Finite Group Databasebeta

← C11×#24098 #14601291

Subgroups — C11×#24098 #14601291

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C22×C11×#107C211yesmaximal, characteristic, complemented
4C11×#2487C211yesmaximal, characteristic
5C11×#2057C212yesmaximal, complemented
6C11×#2036C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic
9C11×#1863C212yesmaximal, complemented
10C11×#1852C212yesmaximal, complemented
11C11×#1824C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C11×#554—24no—
14C11×#554—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#484—24no—
28C2×C11×#107—24no—
29C2×C11×#107C2212yes—
30C2×C11×#107C2212yes—
31C2×C11×#107C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#400—21no—
37C11×#399—21no—
38C11×#389C2212yes—
39C11×#386—21no—
40C11×#385—21no—
41C11×#380C2211yescharacteristic
42C11×#380C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C8×C11—22no—
56C22×C8×C11—24no—
57C22×C8×C11C2312yes—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×#125—28no—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—28no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×D4×C11—28no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4D414yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×#107—24no—
102C11×#107—24no—
103C11×#107—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—24no—
108C11×#95—22no—
109C11×#95—21no—
110C11×#95—22no—
111#24098C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—82no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11Q1614yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—42no—
138C22×C4×C11—82no—
139C22×C4×C11—82no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C8×C11—28no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11#4114yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—82no—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—82no—
180C42×C11—24no—
181C42×C11—21no—
182C42×C11—21no—
183C2×#554C2×C1111yescharacteristic
184C2×#484C2×C1111yescharacteristic, complemented
185C22×#107C2×C1111yescharacteristic, complemented
186#2487C2×C1111yescharacteristic
187#2057C2×C1112yescomplemented
188#2036C2×C1112yescomplemented
189#1892C2×C1111yescharacteristic, complemented
190#1869C2×C1111yescharacteristic
191#1863C2×C1112yescomplemented
192#1852C2×C1112yescomplemented
193#1824C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11#12012yes—
201C23×C11C2×Q1612yes—
202C23×C11C2×Q1612yes—
203C23×C11#13712yes—
204C23×C11C22×D411yescharacteristic
205Q8×C11—24no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—84no—
209D4×C11—28no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11—84no—
239C2×C4×C11—84no—
240C2×C4×C11#12012yes—
241C2×C4×C11C2×Q1612yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C112−1+412yes—
246C8×C11—24no—
247C8×C11—42no—
248C23×C8C22×C1111yescharacteristic
249#554—24no—
250#554—24no—
251C2×C4⋊Q8C22×C1111yescharacteristic
252C2×#125—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8C22×C1111yescharacteristic
256C2×C22⋊Q8C22×C1111yescharacteristic
257C2×C4×Q8C22×C1111yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4C22×C1111yescharacteristic
260C22×C4⋊C4C22×C1111yescharacteristic
261C22×C4⋊C4C22×C1111yescharacteristic
262C22×C4⋊C4C22×C1111yescharacteristic
263#484—24no—
264C2×#107—24no—
265C2×#107C22×C1112yes—
266C2×#107C22×C1112yes—
267C2×#107C22×C1112yes—
268C2×#103C22×C1112yes—
269C2×#103C22×C1112yes—
270C2×C22⋊C8C22×C1111yescharacteristic
271C2×C22⋊C8C22×C1112yes—
272#400—21no—
273#399—21no—
274#389C22×C1112yes—
275#386—21no—
276#385—21no—
277#380C22×C1111yescharacteristic
278#380C22×C1112yes—
279#340C22×C1112yes—
280#340C22×C1112yes—
281#340C22×C1112yes—
282#336C22×C1112yes—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—42no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11#45114yes—
293C22×C11C2×#12011yescharacteristic
294C22×C11#54712yes—
295C22×C11C22×Q1611yescharacteristic
296C22×C11C2×#13711yescharacteristic
297C22×C11#57612yes—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—41no—
301C4×C11—42no—
302C4×C11—41no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—82no—
307C4×C11—82no—
308C4×C11#52511yescharacteristic
309C4×C11#53611yescharacteristic
310C4×C11#54712yes—
311C22×Q8—21no—
312C22×Q8C23×C1111yescharacteristic
313C22×D4D4×C1111yescharacteristic
314C23×C4—21no—
315C23×C4—21no—
316C23×C4—21no—
317C23×C4C23×C1111yescharacteristic
318C23×C4C23×C1111yescharacteristic
319C22×C8—22no—
320C22×C8—24no—
321C22×C8C23×C1112yes—
322C22×C8C23×C1112yes—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325#125—28no—
326C22⋊Q8—28no—
327C22⋊Q8—28no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8D4×C1114yes—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×D4—28no—
335C4×D4—22no—
336C4×D4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C4⋊C4D4×C1114yes—
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4D4×C1111yescharacteristic
362C2×C22⋊C4D4×C1111yescharacteristic
363C2×C42—21no—
364C2×C42C23×C1111yescharacteristic
365#107—24no—
366#107—24no—
367#107—24no—
368#103—24no—
369#103—24no—
370C22⋊C8—22no—
371C22⋊C8—24no—
372#95—22no—
373#95—21no—
374#95—22no—
375C2×C11—24no—
376C2×C11—42no—
377C2×C11#240611yescharacteristic
378C2×C11C2×#45111yescharacteristic
379C2×C11#300811yescharacteristic
380C2×C11#333812yes—
381C2×C11#334612yes—
382C24C2×D4×C1111yescharacteristic
383C24C2×D4×C1111yescharacteristic
384C2×Q8—24no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—82no—
389C2×Q8C2×D4×C1112yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4C11×Q1614yes—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—82no—
409C22×C4—82no—
410C22×C4—82no—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C24×C1111yescharacteristic
418C2×C8—28no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8C11×#4114yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4—82no—
441C4⋊C4C2×D4×C1112yes—
442C4⋊C4C2×D4×C1112yes—
443C4⋊C4C2×D4×C1112yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—42no—
449C22⋊C4—82no—
450C42—24no—
451C42—21no—
452C42—21no—
453C11#2409811yescharacteristic, direct product factor, Sylow
454C23—22no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—21no—
459C23—22no—
460C23C11×#12012yes—
461C23C2×C11×Q1612yes—
462C23C2×C11×Q1612yes—
463C23C11×#13712yes—
464C23C22×D4×C1111yescharacteristic
465Q8—24no—
466Q8—41no—
467Q8—41no—
468Q8—84no—
469D4—28no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—84no—
500C2×C4C11×#12012yes—
501C2×C4C2×C11×Q1612yes—
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C2×C4C2×C11×#4112yes—
505C2×C4C11×2−1+412yes—
506C8—24no—
507C8—42no—
508C22—22no—
509C22—22no—
510C22—24no—
511C22—24no—
512C22—22no—
513C22—24no—
514C22—41no—
515C22—41no—
516C22—42no—
517C22C11×#45114yes—
518C22C2×C11×#12011yescharacteristic
519C22C11×#54712yes—
520C22C22×C11×Q1611yescharacteristic
521C22C2×C11×#13711yescharacteristic
522C22C11×#57612yes—
523C4—22no—
524C4—22no—
525C4—41no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—82no—
532C4—82no—
533C4C11×#52511yescharacteristic
534C4C11×#53611yescharacteristic
535C4C11×#54712yes—
536C2—24no—
537C2—42no—
538C2C11×#240611yescharacteristic
539C2C2×C11×#45111yescharacteristic
540C2C11×#300811yescharacteristic
541C2C11×#333812yes—
542C2C11×#334612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#484C2semidirect
3. C22×C11×#107C2semidirect
5. C11×#2057C2semidirect
6. C11×#2036C2semidirect
7. C11×#1892C2semidirect
9. C11×#1863C2semidirect
10. C11×#1852C2semidirect
11. C11×#1824C2semidirect
111. #24098C11direct (N × H)
184. C2×#484C2×C11semidirect
185. C22×#107C2×C11semidirect
187. #2057C2×C11semidirect
188. #2036C2×C11semidirect
189. #1892C2×C11semidirect
191. #1863C2×C11semidirect
192. #1852C2×C11semidirect
193. #1824C2×C11semidirect
453. C11#24098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4842
C22×C11×#1072
C11×#24872
C11×#20572
C11×#20362
C11×#18922
C11×#18692
C11×#18632
C11×#18522
C11×#18242
#2409811