Finite Group Databasebeta

← C11×#21062 #14598255

Subgroups — C11×#21062 #14598255

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#417C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C11×#2274C211yesmaximal, characteristic, complemented
6C11×#1928C212yesmaximal, complemented
7C11×#1927C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1925C212yesmaximal, complemented
10C2×C11×#340C211yesmaximal, characteristic, complemented
11C11×#1729C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#428—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C11×#417C418yescomplemented
23C11×#416—24no—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2212yes—
30C11×#391C2212yes—
31C11×#390C2212yes—
32C11×#386—22no—
33C11×#380—21no—
34C11×#380—21no—
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C22⋊C4—22no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41C2×C414yes—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C2×C11×M16—22no—
58C2×C11×M16—22no—
59C2×C11×M16C2×C414yes—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2312yes—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117D414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2×C414yes—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—21no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11C2312yes—
90C11×#107—24no—
91C11×#106—24no—
92C11×#103—22no—
93C11×#103—22no—
94C11×#103C2×C418yescomplemented
95C11×#102—22no—
96C11×#102—22no—
97C11×#102C2×C418yescomplemented
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—22no—
101C11×#95—22no—
102#21062C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—44no—
108C11×#41—44no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—24no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11C22×C412yes—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—81no—
135C22×C4×C11—81no—
136C22×C4×C11—81no—
137C22×C4×C11—81no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C11×M16—28no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—44no—
158C2×C8×C11C22×C414yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4C22×C414yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—82no—
174C11×C22⋊C4—82no—
175C42×C11—24no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—82no—
179C42×C11—82no—
180C2×#428C2×C1111yescharacteristic, complemented
181C2×#417C2×C1111yescharacteristic
182C2×#416C2×C1111yescharacteristic
183#2311C2×C1111yescharacteristic
184#2274C2×C1111yescharacteristic, complemented
185#1928C2×C1112yescomplemented
186#1927C2×C1112yescomplemented
187#1926C2×C1112yescomplemented
188#1925C2×C1112yescomplemented
189C2×#340C2×C1111yescharacteristic, complemented
190#1729C2×C1111yescharacteristic, complemented
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11C4×D412yes—
203C23×C11#12112yes—
204C23×C11#12312yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—48no—
213D4×C11—41no—
214D4×C11—41no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11—84no—
239C2×C4×C11#11714yes—
240C2×C4×C11C4×D414yes—
241C2×C4×C11C4×D412yes—
242C2×C4×C11#12112yes—
243C2×C4×C11#12312yes—
244C2×C4×C11#12414yes—
245C2×C4×C11#12614yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C8×C11—24no—
253C8×C11—41no—
254C8×C11—41no—
255C22×#41C22×C1111yescharacteristic
256C22×M16C22×C1111yescharacteristic
257C23×C8C22×C1111yescharacteristic
258C2×#117C22×C1111yescharacteristic
259C2×#117C22×C1111yescharacteristic
260C22×C4⋊C4C22×C1111yescharacteristic
261C22×C4⋊C4C22×C1111yescharacteristic
262#428—24no—
263C2×#107C22×C1112yes—
264C2×#106C22×C1112yes—
265#417C4×C1118yescomplemented
266#416—24no—
267C2×#103C22×C1111yescharacteristic
268C2×#103C22×C1111yescharacteristic
269C2×#103C22×C1112yes—
270C2×#102C22×C1111yescharacteristic
271C2×#102C22×C1111yescharacteristic
272C2×#102C22×C1112yes—
273#391C22×C1112yes—
274#390C22×C1112yes—
275#386—22no—
276#380—21no—
277#380—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4C22×C1112yes—
281C4×C4⋊C4C22×C1112yes—
282C4×C22⋊C4—22no—
283#340C22×C1112yes—
284#340C22×C1112yes—
285#336C22×C1112yes—
286#336C22×C1112yes—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11#38814yes—
301C22×C11C2×C4×D411yescharacteristic
302C22×C11C2×#12111yescharacteristic
303C22×C11C2×#12311yescharacteristic
304C22×C11#57611yescharacteristic
305C22×C11#57711yescharacteristic
306C22×C11#57711yescharacteristic
307C22×C11#57811yescharacteristic
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—82no—
315C4×C11#38814yes—
316C4×C11C2×#11711yescharacteristic
317C4×C11C2×C4×D411yescharacteristic
318C4×C11C2×#12411yescharacteristic
319C4×C11C2×#12611yescharacteristic
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41C2×C4×C1114yes—
326C22×Q8C23×C1111yescharacteristic
327C22×D4—21no—
328C22×D4C23×C1111yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4C23×C1111yescharacteristic
333C2×M16—22no—
334C2×M16—22no—
335C2×M16C2×C4×C1114yes—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8C23×C1111yescharacteristic
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1112yes—
342#117—22no—
343#117—22no—
344#117—22no—
345#117D4×C1114yes—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4C2×C4×C1114yes—
352C2×C4⋊C4D4×C1111yescharacteristic
353C2×C4⋊C4D4×C1111yescharacteristic
354C2×C4⋊C4C23×C1112yes—
355C2×C4⋊C4C23×C1112yes—
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4D4×C1112yes—
362C2×C42—21no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42C23×C1112yes—
366#107—24no—
367#106—24no—
368#103—22no—
369#103—22no—
370#103C2×C4×C1118yescomplemented
371#102—22no—
372#102—22no—
373#102C2×C4×C1118yescomplemented
374#95—22no—
375#95—22no—
376#95—22no—
377#95—22no—
378C2×C11—24no—
379C2×C11—82no—
380C2×C11C2×#38811yescharacteristic
381C2×C11#294611yescharacteristic
382C2×C11#294711yescharacteristic
383C2×C11#304511yescharacteristic
384C2×C11#304611yescharacteristic
385C2×C11#309811yescharacteristic
386C2×C11#309911yescharacteristic
387C24—21no—
388C24C2×D4×C1111yescharacteristic
389#41—28no—
390#41—28no—
391#41—44no—
392#41—44no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8C22×C4×C1112yes—
399C2×D4—24no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4C22×C4×C1112yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—81no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4C22×C4×C1112yes—
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1112yes—
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1112yes—
427C22×C4C11×#4112yes—
428C22×C4C11×#4112yes—
429C22×C4C11×#4112yes—
430C22×C4C11×#4112yes—
431C22×C4C24×C1111yescharacteristic
432M16—28no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—44no—
442C2×C8C22×C4×C1114yes—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4C22×C4×C1114yes—
453C4⋊C4C2×D4×C1112yes—
454C4⋊C4C2×D4×C1112yes—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—82no—
458C22⋊C4—82no—
459C42—24no—
460C42—22no—
461C42—22no—
462C42—82no—
463C42—82no—
464C11#2106211yescharacteristic, direct product factor, Sylow
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C4×D4×C1112yes—
477C23C11×#12112yes—
478C23C11×#12312yes—
479C23C22×D4×C1111yescharacteristic
480Q8—22no—
481Q8—22no—
482Q8—41no—
483Q8—41no—
484D4—22no—
485D4—22no—
486D4—48no—
487D4—41no—
488D4—41no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—84no—
512C2×C4—84no—
513C2×C4C11×#11714yes—
514C2×C4C4×D4×C1114yes—
515C2×C4C4×D4×C1112yes—
516C2×C4C11×#12112yes—
517C2×C4C11×#12312yes—
518C2×C4C11×#12414yes—
519C2×C4C11×#12614yes—
520C2×C4C23×C4×C1111yescharacteristic
521C2×C4C22×D4×C1111yescharacteristic
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C2×C11×#4111yescharacteristic
524C2×C4C2×C11×#4111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C8—24no—
527C8—41no—
528C8—41no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22C11×#38814yes—
543C22C2×C4×D4×C1111yescharacteristic
544C22C2×C11×#12111yescharacteristic
545C22C2×C11×#12311yescharacteristic
546C22C11×#57611yescharacteristic
547C22C11×#57711yescharacteristic
548C22C11×#57711yescharacteristic
549C22C11×#57811yescharacteristic
550C4—44no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—82no—
557C4C11×#38814yes—
558C4C2×C11×#11711yescharacteristic
559C4C2×C4×D4×C1111yescharacteristic
560C4C2×C11×#12411yescharacteristic
561C4C2×C11×#12611yescharacteristic
562C2—24no—
563C2—82no—
564C2C2×C11×#38811yescharacteristic
565C2C11×#294611yescharacteristic
566C2C11×#294711yescharacteristic
567C2C11×#304511yescharacteristic
568C2C11×#304611yescharacteristic
569C2C11×#309811yescharacteristic
570C2C11×#309911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C11×#2274C2semidirect
6. C11×#1928C2semidirect
7. C11×#1927C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C2×C11×#340C2semidirect
11. C11×#1729C2semidirect
22. C11×#417C4semidirect
94. C11×#103C2×C4semidirect
97. C11×#102C2×C4semidirect
102. #21062C11direct (N × H)
180. C2×#428C2×C11semidirect
184. #2274C2×C11semidirect
185. #1928C2×C11semidirect
186. #1927C2×C11semidirect
187. #1926C2×C11semidirect
188. #1925C2×C11semidirect
189. C2×#340C2×C11semidirect
190. #1729C2×C11semidirect
265. #417C4×C11semidirect
370. #103C2×C4×C11semidirect
373. #102C2×C4×C11semidirect
464. C11#21062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4172
C2×C11×#4162
C11×#23112
C11×#22742
C11×#19282
C11×#19272
C11×#19262
C11×#19252
C2×C11×#3402
C11×#17292
#2106211