Finite Group Databasebeta

← C11×#24330 #14601523

Subgroups — C11×#24330 #14601523

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2582C211yesmaximal, characteristic, complemented
5C11×#2058C212yesmaximal, complemented
6C11×#2024C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1984C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal
10C11×#1864C212yesmaximal
11C11×#1802C211yesmaximal, characteristic
12C23×Q8×C11—21no—
13C22×C11×SD16C2211yescharacteristic
14D4×Q8×C11—24no—
15D4×Q8×C11—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#475—24no—
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C11×#398—22no—
35C11×#391—21no—
36C11×#391C2212yes—
37C11×#389—21no—
38C11×#389C2212yes—
39C11×#384C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—28no—
46C22×Q8×C11—22no—
47C22×Q8×C11—21no—
48C22×Q8×C11—44no—
49C22×Q8×C11—44no—
50C22×Q8×C11D411yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—21no—
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16Q814yescomplemented
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C11×C4⋊Q8—24no—
62C11×C4⋊Q8—24no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8D414yes—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—216no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2312yes—
91C2×C42×C11C2311yescharacteristic
92C11×#106—22no—
93C11×#106—24no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—24no—
97C11×#102—22no—
98C11×#102—24no—
99C4×C8×C11—22no—
100C11×#95—22no—
101C11×#95—22no—
102C11×#95—22no—
103#24330C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—21no—
105C2×Q8×C11—28no—
106C2×Q8×C11—22no—
107C2×Q8×C11—24no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—44no—
115C2×Q8×C11—432no—
116C2×Q8×C11—44no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11SD1614yescomplemented
120C2×Q8×C11C2×Q812yescomplemented
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11C2×D412yes—
125C2×D4×C11C2×Q812yes—
126C2×D4×C11#4112yes—
127C22×C4×C11—28no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C11×SD16—28no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11C2×Q812yescomplemented
153C11×C4⋊C4—28no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4—82no—
167C11×C4⋊C4C2×D414yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—24no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—42no—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176C2×D4×Q8C2×C1111yescharacteristic
177C2×#475C2×C1111yescharacteristic, complemented
178C2×C4×SD16C2×C1111yescharacteristic
179#2582C2×C1111yescharacteristic, complemented
180#2058C2×C1112yescomplemented
181#2024C2×C1112yescomplemented
182#1990C2×C1111yescharacteristic, complemented
183#1984C2×C1111yescharacteristic, complemented
184#1877C2×C1112yes—
185#1864C2×C1112yes—
186#1802C2×C1111yescharacteristic
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195Q8×C11—28no—
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—416no—
199Q8×C11—41no—
200Q8×C11—41no—
201Q8×C11—48no—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11C22⋊Q814yes—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—416no—
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—48no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12012yes—
232C2×C4×C11C2×SD1614yes—
233C2×C4×C11C2×SD1612yes—
234C2×C4×C11AGL(1,ℤ/8)12yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C8×C11—22no—
242C8×C11—41no—
243C8×C11—42no—
244C23×Q8—21no—
245C22×SD16C22×C1111yescharacteristic
246D4×Q8—24no—
247D4×Q8—24no—
248C2×C4⋊Q8C22×C1112yes—
249C2×C4⋊Q8C22×C1111yescharacteristic
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—22no—
252C2×C4×Q8C22×C1111yescharacteristic
253C2×C4×Q8C22×C1111yescharacteristic
254C2×C4×D4C22×C1112yes—
255C2×C4×D4C22×C1111yescharacteristic
256#475—24no—
257C4×SD16—24no—
258C2×#106C22×C1112yes—
259C2×#106C22×C1111yescharacteristic
260C2×C4⋊C8C22×C1111yescharacteristic
261C2×#103C22×C1112yes—
262C2×#103C22×C1111yescharacteristic
263C2×#102C22×C1112yes—
264C2×#102C22×C1111yescharacteristic
265C2×C4×C8C22×C1111yescharacteristic
266#398—22no—
267#391—21no—
268#391C22×C1112yes—
269#389—21no—
270#389C22×C1112yes—
271#384C22×C1111yescharacteristic
272#340C22×C1112yes—
273#340C22×C1112yes—
274#340C22×C1112yes—
275#336C22×C1112yes—
276#336C22×C1112yes—
277C22×C11—24no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11C2×#12011yescharacteristic
285C22×C11#54811yescharacteristic
286C22×C11D4×Q811yescharacteristic
287C22×C11C22×SD1611yescharacteristic
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C11#57711yescharacteristic
290C22×C11#57811yescharacteristic
291C4×C11—24no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—44no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—82no—
298C4×C11—81no—
299C4×C11#45014yes—
300C4×C11C2×C22⋊Q811yescharacteristic
301C4×C11#53611yescharacteristic
302C4×C11#54811yescharacteristic
303C4×C11D4×Q811yescharacteristic
304C22×Q8—28no—
305C22×Q8—22no—
306C22×Q8—21no—
307C22×Q8—44no—
308C22×Q8—44no—
309C22×Q8D4×C1111yescharacteristic
310C22×Q8C23×C1111yescharacteristic
311C22×D4C23×C1111yescharacteristic
312C23×C4—22no—
313C23×C4—21no—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×SD16Q8×C1114yescomplemented
317C22×C8C23×C1111yescharacteristic
318C22×C8C23×C1112yes—
319C22×C8C23×C1111yescharacteristic
320C4⋊Q8—24no—
321C4⋊Q8—24no—
322C4⋊Q8—22no—
323C4⋊Q8D4×C1114yes—
324C22⋊Q8—28no—
325C22⋊Q8—216no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—22no—
333C4×D4D4×C1114yes—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4D4×C1111yescharacteristic
341C2×C4⋊C4D4×C1112yes—
342C2×C4⋊C4C23×C1111yescharacteristic
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1112yes—
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C42—21no—
349C2×C42C23×C1112yes—
350C2×C42C23×C1111yescharacteristic
351#106—22no—
352#106—24no—
353C4⋊C8—22no—
354#103—22no—
355#103—24no—
356#102—22no—
357#102—24no—
358C4×C8—22no—
359#95—22no—
360#95—22no—
361#95—22no—
362C2×C11—44no—
363C2×C11#240911yescharacteristic
364C2×C11C2×#45011yescharacteristic
365C2×C11#301311yescharacteristic
366C2×C11#335911yescharacteristic
367C2×C11#337311yescharacteristic
368C2×C11Q8×SD1611yescharacteristic
369C2×C11#338611yescharacteristic
370C24—21no—
371C2×Q8—28no—
372C2×Q8—22no—
373C2×Q8—24no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—44no—
381C2×Q8—432no—
382C2×Q8—44no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8C11×SD1614yescomplemented
386C2×Q8C2×Q8×C1112yescomplemented
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4C2×D4×C1112yes—
391C2×D4C2×Q8×C1112yes—
392C2×D4C11×#4112yes—
393C22×C4—28no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C24×C1111yescharacteristic
409SD16—28no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8C2×Q8×C1112yescomplemented
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—42no—
430C4⋊C4—42no—
431C4⋊C4—81no—
432C4⋊C4—82no—
433C4⋊C4C2×D4×C1114yes—
434C4⋊C4C2×D4×C1112yes—
435C22⋊C4—28no—
436C22⋊C4—24no—
437C42—22no—
438C42—22no—
439C42—42no—
440C42C2×D4×C1112yes—
441C42C2×D4×C1112yes—
442C11#2433011yescharacteristic, direct product factor, Sylow
443C23—22no—
444C23—22no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23C22×D4×C1111yescharacteristic
451Q8—28no—
452Q8—22no—
453Q8—22no—
454Q8—416no—
455Q8—41no—
456Q8—41no—
457Q8—48no—
458D4—22no—
459D4—22no—
460D4—22no—
461D4C11×C22⋊Q814yes—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—416no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—48no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4C11×#12012yes—
487C2×C4C11×#12012yes—
488C2×C4C2×C11×SD1614yes—
489C2×C4C2×C11×SD1612yes—
490C2×C4C11×AGL(1,ℤ/8)12yes—
491C2×C4C22×D4×C1111yescharacteristic
492C2×C4C22×D4×C1111yescharacteristic
493C2×C4C22×Q8×C1111yescharacteristic
494C2×C4C2×C11×#4111yescharacteristic
495C2×C4C11×2−1+411yescharacteristic
496C2×C4C11×2−1+411yescharacteristic
497C8—22no—
498C8—41no—
499C8—42no—
500C22—24no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22C2×C11×#12011yescharacteristic
508C22C11×#54811yescharacteristic
509C22D4×Q8×C1111yescharacteristic
510C22C22×C11×SD1611yescharacteristic
511C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
512C22C11×#57711yescharacteristic
513C22C11×#57811yescharacteristic
514C4—24no—
515C4—22no—
516C4—42no—
517C4—44no—
518C4—42no—
519C4—42no—
520C4—81no—
521C4—82no—
522C4C11×#45014yes—
523C4C2×C11×C22⋊Q811yescharacteristic
524C4C11×#53611yescharacteristic
525C4C11×#54811yescharacteristic
526C4D4×Q8×C1111yescharacteristic
527C2—44no—
528C2C11×#240911yescharacteristic
529C2C2×C11×#45011yescharacteristic
530C2C11×#301311yescharacteristic
531C2C11×#335911yescharacteristic
532C2C11×#337311yescharacteristic
533C2Q8×C11×SD1611yescharacteristic
534C2C11×#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
2. C2×C11×#475C2semidirect
4. C11×#2582C2semidirect
5. C11×#2058C2semidirect
6. C11×#2024C2semidirect
7. C11×#1990C2semidirect
8. C11×#1984C2semidirect
57. C2×C11×SD16Q8semidirect
103. #24330C11direct (N × H)
119. C2×Q8×C11SD16semidirect
120. C2×Q8×C11C2×Q8semidirect
152. C2×C8×C11C2×Q8semidirect
177. C2×#475C2×C11semidirect
179. #2582C2×C11semidirect
180. #2058C2×C11semidirect
181. #2024C2×C11semidirect
182. #1990C2×C11semidirect
183. #1984C2×C11semidirect
316. C2×SD16Q8×C11semidirect
385. C2×Q8C11×SD16semidirect
386. C2×Q8C2×Q8×C11semidirect
418. C2×C8C2×Q8×C11semidirect
442. C11#24330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4752
C2×C4×C11×SD162
C11×#25822
C11×#20582
C11×#20242
C11×#19902
C11×#19842
C11×#18772
C11×#18642
C11×#18022
#2433011