Finite Group Databasebeta

← C11×#24752 #14601945

Subgroups — C11×#24752 #14601945

Order 2816.

992 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
1C2×C11×#467C212yesmaximal
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C22×C11×C4⋊C8C211yesmaximal, characteristic
4C11×#2857C211yesmaximal, characteristic
5C4×C11×C22⋊Q8C211yesmaximal, characteristic
6C11×#2068C212yesmaximal, complemented
7C11×#2056C212yesmaximal, complemented
8C11×#1981C211yesmaximal, characteristic, complemented
9C11×#1947C211yesmaximal, characteristic, complemented
10C11×#1892C212yesmaximal
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C23×C8×C11C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#467—28no—
20C11×#462—24no—
21C2×C11×#107C2212yes—
22C2×C11×C4⋊C8—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C11×#391C2211yescharacteristic
31C11×#391C2212yes—
32C11×#389—21no—
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#387—21no—
36C11×#385—21no—
37C11×#384C2211yescharacteristic
38C11×#380—21no—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C2×C11×Q16—24no—
52C2×C11×Q16—24no—
53C2×C11×Q16—42no—
54C22×C8×C11—24no—
55C22×C8×C11—24no—
56C22×C8×C11—42no—
57C22×C8×C11C2312yes—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8D414yes—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C11×#107—24no—
91C11×C4⋊C8—24no—
92C11×C4⋊C8—22no—
93C11×C4⋊C8D414yes—
94C11×#103—24no—
95C11×#103—24no—
96C11×#103—24no—
97C11×#103—42no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—22no—
104C11×#95—22no—
105#24752C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11C2×D411yescharacteristic
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D412yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—41no—
134C22×C4×C11Q1614yescomplemented
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C11×Q16—48no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—48no—
150C2×C8×C11C2×D414yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—42no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175C42×C11—42no—
176C42×C11C2×D412yes—
177C42×C11#4112yes—
178C2×#467C2×C1112yes—
179C2×#462C2×C1111yescharacteristic, complemented
180C22×C4⋊C8C2×C1111yescharacteristic
181#2857C2×C1111yescharacteristic
182C4×C22⋊Q8C2×C1111yescharacteristic
183#2068C2×C1112yescomplemented
184#2056C2×C1112yescomplemented
185#1981C2×C1111yescharacteristic, complemented
186#1947C2×C1111yescharacteristic, complemented
187#1892C2×C1112yes—
188#1803C2×C1111yescharacteristic, complemented
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11#12112yes—
194C23×C11C2×Q1612yes—
195C23×C11#13712yes—
196C23×C11C22×D411yescharacteristic
197Q8×C11—22no—
198Q8×C11—22no—
199Q8×C11—41no—
200Q8×C11—41no—
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—42no—
204Q8×C11—42no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—28no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—44no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11#12112yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12112yes—
241C2×C4×C11C2×Q1612yes—
242C2×C4×C11C2×Q1612yes—
243C2×C4×C11#13512yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C8×C11—24no—
251C8×C11—42no—
252C22×Q16C22×C1112yes—
253C23×C8C22×C1112yes—
254C2×C4⋊Q8C22×C1111yescharacteristic
255C2×C22⋊Q8C22×C1112yes—
256C2×C22⋊Q8C22×C1111yescharacteristic
257C2×C4×Q8C22×C1111yescharacteristic
258C22×C42C22×C1111yescharacteristic
259#467—28no—
260#462—24no—
261C2×#107C22×C1112yes—
262C2×C4⋊C8—24no—
263C2×C4⋊C8C22×C1112yes—
264C2×C4⋊C8C22×C1111yescharacteristic
265C2×C4⋊C8C22×C1111yescharacteristic
266C2×#103C22×C1112yes—
267C2×#103C22×C1112yes—
268C2×#103C22×C1112yes—
269C2×#103C22×C1112yes—
270#391C22×C1111yescharacteristic
271#391C22×C1112yes—
272#389—21no—
273#389—21no—
274#389C22×C1111yescharacteristic
275#387—21no—
276#385—21no—
277#384C22×C1111yescharacteristic
278#380—21no—
279#380—21no—
280#380C22×C1111yescharacteristic
281C4×C4⋊C4—21no—
282C4×C4⋊C4C22×C1111yescharacteristic
283C4×C22⋊C4—21no—
284#340C22×C1112yes—
285#340C22×C1112yes—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11#46214yescomplemented
293C22×C11C2×#12111yescharacteristic
294C22×C11C2×#12111yescharacteristic
295C22×C11#53711yescharacteristic
296C22×C11C22×Q1611yescharacteristic
297C22×C11C2×#13511yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11#57511yescharacteristic
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—41no—
306C4×C11—82no—
307C4×C11—81no—
308C4×C11—82no—
309C4×C11—81no—
310C4×C11#46714yescomplemented
311C4×C11D4211yescharacteristic
312C4×C11#54711yescharacteristic
313C4×C11#54811yescharacteristic
314C4×C11#55311yescharacteristic
315C22×Q8C23×C1112yes—
316C22×Q8C23×C1111yescharacteristic
317C23×C4D4×C1111yescharacteristic
318C23×C4D4×C1111yescharacteristic
319C23×C4C23×C1111yescharacteristic
320C2×Q16—24no—
321C2×Q16—24no—
322C2×Q16—42no—
323C22×C8—24no—
324C22×C8—24no—
325C22×C8—42no—
326C22×C8C23×C1112yes—
327C22×C8C23×C1112yes—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8D4×C1114yes—
334C4×Q8—22no—
335C4×Q8—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C4⋊C4C23×C1112yes—
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42D4×C1111yescharacteristic
356C2×C42D4×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358C2×C42C23×C1111yescharacteristic
359#107—24no—
360C4⋊C8—24no—
361C4⋊C8—22no—
362C4⋊C8D4×C1114yes—
363#103—24no—
364#103—24no—
365#103—24no—
366#103—42no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—22no—
373#95—22no—
374C2×C11—24no—
375C2×C11#241611yescharacteristic
376C2×C11C2×#46211yescharacteristic
377C2×C11#303511yescharacteristic
378C2×C11C2×#46711yescharacteristic
379C2×C11#305611yescharacteristic
380C2×C11#324811yescharacteristic
381C2×C11#324911yescharacteristic
382C24C2×D4×C1111yescharacteristic
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8C2×D4×C1112yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—41no—
410C22×C4C11×Q1614yescomplemented
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C11×#4112yes—
418C22×C4C24×C1111yescharacteristic
419Q16—48no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—48no—
426C2×C8C2×D4×C1114yes—
427C4⋊C4—24no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4—42no—
438C4⋊C4—44no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4C2×D4×C1112yes—
443C22⋊C4—24no—
444C22⋊C4—44no—
445C22⋊C4—42no—
446C42—22no—
447C42—22no—
448C42—21no—
449C42—21no—
450C42—42no—
451C42—42no—
452C42C2×D4×C1112yes—
453C42C11×#4112yes—
454C11#2475211yescharacteristic, direct product factor, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23C11×#12112yes—
460C23C2×C11×Q1612yes—
461C23C11×#13712yes—
462C23C22×D4×C1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—42no—
468Q8—42no—
469Q8—42no—
470Q8—42no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—28no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4C11×#12112yes—
505C2×C4C11×#12112yes—
506C2×C4C11×#12112yes—
507C2×C4C2×C11×Q1612yes—
508C2×C4C2×C11×Q1612yes—
509C2×C4C11×#13512yes—
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C22×D4×C1111yescharacteristic
512C2×C4C2×C11×#4111yescharacteristic
513C2×C4C2×C11×#4111yescharacteristic
514C2×C4C11×H(5,𝔽2)11yescharacteristic
515C2×C4C11×2−1+411yescharacteristic
516C8—24no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22C11×#46214yescomplemented
525C22C2×C11×#12111yescharacteristic
526C22C2×C11×#12111yescharacteristic
527C22C11×#53711yescharacteristic
528C22C22×C11×Q1611yescharacteristic
529C22C2×C11×#13511yescharacteristic
530C22C2×C11×#13711yescharacteristic
531C22C11×#57511yescharacteristic
532C4—22no—
533C4—22no—
534C4—22no—
535C4—42no—
536C4—42no—
537C4—41no—
538C4—82no—
539C4—81no—
540C4—82no—
541C4—81no—
542C4C11×#46714yescomplemented
543C4D42×C1111yescharacteristic
544C4C11×#54711yescharacteristic
545C4C11×#54811yescharacteristic
546C4C11×#55311yescharacteristic
547C2—24no—
548C2C11×#241611yescharacteristic
549C2C2×C11×#46211yescharacteristic
550C2C11×#303511yescharacteristic
551C2C2×C11×#46711yescharacteristic
552C2C11×#305611yescharacteristic
553C2C11×#324811yescharacteristic
554C2C11×#324911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#462C2semidirect
6. C11×#2068C2semidirect
7. C11×#2056C2semidirect
8. C11×#1981C2semidirect
9. C11×#1947C2semidirect
11. C11×#1803C2semidirect
105. #24752C11direct (N × H)
134. C22×C4×C11Q16semidirect
179. C2×#462C2×C11semidirect
183. #2068C2×C11semidirect
184. #2056C2×C11semidirect
185. #1981C2×C11semidirect
186. #1947C2×C11semidirect
188. #1803C2×C11semidirect
292. C22×C11#462semidirect
310. C4×C11#467semidirect
410. C22×C4C11×Q16semidirect
454. C11#24752direct (N × H)
524. C22C11×#462semidirect
542. C4C11×#467semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×#4622
C22×C11×C4⋊C82
C11×#28572
C4×C11×C22⋊Q82
C11×#20682
C11×#20562
C11×#19812
C11×#19472
C11×#18922
C11×#18032
#2475211