Finite Group Databasebeta

← C11×#60569 #14637762

Subgroups — C11×#60569 #14637762

Order 2816.

2010 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
1C2×C11×#541C211yesmaximal, characteristic, complemented
2C11×#3428C211yesmaximal, characteristic
3C11×#3127C214yesmaximal, complemented
4C11×#3123C214yesmaximal, complemented
5C11×#3120C218yesmaximal, complemented
6C11×#3095C212yesmaximal, complemented
7C11×#3080C212yesmaximal, complemented
8C11×#3039C212yesmaximal, complemented
9C11×#3007C212yesmaximal
10C4×C11×#137C214yesmaximal, complemented
11C11×#2921C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×#137C2214yes—
14C11×#541—22no—
15C11×#541—22no—
16C11×#541C2214yes—
17C11×#541C2214yescomplemented
18C2×C11×C4⋊Q8C2211yescharacteristic, complemented
19C2×C11×#126—22no—
20C2×C11×#125—22no—
21C2×C11×#125C2211yescharacteristic, complemented
22C2×C11×C22⋊Q8C2212yes—
23C11×#520—22no—
24C11×#520C2214yes—
25C11×#519C2212yes—
26C11×#518—22no—
27C11×#518C2212yes—
28C4×C11×#41—22no—
29C4×C11×#41C2212yes—
30C4×C11×#41C2212yes—
31C2×C4×Q8×C11C2212yescomplemented
32C2×C11×#117—22no—
33C2×C11×#117C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C11×#485C2218yes—
36C11×#484C2214yescomplemented
37C11×#483C2214yescomplemented
38C11×#479C2218yescomplemented
39C11×#478C2218yescomplemented
40C11×#462C2218yescomplemented
41C11×#461C2218yescomplemented
42C11×#452C2218yes—
43C11×#451C2214yes—
44C11×#450C2214yes—
45C11×#441C2218yescomplemented
46C11×#440C2218yescomplemented
47C4×C11×Q16C2218yescomplemented
48C4×C11×SD16C2218yescomplemented
49C11×#433C2214yes—
50C11×#433C2214yescomplemented
51C11×#428C2214yescomplemented
52C11×#423C2212yescomplemented
53C11×#419C2214yescomplemented
54C11×#417C2214yes—
55C11×#407C2212yes—
56C4×C11×M16C2212yescomplemented
57C2×C11×#41—28no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41C2312yes—
61C2×C11×#41C2312yes—
62C22×Q8×C11C2312yes—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C11×#137—216no—
69C2×C11×Q16C2318yes—
70C2×C11×SD16C2318yes—
71C2×C11×M16C2314yes—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C11×#126—28no—
75C11×#126—28no—
76C11×#125—28no—
77C11×#125—28no—
78C11×#125—22no—
79C11×#125C2314yes—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8C2314yes—
83C11×C22⋊Q8C2314yes—
84C4×Q8×C11—24no—
85C4×Q8×C11—24no—
86C4×Q8×C11C2318yes—
87C4×Q8×C11C2314yes—
88C4×Q8×C11C2314yes—
89C4×D4×C11—24no—
90C4×D4×C11—24no—
91C4×D4×C11—24no—
92C4×D4×C11—24no—
93C4×D4×C11—24no—
94C4×D4×C11C2314yes—
95C4×D4×C11C2314yes—
96C11×#117—21no—
97C11×#117—21no—
98C11×#117—24no—
99C11×#117—24no—
100C11×#117—22no—
101C11×#117—22no—
102C11×#117D412yes—
103C11×#117D412yes—
104C11×#117C2312yes—
105C11×#117C2312yes—
106C11×#117C2312yes—
107C11×#117C2312yes—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4D412yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4D412yes—
120C2×C42×C11—21no—
121C2×C42×C11—22no—
122C2×C42×C11—22no—
123C2×C42×C11—22no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C11×#107C2318yes—
127C11×#106C2318yes—
128C11×C4⋊C8C2318yes—
129C11×#103C2318yes—
130C11×#103C2318yes—
131C11×#103C2318yes—
132C11×#102C2318yes—
133C11×C22⋊C8C2314yes—
134C11×C22⋊C8C2314yes—
135C11×#97C2314yes—
136C4×C8×C11C2314yes—
137#60569C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C11×#41—28no—
141C11×#41—28no—
142C11×#41—24no—
143C11×#41—24no—
144C11×#41—24no—
145C11×#41#4118yes—
146C2×Q8×C11—24no—
147C2×Q8×C11—21no—
148C2×Q8×C11—22no—
149C2×Q8×C11—28no—
150C2×Q8×C11C2414yes—
151C2×Q8×C11C2412yes—
152C2×D4×C11—28no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—24no—
156C2×D4×C11—21no—
157C2×D4×C11C2412yes—
158C22×C4×C11—28no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—24no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C11×Q16—216no—
177C11×SD16—216no—
178C11×M16—28no—
179C2×C8×C11C2418yes—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—28no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D414yes—
190C11×C4⋊C4C2×D414yes—
191C11×C4⋊C4C2414yes—
192C11×C4⋊C4C2414yes—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4C2×D414yes—
200C11×C22⋊C4C2×D414yes—
201C42×C11—22no—
202C42×C11—24no—
203C42×C11—24no—
204C42×C11—22no—
205C42×C11—28no—
206C42×C11C2×D412yes—
207C42×C11C2×D412yes—
208C42×C11C2412yes—
209C42×C11C2412yes—
210C2×#541C2×C1111yescharacteristic, complemented
211#3428C2×C1111yescharacteristic
212#3127C2×C1114yescomplemented
213#3123C2×C1114yescomplemented
214#3120C2×C1118yescomplemented
215#3095C2×C1112yescomplemented
216#3080C2×C1112yescomplemented
217#3039C2×C1112yescomplemented
218#3007C2×C1112yes—
219C4×#137C2×C1114yescomplemented
220#2921C2×C1111yescharacteristic, complemented
221C23×C11—24no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—42no—
225C23×C11—82no—
226C23×C11C22×D411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D411yescharacteristic
229Q8×C11—24no—
230Q8×C11—22no—
231Q8×C11—28no—
232Q8×C11—44no—
233Q8×C11C2×#4114yes—
234D4×C11—28no—
235D4×C11—24no—
236D4×C11—28no—
237D4×C11—22no—
238D4×C11C2×#4114yes—
239C2×C4×C11—24no—
240C2×C4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—28no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—84no—
256C2×C4×C11—84no—
257C2×C4×C11—82no—
258C2×C4×C11C22×D414yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D414yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4114yes—
264C2×C4×C11C2511yescharacteristic
265C8×C11—28no—
266C22×#41C22×C1111yescharacteristic
267C2×#137C22×C1114yes—
268#541—22no—
269#541—22no—
270#541C22×C1114yes—
271#541C22×C1114yescomplemented
272C2×C4⋊Q8C22×C1111yescharacteristic, complemented
273C2×#126—22no—
274C2×#125—22no—
275C2×#125C22×C1111yescharacteristic, complemented
276C2×C22⋊Q8C22×C1112yes—
277#520—22no—
278#520C22×C1114yes—
279#519C22×C1112yes—
280#518—22no—
281#518C22×C1112yes—
282C4×#41—22no—
283C4×#41C22×C1112yes—
284C4×#41C22×C1112yes—
285C2×C4×Q8C22×C1112yescomplemented
286C2×#117—22no—
287C2×#117C22×C1111yescharacteristic
288C2×#117C22×C1111yescharacteristic
289#485C22×C1118yes—
290#484C22×C1114yescomplemented
291#483C22×C1114yescomplemented
292#479C22×C1118yescomplemented
293#478C22×C1118yescomplemented
294#462C22×C1118yescomplemented
295#461C22×C1118yescomplemented
296#452C22×C1118yes—
297#451C22×C1114yes—
298#450C22×C1114yes—
299#441C22×C1118yescomplemented
300#440C22×C1118yescomplemented
301C4×Q16C22×C1118yescomplemented
302C4×SD16C22×C1118yescomplemented
303#433C22×C1114yes—
304#433C22×C1114yescomplemented
305#428C22×C1114yescomplemented
306#423C22×C1112yescomplemented
307#419C22×C1114yescomplemented
308#417C22×C1114yes—
309#407C22×C1112yes—
310C4×M16C22×C1112yescomplemented
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—24no—
317C22×C11—44no—
318C22×C11—82no—
319C22×C11—84no—
320C22×C11#52512yes—
321C22×C11C23×D411yescharacteristic
322C4×C11—24no—
323C4×C11—24no—
324C4×C11—21no—
325C4×C11—24no—
326C4×C11—21no—
327C4×C11—44no—
328C4×C11—44no—
329C4×C11—44no—
330C4×C11#52512yes—
331C4×C11C22×#4112yes—
332C2×#41—28no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41C23×C1112yes—
336C2×#41C23×C1112yes—
337C22×Q8C23×C1112yes—
338C22×Q8C23×C1111yescharacteristic
339C22×D4—21no—
340C22×D4C23×C1111yescharacteristic
341C23×C4—21no—
342C23×C4C23×C1111yescharacteristic
343#137—216no—
344C2×Q16C23×C1118yes—
345C2×SD16C23×C1118yes—
346C2×M16C23×C1114yes—
347C4⋊Q8—22no—
348C4⋊Q8C23×C1114yes—
349#126—28no—
350#126—28no—
351#125—28no—
352#125—28no—
353#125—22no—
354#125C23×C1114yes—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8C23×C1114yes—
358C22⋊Q8C23×C1114yes—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8C23×C1118yes—
362C4×Q8C23×C1114yes—
363C4×Q8C23×C1114yes—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4C23×C1114yes—
370C4×D4C23×C1114yes—
371#117—21no—
372#117—21no—
373#117—24no—
374#117—24no—
375#117—22no—
376#117—22no—
377#117D4×C1112yes—
378#117D4×C1112yes—
379#117C23×C1112yes—
380#117C23×C1112yes—
381#117C23×C1112yes—
382#117C23×C1112yes—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4D4×C1112yes—
389C2×C4⋊C4C23×C1112yes—
390C2×C4⋊C4C23×C1112yes—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4D4×C1112yes—
395C2×C42—21no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42C23×C1111yescharacteristic
400C2×C42C23×C1111yescharacteristic
401#107C23×C1118yes—
402#106C23×C1118yes—
403C4⋊C8C23×C1118yes—
404#103C23×C1118yes—
405#103C23×C1118yes—
406#103C23×C1118yes—
407#102C23×C1118yes—
408C22⋊C8C23×C1114yes—
409C22⋊C8C23×C1114yes—
410#97C23×C1114yes—
411C4×C8C23×C1114yes—
412C2×C11—22no—
413C2×C11—41no—
414C2×C11—41no—
415C2×C11—44no—
416C2×C11C2×#52511yescharacteristic
417C2×C11#358612yes—
418C24—21no—
419C24C2×D4×C1111yescharacteristic
420#41—28no—
421#41—28no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41C11×#4118yes—
426C2×Q8—24no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—28no—
430C2×Q8C24×C1114yes—
431C2×Q8C24×C1112yes—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—24no—
436C2×D4—21no—
437C2×D4C24×C1112yes—
438C22×C4—28no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1112yes—
452C22×C4C2×D4×C1112yes—
453C22×C4C24×C1111yescharacteristic
454C22×C4C24×C1111yescharacteristic
455C22×C4C24×C1111yescharacteristic
456Q16—216no—
457SD16—216no—
458M16—28no—
459C2×C8C24×C1118yes—
460C4⋊C4—22no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—28no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—28no—
467C4⋊C4—28no—
468C4⋊C4—22no—
469C4⋊C4C2×D4×C1114yes—
470C4⋊C4C2×D4×C1114yes—
471C4⋊C4C24×C1114yes—
472C4⋊C4C24×C1114yes—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4C2×D4×C1114yes—
480C22⋊C4C2×D4×C1114yes—
481C42—22no—
482C42—24no—
483C42—24no—
484C42—22no—
485C42—28no—
486C42C2×D4×C1112yes—
487C42C2×D4×C1112yes—
488C42C24×C1112yes—
489C42C24×C1112yes—
490C11#6056911yescharacteristic, direct product factor, Sylow
491C23—24no—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—82no—
496C23C22×D4×C1111yescharacteristic
497C23C22×D4×C1111yescharacteristic
498C23C22×D4×C1111yescharacteristic
499Q8—24no—
500Q8—22no—
501Q8—28no—
502Q8—44no—
503Q8C2×C11×#4114yes—
504D4—28no—
505D4—24no—
506D4—28no—
507D4—22no—
508D4C2×C11×#4114yes—
509C2×C4—24no—
510C2×C4—28no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—28no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—84no—
526C2×C4—84no—
527C2×C4—82no—
528C2×C4C22×D4×C1114yes—
529C2×C4C22×D4×C1111yescharacteristic
530C2×C4C22×D4×C1114yes—
531C2×C4C22×D4×C1111yescharacteristic
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C2×C11×#4114yes—
534C2×C4C25×C1111yescharacteristic
535C8—28no—
536C22—22no—
537C22—21no—
538C22—21no—
539C22—24no—
540C22—22no—
541C22—22no—
542C22—44no—
543C22—82no—
544C22—84no—
545C22C11×#52512yes—
546C22C23×D4×C1111yescharacteristic
547C4—21no—
548C4—24no—
549C4—21no—
550C4—24no—
551C4—24no—
552C4—44no—
553C4—44no—
554C4—44no—
555C4C11×#52512yes—
556C4C22×C11×#4112yes—
557C2—22no—
558C2—41no—
559C2—41no—
560C2—44no—
561C2C2×C11×#52511yescharacteristic
562C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#541C2semidirect
3. C11×#3127C2semidirect
4. C11×#3123C2semidirect
5. C11×#3120C2semidirect
6. C11×#3095C2semidirect
7. C11×#3080C2semidirect
8. C11×#3039C2semidirect
10. C4×C11×#137C2semidirect
11. C11×#2921C2semidirect
17. C11×#541C22semidirect
18. C2×C11×C4⋊Q8C22semidirect
21. C2×C11×#125C22semidirect
31. C2×C4×Q8×C11C22semidirect
36. C11×#484C22semidirect
37. C11×#483C22semidirect
38. C11×#479C22semidirect
39. C11×#478C22semidirect
40. C11×#462C22semidirect
41. C11×#461C22semidirect
45. C11×#441C22semidirect
46. C11×#440C22semidirect
47. C4×C11×Q16C22semidirect
48. C4×C11×SD16C22semidirect
50. C11×#433C22semidirect
51. C11×#428C22semidirect
52. C11×#423C22semidirect
53. C11×#419C22semidirect
56. C4×C11×M16C22semidirect
137. #60569C11direct (N × H)
210. C2×#541C2×C11semidirect
212. #3127C2×C11semidirect
213. #3123C2×C11semidirect
214. #3120C2×C11semidirect
215. #3095C2×C11semidirect
216. #3080C2×C11semidirect
217. #3039C2×C11semidirect
219. C4×#137C2×C11semidirect
220. #2921C2×C11semidirect
271. #541C22×C11semidirect
272. C2×C4⋊Q8C22×C11semidirect
275. C2×#125C22×C11semidirect
285. C2×C4×Q8C22×C11semidirect
290. #484C22×C11semidirect
291. #483C22×C11semidirect
292. #479C22×C11semidirect
293. #478C22×C11semidirect
294. #462C22×C11semidirect
295. #461C22×C11semidirect
299. #441C22×C11semidirect
300. #440C22×C11semidirect
301. C4×Q16C22×C11semidirect
302. C4×SD16C22×C11semidirect
304. #433C22×C11semidirect
305. #428C22×C11semidirect
306. #423C22×C11semidirect
307. #419C22×C11semidirect
310. C4×M16C22×C11semidirect
490. C11#60569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C11×#34282
C11×#31272
C11×#31232
C11×#31202
C11×#30952
C11×#30802
C11×#30392
C11×#30072
C4×C11×#1372
C11×#29212
#6056911