Finite Group Databasebeta

← C11×#24376 #14601569

Subgroups — C11×#24376 #14601569

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic
2C2×C11×#461C212yesmaximal, complemented
3C2×C11×#452C211yesmaximal, characteristic
4C11×#2434C211yesmaximal, characteristic, complemented
5C11×#2339C211yesmaximal, characteristic
6C11×#2056C212yesmaximal, complemented
7C11×#2016C212yesmaximal, complemented
8C11×#1894C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C2×C11×#137—24no—
15C2×C11×#137—28no—
16C22×C11×Q16C2212yes—
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2212yes—
20C22×C11×M16C2211yescharacteristic
21C2×C11×C4⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C11×#461—28no—
25C11×#452—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#395—21no—
34C11×#395—21no—
35C11×#391C2212yes—
36C11×#391C2212yes—
37C11×#386—22no—
38C11×#385—22no—
39C11×#381—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4C2211yescharacteristic
42C2×C11×#95—21no—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—24no—
47C2×C11×#41—42no—
48C2×C11×#41D414yes—
49C22×Q8×C11—21no—
50C22×Q8×C11—24no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—42no—
54C22×Q8×C11C2311yescharacteristic
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11—22no—
62C23×C4×C11C2311yescharacteristic
63C11×#137—232no—
64C2×C11×Q16—24no—
65C2×C11×Q16—24no—
66C2×C11×Q16—22no—
67C2×C11×Q16—24no—
68C2×C11×Q16—42no—
69C2×C11×SD16—24no—
70C2×C11×SD16—24no—
71C2×C11×SD16—22no—
72C2×C11×SD16—24no—
73C2×C11×SD16D418yes—
74C2×C11×M16—22no—
75C2×C11×M16—24no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×C4⋊Q8—24no—
80C11×C4⋊Q8—42no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C4×D4×C11—24no—
84C4×D4×C11—42no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11C2312yes—
95C11×C4⋊C8—24no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#103—24no—
99C11×#103—42no—
100C11×#102—22no—
101C11×C22⋊C8—22no—
102C11×#95—21no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#24376C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—21no—
111C24×C11C2×D411yescharacteristic
112C11×#41—28no—
113C11×#41—44no—
114C11×#41—48no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—48no—
130C2×Q8×C11—44no—
131C2×Q8×C11—42no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—44no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11—42no—
152C22×C4×C11—44no—
153C22×C4×C11—82no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C11×Q16—216no—
161C11×Q16—44no—
162C11×SD16—216no—
163C11×SD16—44no—
164C11×M16—28no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C2×D414yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—44no—
177C11×C4⋊C4—44no—
178C11×C4⋊C4—42no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—81no—
183C42×C11—22no—
184C42×C11—22no—
185C22×#137C2×C1111yescharacteristic
186C2×#461C2×C1112yescomplemented
187C2×#452C2×C1111yescharacteristic
188#2434C2×C1111yescharacteristic, complemented
189#2339C2×C1111yescharacteristic
190#2056C2×C1112yescomplemented
191#2016C2×C1112yescomplemented
192#1894C2×C1111yescharacteristic, complemented
193#1877C2×C1112yescomplemented
194#1851C2×C1111yescharacteristic, complemented
195#1787C2×C1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11#12112yes—
206C23×C11C22×D411yescharacteristic
207Q8×C11—24no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—24no—
211Q8×C11—48no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—42no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—42no—
218D4×C11—22no—
219D4×C11—24no—
220D4×C11—48no—
221D4×C11#12014yes—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—48no—
234C2×C4×C11—48no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—88no—
247C2×C4×C11#12112yes—
248C2×C4×C11#13714yescomplemented
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D412yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)12yes—
253C8×C11—24no—
254C8×C11—41no—
255C8×C11—41no—
256C22×#41C22×C1111yescharacteristic
257C23×Q8C22×C1111yescharacteristic
258C2×#137—24no—
259C2×#137—28no—
260C22×Q16C22×C1112yes—
261C22×Q16C22×C1111yescharacteristic
262C22×SD16C22×C1111yescharacteristic
263C22×SD16C22×C1112yes—
264C22×M16C22×C1111yescharacteristic
265C2×C4⋊Q8C22×C1112yes—
266C2×C22⋊Q8C22×C1111yescharacteristic
267C2×C4×D4C22×C1112yes—
268#461—28no—
269#452—24no—
270C2×C4⋊C8C22×C1112yes—
271C2×#103C22×C1111yescharacteristic
272C2×#103C22×C1112yes—
273C2×#103C22×C1112yes—
274C2×#103C22×C1112yes—
275C2×#102C22×C1111yescharacteristic
276C2×C22⋊C8C22×C1111yescharacteristic
277#395—21no—
278#395—21no—
279#391C22×C1112yes—
280#391C22×C1112yes—
281#386—22no—
282#385—22no—
283#381—21no—
284#380C22×C1111yescharacteristic
285C4×C22⋊C4C22×C1111yescharacteristic
286C2×#95—21no—
287#340C22×C1112yes—
288#336C22×C1112yes—
289C22×C11—22no—
290C22×C11—24no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11C2×#12111yescharacteristic
300C22×C11D4212yes—
301C22×C11C2×#13712yes—
302C22×C11#57711yescharacteristic
303C22×C11#57811yescharacteristic
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—42no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11—81no—
310C4×C11—82no—
311C4×C11—81no—
312C4×C11C2×#12011yescharacteristic
313C4×C11#53411yescharacteristic
314C4×C11#54612yes—
315C2×#41—22no—
316C2×#41—24no—
317C2×#41—42no—
318C2×#41D4×C1114yes—
319C22×Q8—21no—
320C22×Q8—24no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—42no—
324C22×Q8C23×C1111yescharacteristic
325C22×Q8C23×C1112yes—
326C22×Q8C23×C1111yescharacteristic
327C22×D4—21no—
328C22×D4C23×C1111yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—22no—
332C23×C4C23×C1111yescharacteristic
333#137—232no—
334C2×Q16—24no—
335C2×Q16—24no—
336C2×Q16—22no—
337C2×Q16—24no—
338C2×Q16—42no—
339C2×SD16—24no—
340C2×SD16—24no—
341C2×SD16—22no—
342C2×SD16—24no—
343C2×SD16D4×C1118yes—
344C2×M16—22no—
345C2×M16—24no—
346C22×C8C23×C1111yescharacteristic
347C22×C8C23×C1111yescharacteristic
348C22×C8C23×C1112yes—
349C4⋊Q8—24no—
350C4⋊Q8—42no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C4×D4—24no—
354C4×D4—42no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4C23×C1112yes—
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4D4×C1112yes—
364C2×C42C23×C1112yes—
365C4⋊C8—24no—
366#103—22no—
367#103—24no—
368#103—24no—
369#103—42no—
370#102—22no—
371C22⋊C8—22no—
372#95—21no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—22no—
377#95D4×C1111yescharacteristic
378#95D4×C1111yescharacteristic
379C2×C11—42no—
380C2×C11—44no—
381C2×C11#241011yescharacteristic
382C2×C11#303911yescharacteristic
383C2×C11#304611yescharacteristic
384C2×C11#326612yes—
385C2×C11#327612yes—
386C24—21no—
387C24C2×D4×C1111yescharacteristic
388#41—28no—
389#41—44no—
390#41—48no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—28no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—44no—
405C2×Q8—48no—
406C2×Q8—44no—
407C2×Q8—42no—
408C2×Q8C2×D4×C1114yes—
409C2×Q8C2×D4×C1112yes—
410C2×D4—24no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—44no—
414C2×D4C2×D4×C1112yes—
415C2×D4C2×D4×C1114yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—42no—
428C22×C4—44no—
429C22×C4—82no—
430C22×C4C2×D4×C1112yes—
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1112yes—
433C22×C4C2×D4×C1112yes—
434C22×C4C11×#4112yes—
435C22×C4C24×C1111yescharacteristic
436Q16—216no—
437Q16—44no—
438SD16—216no—
439SD16—44no—
440M16—28no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8C2×D4×C1114yes—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—42no—
455C22⋊C4—24no—
456C22⋊C4—44no—
457C22⋊C4—42no—
458C22⋊C4—81no—
459C42—22no—
460C42—22no—
461C11#2437611yescharacteristic, direct product factor, Sylow
462C23—22no—
463C23—24no—
464C23—22no—
465C23—22no—
466C23—21no—
467C23—21no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23C11×#12112yes—
472C23C22×D4×C1111yescharacteristic
473Q8—24no—
474Q8—22no—
475Q8—22no—
476Q8—24no—
477Q8—48no—
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—41no—
482Q8—41no—
483Q8—42no—
484D4—22no—
485D4—24no—
486D4—48no—
487D4C11×#12014yes—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—48no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—88no—
513C2×C4C11×#12112yes—
514C2×C4C11×#13714yescomplemented
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C22×D4×C1112yes—
517C2×C4C2×C11×#4111yescharacteristic
518C2×C4C11×H(5,𝔽2)12yes—
519C8—24no—
520C8—41no—
521C8—41no—
522C22—22no—
523C22—24no—
524C22—22no—
525C22—22no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—42no—
531C22—42no—
532C22C2×C11×#12111yescharacteristic
533C22D42×C1112yes—
534C22C2×C11×#13712yes—
535C22C11×#57711yescharacteristic
536C22C11×#57811yescharacteristic
537C4—22no—
538C4—24no—
539C4—42no—
540C4—44no—
541C4—42no—
542C4—81no—
543C4—82no—
544C4—81no—
545C4C2×C11×#12011yescharacteristic
546C4C11×#53411yescharacteristic
547C4C11×#54612yes—
548C2—42no—
549C2—44no—
550C2C11×#241011yescharacteristic
551C2C11×#303911yescharacteristic
552C2C11×#304611yescharacteristic
553C2C11×#326612yes—
554C2C11×#327612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#461C2semidirect
4. C11×#2434C2semidirect
6. C11×#2056C2semidirect
7. C11×#2016C2semidirect
8. C11×#1894C2semidirect
9. C11×#1877C2semidirect
10. C11×#1851C2semidirect
11. C11×#1787C2semidirect
109. #24376C11direct (N × H)
186. C2×#461C2×C11semidirect
188. #2434C2×C11semidirect
190. #2056C2×C11semidirect
191. #2016C2×C11semidirect
192. #1894C2×C11semidirect
193. #1877C2×C11semidirect
194. #1851C2×C11semidirect
195. #1787C2×C11semidirect
248. C2×C4×C11#137semidirect
461. C11#24376direct (N × H)
514. C2×C4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4612
C2×C11×#4522
C11×#24342
C11×#23392
C11×#20562
C11×#20162
C11×#18942
C11×#18772
C11×#18512
C11×#17872
#2437611