Finite Group Databasebeta

← C11×#18194 #14595387

Subgroups — C11×#18194 #14595387

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic, complemented
2C2×C11×#447C212yesmaximal, complemented
3C11×#2408C211yesmaximal, characteristic, complemented
4C11×#1598C214yesmaximal, complemented
5C11×#1595C214yesmaximal, complemented
6C11×#1519C212yesmaximal, complemented
7C11×#1459C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—21no—
9C23×D4×C11C2211yescharacteristic, complemented
10C22×C11×D8—22no—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yescomplemented
15C11×#534—21no—
16C11×#534C2212yescomplemented
17C11×#532—21no—
18C2×C11×#121—21no—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C11×#120—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#447—24no—
24C11×#447C2218yescomplemented
25C2×C11×#102—22no—
26C2×C11×C22⋊C8C2212yescomplemented
27C11×#394C2212yescomplemented
28C11×#392C2212yescomplemented
29C11×#390—21no—
30C11×#380C2211yescharacteristic, complemented
31C11×#379—21no—
32C11×#327C2218yescomplemented
33C11×#324C2212yescomplemented
34C11×#323C2212yescomplemented
35C25×C11—21no—
36C11×H(5,𝔽2)—44no—
37C11×H(5,𝔽2)—44no—
38C2×C11×#41—24no—
39C2×C11×#41—22no—
40C22×D4×C11—24no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—44no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D412yescomplemented
51C22×D4×C11C2312yes—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C2×C11×D8—28no—
55C2×C11×D8—48no—
56C22×C8×C11—22no—
57C11×C4⋊Q8—21no—
58C11×#127—21no—
59C11×#124—22no—
60C11×#123—24no—
61C11×#123—24no—
62C11×C22⋊Q8—24no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—24no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—44no—
71C11×#121D414yescomplemented
72C11×#121C2314yes—
73C11×#120—24no—
74C11×#120—24no—
75C11×#120—44no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yescomplemented
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4C2311yescharacteristic
92C2×C42×C11D411yescharacteristic
93C11×#102—28no—
94C11×C22⋊C8—22no—
95C11×C22⋊C8C2314yes—
96C11×#95C2312yes—
97#18194C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—44no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—82no—
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C11×#41—44no—
109C11×#41—416no—
110C11×#41—44no—
111C2×Q8×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—42no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—48no—
129C2×D4×C11—416no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—82no—
139C2×D4×C11—82no—
140C2×D4×C11D814yescomplemented
141C2×D4×C11C2×D414yes—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C11×D8—416no—
158C2×C8×C11—24no—
159C2×C8×C11—44no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D414yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—82no—
176C42×C11—21no—
177C42×C11—21no—
178#3496C2×C1111yescharacteristic, complemented
179C2×#447C2×C1112yescomplemented
180#2408C2×C1111yescharacteristic, complemented
181#1598C2×C1114yescomplemented
182#1595C2×C1114yescomplemented
183#1519C2×C1112yescomplemented
184#1459C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—48no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—44no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—84no—
205C23×C11—82no—
206C23×C11—82no—
207C23×C11—88no—
208C23×C11—88no—
209C23×C11—84no—
210C23×C11#12012yes—
211C23×C11C2×D812yes—
212C23×C11C2×D812yescomplemented
213C23×C11AGL(1,ℤ/8)12yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—44no—
216D4×C11—28no—
217D4×C11—28no—
218D4×C11—44no—
219D4×C11—44no—
220D4×C11—44no—
221D4×C11—44no—
222D4×C11—48no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—48no—
226D4×C11—44no—
227D4×C11—44no—
228D4×C11—82no—
229D4×C11—82no—
230D4×C11—88no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—24no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—48no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—81no—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11C2×D812yescomplemented
253C2×C4×C11C22×D412yes—
254C8×C11—44no—
255C2×H(5,𝔽2)—21no—
256C23×D4C22×C1111yescharacteristic, complemented
257C22×D8—22no—
258#547—22no—
259#546—24no—
260D42—22no—
261#537C22×C1112yescomplemented
262#534—21no—
263#534C22×C1112yescomplemented
264#532—21no—
265C2×#121—21no—
266C2×#121—21no—
267C2×#121C22×C1112yes—
268C2×#120—21no—
269C2×C4×D4C22×C1111yescharacteristic
270#447—24no—
271#447C22×C1118yescomplemented
272C2×#102—22no—
273C2×C22⋊C8C22×C1112yescomplemented
274#394C22×C1112yescomplemented
275#392C22×C1112yescomplemented
276#390—21no—
277#380C22×C1111yescharacteristic, complemented
278#379—21no—
279#327C22×C1118yescomplemented
280#324C22×C1112yescomplemented
281#323C22×C1112yescomplemented
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—81no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—816no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—164no—
305C22×C11—164no—
306C22×C11#44714yes—
307C22×C11C2×#12011yescharacteristic
308C22×C11C22×D811yescharacteristic
309C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C11—22no—
311C4×C11—21no—
312C4×C11—22no—
313C4×C11—44no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11—82no—
317C4×C11B(4,𝔽2)12yes—
318C25—21no—
319H(5,𝔽2)—44no—
320H(5,𝔽2)—44no—
321C2×#41—24no—
322C2×#41—22no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—44no—
332C22×D4D4×C1111yescharacteristic
333C22×D4D4×C1112yescomplemented
334C22×D4C23×C1112yes—
335C23×C4D4×C1111yescharacteristic
336C23×C4C23×C1111yescharacteristic
337C2×D8—28no—
338C2×D8—48no—
339C22×C8—22no—
340C4⋊Q8—21no—
341#127—21no—
342#124—22no—
343#123—24no—
344#123—24no—
345C22⋊Q8—24no—
346#121—22no—
347#121—22no—
348#121—24no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—44no—
354#121D4×C1114yescomplemented
355#121C23×C1114yes—
356#120—24no—
357#120—24no—
358#120—44no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C1112yescomplemented
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4D4×C1111yescharacteristic
374C2×C22⋊C4C23×C1111yescharacteristic
375C2×C42D4×C1111yescharacteristic
376#102—28no—
377C22⋊C8—22no—
378C22⋊C8C23×C1114yes—
379#95C23×C1112yes—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—24no—
383C2×C11—42no—
384C2×C11—84no—
385C2×C11—84no—
386C2×C11C2×#44711yescharacteristic
387C2×C11#302111yescharacteristic
388C2×C11C2×B(4,𝔽2)11yescharacteristic
389C24—22no—
390C24—22no—
391C24—22no—
392C24—44no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—82no—
397C24C2×D4×C1111yescharacteristic
398C24C2×D4×C1111yescharacteristic
399#41—44no—
400#41—416no—
401#41—44no—
402C2×Q8—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—28no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—24no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—48no—
420C2×D4—416no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—82no—
430C2×D4—82no—
431C2×D4C11×D814yescomplemented
432C2×D4C2×D4×C1114yes—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1112yes—
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1112yes—
447C22×C4C24×C1111yescharacteristic
448D8—416no—
449C2×C8—24no—
450C2×C8—44no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4C2×D4×C1114yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—44no—
464C22⋊C4—42no—
465C22⋊C4—44no—
466C22⋊C4—82no—
467C42—21no—
468C42—21no—
469C11#1819411yescharacteristic, direct product factor, Sylow
470C23—21no—
471C23—21no—
472C23—24no—
473C23—24no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—42no—
479C23—48no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—82no—
488C23—82no—
489C23—84no—
490C23—82no—
491C23—82no—
492C23—88no—
493C23—88no—
494C23—84no—
495C23C11×#12012yes—
496C23C2×C11×D812yes—
497C23C2×C11×D812yescomplemented
498C23C11×AGL(1,ℤ/8)12yes—
499C23C22×D4×C1111yescharacteristic
500Q8—44no—
501D4—28no—
502D4—28no—
503D4—44no—
504D4—44no—
505D4—44no—
506D4—44no—
507D4—48no—
508D4—44no—
509D4—44no—
510D4—48no—
511D4—44no—
512D4—44no—
513D4—82no—
514D4—82no—
515D4—88no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—24no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—48no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—81no—
535C2×C4C11×#12011yescharacteristic
536C2×C4C11×#12011yescharacteristic
537C2×C4C2×C11×D812yescomplemented
538C2×C4C22×D4×C1112yes—
539C8—44no—
540C22—21no—
541C22—22no—
542C22—21no—
543C22—22no—
544C22—22no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—44no—
549C22—44no—
550C22—41no—
551C22—41no—
552C22—44no—
553C22—44no—
554C22—44no—
555C22—44no—
556C22—81no—
557C22—82no—
558C22—82no—
559C22—816no—
560C22—82no—
561C22—82no—
562C22—164no—
563C22—164no—
564C22C11×#44714yes—
565C22C2×C11×#12011yescharacteristic
566C22C22×C11×D811yescharacteristic
567C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—44no—
572C4—41no—
573C4—41no—
574C4—82no—
575C4C11×B(4,𝔽2)12yes—
576C2—21no—
577C2—21no—
578C2—24no—
579C2—42no—
580C2—84no—
581C2—84no—
582C2C2×C11×#44711yescharacteristic
583C2C11×#302111yescharacteristic
584C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3496C2semidirect
2. C2×C11×#447C2semidirect
3. C11×#2408C2semidirect
4. C11×#1598C2semidirect
5. C11×#1595C2semidirect
6. C11×#1519C2semidirect
7. C11×#1459C2semidirect
9. C23×D4×C11C22semidirect
14. C11×#537C22semidirect
16. C11×#534C22semidirect
24. C11×#447C22semidirect
26. C2×C11×C22⋊C8C22semidirect
27. C11×#394C22semidirect
28. C11×#392C22semidirect
30. C11×#380C22semidirect
32. C11×#327C22semidirect
33. C11×#324C22semidirect
34. C11×#323C22semidirect
50. C22×D4×C11D4semidirect
71. C11×#121D4semidirect
82. C2×C11×C4⋊C4D4semidirect
97. #18194C11direct (N × H)
140. C2×D4×C11D8semidirect
178. #3496C2×C11semidirect
179. C2×#447C2×C11semidirect
180. #2408C2×C11semidirect
181. #1598C2×C11semidirect
182. #1595C2×C11semidirect
183. #1519C2×C11semidirect
184. #1459C2×C11semidirect
212. C23×C11C2×D8semidirect
252. C2×C4×C11C2×D8semidirect
256. C23×D4C22×C11semidirect
261. #537C22×C11semidirect
263. #534C22×C11semidirect
271. #447C22×C11semidirect
273. C2×C22⋊C8C22×C11semidirect
274. #394C22×C11semidirect
275. #392C22×C11semidirect
277. #380C22×C11semidirect
279. #327C22×C11semidirect
280. #324C22×C11semidirect
281. #323C22×C11semidirect
333. C22×D4D4×C11semidirect
354. #121D4×C11semidirect
365. C2×C4⋊C4D4×C11semidirect
431. C2×D4C11×D8semidirect
469. C11#18194direct (N × H)
497. C23C2×C11×D8semidirect
537. C2×C4C2×C11×D8semidirect

Maximal subgroups

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

subgroupindex
C11×#34962
C2×C11×#4472
C11×#24082
C11×#15982
C11×#15952
C11×#15192
C11×#14592
#1819411