Finite Group Databasebeta

← C11×#32973 #14610166

Subgroups — C11×#32973 #14610166

Order 2816.

1286 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
2C11×#3080C212yesmaximal, complemented
3C11×#2566C211yesmaximal, characteristic, complemented
4C11×#1860C212yesmaximal, complemented
5C11×#1859C212yesmaximal, complemented
6C11×#1856C211yesmaximal, characteristic, complemented
7C11×#1856C211yesmaximal, characteristic, complemented
8C11×#1806C212yesmaximal, complemented
9C11×#1800C211yesmaximal, characteristic, complemented
10C11×#1792C211yesmaximal, characteristic
11C11×#1792C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic, complemented
14C11×#520—22no—
15C11×#520C2212yes—
16C11×#518—22no—
17C11×#518—22no—
18C11×#518C2211yescharacteristic
19C4×C11×#41—22no—
20C4×C11×#41C2212yes—
21C2×C4×D4×C11—22no—
22C2×C4×D4×C11—22no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#479—22no—
25C11×#479—22no—
26C11×#478—22no—
27C11×#478—22no—
28C11×#428C2212yescomplemented
29C11×#428C2212yescomplemented
30C11×#423C2212yescomplemented
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#417C2212yes—
34C11×#417C2212yes—
35C2×C11×#100C2211yescharacteristic
36C2×C11×#100C2211yescharacteristic
37C11×#396—22no—
38C11×#390C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#385—22no—
41C11×#384C2211yescharacteristic, complemented
42C11×#382C2211yescharacteristic, complemented
43C4×C11×C4⋊C4C2211yescharacteristic, complemented
44C11×#343C2212yescomplemented
45C11×#339C2212yescomplemented
46C11×#339C2212yescomplemented
47C11×H(5,𝔽2)—24no—
48C11×H(5,𝔽2)—22no—
49C11×H(5,𝔽2)Q814yes—
50C2×C11×#41—22no—
51C2×C11×#41C2312yes—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11D412yes—
57C2×C11×M16C2312yes—
58C2×C11×M16C2312yes—
59C11×#125—22no—
60C11×#125—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D412yes—
63C4×Q8×C11D412yes—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—24no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11D412yes—
77C4×D4×C11D412yes—
78C11×#117—24no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4D412yes—
97C2×C42×C11—22no—
98C2×C42×C11—22no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107—22no—
103C11×#107—22no—
104C11×#106—22no—
105C11×#106—22no—
106C11×C4⋊C8—22no—
107C11×C4⋊C8—22no—
108C11×#104—24no—
109C11×#104—24no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×#100—22no—
115C11×#100—22no—
116C11×#95—21no—
117C11×#95—22no—
118#32973C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—22no—
120C24×C11C2×D412yes—
121C11×#41—28no—
122C11×#41—28no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41C2×Q814yes—
126C11×#41#4114yes—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—24no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—22no—
133C2×D4×C11—28no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11C2×D412yes—
137C2×D4×C11C2×Q812yes—
138C2×D4×C11#4112yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—82no—
153C22×C4×C11—84no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—82no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—44no—
184C11×C22⋊C4—82no—
185C42×C11—24no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11C2×D412yes—
192C42×C11C2×D412yes—
193C4×H(5,𝔽2)C2×C1111yescharacteristic
194#3080C2×C1112yescomplemented
195#2566C2×C1111yescharacteristic, complemented
196#1860C2×C1112yescomplemented
197#1859C2×C1112yescomplemented
198#1856C2×C1111yescharacteristic, complemented
199#1856C2×C1111yescharacteristic, complemented
200#1806C2×C1112yescomplemented
201#1800C2×C1111yescharacteristic, complemented
202#1792C2×C1111yescharacteristic
203#1792C2×C1111yescharacteristic
204C23×C11—28no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—82no—
211C23×C11—82no—
212C23×C11C22⋊Q814yes—
213C23×C11C22×D411yescharacteristic
214Q8×C11—22no—
215Q8×C11C22⋊Q814yes—
216D4×C11—216no—
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—22no—
221D4×C11—24no—
222D4×C11C22⋊Q814yes—
223C2×C4×C11—28no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11—84no—
249C2×C4×C11—82no—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12012yes—
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11C2×#4112yes—
256C2×C4×C11C2×#4111yescharacteristic
257C8×C11—42no—
258C8×C11—42no—
259C2×H(5,𝔽2)C22×C1111yescharacteristic
260C2×#125C22×C1111yescharacteristic, complemented
261#520—22no—
262#520C22×C1112yes—
263#518—22no—
264#518—22no—
265#518C22×C1111yescharacteristic
266C4×#41—22no—
267C4×#41C22×C1112yes—
268C2×C4×D4—22no—
269C2×C4×D4—22no—
270C2×C4×D4C22×C1111yescharacteristic
271#479—22no—
272#479—22no—
273#478—22no—
274#478—22no—
275#428C22×C1112yescomplemented
276#428C22×C1112yescomplemented
277#423C22×C1112yescomplemented
278C2×#104C22×C1112yes—
279C2×#104C22×C1112yes—
280#417C22×C1112yes—
281#417C22×C1112yes—
282C2×#100C22×C1111yescharacteristic
283C2×#100C22×C1111yescharacteristic
284#396—22no—
285#390C22×C1111yescharacteristic
286#390C22×C1111yescharacteristic
287#385—22no—
288#384C22×C1111yescharacteristic, complemented
289#382C22×C1111yescharacteristic, complemented
290C4×C4⋊C4C22×C1111yescharacteristic, complemented
291#343C22×C1112yescomplemented
292#339C22×C1112yescomplemented
293#339C22×C1112yescomplemented
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—44no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—82no—
304C22×C11—88no—
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×C22⋊Q811yescharacteristic
307C22×C11#52511yescharacteristic
308C4×C11—24no—
309C4×C11—22no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11C2×C22⋊Q812yes—
320C4×C11#52512yes—
321H(5,𝔽2)—24no—
322H(5,𝔽2)—22no—
323H(5,𝔽2)Q8×C1114yes—
324C2×#41—22no—
325C2×#41C23×C1112yes—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4C23×C1111yescharacteristic
329C23×C4—22no—
330C23×C4D4×C1112yes—
331C2×M16C23×C1112yes—
332C2×M16C23×C1112yes—
333#125—22no—
334#125—22no—
335C4×Q8—22no—
336C4×Q8D4×C1112yes—
337C4×Q8D4×C1112yes—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—24no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4D4×C1112yes—
351C4×D4D4×C1112yes—
352#117—24no—
353#117—22no—
354#117—22no—
355#117C23×C1112yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4D4×C1112yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42C23×C1111yescharacteristic
374C2×C42C23×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376#107—22no—
377#107—22no—
378#106—22no—
379#106—22no—
380C4⋊C8—22no—
381C4⋊C8—22no—
382#104—24no—
383#104—24no—
384#103—22no—
385#103—22no—
386#102—22no—
387#102—22no—
388#100—22no—
389#100—22no—
390#95—21no—
391#95—22no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—44no—
395C2×C11—44no—
396C2×C11#284811yescharacteristic
397C2×C11#301811yescharacteristic
398C2×C11#301911yescharacteristic
399C24—22no—
400C24C2×D4×C1112yes—
401#41—28no—
402#41—28no—
403#41—22no—
404#41—22no—
405#41C2×Q8×C1114yes—
406#41C11×#4114yes—
407C2×Q8C2×D4×C1112yes—
408C2×D4—24no—
409C2×D4—28no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—22no—
413C2×D4—28no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4C2×D4×C1112yes—
417C2×D4C2×Q8×C1112yes—
418C2×D4C11×#4112yes—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—82no—
433C22×C4—84no—
434C22×C4C2×D4×C1112yes—
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C24×C1111yescharacteristic
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—41no—
452C4⋊C4—42no—
453C4⋊C4—41no—
454C4⋊C4—82no—
455C4⋊C4C2×D4×C1112yes—
456C4⋊C4C2×D4×C1112yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—24no—
463C22⋊C4—44no—
464C22⋊C4—82no—
465C42—24no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42C2×D4×C1112yes—
472C42C2×D4×C1112yes—
473C11#3297311yescharacteristic, direct product factor, Sylow
474C23—28no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—42no—
479C23—42no—
480C23—82no—
481C23—82no—
482C23C11×C22⋊Q814yes—
483C23C22×D4×C1111yescharacteristic
484Q8—22no—
485Q8C11×C22⋊Q814yes—
486D4—216no—
487D4—24no—
488D4—24no—
489D4—24no—
490D4—22no—
491D4—24no—
492D4C11×C22⋊Q814yes—
493C2×C4—28no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4—82no—
520C2×C4C11×#12011yescharacteristic
521C2×C4C11×#12012yes—
522C2×C4C11×#12011yescharacteristic
523C2×C4C22×D4×C1112yes—
524C2×C4C22×Q8×C1111yescharacteristic
525C2×C4C2×C11×#4112yes—
526C2×C4C2×C11×#4111yescharacteristic
527C8—42no—
528C8—42no—
529C22—21no—
530C22—21no—
531C22—24no—
532C22—24no—
533C22—44no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—82no—
539C22—88no—
540C22C2×C11×#12011yescharacteristic
541C22C2×C11×C22⋊Q811yescharacteristic
542C22C11×#52511yescharacteristic
543C4—22no—
544C4—21no—
545C4—21no—
546C4—24no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4C2×C11×C22⋊Q812yes—
555C4C11×#52512yes—
556C2—21no—
557C2—21no—
558C2—44no—
559C2—44no—
560C2C11×#284811yescharacteristic
561C2C11×#301811yescharacteristic
562C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×H(5,𝔽2)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3080C2semidirect
3. C11×#2566C2semidirect
4. C11×#1860C2semidirect
5. C11×#1859C2semidirect
6. C11×#1856C2semidirect
7. C11×#1856C2semidirect
8. C11×#1806C2semidirect
9. C11×#1800C2semidirect
13. C2×C11×#125C22semidirect
28. C11×#428C22semidirect
29. C11×#428C22semidirect
30. C11×#423C22semidirect
41. C11×#384C22semidirect
42. C11×#382C22semidirect
43. C4×C11×C4⋊C4C22semidirect
44. C11×#343C22semidirect
45. C11×#339C22semidirect
46. C11×#339C22semidirect
118. #32973C11direct (N × H)
194. #3080C2×C11semidirect
195. #2566C2×C11semidirect
196. #1860C2×C11semidirect
197. #1859C2×C11semidirect
198. #1856C2×C11semidirect
199. #1856C2×C11semidirect
200. #1806C2×C11semidirect
201. #1800C2×C11semidirect
260. C2×#125C22×C11semidirect
275. #428C22×C11semidirect
276. #428C22×C11semidirect
277. #423C22×C11semidirect
288. #384C22×C11semidirect
289. #382C22×C11semidirect
290. C4×C4⋊C4C22×C11semidirect
291. #343C22×C11semidirect
292. #339C22×C11semidirect
293. #339C22×C11semidirect
473. C11#32973direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×H(5,𝔽2)2
C11×#30802
C11×#25662
C11×#18602
C11×#18592
C11×#18562
C11×#18062
C11×#18002
C11×#17922
#3297311