Finite Group Databasebeta

← C11×#20947 #14598140

Subgroups — C11×#20947 #14598140

Order 2816.

1708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C11×#3449C211yesmaximal, characteristic
3C2×C11×#421C212yesmaximal, complemented
4C2×C11×#410C211yesmaximal, characteristic, complemented
5C11×#1884C218yesmaximal, complemented
6C11×#1733C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C22×C11×#41C2211yescharacteristic
9C11×#568—22no—
10C11×#568—24no—
11C11×#568C2214yescomplemented
12C2×C11×#131—24no—
13C22×C11×M16—22no—
14C22×C11×M16C2212yes—
15C11×#537—22no—
16C11×#536C412yescomplemented
17C11×#536C412yescomplemented
18C11×#535C412yescomplemented
19C11×#535C412yescomplemented
20C11×#534—22no—
21C11×#532C2214yes—
22C11×#525—22no—
23C11×#525—22no—
24C2×C11×#117C2212yes—
25C2×C11×#117C2211yescharacteristic
26C11×#421—24no—
27C11×#421C2218yescomplemented
28C2×C11×#104—24no—
29C11×#410—22no—
30C11×#410C2214yescomplemented
31C2×C11×#99—22no—
32C11×#339C2218yescomplemented
33C2×C11×#41—22no—
34C2×C11×#41—22no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41C2×C412yes—
44C2×C11×#41C2×C412yes—
45C2×C11×#41D412yes—
46C2×C11×#41D412yes—
47C2×C11×#41C2312yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11C2×C411yescharacteristic
50C22×Q8×C11C2×C411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11C2×C411yescharacteristic
53C22×D4×C11C2×C411yescharacteristic
54C22×D4×C11D412yes—
55C23×C4×C11—21no—
56C23×C4×C11D412yes—
57C23×C4×C11C2311yescharacteristic
58C11×#131—216no—
59C11×#131—216no—
60C2×C11×M16—24no—
61C2×C11×M16—28no—
62C2×C11×M16—22no—
63C2×C11×M16—28no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16D414yescomplemented
67C2×C11×M16D414yescomplemented
68C2×C11×M16C2314yes—
69C22×C8×C11—24no—
70C22×C8×C11—22no—
71C11×C4⋊Q8C2×C414yescomplemented
72C11×#127C2×C414yescomplemented
73C11×#124C2×C414yescomplemented
74C11×#124C2×C414yescomplemented
75C11×#123—24no—
76C11×#123—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×#121—24no—
80C11×#121—28no—
81C11×#121—24no—
82C11×#120—24no—
83C11×#120—24no—
84C4×D4×C11—28no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117—22no—
88C11×#117—22no—
89C11×#117—22no—
90C11×#117C2×C412yes—
91C11×#117C2×C412yes—
92C11×#117C2314yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C42×C11—22no—
98C2×C42×C11C2312yes—
99C11×#104—216no—
100C11×#99—28no—
101#20947C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11C22⋊C412yes—
104C24×C11C2×D411yescharacteristic
105C11×#41—24no—
106C11×#41—24no—
107C11×#41—24no—
108C11×#41—24no—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—41no—
122C11×#41—41no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11C22⋊C412yes—
129C2×Q8×C11C22×C412yes—
130C2×Q8×C11C22×C412yes—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—28no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11C22⋊C414yes—
144C2×D4×C11C22⋊C412yes—
145C2×D4×C11C22×C412yes—
146C2×D4×C11C22×C412yes—
147C2×D4×C11C2×D414yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22⋊C414yes—
160C22×C4×C11C22⋊C412yes—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C11×M16—216no—
173C11×M16—24no—
174C11×M16—24no—
175C11×M16—24no—
176C11×M16C2×D418yes—
177C2×C8×C11—216no—
178C2×C8×C11—24no—
179C2×C8×C11—24no—
180C2×C8×C11—24no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—42no—
192C42×C11—22no—
193C42×C11—24no—
194C42×C11—42no—
195C42×C11C22×C414yes—
196C2×#568C2×C1111yescharacteristic, complemented
197#3449C2×C1111yescharacteristic
198C2×#421C2×C1112yescomplemented
199C2×#410C2×C1111yescharacteristic, complemented
200#1884C2×C1118yescomplemented
201#1733C2×C1112yescomplemented
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—81no—
207C23×C11—82no—
208C23×C11—82no—
209C23×C11C2×C22⋊C414yes—
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11#12112yes—
213C23×C11#12112yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—24no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—28no—
221D4×C11—28no—
222D4×C11—24no—
223D4×C11—24no—
224D4×C11—24no—
225D4×C11—44no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—41no—
230D4×C11—88no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—82no—
245C2×C4×C11—84no—
246C2×C4×C11C2×C22⋊C414yes—
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C4×D412yes—
250C2×C4×C11C4×D412yes—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C4×D412yes—
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12012yes—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12312yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4112yes—
265C8×C11—28no—
266C22×#41C22×C1111yescharacteristic
267C22×#41C22×C1111yescharacteristic
268#568—22no—
269#568—24no—
270#568C22×C1114yescomplemented
271C2×#131—24no—
272C22×M16—22no—
273C22×M16C22×C1112yes—
274#537—22no—
275#536C4×C1112yescomplemented
276#536C4×C1112yescomplemented
277#535C4×C1112yescomplemented
278#535C4×C1112yescomplemented
279#534—22no—
280#532C22×C1114yes—
281#525—22no—
282#525—22no—
283C2×#117C22×C1112yes—
284C2×#117C22×C1111yescharacteristic
285#421—24no—
286#421C22×C1118yescomplemented
287C2×#104—24no—
288#410—22no—
289#410C22×C1114yescomplemented
290C2×#99—22no—
291#339C22×C1118yescomplemented
292C22×C11—24no—
293C22×C11—42no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—82no—
303C22×C11—84no—
304C22×C11#38611yescharacteristic
305C22×C11#38611yescharacteristic
306C22×C11#38612yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C2×#12112yes—
309C4×C11—24no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—84no—
313C4×C11#38611yescharacteristic
314C4×C11#38611yescharacteristic
315C4×C11#38612yes—
316C4×C11C2×C4×D412yes—
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12311yescharacteristic
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41C2×C4×C1112yes—
330C2×#41C2×C4×C1112yes—
331C2×#41D4×C1112yes—
332C2×#41D4×C1112yes—
333C2×#41C23×C1112yes—
334C2×#41C23×C1112yes—
335C22×Q8C2×C4×C1111yescharacteristic
336C22×Q8C2×C4×C1111yescharacteristic
337C22×D4—21no—
338C22×D4C2×C4×C1111yescharacteristic
339C22×D4C2×C4×C1111yescharacteristic
340C22×D4D4×C1112yes—
341C23×C4—21no—
342C23×C4D4×C1112yes—
343C23×C4C23×C1111yescharacteristic
344#131—216no—
345#131—216no—
346C2×M16—24no—
347C2×M16—28no—
348C2×M16—22no—
349C2×M16—28no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16D4×C1114yescomplemented
353C2×M16D4×C1114yescomplemented
354C2×M16C23×C1114yes—
355C22×C8—24no—
356C22×C8—22no—
357C4⋊Q8C2×C4×C1114yescomplemented
358#127C2×C4×C1114yescomplemented
359#124C2×C4×C1114yescomplemented
360#124C2×C4×C1114yescomplemented
361#123—24no—
362#123—24no—
363C22⋊Q8—24no—
364C22⋊Q8—24no—
365#121—24no—
366#121—28no—
367#121—24no—
368#120—24no—
369#120—24no—
370C4×D4—28no—
371#117—21no—
372#117—21no—
373#117—22no—
374#117—22no—
375#117—22no—
376#117C2×C4×C1112yes—
377#117C2×C4×C1112yes—
378#117C23×C1114yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C42—22no—
384C2×C42C23×C1112yes—
385#104—216no—
386#99—28no—
387C2×C11—21no—
388C2×C11—22no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—22no—
392C2×C11—44no—
393C2×C11—82no—
394C2×C11C2×#38611yescharacteristic
395C24—21no—
396C24C11×C22⋊C412yes—
397C24C2×D4×C1111yescharacteristic
398#41—24no—
399#41—24no—
400#41—24no—
401#41—24no—
402#41—24no—
403#41—24no—
404#41—24no—
405#41—24no—
406#41—24no—
407#41—24no—
408#41—24no—
409#41—24no—
410#41—41no—
411#41—41no—
412#41—42no—
413#41—42no—
414#41—41no—
415#41—41no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8C11×C22⋊C412yes—
422C2×Q8C22×C4×C1112yes—
423C2×Q8C22×C4×C1112yes—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—28no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4C11×C22⋊C414yes—
437C2×D4C11×C22⋊C412yes—
438C2×D4C22×C4×C1112yes—
439C2×D4C22×C4×C1112yes—
440C2×D4C2×D4×C1114yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4C11×C22⋊C414yes—
453C22×C4C11×C22⋊C412yes—
454C22×C4C22×C4×C1111yescharacteristic
455C22×C4C22×C4×C1111yescharacteristic
456C22×C4C2×D4×C1114yes—
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1112yes—
461C22×C4C2×D4×C1112yes—
462C22×C4C11×#4112yes—
463C22×C4C11×#4112yes—
464C22×C4C24×C1111yescharacteristic
465M16—216no—
466M16—24no—
467M16—24no—
468M16—24no—
469M16C2×D4×C1118yes—
470C2×C8—216no—
471C2×C8—24no—
472C2×C8—24no—
473C2×C8—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—28no—
477C4⋊C4—24no—
478C4⋊C4—42no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—42no—
485C42—22no—
486C42—24no—
487C42—42no—
488C42C22×C4×C1114yes—
489C11#2094711yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—81no—
495C23—82no—
496C23—82no—
497C23C2×C11×C22⋊C414yes—
498C23C2×C11×C22⋊C411yescharacteristic
499C23C2×C11×C22⋊C411yescharacteristic
500C23C11×#12112yes—
501C23C11×#12112yes—
502C23C22×D4×C1111yescharacteristic
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8—41no—
507Q8—41no—
508D4—28no—
509D4—28no—
510D4—24no—
511D4—24no—
512D4—24no—
513D4—44no—
514D4—42no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—88no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—82no—
533C2×C4—84no—
534C2×C4C2×C11×C22⋊C414yes—
535C2×C4C2×C11×C22⋊C411yescharacteristic
536C2×C4C2×C11×C22⋊C411yescharacteristic
537C2×C4C4×D4×C1112yes—
538C2×C4C4×D4×C1112yes—
539C2×C4C4×D4×C1112yes—
540C2×C4C4×D4×C1112yes—
541C2×C4C11×#12011yescharacteristic
542C2×C4C11×#12012yes—
543C2×C4C11×#12011yescharacteristic
544C2×C4C11×#12112yes—
545C2×C4C11×#12112yes—
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12311yescharacteristic
548C2×C4C11×#12312yes—
549C2×C4C23×C4×C1111yescharacteristic
550C2×C4C22×D4×C1112yes—
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C2×C11×#4112yes—
553C8—28no—
554C22—24no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—42no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—42no—
564C22—82no—
565C22—84no—
566C22C11×#38611yescharacteristic
567C22C11×#38611yescharacteristic
568C22C11×#38612yes—
569C22C22×C11×C22⋊C411yescharacteristic
570C22C2×C11×#12112yes—
571C4—24no—
572C4—44no—
573C4—42no—
574C4—84no—
575C4C11×#38611yescharacteristic
576C4C11×#38611yescharacteristic
577C4C11×#38612yes—
578C4C2×C4×D4×C1112yes—
579C4C2×C11×#12011yescharacteristic
580C4C2×C11×#12311yescharacteristic
581C2—21no—
582C2—22no—
583C2—21no—
584C2—21no—
585C2—22no—
586C2—44no—
587C2—82no—
588C2C2×C11×#38611yescharacteristic
subgroupG/H
centerC4×C11C2×#120
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC2×C11C2×#386
prime radicalC11×#3449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
3. C2×C11×#421C2semidirect
4. C2×C11×#410C2semidirect
5. C11×#1884C2semidirect
6. C11×#1733C2semidirect
11. C11×#568C22semidirect
16. C11×#536C4semidirect
17. C11×#536C4semidirect
18. C11×#535C4semidirect
19. C11×#535C4semidirect
27. C11×#421C22semidirect
30. C11×#410C22semidirect
32. C11×#339C22semidirect
66. C2×C11×M16D4semidirect
67. C2×C11×M16D4semidirect
71. C11×C4⋊Q8C2×C4semidirect
72. C11×#127C2×C4semidirect
73. C11×#124C2×C4semidirect
74. C11×#124C2×C4semidirect
101. #20947C11direct (N × H)
196. C2×#568C2×C11semidirect
198. C2×#421C2×C11semidirect
199. C2×#410C2×C11semidirect
200. #1884C2×C11semidirect
201. #1733C2×C11semidirect
270. #568C22×C11semidirect
275. #536C4×C11semidirect
276. #536C4×C11semidirect
277. #535C4×C11semidirect
278. #535C4×C11semidirect
286. #421C22×C11semidirect
289. #410C22×C11semidirect
291. #339C22×C11semidirect
352. C2×M16D4×C11semidirect
353. C2×M16D4×C11semidirect
357. C4⋊Q8C2×C4×C11semidirect
358. #127C2×C4×C11semidirect
359. #124C2×C4×C11semidirect
360. #124C2×C4×C11semidirect
489. C11#20947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C11×#34492
C2×C11×#4212
C2×C11×#4102
C11×#18842
C11×#17332
#2094711