Finite Group Databasebeta

← C11×#10931 #14588124

Subgroups — C11×#10931 #14588124

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#102C212yesmaximal
2C2×C11×#390C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C11×#340C212yesmaximal, complemented
5C2×C11×#336C211yesmaximal, characteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C23×C8×C11C2212yes—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C22⋊C4—21no—
11C22×C11×C22⋊C4—21no—
12C22×C42×C11—21no—
13C22×C42×C11C2211yescharacteristic
14C2×C11×#102—24no—
15C2×C11×#102—24no—
16C2×C11×#102C418yescomplemented
17C11×#390—22no—
18C11×#390C414yescomplemented
19C4×C11×C4⋊C4—24no—
20C2×C11×#95—21no—
21C11×#340—24no—
22C11×#336—22no—
23C25×C11—21no—
24C22×D4×C11—22no—
25C22×D4×C11—22no—
26C22×D4×C11—21no—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11C2×C412yes—
31C22×D4×C11C2×C414yes—
32C23×C4×C11—22no—
33C23×C4×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—22no—
38C22×C8×C11—22no—
39C22×C8×C11—22no—
40C22×C8×C11—22no—
41C22×C8×C11—22no—
42C22×C8×C11—22no—
43C22×C8×C11C2×C414yes—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C4⋊C4D414yes—
53C2×C11×C4⋊C4D414yes—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—44no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C42×C11—22no—
60C2×C42×C11—22no—
61C2×C42×C11—24no—
62C2×C42×C11—42no—
63C2×C42×C11—42no—
64C2×C42×C11C2×C412yes—
65C2×C42×C11D412yes—
66C11×#102—216no—
67C11×#95—24no—
68#10931C1111yesmaximal, characteristic, direct product factor, Sylow
69C24×C11—22no—
70C24×C11—24no—
71C24×C11—41no—
72C24×C11—42no—
73C24×C11—41no—
74C24×C11—41no—
75C24×C11—41no—
76C24×C11—42no—
77C24×C11—42no—
78C24×C11—41no—
79C24×C11—41no—
80C24×C11C2×D411yescharacteristic
81C2×D4×C11—24no—
82C2×D4×C11—24no—
83C2×D4×C11—22no—
84C2×D4×C11—24no—
85C2×D4×C11—24no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—24no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11C4214yescomplemented
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11—42no—
117C22×C4×C11C22⋊C412yes—
118C22×C4×C11C22⋊C412yes—
119C22×C4×C11D812yes—
120C22×C4×C11SD1612yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C2×C8×C11—24no—
130C2×C8×C11—24no—
131C2×C8×C11—24no—
132C2×C8×C11—42no—
133C2×C8×C11—42no—
134C2×C8×C11—42no—
135C2×C8×C11—42no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4C22⋊C418yescomplemented
143C11×C22⋊C4—48no—
144C11×C22⋊C4—48no—
145C42×C11—24no—
146C42×C11—24no—
147C42×C11—48no—
148C22×#102C2×C1112yes—
149C2×#390C2×C1111yescharacteristic
150C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
151C2×#340C2×C1112yescomplemented
152C2×#336C2×C1111yescharacteristic, complemented
153C23×C11—24no—
154C23×C11—42no—
155C23×C11—44no—
156C23×C11—44no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—44no—
163C23×C11—44no—
164C23×C11—44no—
165C23×C11—44no—
166C23×C11—81no—
167C23×C11—81no—
168C23×C11—82no—
169C23×C11—82no—
170C23×C11—82no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11—81no—
174C23×C11—81no—
175C23×C11—82no—
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11C4×D412yes—
178C23×C11#12011yescharacteristic
179C23×C11#12112yes—
180C23×C11#12311yescharacteristic
181C23×C11C2×D811yescharacteristic
182C23×C11C2×SD1611yescharacteristic
183C23×C11#13512yes—
184C23×C11AGL(1,ℤ/8)11yescharacteristic
185C23×C11AGL(1,ℤ/8)12yes—
186C23×C11#13711yescharacteristic
187D4×C11—28no—
188D4×C11—44no—
189D4×C11—44no—
190D4×C11—44no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—44no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—82no—
213C2×C4×C11—82no—
214C2×C4×C11#10214yescomplemented
215C2×C4×C11C2×C4211yescharacteristic
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11#11712yes—
218C2×C4×C11#11711yescharacteristic
219C2×C4×C11C4×D412yes—
220C2×C4×C11C4×D412yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C4×D412yes—
223C2×C4×C11C4×D412yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11#12312yes—
227C2×C4×C11#12411yescharacteristic
228C2×C4×C11#12412yes—
229C2×C4×C11#12612yes—
230C2×C4×C11#12711yescharacteristic
231C8×C11—44no—
232C23×D4C22×C1111yescharacteristic
233C23×C8C22×C1112yes—
234C22×C4⋊C4C22×C1111yescharacteristic
235C22×C4⋊C4C22×C1112yes—
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C42—21no—
239C22×C42C22×C1111yescharacteristic
240C2×#102—24no—
241C2×#102—24no—
242C2×#102C4×C1118yescomplemented
243#390—22no—
244#390C4×C1114yescomplemented
245C4×C4⋊C4—24no—
246C2×#95—21no—
247#340—24no—
248#336—22no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11—44no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11—84no—
255C22×C11—84no—
256C22×C11—84no—
257C22×C11—84no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11C4×C22⋊C411yescharacteristic
261C22×C11#38611yescharacteristic
262C22×C11#38612yes—
263C22×C11#38812yes—
264C22×C11#39011yescharacteristic
265C22×C11C2×#10211yescharacteristic
266C22×C11#41611yescharacteristic
267C22×C11#41711yescharacteristic
268C22×C11#41811yescharacteristic
269C22×C11C4×D812yes—
270C22×C11C4×SD1612yes—
271C22×C11#44012yes—
272C22×C11#44212yes—
273C22×C11#44711yescharacteristic
274C22×C11#44811yescharacteristic
275C22×C11#44912yes—
276C22×C11#45912yes—
277C22×C11#46012yes—
278C22×C11#46312yes—
279C22×C11#46412yes—
280C22×C11#48011yescharacteristic
281C22×C11#48111yescharacteristic
282C22×C11#48212yes—
283C4×C11—24no—
284C4×C11—42no—
285C4×C11—48no—
286C4×C11—82no—
287C4×C11C4×C22⋊C412yes—
288C4×C11#38812yes—
289C4×C11#38812yes—
290C4×C11#39012yes—
291C25—21no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4C2×C4×C1112yes—
299C22×D4C2×C4×C1114yes—
300C23×C4—22no—
301C23×C4—21no—
302C23×C4D4×C1111yescharacteristic
303C23×C4D4×C1111yescharacteristic
304C23×C4C23×C1111yescharacteristic
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8C2×C4×C1114yes—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4C2×C4×C1112yes—
319C2×C4⋊C4C2×C4×C1114yes—
320C2×C4⋊C4D4×C1114yes—
321C2×C4⋊C4D4×C1114yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—24no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42C2×C4×C1112yes—
333C2×C42D4×C1112yes—
334#102—216no—
335#95—24no—
336C2×C11—84no—
337C2×C11#143711yescharacteristic
338C2×C11C4×#10211yescharacteristic
339C2×C11#176211yescharacteristic
340C2×C11#187411yescharacteristic
341C2×C11#187511yescharacteristic
342C2×C11#187912yes—
343C2×C11#188012yes—
344C2×C11#192512yes—
345C2×C11#192612yes—
346C2×C11#198211yescharacteristic
347C2×C11#198311yescharacteristic
348C24—22no—
349C24—24no—
350C24—41no—
351C24—42no—
352C24—41no—
353C24—41no—
354C24—41no—
355C24—42no—
356C24—42no—
357C24—41no—
358C24—41no—
359C24C2×D4×C1111yescharacteristic
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—24no—
367C2×D4—24no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4C42×C1114yescomplemented
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C11×C22⋊C412yes—
397C22×C4C11×C22⋊C412yes—
398C22×C4C11×D812yes—
399C22×C4C11×SD1612yes—
400C22×C4C22×C4×C1112yes—
401C22×C4C22×C4×C1111yescharacteristic
402C22×C4C2×D4×C1112yes—
403C22×C4C2×D4×C1112yes—
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C11×#4112yes—
406C22×C4C11×#4112yes—
407C22×C4C11×#4112yes—
408C2×C8—24no—
409C2×C8—24no—
410C2×C8—24no—
411C2×C8—42no—
412C2×C8—42no—
413C2×C8—42no—
414C2×C8—42no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C11×C22⋊C418yescomplemented
422C22⋊C4—48no—
423C22⋊C4—48no—
424C42—24no—
425C42—24no—
426C42—48no—
427C11#1093111yescharacteristic, direct product factor, Sylow
428C23—24no—
429C23—42no—
430C23—44no—
431C23—44no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—44no—
438C23—44no—
439C23—44no—
440C23—44no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—81no—
449C23—81no—
450C23—82no—
451C23C2×C11×C22⋊C411yescharacteristic
452C23C4×D4×C1112yes—
453C23C11×#12011yescharacteristic
454C23C11×#12112yes—
455C23C11×#12311yescharacteristic
456C23C2×C11×D811yescharacteristic
457C23C2×C11×SD1611yescharacteristic
458C23C11×#13512yes—
459C23C11×AGL(1,ℤ/8)11yescharacteristic
460C23C11×AGL(1,ℤ/8)12yes—
461C23C11×#13711yescharacteristic
462D4—28no—
463D4—44no—
464D4—44no—
465D4—44no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—28no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4C11×#10214yescomplemented
490C2×C4C2×C42×C1111yescharacteristic
491C2×C4C2×C11×C22⋊C412yes—
492C2×C4C11×#11712yes—
493C2×C4C11×#11711yescharacteristic
494C2×C4C4×D4×C1112yes—
495C2×C4C4×D4×C1112yes—
496C2×C4C4×D4×C1112yes—
497C2×C4C4×D4×C1112yes—
498C2×C4C4×D4×C1112yes—
499C2×C4C11×#12112yes—
500C2×C4C11×#12112yes—
501C2×C4C11×#12312yes—
502C2×C4C11×#12411yescharacteristic
503C2×C4C11×#12412yes—
504C2×C4C11×#12612yes—
505C2×C4C11×#12711yescharacteristic
506C8—44no—
507C22—44no—
508C22—44no—
509C22—44no—
510C22—82no—
511C22—82no—
512C22—84no—
513C22—84no—
514C22—84no—
515C22—84no—
516C22—82no—
517C22—82no—
518C22C4×C11×C22⋊C411yescharacteristic
519C22C11×#38611yescharacteristic
520C22C11×#38612yes—
521C22C11×#38812yes—
522C22C11×#39011yescharacteristic
523C22C2×C11×#10211yescharacteristic
524C22C11×#41611yescharacteristic
525C22C11×#41711yescharacteristic
526C22C11×#41811yescharacteristic
527C22C4×C11×D812yes—
528C22C4×C11×SD1612yes—
529C22C11×#44012yes—
530C22C11×#44212yes—
531C22C11×#44711yescharacteristic
532C22C11×#44811yescharacteristic
533C22C11×#44912yes—
534C22C11×#45912yes—
535C22C11×#46012yes—
536C22C11×#46312yes—
537C22C11×#46412yes—
538C22C11×#48011yescharacteristic
539C22C11×#48111yescharacteristic
540C22C11×#48212yes—
541C4—24no—
542C4—42no—
543C4—48no—
544C4—82no—
545C4C4×C11×C22⋊C412yes—
546C4C11×#38812yes—
547C4C11×#38812yes—
548C4C11×#39012yes—
549C2—84no—
550C2C11×#143711yescharacteristic
551C2C4×C11×#10211yescharacteristic
552C2C11×#176211yescharacteristic
553C2C11×#187411yescharacteristic
554C2C11×#187511yescharacteristic
555C2C11×#187912yes—
556C2C11×#188012yes—
557C2C11×#192512yes—
558C2C11×#192612yes—
559C2C11×#198211yescharacteristic
560C2C11×#198311yescharacteristic
subgroupG/H
center, socleC24×C11C2×D4
commutatorC2×C4C2×C42×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×C4⋊C4C2semidirect
4. C2×C11×#340C2semidirect
5. C2×C11×#336C2semidirect
16. C2×C11×#102C4semidirect
18. C11×#390C4semidirect
68. #10931C11direct (N × H)
96. C2×D4×C11C42semidirect
142. C11×C4⋊C4C22⋊C4semidirect
150. C2×C4×C4⋊C4C2×C11semidirect
151. C2×#340C2×C11semidirect
152. C2×#336C2×C11semidirect
214. C2×C4×C11#102semidirect
242. C2×#102C4×C11semidirect
244. #390C4×C11semidirect
375. C2×D4C42×C11semidirect
421. C4⋊C4C11×C22⋊C4semidirect
427. C11#10931direct (N × H)
489. C2×C4C11×#102semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1022
C2×C11×#3902
C2×C4×C11×C4⋊C42
C2×C11×#3402
C2×C11×#3362
#1093111