Finite Group Databasebeta

← C11×#19007 #14596200

Subgroups — C11×#19007 #14596200

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#563C211yesmaximal, characteristic
2C11×#3236C211yesmaximal, characteristic, complemented
3C11×#3215C211yesmaximal, characteristic
4C11×#3166C211yesmaximal, characteristic, complemented
5C11×#1664C214yesmaximal, complemented
6C11×#1660C214yesmaximal, complemented
7C11×#1534C211yesmaximal, characteristic, complemented
8C11×#1528C211yesmaximal, characteristic, complemented
9C11×#1527C211yesmaximal, characteristic
10C11×#563—22no—
11C11×#563—22no—
12C11×#563—22no—
13C11×#563C2214yes—
14C11×#533C2211yescharacteristic
15C2×C11×C4⋊Q8—21no—
16C2×C11×#126—21no—
17C2×C11×#126—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C11×#501C2212yescomplemented
25C11×#501C2212yescomplemented
26C11×#501C2212yescomplemented
27C11×#499—22no—
28C11×#497C2212yes—
29C11×#491C2212yescomplemented
30C11×#489C2212yes—
31C11×#484—21no—
32C11×#483—21no—
33C11×#479—22no—
34C11×#464—22no—
35C11×#451—21no—
36C11×#450—21no—
37C11×#432C2211yescharacteristic
38C11×#432C2211yescharacteristic
39C11×#428—21no—
40C11×#428—21no—
41C4×C11×M16C2211yescharacteristic
42C11×#330C2214yescomplemented
43C11×#330C2214yescomplemented
44C11×#329C2214yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C2×C11×Q16—22no—
50C2×C11×SD16—22no—
51C2×C11×M16—21no—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#126—24no—
57C11×#126—24no—
58C11×#126—24no—
59C11×#126—24no—
60C11×#125—21no—
61C11×#125—21no—
62C11×#125—21no—
63C11×#125—21no—
64C11×#125—21no—
65C11×#125D412yes—
66C11×#125D412yes—
67C11×#125C2312yes—
68C11×#125C2312yes—
69C11×#124—21no—
70C11×#124—21no—
71C11×#124D412yes—
72C11×#124C2312yes—
73C11×#123—24no—
74C11×#123—24no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C11×#117—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#107—22no—
103C11×#107—22no—
104C11×#106—22no—
105C11×#106—22no—
106C11×#106—22no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#102—22no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97C2312yes—
116C11×#97C2312yes—
117C11×#97C2312yes—
118C4×C8×C11—21no—
119#19007C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—81no—
126C2×Q8×C11—82no—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—21no—
129C2×D4×C11—81no—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—82no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C11×Q16—82no—
142C11×SD16—82no—
143C11×M16—24no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—41no—
179C42×C11—24no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2411yescharacteristic
185C2×#563C2×C1111yescharacteristic
186#3236C2×C1111yescharacteristic, complemented
187#3215C2×C1111yescharacteristic
188#3166C2×C1111yescharacteristic, complemented
189#1664C2×C1114yescomplemented
190#1660C2×C1114yescomplemented
191#1534C2×C1111yescharacteristic, complemented
192#1528C2×C1111yescharacteristic, complemented
193#1527C2×C1111yescharacteristic
194C23×C11—22no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11#12011yescharacteristic
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—81no—
203Q8×C11—84no—
204D4×C11—42no—
205D4×C11—81no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—84no—
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C8×C11—24no—
229C8×C11—42no—
230C8×C11—42no—
231#563—22no—
232#563—22no—
233#563—22no—
234#563C22×C1114yes—
235#533C22×C1111yescharacteristic
236C2×C4⋊Q8—21no—
237C2×#126—21no—
238C2×#126—21no—
239C2×#125C22×C1111yescharacteristic
240C2×#125C22×C1111yescharacteristic
241C2×#124C22×C1111yescharacteristic
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245#501C22×C1112yescomplemented
246#501C22×C1112yescomplemented
247#501C22×C1112yescomplemented
248#499—22no—
249#497C22×C1112yes—
250#491C22×C1112yescomplemented
251#489C22×C1112yes—
252#484—21no—
253#483—21no—
254#479—22no—
255#464—22no—
256#451—21no—
257#450—21no—
258#432C22×C1111yescharacteristic
259#432C22×C1111yescharacteristic
260#428—21no—
261#428—21no—
262C4×M16C22×C1111yescharacteristic
263#330C22×C1114yescomplemented
264#330C22×C1114yescomplemented
265#329C22×C1114yes—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—84no—
272C22×C11#45612yes—
273C22×C11C2×#12011yescharacteristic
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—81no—
286C4×C11—81no—
287C22×Q8—21no—
288C22×Q8D4×C1111yescharacteristic
289C22×D4D4×C1111yescharacteristic
290C23×C4—21no—
291C2×Q16—22no—
292C2×SD16—22no—
293C2×M16—21no—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296C4⋊Q8C23×C1111yescharacteristic
297C4⋊Q8C23×C1111yescharacteristic
298#126—24no—
299#126—24no—
300#126—24no—
301#126—24no—
302#125—21no—
303#125—21no—
304#125—21no—
305#125—21no—
306#125—21no—
307#125D4×C1112yes—
308#125D4×C1112yes—
309#125C23×C1112yes—
310#125C23×C1112yes—
311#124—21no—
312#124—21no—
313#124D4×C1112yes—
314#124C23×C1112yes—
315#123—24no—
316#123—24no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325#117—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4D4×C1111yescharacteristic
333C2×C4⋊C4D4×C1111yescharacteristic
334C2×C4⋊C4D4×C1111yescharacteristic
335C2×C4⋊C4D4×C1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C42—21no—
342C2×C42C23×C1111yescharacteristic
343#107—22no—
344#107—22no—
345#107—22no—
346#106—22no—
347#106—22no—
348#106—22no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351#103—22no—
352#103—22no—
353#103—22no—
354#102—22no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357#97C23×C1112yes—
358#97C23×C1112yes—
359#97C23×C1112yes—
360C4×C8—21no—
361C2×C11—22no—
362C2×C11—82no—
363C2×C11C2×#45611yescharacteristic
364C2×C11#301911yescharacteristic
365C2×C11#302011yescharacteristic
366C24—21no—
367C2×Q8—24no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—81no—
372C2×Q8—82no—
373C2×Q8C2×D4×C1112yes—
374C2×D4—21no—
375C2×D4—81no—
376C2×D4C2×D4×C1112yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—82no—
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387Q16—82no—
388SD16—82no—
389M16—24no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C2×D4×C1112yes—
414C4⋊C4C2×D4×C1112yes—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C2×D4×C1112yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—41no—
425C42—24no—
426C42—41no—
427C42C2×D4×C1111yescharacteristic
428C42C2×D4×C1111yescharacteristic
429C42C2×D4×C1111yescharacteristic
430C42C24×C1111yescharacteristic
431C11#1900711yescharacteristic, direct product factor, Sylow
432C23—22no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23C11×#12011yescharacteristic
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—81no—
441Q8—84no—
442D4—42no—
443D4—81no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—84no—
460C2×C4C11×#12011yescharacteristic
461C2×C4C11×#12011yescharacteristic
462C2×C4C11×#12011yescharacteristic
463C2×C4C22×D4×C1111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1111yescharacteristic
466C8—24no—
467C8—42no—
468C8—42no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—84no—
475C22C11×#45612yes—
476C22C2×C11×#12011yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—81no—
489C4—81no—
490C2—22no—
491C2—82no—
492C2C2×C11×#45611yescharacteristic
493C2C11×#301911yescharacteristic
494C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3236C2semidirect
4. C11×#3166C2semidirect
5. C11×#1664C2semidirect
6. C11×#1660C2semidirect
7. C11×#1534C2semidirect
8. C11×#1528C2semidirect
24. C11×#501C22semidirect
25. C11×#501C22semidirect
26. C11×#501C22semidirect
29. C11×#491C22semidirect
42. C11×#330C22semidirect
43. C11×#330C22semidirect
119. #19007C11direct (N × H)
186. #3236C2×C11semidirect
188. #3166C2×C11semidirect
189. #1664C2×C11semidirect
190. #1660C2×C11semidirect
191. #1534C2×C11semidirect
192. #1528C2×C11semidirect
245. #501C22×C11semidirect
246. #501C22×C11semidirect
247. #501C22×C11semidirect
250. #491C22×C11semidirect
263. #330C22×C11semidirect
264. #330C22×C11semidirect
431. C11#19007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5632
C11×#32362
C11×#32152
C11×#31662
C11×#16642
C11×#16602
C11×#15342
C11×#15282
C11×#15272
#1900711