Finite Group Databasebeta

← C11×#23930 #14601123

Subgroups — C11×#23930 #14601123

Order 2816.

1768 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic, complemented
2C2×C11×#447C212yesmaximal, complemented
3C2×C11×#390C211yesmaximal, characteristic, complemented
4C11×#2023C212yesmaximal, complemented
5C11×#2011C212yesmaximal, complemented
6C11×#1879C214yesmaximal, complemented
7C11×#1874C212yesmaximal, complemented
8C11×#1817C211yesmaximal, characteristic, complemented
9C22×C11×#41—21no—
10C23×D4×C11C2211yescharacteristic
11C22×C11×D8C2214yes—
12C11×#532—28no—
13C2×C11×C4⋊Q8C2211yescharacteristic, complemented
14C2×C11×#127C2211yescharacteristic, complemented
15C2×C11×#124—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2212yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4—21no—
22C22×C11×C22⋊C4—21no—
23C22×C42×C11C2211yescharacteristic
24C11×#447—28no—
25C2×C11×#102C2214yes—
26C2×C11×#102C2214yescomplemented
27C2×C11×C22⋊C8C2212yes—
28C11×#390—21no—
29C11×#390—21no—
30C11×#390C2212yes—
31C11×#390C2212yes—
32C11×#340C2214yescomplemented
33C11×#336C2212yescomplemented
34C11×#336C2212yescomplemented
35C25×C11—21no—
36C2×C11×#41—28no—
37C2×C11×#41—44no—
38C2×C11×#41—44no—
39C22×Q8×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—24no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—24no—
46C22×D4×C11—42no—
47C22×D4×C11C2312yes—
48C22×D4×C11C2312yes—
49C23×C4×C11—22no—
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C2×C11×D8—28no—
55C2×C11×D8—28no—
56C2×C11×D8—44no—
57C22×C8×C11C2314yes—
58C11×C4⋊Q8—24no—
59C11×#127—24no—
60C11×#124—28no—
61C11×#121—28no—
62C11×#121—24no—
63C11×#121D418yes—
64C4×D4×C11—28no—
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4—44no—
80C2×C42×C11—24no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×#102—28no—
86C11×#102—44no—
87C11×C22⋊C8—24no—
88#23930C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—24no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11C2×D411yescharacteristic
99C11×#41—432no—
100C2×Q8×C11—24no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—28no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—416no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11C2×D414yes—
123C2×D4×C11#4114yescomplemented
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—28no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—41no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11D814yescomplemented
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×D8—416no—
148C2×C8×C11—24no—
149C2×C8×C11—24no—
150C2×C8×C11—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—44no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C2×#532C2×C1111yescharacteristic, complemented
167C2×#447C2×C1112yescomplemented
168C2×#390C2×C1111yescharacteristic, complemented
169#2023C2×C1112yescomplemented
170#2011C2×C1112yescomplemented
171#1879C2×C1114yescomplemented
172#1874C2×C1112yescomplemented
173#1817C2×C1111yescharacteristic, complemented
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—48no—
181C23×C11—48no—
182C23×C11—48no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—84no—
196C23×C11—84no—
197C23×C11—84no—
198C23×C11—84no—
199C23×C11#12012yes—
200C23×C11C2×D812yes—
201C23×C11AGL(1,ℤ/8)12yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—48no—
204D4×C11—28no—
205D4×C11—28no—
206D4×C11—48no—
207D4×C11—48no—
208D4×C11—48no—
209D4×C11—416no—
210D4×C11—44no—
211D4×C11—44no—
212C2×C4×C11—21no—
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—28no—
221C2×C4×C11—28no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—44no—
227C2×C4×C11—416no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—84no—
234C2×C4×C11#12012yes—
235C2×C4×C11C2×D812yes—
236C2×C4×C11C2×D812yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C2×#4112yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C8×C11—44no—
242C22×#41—21no—
243C23×D4C22×C1111yescharacteristic
244C22×D8C22×C1114yes—
245#532—28no—
246C2×C4⋊Q8C22×C1111yescharacteristic, complemented
247C2×#127C22×C1111yescharacteristic, complemented
248C2×#124—21no—
249C2×#121—21no—
250C2×#121C22×C1112yes—
251C2×C4×D4—21no—
252C2×C4×D4C22×C1112yescomplemented
253C22×C4⋊C4C22×C1111yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42C22×C1111yescharacteristic
257#447—28no—
258C2×#102C22×C1114yes—
259C2×#102C22×C1114yescomplemented
260C2×C22⋊C8C22×C1112yes—
261#390—21no—
262#390—21no—
263#390C22×C1112yes—
264#390C22×C1112yes—
265#340C22×C1114yescomplemented
266#336C22×C1112yescomplemented
267#336C22×C1112yescomplemented
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—816no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11#44714yes—
290C22×C11C2×#12011yescharacteristic
291C22×C11#52511yescharacteristic
292C22×C11#53511yescharacteristic
293C22×C11C22×D811yescharacteristic
294C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11#57511yescharacteristic
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—44no—
302C4×C11—41no—
303C4×C11—82no—
304C4×C11#54614yes—
305C25—21no—
306C2×#41—28no—
307C2×#41—44no—
308C2×#41—44no—
309C22×Q8—21no—
310C22×D4—22no—
311C22×D4—24no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—24no—
316C22×D4—42no—
317C22×D4C23×C1112yes—
318C22×D4C23×C1112yes—
319C23×C4—22no—
320C23×C4—21no—
321C23×C4D4×C1111yescharacteristic
322C23×C4D4×C1111yescharacteristic
323C23×C4C23×C1111yescharacteristic
324C2×D8—28no—
325C2×D8—28no—
326C2×D8—44no—
327C22×C8C23×C1114yes—
328C4⋊Q8—24no—
329#127—24no—
330#124—28no—
331#121—28no—
332#121—24no—
333#121D4×C1118yes—
334C4×D4—28no—
335C4×D4—24no—
336C4×D4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C23×C1112yes—
341C2×C4⋊C4C23×C1112yes—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C42—24no—
351C2×C42D4×C1111yescharacteristic
352C2×C42D4×C1111yescharacteristic
353C2×C42C23×C1111yescharacteristic
354C2×C42C23×C1111yescharacteristic
355#102—28no—
356#102—44no—
357C22⋊C8—24no—
358C2×C11—24no—
359C2×C11—84no—
360C2×C11—84no—
361C2×C11#240411yescharacteristic
362C2×C11C2×#44711yescharacteristic
363C2×C11#300611yescharacteristic
364C2×C11#310011yescharacteristic
365C2×C11#310911yescharacteristic
366C2×C11#320511yescharacteristic
367C2×C11#321311yescharacteristic
368C24—24no—
369C24—22no—
370C24—22no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24—42no—
377C24C2×D4×C1111yescharacteristic
378#41—432no—
379C2×Q8—24no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—28no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—24no—
389C2×D4—22no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—416no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4C2×D4×C1114yes—
402C2×D4C11×#4114yescomplemented
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—28no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—41no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4C11×D814yescomplemented
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1114yes—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C24×C1111yescharacteristic
426D8—416no—
427C2×C8—24no—
428C2×C8—24no—
429C2×C8—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—42no—
434C4⋊C4C2×D4×C1114yes—
435C22⋊C4—28no—
436C22⋊C4—28no—
437C22⋊C4—44no—
438C22⋊C4—44no—
439C22⋊C4—44no—
440C22⋊C4—44no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C11#2393011yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—24no—
451C23—24no—
452C23—48no—
453C23—48no—
454C23—48no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C11×#12012yes—
472C23C2×C11×D812yes—
473C23C11×AGL(1,ℤ/8)12yes—
474C23C22×D4×C1111yescharacteristic
475Q8—48no—
476D4—28no—
477D4—28no—
478D4—48no—
479D4—48no—
480D4—48no—
481D4—416no—
482D4—44no—
483D4—44no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—28no—
493C2×C4—28no—
494C2×C4—21no—
495C2×C4—24no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—44no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—84no—
506C2×C4C11×#12012yes—
507C2×C4C2×C11×D812yes—
508C2×C4C2×C11×D812yes—
509C2×C4C11×AGL(1,ℤ/8)12yes—
510C2×C4C22×D4×C1112yes—
511C2×C4C2×C11×#4112yes—
512C2×C4C11×H(5,𝔽2)12yes—
513C8—44no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—44no—
526C22—816no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22C11×#44714yes—
536C22C2×C11×#12011yescharacteristic
537C22C11×#52511yescharacteristic
538C22C11×#53511yescharacteristic
539C22C22×C11×D811yescharacteristic
540C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
541C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
542C22C11×#57511yescharacteristic
543C4—22no—
544C4—22no—
545C4—22no—
546C4—22no—
547C4—44no—
548C4—41no—
549C4—82no—
550C4C11×#54614yes—
551C2—24no—
552C2—84no—
553C2—84no—
554C2C11×#240411yescharacteristic
555C2C2×C11×#44711yescharacteristic
556C2C11×#300611yescharacteristic
557C2C11×#310011yescharacteristic
558C2C11×#310911yescharacteristic
559C2C11×#320511yescharacteristic
560C2C11×#321311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#532C2semidirect
2. C2×C11×#447C2semidirect
3. C2×C11×#390C2semidirect
4. C11×#2023C2semidirect
5. C11×#2011C2semidirect
6. C11×#1879C2semidirect
7. C11×#1874C2semidirect
8. C11×#1817C2semidirect
13. C2×C11×C4⋊Q8C22semidirect
14. C2×C11×#127C22semidirect
19. C2×C4×D4×C11C22semidirect
26. C2×C11×#102C22semidirect
32. C11×#340C22semidirect
33. C11×#336C22semidirect
34. C11×#336C22semidirect
88. #23930C11direct (N × H)
123. C2×D4×C11#41semidirect
139. C22×C4×C11D8semidirect
166. C2×#532C2×C11semidirect
167. C2×#447C2×C11semidirect
168. C2×#390C2×C11semidirect
169. #2023C2×C11semidirect
170. #2011C2×C11semidirect
171. #1879C2×C11semidirect
172. #1874C2×C11semidirect
173. #1817C2×C11semidirect
246. C2×C4⋊Q8C22×C11semidirect
247. C2×#127C22×C11semidirect
252. C2×C4×D4C22×C11semidirect
259. C2×#102C22×C11semidirect
265. #340C22×C11semidirect
266. #336C22×C11semidirect
267. #336C22×C11semidirect
402. C2×D4C11×#41semidirect
418. C22×C4C11×D8semidirect
445. C11#23930direct (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×#4472
C2×C11×#3902
C11×#20232
C11×#20112
C11×#18792
C11×#18742
C11×#18172
#2393011