Finite Group Databasebeta

← C11×#24328 #14601521

Subgroups — C11×#24328 #14601521

Order 2816.

1070 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic
5C11×#2059C212yesmaximal, complemented
6C11×#2025C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1984C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1863C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C11×#557—24no—
14C11×#557—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—22no—
18C2×C11×#125C2212yes—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#474—24no—
26C4×C11×SD16—24no—
27C2×C11×#107C2212yes—
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#396—22no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#384C2211yescharacteristic
39C11×#380—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16Q814yescomplemented
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—28no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C11×#125—216no—
60C11×#125—24no—
61C11×#125—24no—
62C11×C22⋊Q8—44no—
63C4×Q8×C11—28no—
64C4×Q8×C11—24no—
65C4×Q8×C11—24no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yes—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11—22no—
90C2×C42×C11—21no—
91C2×C42×C11C2312yes—
92C2×C42×C11C2311yescharacteristic
93C11×#107—24no—
94C11×#106—22no—
95C11×C4⋊C8—22no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#102—22no—
99C11×#102—24no—
100C4×C8×C11—22no—
101C11×#95—22no—
102#24328C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11C2×Q812yes—
115C2×Q8×C11#4112yes—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×Q812yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C11×SD16—28no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11C2×Q812yes—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D414yes—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—82no—
166C42×C11—28no—
167C42×C11—24no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C2×#557C2×C1111yescharacteristic, complemented
173C2×#474C2×C1111yescharacteristic
174C2×C4×SD16C2×C1111yescharacteristic
175#2538C2×C1111yescharacteristic
176#2059C2×C1112yescomplemented
177#2025C2×C1112yes—
178#1990C2×C1111yescharacteristic, complemented
179#1984C2×C1111yescharacteristic, complemented
180#1880C2×C1112yes—
181#1863C2×C1112yescomplemented
182#1803C2×C1111yescharacteristic, complemented
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—44no—
195Q8×C11—48no—
196Q8×C11C22⋊Q814yescomplemented
197D4×C11—22no—
198D4×C11—22no—
199D4×C11—41no—
200D4×C11—41no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12012yes—
227C2×C4×C11#13512yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×Q811yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C8×C11—22no—
236C8×C11—41no—
237C8×C11—42no—
238C22×SD16C22×C1111yescharacteristic
239#557—24no—
240#557—24no—
241C2×C4⋊Q8—21no—
242C2×C4⋊Q8C22×C1111yescharacteristic
243C2×#125—22no—
244C2×#125C22×C1112yes—
245C2×C22⋊Q8—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8C22×C1112yes—
248C2×C4×Q8C22×C1111yescharacteristic
249C2×C4×Q8C22×C1111yescharacteristic
250C2×C4×D4C22×C1111yescharacteristic
251#474—24no—
252C4×SD16—24no—
253C2×#107C22×C1112yes—
254C2×#106C22×C1111yescharacteristic
255C2×C4⋊C8C22×C1111yescharacteristic
256C2×#103C22×C1112yes—
257C2×#103C22×C1111yescharacteristic
258C2×#102C22×C1112yes—
259C2×#102C22×C1111yescharacteristic
260C2×C4×C8C22×C1111yescharacteristic
261#396—22no—
262#390C22×C1112yes—
263#389C22×C1112yes—
264#384C22×C1111yescharacteristic
265#380—21no—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269#336C22×C1112yes—
270#336C22×C1112yes—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C2×#12011yescharacteristic
279C22×C11#54811yescharacteristic
280C22×C11D4×Q811yescharacteristic
281C22×C11C2×#13511yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57811yescharacteristic
285C4×C11—24no—
286C4×C11—22no—
287C4×C11—42no—
288C4×C11—44no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—82no—
292C4×C11—81no—
293C4×C11#44914yes—
294C4×C11C2×C22⋊Q811yescharacteristic
295C4×C11#53611yescharacteristic
296C4×C11#54811yescharacteristic
297C4×C11D4×Q811yescharacteristic
298C22×Q8—21no—
299C22×Q8D4×C1111yescharacteristic
300C22×Q8C23×C1111yescharacteristic
301C22×D4C23×C1111yescharacteristic
302C23×C4—21no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16Q8×C1114yescomplemented
306C22×C8C23×C1111yescharacteristic
307C22×C8C23×C1112yes—
308C22×C8C23×C1111yescharacteristic
309C4⋊Q8—28no—
310C4⋊Q8—22no—
311C4⋊Q8D4×C1114yes—
312#125—216no—
313#125—24no—
314#125—24no—
315C22⋊Q8—44no—
316C4×Q8—28no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8D4×C1114yes—
323C4×D4—22no—
324C4×D4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4D4×C1111yescharacteristic
334C2×C4⋊C4D4×C1112yes—
335C2×C4⋊C4C23×C1111yescharacteristic
336C2×C4⋊C4C23×C1112yes—
337C2×C4⋊C4C23×C1111yescharacteristic
338C2×C4⋊C4C23×C1112yes—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C42—22no—
343C2×C42—21no—
344C2×C42C23×C1112yes—
345C2×C42C23×C1111yescharacteristic
346#107—24no—
347#106—22no—
348C4⋊C8—22no—
349#103—22no—
350#103—24no—
351#102—22no—
352#102—24no—
353C4×C8—22no—
354#95—22no—
355C2×C11—82no—
356C2×C11#240911yescharacteristic
357C2×C11C2×#44911yescharacteristic
358C2×C11#301311yescharacteristic
359C2×C11#336411yescharacteristic
360C2×C11#336811yescharacteristic
361C2×C11#338111yescharacteristic
362C2×C11#338611yescharacteristic
363C24—21no—
364C2×Q8—22no—
365C2×Q8—24no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8C2×D4×C1112yes—
374C2×Q8C2×Q8×C1112yes—
375C2×Q8C11×#4112yes—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4C2×Q8×C1112yes—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4C2×D4×C1112yes—
391C22×C4C2×D4×C1112yes—
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C24×C1111yescharacteristic
395SD16—28no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—22no—
404C2×C8C2×Q8×C1112yes—
405C4⋊C4—28no—
406C4⋊C4—28no—
407C4⋊C4—28no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—44no—
419C4⋊C4—42no—
420C4⋊C4—81no—
421C4⋊C4C2×D4×C1112yes—
422C4⋊C4C2×D4×C1114yes—
423C22⋊C4—44no—
424C22⋊C4—42no—
425C22⋊C4—82no—
426C42—28no—
427C42—24no—
428C42—22no—
429C42—22no—
430C42C2×D4×C1112yes—
431C42C2×D4×C1112yes—
432C11#2432811yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23C22×D4×C1111yescharacteristic
441Q8—22no—
442Q8—22no—
443Q8—22no—
444Q8—44no—
445Q8—48no—
446Q8C11×C22⋊Q814yescomplemented
447D4—22no—
448D4—22no—
449D4—41no—
450D4—41no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4C11×#12012yes—
476C2×C4C11×#12012yes—
477C2×C4C11×#13512yes—
478C2×C4C11×AGL(1,ℤ/8)12yes—
479C2×C4C22×D4×C1111yescharacteristic
480C2×C4C22×D4×C1111yescharacteristic
481C2×C4C22×Q8×C1111yescharacteristic
482C2×C4C2×C11×#4111yescharacteristic
483C2×C4C11×2−1+411yescharacteristic
484C2×C4C11×2−1+411yescharacteristic
485C8—22no—
486C8—41no—
487C8—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22C2×C11×#12011yescharacteristic
496C22C11×#54811yescharacteristic
497C22D4×Q8×C1111yescharacteristic
498C22C2×C11×#13511yescharacteristic
499C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
500C22C11×#57711yescharacteristic
501C22C11×#57811yescharacteristic
502C4—24no—
503C4—22no—
504C4—42no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—81no—
509C4—82no—
510C4C11×#44914yes—
511C4C2×C11×C22⋊Q811yescharacteristic
512C4C11×#53611yescharacteristic
513C4C11×#54811yescharacteristic
514C4D4×Q8×C1111yescharacteristic
515C2—82no—
516C2C11×#240911yescharacteristic
517C2C2×C11×#44911yescharacteristic
518C2C11×#301311yescharacteristic
519C2C11×#336411yescharacteristic
520C2C11×#336811yescharacteristic
521C2C11×#338111yescharacteristic
522C2C11×#338611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×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
1. C2×C11×#557C2semidirect
5. C11×#2059C2semidirect
7. C11×#1990C2semidirect
8. C11×#1984C2semidirect
10. C11×#1863C2semidirect
11. C11×#1803C2semidirect
52. C2×C11×SD16Q8semidirect
102. #24328C11direct (N × H)
172. C2×#557C2×C11semidirect
176. #2059C2×C11semidirect
178. #1990C2×C11semidirect
179. #1984C2×C11semidirect
181. #1863C2×C11semidirect
182. #1803C2×C11semidirect
196. Q8×C11C22⋊Q8semidirect
305. C2×SD16Q8×C11semidirect
432. C11#24328direct (N × H)
446. Q8C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4742
C2×C4×C11×SD162
C11×#25382
C11×#20592
C11×#20252
C11×#19902
C11×#19842
C11×#18802
C11×#18632
C11×#18032
#2432811