Finite Group Databasebeta

← C11×#22500 #14599693

Subgroups — C11×#22500 #14599693

Order 2816.

1370 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
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#436C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic, complemented
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1988C211yesmaximal, characteristic, complemented
6C11×#1895C212yesmaximal, complemented
7C11×#1875C212yesmaximal, complemented
8C11×#1824C212yesmaximal, complemented
9C11×#1802C211yesmaximal, characteristic, complemented
10C4×C11×#102C211yesmaximal, characteristic, complemented
11C11×#1736C212yesmaximal, complemented
12C22×C11×#41—21no—
13C22×C11×M16C2212yes—
14C11×#547—24no—
15C11×#547C418yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2212yes—
23C22×C11×C4⋊C4C2212yes—
24C11×#436—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390—21no—
32C11×#388—22no—
33C11×#384C2211yescharacteristic
34C11×#380C2212yes—
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C2×C11×#41—28no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C23×C4×C11C2312yes—
54C2×C11×M16—24no—
55C2×C11×M16—24no—
56C2×C11×M16—42no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8C2×C414yes—
62C11×#123—216no—
63C11×C22⋊Q8—28no—
64C11×#121—24no—
65C11×#121C2×C418yes—
66C4×D4×C11—22no—
67C4×D4×C11C2×C414yes—
68C4×D4×C11C2×C414yes—
69C4×D4×C11D414yes—
70C11×#117—24no—
71C11×#117—42no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2×C418yes—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—22no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×C4⋊C8—22no—
93C11×#102—22no—
94C11×#102—22no—
95C11×#102—42no—
96C11×C22⋊C8—24no—
97C4×C8×C11—22no—
98C11×#95—22no—
99C11×#95—21no—
100#22500C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11C2×D412yes—
103C11×#41—432no—
104C2×Q8×C11—24no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×D4×C11—28no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11C22⋊C414yes—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—44no—
131C22×C4×C11—44no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C11×M16—48no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11#4112yescomplemented
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4C22⋊C414yes—
162C11×C4⋊C4C22×C412yes—
163C11×C4⋊C4C22×C414yes—
164C11×C4⋊C4#4112yescomplemented
165C11×C22⋊C4—24no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—82no—
169C11×C22⋊C4C22⋊C418yes—
170C42×C11—44no—
171C42×C11—42no—
172C42×C11C22×C412yes—
173C42×C11C2×D412yes—
174C2×#547C2×C1111yescharacteristic
175C2×#436C2×C1111yescharacteristic, complemented
176#2354C2×C1111yescharacteristic, complemented
177#1990C2×C1111yescharacteristic, complemented
178#1988C2×C1111yescharacteristic, complemented
179#1895C2×C1112yescomplemented
180#1875C2×C1112yescomplemented
181#1824C2×C1112yescomplemented
182#1802C2×C1111yescharacteristic, complemented
183C4×#102C2×C1111yescharacteristic, complemented
184#1736C2×C1112yescomplemented
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C2×C22⋊C414yes—
199C23×C11C22×D411yescharacteristic
200Q8×C11—48no—
201D4×C11—22no—
202D4×C11—22no—
203D4×C11—28no—
204D4×C11—416no—
205D4×C11—41no—
206D4×C11—41no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—416no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—48no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11C2×C22⋊C414yes—
234C2×C4×C11C2×C22⋊C412yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11AGL(1,ℤ/8)12yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C8×C11—22no—
244C8×C11—42no—
245C8×C11—41no—
246C22×#41—21no—
247C22×M16C22×C1112yes—
248#547—24no—
249#547C4×C1118yescomplemented
250C2×C4⋊Q8C22×C1111yescharacteristic
251C2×#123—22no—
252C2×C22⋊Q8—21no—
253C2×#121C22×C1112yes—
254C2×C4×D4C22×C1111yescharacteristic
255C2×C4×D4C22×C1111yescharacteristic
256C2×#117C22×C1112yes—
257C22×C4⋊C4C22×C1112yes—
258#436—24no—
259C2×C4⋊C8C22×C1111yescharacteristic
260C2×#102C22×C1111yescharacteristic
261C2×#102C22×C1111yescharacteristic
262C2×#102C22×C1112yes—
263C2×C22⋊C8C22×C1112yes—
264C2×C4×C8C22×C1111yescharacteristic
265#390—21no—
266#388—22no—
267#384C22×C1111yescharacteristic
268#380C22×C1112yes—
269C4×C4⋊C4—21no—
270C4×C4⋊C4C22×C1111yescharacteristic
271#340C22×C1112yes—
272#340C22×C1111yescharacteristic
273#340C22×C1112yes—
274#340C22×C1112yes—
275#340C22×C1112yes—
276#340C22×C1112yes—
277#340C22×C1111yescharacteristic
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×C22⋊C411yescharacteristic
293C22×C11#54611yescharacteristic
294C22×C11#54711yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11#57711yescharacteristic
298C22×C11#57811yescharacteristic
299C4×C11—24no—
300C4×C11—22no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—44no—
304C4×C11—82no—
305C4×C11—81no—
306C4×C11#41814yes—
307C4×C11C4×#4111yescharacteristic
308C4×C11#52011yescharacteristic
309C4×C11#54611yescharacteristic
310C4×C11#54711yescharacteristic
311C2×#41—28no—
312C2×#41—44no—
313C2×#41—44no—
314C22×Q8—21no—
315C22×D4—22no—
316C22×D4D4×C1111yescharacteristic
317C22×D4C23×C1111yescharacteristic
318C23×C4—22no—
319C23×C4—21no—
320C23×C4C23×C1112yes—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—42no—
324C22×C8C23×C1112yes—
325C22×C8C23×C1111yescharacteristic
326C22×C8C23×C1111yescharacteristic
327C4⋊Q8—22no—
328C4⋊Q8C2×C4×C1114yes—
329#123—216no—
330C22⋊Q8—28no—
331#121—24no—
332#121C2×C4×C1118yes—
333C4×D4—22no—
334C4×D4C2×C4×C1114yes—
335C4×D4C2×C4×C1114yes—
336C4×D4D4×C1114yes—
337#117—24no—
338#117—42no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4C2×C4×C1118yes—
345C2×C4⋊C4D4×C1111yescharacteristic
346C2×C4⋊C4C23×C1112yes—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4D4×C1112yes—
356C2×C42—22no—
357C2×C42—21no—
358C2×C42C23×C1111yescharacteristic
359C4⋊C8—22no—
360#102—22no—
361#102—22no—
362#102—42no—
363C22⋊C8—24no—
364C4×C8—22no—
365#95—22no—
366#95—21no—
367C2×C11—44no—
368C2×C11—82no—
369C2×C11#233911yescharacteristic
370C2×C11C2×#41811yescharacteristic
371C2×C11#289811yescharacteristic
372C2×C11#333011yescharacteristic
373C2×C11#333211yescharacteristic
374C2×C11#335311yescharacteristic
375C2×C11#335411yescharacteristic
376C24—21no—
377C24C2×D4×C1112yes—
378#41—432no—
379C2×Q8—24no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×D4—28no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4C11×C22⋊C414yes—
393C2×D4C22×C4×C1112yes—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—28no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4C22×C4×C1114yes—
410C22×C4C2×D4×C1112yes—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1114yes—
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C24×C1111yescharacteristic
415M16—48no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—21no—
424C2×C8C11×#4112yescomplemented
425C4⋊C4—28no—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—42no—
435C4⋊C4—81no—
436C4⋊C4C11×C22⋊C414yes—
437C4⋊C4C22×C4×C1112yes—
438C4⋊C4C22×C4×C1114yes—
439C4⋊C4C11×#4112yescomplemented
440C22⋊C4—24no—
441C22⋊C4—28no—
442C22⋊C4—44no—
443C22⋊C4—82no—
444C22⋊C4C11×C22⋊C418yes—
445C42—44no—
446C42—42no—
447C42C22×C4×C1112yes—
448C42C2×D4×C1112yes—
449C11#2250011yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23C2×C11×C22⋊C414yes—
464C23C22×D4×C1111yescharacteristic
465Q8—48no—
466D4—22no—
467D4—22no—
468D4—28no—
469D4—416no—
470D4—41no—
471D4—41no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—416no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—48no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4C2×C11×C22⋊C412yes—
498C2×C4C2×C11×C22⋊C414yes—
499C2×C4C2×C11×C22⋊C412yes—
500C2×C4C11×AGL(1,ℤ/8)12yes—
501C2×C4C11×AGL(1,ℤ/8)12yes—
502C2×C4C23×C4×C1111yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C2×C4C2×C11×#4111yescharacteristic
505C2×C4C2×C11×#4111yescharacteristic
506C2×C4C11×H(5,𝔽2)11yescharacteristic
507C2×C4C11×2−1+411yescharacteristic
508C8—22no—
509C8—42no—
510C8—41no—
511C22—24no—
512C22—24no—
513C22—24no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22C22×C11×C22⋊C411yescharacteristic
526C22C11×#54611yescharacteristic
527C22C11×#54711yescharacteristic
528C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
529C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
530C22C11×#57711yescharacteristic
531C22C11×#57811yescharacteristic
532C4—22no—
533C4—24no—
534C4—42no—
535C4—44no—
536C4—42no—
537C4—82no—
538C4—81no—
539C4C11×#41814yes—
540C4C4×C11×#4111yescharacteristic
541C4C11×#52011yescharacteristic
542C4C11×#54611yescharacteristic
543C4C11×#54711yescharacteristic
544C2—44no—
545C2—82no—
546C2C11×#233911yescharacteristic
547C2C2×C11×#41811yescharacteristic
548C2C11×#289811yescharacteristic
549C2C11×#333011yescharacteristic
550C2C11×#333211yescharacteristic
551C2C11×#335311yescharacteristic
552C2C11×#335411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
LCSG ▷ C2×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×#436C2semidirect
3. C11×#2354C2semidirect
4. C11×#1990C2semidirect
5. C11×#1988C2semidirect
6. C11×#1895C2semidirect
7. C11×#1875C2semidirect
8. C11×#1824C2semidirect
9. C11×#1802C2semidirect
10. C4×C11×#102C2semidirect
11. C11×#1736C2semidirect
15. C11×#547C4semidirect
100. #22500C11direct (N × H)
149. C2×C8×C11#41semidirect
164. C11×C4⋊C4#41semidirect
175. C2×#436C2×C11semidirect
176. #2354C2×C11semidirect
177. #1990C2×C11semidirect
178. #1988C2×C11semidirect
179. #1895C2×C11semidirect
180. #1875C2×C11semidirect
181. #1824C2×C11semidirect
182. #1802C2×C11semidirect
183. C4×#102C2×C11semidirect
184. #1736C2×C11semidirect
249. #547C4×C11semidirect
424. C2×C8C11×#41semidirect
439. C4⋊C4C11×#41semidirect
449. C11#22500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4362
C11×#23542
C11×#19902
C11×#19882
C11×#18952
C11×#18752
C11×#18242
C11×#18022
C4×C11×#1022
C11×#17362
#2250011