Finite Group Databasebeta

← C11×#24676 #14601869

Subgroups — C11×#24676 #14601869

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#474C211yesmaximal, characteristic, complemented
2C2×C4×C11×D8C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic, complemented
5C11×#2071C212yesmaximal, complemented
6C11×#2054C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1947C212yesmaximal, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117—21no—
19C11×#474—24no—
20C4×C11×D8—24no—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2212yes—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#399—22no—
31C11×#390C2212yes—
32C11×#390C2212yes—
33C11×#388—22no—
34C11×#384C2212yes—
35C11×#384C2211yescharacteristic
36C11×#380—21no—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C2×C11×D8—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C22⋊Q8—44no—
57C11×C22⋊Q8—44no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11D414yes—
62C11×#117—44no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—22no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#107—22no—
84C11×#107—24no—
85C11×C4⋊C8—24no—
86C11×C4⋊C8—22no—
87C11×#102—22no—
88C11×#102—24no—
89C11×#102—24no—
90C11×#102—22no—
91C4×C8×C11—22no—
92C11×#95—22no—
93C11×#95D412yes—
94#24676C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11—21no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11C2×D412yes—
111C2×D4×C11#4112yes—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C11×D8—28no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11#4112yes—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4D814yescomplemented
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—82no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—44no—
161C42×C11C2×D412yes—
162C42×C11#4112yes—
163C2×#474C2×C1111yescharacteristic, complemented
164C2×C4×D8C2×C1111yescharacteristic
165#2542C2×C1111yescharacteristic, complemented
166#2354C2×C1111yescharacteristic, complemented
167#2071C2×C1112yescomplemented
168#2054C2×C1112yes—
169#1990C2×C1111yescharacteristic, complemented
170#1947C2×C1112yescomplemented
171#1939C2×C1111yescharacteristic, complemented
172#1925C2×C1112yescomplemented
173#1802C2×C1111yescharacteristic, complemented
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11C22×D411yescharacteristic
189Q8×C11—84no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—48no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—84no—
219C2×C4×C11#12112yes—
220C2×C4×C11#12112yes—
221C2×C4×C11C2×D814yes—
222C2×C4×C11C2×D812yes—
223C2×C4×C11AGL(1,ℤ/8)12yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C8×C11—22no—
231C8×C11—42no—
232C8×C11—41no—
233C22×D8C22×C1111yescharacteristic
234C2×C4⋊Q8C22×C1111yescharacteristic
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C4×D4C22×C1111yescharacteristic
238C2×C4×D4C22×C1111yescharacteristic
239C2×#117—21no—
240#474—24no—
241C4×D8—24no—
242C2×#107C22×C1111yescharacteristic
243C2×#107C22×C1112yes—
244C2×C4⋊C8C22×C1112yes—
245C2×C4⋊C8C22×C1111yescharacteristic
246C2×#102C22×C1112yes—
247C2×#102C22×C1112yes—
248C2×#102C22×C1111yescharacteristic
249C2×#102C22×C1111yescharacteristic
250C2×C4×C8C22×C1111yescharacteristic
251#399—22no—
252#390C22×C1112yes—
253#390C22×C1112yes—
254#388—22no—
255#384C22×C1111yescharacteristic
256#384C22×C1112yes—
257#380—21no—
258C4×C4⋊C4C22×C1112yes—
259C4×C4⋊C4C22×C1111yescharacteristic
260#340C22×C1112yes—
261#340C22×C1112yes—
262#340C22×C1112yes—
263#336C22×C1112yes—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C2×#12111yescharacteristic
279C22×C11#54711yescharacteristic
280C22×C11#54811yescharacteristic
281C22×C11C22×D811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57811yescharacteristic
285C4×C11—24no—
286C4×C11—22no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11—81no—
291C4×C11—82no—
292C4×C11#45914yes—
293C4×C11#52511yescharacteristic
294C4×C11#53611yescharacteristic
295C4×C11#55211yescharacteristic
296C4×C11#55611yescharacteristic
297C22×Q8—21no—
298C22×D4C23×C1111yescharacteristic
299C22×D4C23×C1111yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C2×D8—22no—
303C2×D8—22no—
304C2×D8—22no—
305C22×C8C23×C1111yescharacteristic
306C22×C8C23×C1112yes—
307C22×C8C23×C1111yescharacteristic
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C22⋊Q8—44no—
311C22⋊Q8—44no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4D4×C1114yes—
316#117—44no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C1111yescharacteristic
323C2×C4⋊C4D4×C1111yescharacteristic
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1112yes—
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C42—22no—
335C2×C42C23×C1112yes—
336C2×C42C23×C1111yescharacteristic
337#107—22no—
338#107—24no—
339C4⋊C8—24no—
340C4⋊C8—22no—
341#102—22no—
342#102—24no—
343#102—24no—
344#102—22no—
345C4×C8—22no—
346#95—22no—
347#95D4×C1112yes—
348C2×C11—82no—
349C2×C11—82no—
350C2×C11#241511yescharacteristic
351C2×C11C2×#45911yescharacteristic
352C2×C11#304611yescharacteristic
353C2×C11#333411yescharacteristic
354C2×C11#335411yescharacteristic
355C2×C11#335811yescharacteristic
356C2×C11#336711yescharacteristic
357C24—21no—
358C24—21no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4C2×D4×C1112yes—
373C2×D4C11×#4112yes—
374C22×C4—21no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4C2×D4×C1112yes—
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C24×C1111yescharacteristic
389D8—28no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C11×#4112yes—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—44no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—44no—
411C4⋊C4—81no—
412C4⋊C4C11×D814yescomplemented
413C4⋊C4C2×D4×C1112yes—
414C22⋊C4—24no—
415C22⋊C4—44no—
416C22⋊C4—42no—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C22⋊C4—82no—
420C42—22no—
421C42—22no—
422C42—44no—
423C42C2×D4×C1112yes—
424C42C11×#4112yes—
425C11#2467611yescharacteristic, direct product factor, Sylow
426C23—22no—
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23C22×D4×C1111yescharacteristic
441Q8—84no—
442D4—22no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—41no—
447D4—41no—
448D4—41no—
449D4—41no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—48no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4C11×#12112yes—
472C2×C4C11×#12112yes—
473C2×C4C2×C11×D814yes—
474C2×C4C2×C11×D812yes—
475C2×C4C11×AGL(1,ℤ/8)12yes—
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C2×C11×#4111yescharacteristic
478C2×C4C2×C11×#4111yescharacteristic
479C2×C4C2×C11×#4111yescharacteristic
480C2×C4C11×2−1+411yescharacteristic
481C2×C4C11×2−1+411yescharacteristic
482C8—22no—
483C8—42no—
484C8—41no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22C2×C11×#12111yescharacteristic
500C22C11×#54711yescharacteristic
501C22C11×#54811yescharacteristic
502C22C22×C11×D811yescharacteristic
503C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
504C22C11×#57711yescharacteristic
505C22C11×#57811yescharacteristic
506C4—22no—
507C4—24no—
508C4—42no—
509C4—42no—
510C4—81no—
511C4—82no—
512C4—82no—
513C4C11×#45914yes—
514C4C11×#52511yescharacteristic
515C4C11×#53611yescharacteristic
516C4C11×#55211yescharacteristic
517C4C11×#55611yescharacteristic
518C2—82no—
519C2—82no—
520C2C11×#241511yescharacteristic
521C2C2×C11×#45911yescharacteristic
522C2C11×#304611yescharacteristic
523C2C11×#333411yescharacteristic
524C2C11×#335411yescharacteristic
525C2C11×#335811yescharacteristic
526C2C11×#336711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×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
1. C2×C11×#474C2semidirect
3. C11×#2542C2semidirect
4. C11×#2354C2semidirect
5. C11×#2071C2semidirect
7. C11×#1990C2semidirect
8. C11×#1947C2semidirect
9. C11×#1939C2semidirect
10. C11×#1925C2semidirect
11. C11×#1802C2semidirect
94. #24676C11direct (N × H)
150. C11×C4⋊C4D8semidirect
163. C2×#474C2×C11semidirect
165. #2542C2×C11semidirect
166. #2354C2×C11semidirect
167. #2071C2×C11semidirect
169. #1990C2×C11semidirect
170. #1947C2×C11semidirect
171. #1939C2×C11semidirect
172. #1925C2×C11semidirect
173. #1802C2×C11semidirect
412. C4⋊C4C11×D8semidirect
425. C11#24676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4742
C2×C4×C11×D82
C11×#25422
C11×#23542
C11×#20712
C11×#20542
C11×#19902
C11×#19472
C11×#19392
C11×#19252
C11×#18022
#2467611