Finite Group Databasebeta

← C11×#24811 #14602004

Subgroups — C11×#24811 #14602004

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 538 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
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2083C212yesmaximal, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1939C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1802C212yesmaximal, 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×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C11×#474—24no—
21C4×C11×D8—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2212yes—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#399—22no—
32C11×#390C2212yes—
33C11×#389C2212yes—
34C11×#385—22no—
35C11×#384C2211yescharacteristic
36C11×#384C2212yes—
37C11×#380—21no—
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—
48C23×C4×C11—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C2×C11×D8Q814yescomplemented
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C22⋊Q8—44no—
58C11×C22⋊Q8—44no—
59C4×D4×C11—24no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—42no—
64C4×D4×C11D414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—44no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C42×C11C2312yes—
84C2×C42×C11C2311yescharacteristic
85C11×#107—22no—
86C11×#107—24no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8—42no—
89C11×#102—22no—
90C11×#102—24no—
91C11×#102—22no—
92C11×#102—42no—
93C4×C8×C11—22no—
94C11×#95—22no—
95C11×#95D412yes—
96#24811C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11—21no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
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×C11C2×Q812yes—
112C2×D4×C11C2×Q812yes—
113C2×D4×C11#4112yes—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—44no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—44no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—82no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C11×D8—28no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11C2×Q812yes—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4D814yescomplemented
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—44no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11C2×D412yes—
166C42×C11#4112yes—
167C2×#474C2×C1111yescharacteristic, complemented
168C2×C4×D8C2×C1111yescharacteristic
169#2542C2×C1111yescharacteristic, complemented
170D4×C4⋊C4C2×C1111yescharacteristic, complemented
171#2083C2×C1112yescomplemented
172#2067C2×C1112yescomplemented
173#1990C2×C1111yescharacteristic, complemented
174#1939C2×C1111yescharacteristic, complemented
175#1879C2×C1112yes—
176#1802C2×C1111yescharacteristic, complemented
177#1802C2×C1112yescomplemented
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11C22×D411yescharacteristic
193Q8×C11—84no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—22no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11C22⋊Q814yescomplemented
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—48no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—88no—
223C2×C4×C11—84no—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11C2×D814yes—
227C2×C4×C11C2×D812yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×Q811yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C8×C11—22no—
236C8×C11—41no—
237C8×C11—42no—
238C22×D8C22×C1111yescharacteristic
239C2×C4⋊Q8C22×C1111yescharacteristic
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C4×D4C22×C1111yescharacteristic
243C2×C4×D4C22×C1112yes—
244C2×C4×D4C22×C1111yescharacteristic
245C22×C4⋊C4—21no—
246#474—24no—
247C4×D8—24no—
248C2×#107C22×C1112yes—
249C2×#107C22×C1111yescharacteristic
250C2×C4⋊C8C22×C1111yescharacteristic
251C2×C4⋊C8C22×C1112yes—
252C2×#102C22×C1111yescharacteristic
253C2×#102C22×C1112yes—
254C2×#102C22×C1111yescharacteristic
255C2×#102C22×C1112yes—
256C2×C4×C8C22×C1111yescharacteristic
257#399—22no—
258#390C22×C1112yes—
259#389C22×C1112yes—
260#385—22no—
261#384C22×C1112yes—
262#384C22×C1111yescharacteristic
263#380—21no—
264C4×C4⋊C4C22×C1111yescharacteristic
265#340C22×C1112yes—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#336C22×C1112yes—
269C22×C11—24no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C2×#12111yescharacteristic
284C22×C11#54611yescharacteristic
285C22×C11D4×Q811yescharacteristic
286C22×C11C22×D811yescharacteristic
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C11#57711yescharacteristic
289C22×C11#57811yescharacteristic
290C4×C11—24no—
291C4×C11—22no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—81no—
295C4×C11—82no—
296C4×C11—82no—
297C4×C11#45914yes—
298C4×C11C2×C22⋊Q811yescharacteristic
299C4×C11#53711yescharacteristic
300C4×C11#55211yescharacteristic
301C4×C11#55411yescharacteristic
302C22×Q8—21no—
303C22×D4C23×C1111yescharacteristic
304C22×D4C23×C1111yescharacteristic
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—22no—
308C2×D8—22no—
309C2×D8—22no—
310C2×D8Q8×C1114yescomplemented
311C22×C8C23×C1112yes—
312C22×C8C23×C1111yescharacteristic
313C22×C8C23×C1111yescharacteristic
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C4×D4—24no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—42no—
323C4×D4D4×C1114yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4D4×C1111yescharacteristic
332C2×C4⋊C4D4×C1111yescharacteristic
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C4⋊C4C23×C1112yes—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C42C23×C1112yes—
343C2×C42C23×C1111yescharacteristic
344#107—22no—
345#107—24no—
346C4⋊C8—22no—
347C4⋊C8—42no—
348#102—22no—
349#102—24no—
350#102—22no—
351#102—42no—
352C4×C8—22no—
353#95—22no—
354#95D4×C1112yes—
355C2×C11—44no—
356C2×C11—82no—
357C2×C11#241711yescharacteristic
358C2×C11C2×#45911yescharacteristic
359C2×C11#304611yescharacteristic
360C2×C11#329411yescharacteristic
361C2×C11#333011yescharacteristic
362C2×C11Q8×D811yescharacteristic
363C2×C11#338411yescharacteristic
364C24—21no—
365C24—21no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4C2×D4×C1112yes—
378C2×D4C2×Q8×C1112yes—
379C2×D4C2×Q8×C1112yes—
380C2×D4C11×#4112yes—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—44no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—82no—
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C24×C1111yescharacteristic
399D8—28no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—21no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8C2×Q8×C1112yes—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—44no—
418C4⋊C4—42no—
419C4⋊C4—44no—
420C4⋊C4—42no—
421C4⋊C4—44no—
422C4⋊C4—81no—
423C4⋊C4C11×D814yescomplemented
424C4⋊C4C2×D4×C1112yes—
425C22⋊C4—24no—
426C22⋊C4—44no—
427C22⋊C4—44no—
428C22⋊C4—42no—
429C22⋊C4—44no—
430C42—22no—
431C42—22no—
432C42C2×D4×C1112yes—
433C42C11×#4112yes—
434C11#2481111yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23C22×D4×C1111yescharacteristic
450Q8—84no—
451D4—22no—
452D4—22no—
453D4—22no—
454D4—22no—
455D4—22no—
456D4—41no—
457D4—41no—
458D4C11×C22⋊Q814yescomplemented
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—48no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—88no—
480C2×C4—84no—
481C2×C4C11×#12112yes—
482C2×C4C11×#12112yes—
483C2×C4C2×C11×D814yes—
484C2×C4C2×C11×D812yes—
485C2×C4C11×AGL(1,ℤ/8)12yes—
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C22×Q8×C1111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C2×C11×#4111yescharacteristic
490C2×C4C11×H(5,𝔽2)11yescharacteristic
491C2×C4C11×2−1+411yescharacteristic
492C8—22no—
493C8—41no—
494C8—42no—
495C22—24no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22C2×C11×#12111yescharacteristic
510C22C11×#54611yescharacteristic
511C22D4×Q8×C1111yescharacteristic
512C22C22×C11×D811yescharacteristic
513C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
514C22C11×#57711yescharacteristic
515C22C11×#57811yescharacteristic
516C4—24no—
517C4—22no—
518C4—42no—
519C4—42no—
520C4—81no—
521C4—82no—
522C4—82no—
523C4C11×#45914yes—
524C4C2×C11×C22⋊Q811yescharacteristic
525C4C11×#53711yescharacteristic
526C4C11×#55211yescharacteristic
527C4C11×#55411yescharacteristic
528C2—44no—
529C2—82no—
530C2C11×#241711yescharacteristic
531C2C2×C11×#45911yescharacteristic
532C2C11×#304611yescharacteristic
533C2C11×#329411yescharacteristic
534C2C11×#333011yescharacteristic
535C2Q8×C11×D811yescharacteristic
536C2C11×#338411yescharacteristic
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. D4×C11×C4⋊C4C2semidirect
5. C11×#2083C2semidirect
6. C11×#2067C2semidirect
7. C11×#1990C2semidirect
8. C11×#1939C2semidirect
10. C11×#1802C2semidirect
11. C11×#1802C2semidirect
51. C2×C11×D8Q8semidirect
96. #24811C11direct (N × H)
156. C11×C4⋊C4D8semidirect
167. C2×#474C2×C11semidirect
169. #2542C2×C11semidirect
170. D4×C4⋊C4C2×C11semidirect
171. #2083C2×C11semidirect
172. #2067C2×C11semidirect
173. #1990C2×C11semidirect
174. #1939C2×C11semidirect
176. #1802C2×C11semidirect
177. #1802C2×C11semidirect
201. D4×C11C22⋊Q8semidirect
310. C2×D8Q8×C11semidirect
423. C4⋊C4C11×D8semidirect
434. C11#24811direct (N × H)
458. D4C11×C22⋊Q8semidirect

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
D4×C11×C4⋊C42
C11×#20832
C11×#20672
C11×#19902
C11×#19392
C11×#18792
C11×#18022
#2481111