Finite Group Databasebeta

← C11×#24374 #14601567

Subgroups — C11×#24374 #14601567

Order 2816.

1396 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic
2C2×C11×#462C212yesmaximal, complemented
3C2×C11×#452C211yesmaximal, characteristic
4C11×#2434C211yesmaximal, characteristic, complemented
5C11×#2341C211yesmaximal, characteristic
6C11×#2055C212yesmaximal, complemented
7C11×#2013C212yesmaximal, complemented
8C11×#1894C211yesmaximal, characteristic, complemented
9C11×#1878C212yesmaximal, 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×Q16C2211yescharacteristic
17C22×C11×Q16C2212yes—
18C22×C11×SD16C2212yes—
19C22×C11×SD16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C2×C11×C4⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C4×Q8×C11C2212yes—
24C11×#462—28no—
25C11×#452—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#395—21no—
34C11×#395—21no—
35C11×#391C2212yes—
36C11×#390—22no—
37C11×#390C2212yes—
38C11×#385—22no—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
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×C11C2312yes—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C11×#137—232no—
63C2×C11×Q16—24no—
64C2×C11×Q16—24no—
65C2×C11×Q16—22no—
66C2×C11×Q16—24no—
67C2×C11×Q16D418yes—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16—22no—
71C2×C11×SD16—24no—
72C2×C11×SD16—42no—
73C2×C11×M16—22no—
74C2×C11×M16—24no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2312yes—
78C11×C4⋊Q8—24no—
79C11×C4⋊Q8—42no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C4×Q8×C11—24no—
83C4×Q8×C11—42no—
84C2×C11×C4⋊C4—22no—
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⋊C4—22no—
94C2×C11×C22⋊C4D412yes—
95C2×C42×C11—22no—
96C2×C42×C11C2312yes—
97C11×C4⋊C8—24no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—24no—
101C11×#103—42no—
102C11×#102—22no—
103C11×C22⋊C8—22no—
104C11×#95—21no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#24374C1111yesmaximal, 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—22no—
118C2×Q8×C11—28no—
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—44no—
128C2×Q8×C11—48no—
129C2×Q8×C11—44no—
130C2×Q8×C11—42no—
131C2×Q8×C11C2×D414yes—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D414yes—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—44no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
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—42no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C11×Q16—216no—
158C11×Q16—44no—
159C11×SD16—216no—
160C11×SD16—44no—
161C11×M16—28no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11C2×D414yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C4⋊C4—44no—
176C11×C4⋊C4—42no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—44no—
180C11×C22⋊C4—82no—
181C11×C22⋊C4—81no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—44no—
185C22×#137C2×C1111yescharacteristic
186C2×#462C2×C1112yescomplemented
187C2×#452C2×C1111yescharacteristic
188#2434C2×C1111yescharacteristic, complemented
189#2341C2×C1111yescharacteristic
190#2055C2×C1112yescomplemented
191#2013C2×C1112yescomplemented
192#1894C2×C1111yescharacteristic, complemented
193#1878C2×C1112yescomplemented
194#1851C2×C1111yescharacteristic, complemented
195#1787C2×C1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11#12112yes—
206C23×C11C22×D411yescharacteristic
207Q8×C11—22no—
208Q8×C11—24no—
209Q8×C11—24no—
210Q8×C11—24no—
211Q8×C11—48no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—41no—
215Q8×C11—41no—
216Q8×C11—42no—
217Q8×C11#12014yes—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—48no—
221D4×C11—42no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—48no—
235C2×C4×C11—48no—
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#12112yes—
247C2×C4×C11#13714yescomplemented
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)12yes—
252C8×C11—24no—
253C8×C11—41no—
254C8×C11—41no—
255C22×#41C22×C1111yescharacteristic
256C23×Q8C22×C1111yescharacteristic
257C2×#137—24no—
258C2×#137—28no—
259C22×Q16C22×C1111yescharacteristic
260C22×Q16C22×C1112yes—
261C22×SD16C22×C1112yes—
262C22×SD16C22×C1111yescharacteristic
263C22×M16C22×C1111yescharacteristic
264C2×C4⋊Q8C22×C1112yes—
265C2×C22⋊Q8C22×C1111yescharacteristic
266C2×C4×Q8C22×C1112yes—
267#462—28no—
268#452—24no—
269C2×C4⋊C8C22×C1112yes—
270C2×#103C22×C1112yes—
271C2×#103C22×C1111yescharacteristic
272C2×#103C22×C1112yes—
273C2×#103C22×C1112yes—
274C2×#102C22×C1111yescharacteristic
275C2×C22⋊C8C22×C1111yescharacteristic
276#395—21no—
277#395—21no—
278#391C22×C1112yes—
279#390—22no—
280#390C22×C1112yes—
281#385—22no—
282#380—21no—
283#380C22×C1111yescharacteristic
284C4×C22⋊C4—21no—
285C4×C22⋊C4C22×C1111yescharacteristic
286#340C22×C1112yes—
287#336C22×C1112yes—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11C2×#12111yescharacteristic
299C22×C11D4212yes—
300C22×C11C2×#13712yes—
301C22×C11#57711yescharacteristic
302C22×C11#57811yescharacteristic
303C4×C11—22no—
304C4×C11—24no—
305C4×C11—24no—
306C4×C11—44no—
307C4×C11—42no—
308C4×C11—81no—
309C4×C11—82no—
310C4×C11—81no—
311C4×C11C2×#12011yescharacteristic
312C4×C11#53411yescharacteristic
313C4×C11#54612yes—
314C2×#41—22no—
315C2×#41—24no—
316C2×#41—42no—
317C2×#41D4×C1114yes—
318C22×Q8—21no—
319C22×Q8—24no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—42no—
323C22×Q8C23×C1111yescharacteristic
324C22×Q8C23×C1112yes—
325C22×Q8C23×C1111yescharacteristic
326C22×D4—21no—
327C22×D4C23×C1111yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C23×C1111yescharacteristic
331#137—232no—
332C2×Q16—24no—
333C2×Q16—24no—
334C2×Q16—22no—
335C2×Q16—24no—
336C2×Q16D4×C1118yes—
337C2×SD16—24no—
338C2×SD16—24no—
339C2×SD16—22no—
340C2×SD16—24no—
341C2×SD16—42no—
342C2×M16—22no—
343C2×M16—24no—
344C22×C8C23×C1111yescharacteristic
345C22×C8C23×C1111yescharacteristic
346C22×C8C23×C1112yes—
347C4⋊Q8—24no—
348C4⋊Q8—42no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C4×Q8—24no—
352C4×Q8—42no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4C23×C1112yes—
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4D4×C1112yes—
364C2×C42—22no—
365C2×C42C23×C1112yes—
366C4⋊C8—24no—
367#103—22no—
368#103—24no—
369#103—24no—
370#103—42no—
371#102—22no—
372C22⋊C8—22no—
373#95—21no—
374#95—22no—
375#95—22no—
376#95D4×C1111yescharacteristic
377#95D4×C1111yescharacteristic
378C2×C11—42no—
379C2×C11—82no—
380C2×C11#241011yescharacteristic
381C2×C11#303911yescharacteristic
382C2×C11#304611yescharacteristic
383C2×C11#327012yes—
384C2×C11#327812yes—
385C24—21no—
386C24C2×D4×C1111yescharacteristic
387#41—28no—
388#41—44no—
389#41—48no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—28no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8—48no—
404C2×Q8—44no—
405C2×Q8—42no—
406C2×Q8C2×D4×C1114yes—
407C2×Q8C2×D4×C1112yes—
408C2×Q8C2×D4×C1114yes—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—44no—
414C2×D4C2×D4×C1112yes—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—42no—
426C22×C4C2×D4×C1112yes—
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1112yes—
429C22×C4C2×D4×C1112yes—
430C22×C4C11×#4112yes—
431C22×C4C24×C1111yescharacteristic
432Q16—216no—
433Q16—44no—
434SD16—216no—
435SD16—44no—
436M16—28no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8C2×D4×C1114yes—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—44no—
451C4⋊C4—42no—
452C22⋊C4—24no—
453C22⋊C4—42no—
454C22⋊C4—44no—
455C22⋊C4—82no—
456C22⋊C4—81no—
457C42—22no—
458C42—22no—
459C42—44no—
460C11#2437411yescharacteristic, direct product factor, Sylow
461C23—22no—
462C23—22no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23C11×#12112yes—
471C23C22×D4×C1111yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479Q8—41no—
480Q8—41no—
481Q8—42no—
482Q8C11×#12014yes—
483D4—22no—
484D4—22no—
485D4—48no—
486D4—42no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
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—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4C11×#12112yes—
512C2×C4C11×#13714yescomplemented
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C22×D4×C1112yes—
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C11×H(5,𝔽2)12yes—
517C8—24no—
518C8—41no—
519C8—41no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—82no—
529C22—82no—
530C22C2×C11×#12111yescharacteristic
531C22D42×C1112yes—
532C22C2×C11×#13712yes—
533C22C11×#57711yescharacteristic
534C22C11×#57811yescharacteristic
535C4—22no—
536C4—24no—
537C4—24no—
538C4—44no—
539C4—42no—
540C4—81no—
541C4—82no—
542C4—81no—
543C4C2×C11×#12011yescharacteristic
544C4C11×#53411yescharacteristic
545C4C11×#54612yes—
546C2—42no—
547C2—82no—
548C2C11×#241011yescharacteristic
549C2C11×#303911yescharacteristic
550C2C11×#304611yescharacteristic
551C2C11×#327012yes—
552C2C11×#327812yes—
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×#462C2semidirect
4. C11×#2434C2semidirect
6. C11×#2055C2semidirect
7. C11×#2013C2semidirect
8. C11×#1894C2semidirect
9. C11×#1878C2semidirect
10. C11×#1851C2semidirect
11. C11×#1787C2semidirect
109. #24374C11direct (N × H)
186. C2×#462C2×C11semidirect
188. #2434C2×C11semidirect
190. #2055C2×C11semidirect
191. #2013C2×C11semidirect
192. #1894C2×C11semidirect
193. #1878C2×C11semidirect
194. #1851C2×C11semidirect
195. #1787C2×C11semidirect
247. C2×C4×C11#137semidirect
460. C11#24374direct (N × H)
512. 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×#4622
C2×C11×#4522
C11×#24342
C11×#23412
C11×#20552
C11×#20132
C11×#18942
C11×#18782
C11×#18512
C11×#17872
#2437411