Finite Group Databasebeta

← C11×#24062 #14601255

Subgroups — C11×#24062 #14601255

Order 2816.

1352 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#482C212yesmaximal, complemented
3C11×#2296C211yesmaximal, characteristic, complemented
4C11×#2058C211yesmaximal, characteristic, complemented
5C11×#2057C211yesmaximal, characteristic, complemented
6C11×#2041C211yesmaximal, characteristic, complemented
7C11×#2041C211yesmaximal, characteristic, complemented
8C11×#1875C212yesmaximal, complemented
9C11×#1864C212yesmaximal, complemented
10C11×#1862C212yesmaximal, complemented
11C11×#1817C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C11×#532—28no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124—21no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2212yes—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C11×#482—28no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C11×#389C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#385—21no—
37C11×#385—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2211yescharacteristic
43C11×#336C2211yescharacteristic
44C11×#336C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11C2312yes—
53C23×C4×C11—22no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—24no—
60C11×#127—24no—
61C11×#124—28no—
62C11×#121—28no—
63C11×#121—24no—
64C11×#121D418yes—
65C4×D4×C11—28no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—24no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C11×#107—24no—
93C11×#106—24no—
94C11×#102—24no—
95C11×#102—24no—
96C11×#102—24no—
97C11×#102—24no—
98C11×C22⋊C8—24no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103#24062C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C24×C11C2×D411yescharacteristic
106C11×#41—432no—
107C2×Q8×C11—24no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—28no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11C2×D414yes—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—28no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—41no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4#4112yescomplemented
167C11×C4⋊C4#4112yescomplemented
168C11×C22⋊C4—24no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—42no—
172C42×C11—24no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—42no—
178C2×#532C2×C1111yescharacteristic
179C2×#482C2×C1112yescomplemented
180#2296C2×C1111yescharacteristic, complemented
181#2058C2×C1111yescharacteristic, complemented
182#2057C2×C1111yescharacteristic, complemented
183#2041C2×C1111yescharacteristic, complemented
184#2041C2×C1111yescharacteristic, complemented
185#1875C2×C1112yescomplemented
186#1864C2×C1112yescomplemented
187#1862C2×C1112yescomplemented
188#1817C2×C1111yescharacteristic, complemented
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11#12012yes—
203C23×C11C22×D411yescharacteristic
204Q8×C11—48no—
205D4×C11—24no—
206D4×C11—24no—
207D4×C11—48no—
208D4×C11—48no—
209D4×C11—416no—
210D4×C11—42no—
211D4×C11—42no—
212C2×C4×C11—28no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—21no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—44no—
230C2×C4×C11—416no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11#12012yes—
244C2×C4×C11#13512yes—
245C2×C4×C11AGL(1,ℤ/8)12yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C112−1+412yes—
251C8×C11—42no—
252C8×C11—42no—
253C22×#41—21no—
254#532—28no—
255C2×C4⋊Q8C22×C1111yescharacteristic
256C2×#127C22×C1111yescharacteristic
257C2×#124—21no—
258C2×#121—21no—
259C2×#121C22×C1112yes—
260C2×C4×D4—21no—
261C2×C4×D4C22×C1112yes—
262C2×#117C22×C1111yescharacteristic
263C2×#117C22×C1111yescharacteristic
264C22×C42C22×C1111yescharacteristic
265#482—28no—
266C2×#107C22×C1112yes—
267C2×#106C22×C1112yes—
268C2×#102C22×C1112yes—
269C2×#102C22×C1112yes—
270C2×#102C22×C1112yes—
271C2×#102C22×C1112yes—
272C2×C22⋊C8C22×C1112yes—
273#389C22×C1111yescharacteristic
274#389C22×C1111yescharacteristic
275#389C22×C1111yescharacteristic
276#389C22×C1111yescharacteristic
277#385—21no—
278#385—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281#340C22×C1112yes—
282#340C22×C1112yes—
283#336C22×C1111yescharacteristic
284#336C22×C1111yescharacteristic
285#336C22×C1112yes—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#52511yescharacteristic
302C22×C11#53611yescharacteristic
303C22×C11C2×#13511yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11#57511yescharacteristic
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—41no—
314C4×C11—44no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11#54712yes—
318C4×C11#54712yes—
319C2×#41—28no—
320C2×#41—44no—
321C2×#41—44no—
322C22×Q8—21no—
323C22×D4—22no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C23×C1112yes—
327C23×C4—22no—
328C23×C4D4×C1111yescharacteristic
329C23×C4D4×C1111yescharacteristic
330C23×C4C23×C1111yescharacteristic
331C22×C8C23×C1112yes—
332C22×C8C23×C1112yes—
333C4⋊Q8—24no—
334#127—24no—
335#124—28no—
336#121—28no—
337#121—24no—
338#121D4×C1118yes—
339C4×D4—28no—
340C4×D4—24no—
341C4×D4—24no—
342#117—22no—
343#117—22no—
344#117—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C42—21no—
360C2×C42—24no—
361C2×C42—21no—
362C2×C42D4×C1111yescharacteristic
363C2×C42D4×C1111yescharacteristic
364C2×C42C23×C1111yescharacteristic
365C2×C42C23×C1111yescharacteristic
366#107—24no—
367#106—24no—
368#102—24no—
369#102—24no—
370#102—24no—
371#102—24no—
372C22⋊C8—24no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377C2×C11—42no—
378C2×C11—84no—
379C2×C11#240611yescharacteristic
380C2×C11#300211yescharacteristic
381C2×C11#300311yescharacteristic
382C2×C11#310611yescharacteristic
383C2×C11#311511yescharacteristic
384C2×C11#322811yescharacteristic
385C2×C11#323511yescharacteristic
386C24—22no—
387C24C2×D4×C1111yescharacteristic
388#41—432no—
389C2×Q8—24no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—28no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—44no—
403C2×D4—44no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4C2×D4×C1114yes—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—28no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—41no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1114yes—
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C24×C1111yescharacteristic
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4C2×D4×C1114yes—
448C4⋊C4C11×#4112yescomplemented
449C4⋊C4C11×#4112yescomplemented
450C22⋊C4—24no—
451C22⋊C4—28no—
452C22⋊C4—28no—
453C22⋊C4—42no—
454C42—24no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—42no—
460C11#2406211yescharacteristic, direct product factor, Sylow
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23C11×#12012yes—
475C23C22×D4×C1111yescharacteristic
476Q8—48no—
477D4—24no—
478D4—24no—
479D4—48no—
480D4—48no—
481D4—416no—
482D4—42no—
483D4—42no—
484C2×C4—28no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—44no—
502C2×C4—416no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4C11×#12012yes—
516C2×C4C11×#13512yes—
517C2×C4C11×AGL(1,ℤ/8)12yes—
518C2×C4C11×AGL(1,ℤ/8)12yes—
519C2×C4C22×D4×C1112yes—
520C2×C4C2×C11×#4111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C2×C4C11×2−1+412yes—
523C8—42no—
524C8—42no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—44no—
534C22—44no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22C2×C11×#12011yescharacteristic
540C22C11×#52511yescharacteristic
541C22C11×#53611yescharacteristic
542C22C2×C11×#13511yescharacteristic
543C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
544C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
545C22C11×#57511yescharacteristic
546C4—22no—
547C4—22no—
548C4—22no—
549C4—22no—
550C4—41no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—81no—
555C4—81no—
556C4C11×#54712yes—
557C4C11×#54712yes—
558C2—42no—
559C2—84no—
560C2C11×#240611yescharacteristic
561C2C11×#300211yescharacteristic
562C2C11×#300311yescharacteristic
563C2C11×#310611yescharacteristic
564C2C11×#311511yescharacteristic
565C2C11×#322811yescharacteristic
566C2C11×#323511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#482C2semidirect
3. C11×#2296C2semidirect
4. C11×#2058C2semidirect
5. C11×#2057C2semidirect
6. C11×#2041C2semidirect
7. C11×#2041C2semidirect
8. C11×#1875C2semidirect
9. C11×#1864C2semidirect
10. C11×#1862C2semidirect
11. C11×#1817C2semidirect
103. #24062C11direct (N × H)
166. C11×C4⋊C4#41semidirect
167. C11×C4⋊C4#41semidirect
179. C2×#482C2×C11semidirect
180. #2296C2×C11semidirect
181. #2058C2×C11semidirect
182. #2057C2×C11semidirect
183. #2041C2×C11semidirect
184. #2041C2×C11semidirect
185. #1875C2×C11semidirect
186. #1864C2×C11semidirect
187. #1862C2×C11semidirect
188. #1817C2×C11semidirect
448. C4⋊C4C11×#41semidirect
449. C4⋊C4C11×#41semidirect
460. C11#24062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4822
C11×#22962
C11×#20582
C11×#20572
C11×#20412
C11×#18752
C11×#18642
C11×#18622
C11×#18172
#2406211