—
473C2×C4C11×#13712yes—
474C2×C4C23×C4×C1111yescharacteristic
475C2×C4C2×C11×#4111yescharacteristic
476C2×C4C11×H(5,𝔽2)11yescharacteristic
477C2×C4C11×H(5,𝔽2)11yescharacteristic
478C2×C4C11×H(5,𝔽2)11yescharacteristic
479C2×C4C11×2−1+411yescharacteristic
480C8—24no—
481C8—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22C2×C4×D4×C1111yescharacteristic
490C22C11×#53511yescharacteristic
491C22C11×#53711yescharacteristic
492C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
493C22C2×C11×#13711yescharacteristic
494C22C2×C11×#13711yescharacteristic
495C22C11×#57511yescharacteristic
496C4—22no—
497C4—22no—
498C4—42no—
499C4—41no—
500C4—41no—
501C4—41no—
502C4—44no—
503C4—82no—
504C4—81no—
505C4—81no—
506C4C11×#44014yes—
507C4C11×#51811yescharacteristic
508C4C11×#52011yescharacteristic
509C4C11×#54011yescharacteristic
510C4C11×#54211yescharacteristic
511C2—82no—
512C2C11×#232411yescharacteristic
513C2C2×C11×#44011yescharacteristic
514C2C4×C11×#13711yescharacteristic
515C2C11×#321411yescharacteristic
516C2C11×#321811yescharacteristic
517C2C11×#325211yescharacteristic
518C2C11×#325411yescharacteristic
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 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×C4⋊Q8C2semidirect
4. C11×#1981C2semidirect
6. C11×#1947C2semidirect
7. C11×#1935C2semidirect
9. C11×#1863C2semidirect
11. C11×#1767C2semidirect
17. C11×#461C4semidirect
97. #22152C11direct (N × H)
166. C4×C4⋊Q8C2×C11semidirect
168. #1981C2×C11semidirect
170. #1947C2×C11semidirect
171. #1935C2×C11semidirect
173. #1863C2×C11semidirect
175. #1767C2×C11semidirect
239. #461C4×C11semidirect
423. C11#22152direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C4×C11×C4⋊Q82
C11×#22932
C11×#19812
C11×#19732
C11×#19472
C11×#19352
C11×#18802
C11×#18632
C11×#18022
C11×#17672
#2215211