Finite Group Databasebeta

← C11×#7943 #14585136

Subgroups — C11×#7943 #14585136

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#407C211yesmaximal, characteristic
2C11×#2280C211yesmaximal, characteristic
3C2×C11×#381C211yesmaximal, characteristic
4C11×#1284C214yesmaximal, complemented
5C24×C4×C11C2211yescharacteristic
6C22×C11×M16—21no—
7C2×C11×#117C412yescomplemented
8C22×C11×C22⋊C4—21no—
9C11×#407—21no—
10C11×#407—21no—
11C11×#407C412yescomplemented
12C11×#407C2212yes—
13C2×C11×C22⋊C8—21no—
14C2×C11×C22⋊C8C412yescomplemented
15C11×#381—21no—
16C11×#381—21no—
17C11×#381—21no—
18C11×#381C412yescomplemented
19C11×#381C2212yes—
20C11×#380—21no—
21C11×#380—21no—
22C11×#379—21no—
23C4×C11×C22⋊C4C412yescomplemented
24C4×C11×C22⋊C4C2212yes—
25C2×C11×#95—21no—
26C2×C11×#95C412yescomplemented
27C25×C11D411yescharacteristic
28C23×C4×C11—22no—
29C23×C4×C11—44no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11Q811yescharacteristic
42C23×C4×C11Q811yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C2×C11×M16—22no—
45C2×C11×M16—22no—
46C2×C11×M16—44no—
47C22×C8×C11—22no—
48C11×#117—44no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—44no—
56C2×C42×C11C2×C414yescomplemented
57C11×C22⋊C8—22no—
58C11×C22⋊C8—22no—
59C11×C22⋊C8—22no—
60C11×C22⋊C8C2×C414yescomplemented
61C11×#95—22no—
62C11×#95—22no—
63C11×#95—22no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95C2×C414yes—
67#7943C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—24no—
69C24×C11—42no—
70C24×C11—42no—
71C24×C11C22⋊C411yescharacteristic
72C24×C11C22⋊C411yescharacteristic
73C24×C11C22⋊C411yescharacteristic
74C24×C11C22⋊C411yescharacteristic
75C24×C11C4⋊C411yescharacteristic
76C24×C11C4⋊C411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—44no—
95C22×C4×C11—44no—
96C22×C4×C11—44no—
97C22×C4×C11C4211yescharacteristic
98C22×C4×C11C4211yescharacteristic
99C22×C4×C11C4211yescharacteristic
100C22×C4×C11C4211yescharacteristic
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C411yescharacteristic
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C4⋊C411yescharacteristic
110C22×C4×C11C4⋊C411yescharacteristic
111C22×C4×C11C4⋊C411yescharacteristic
112C22×C4×C11C4⋊C411yescharacteristic
113C22×C4×C11C4⋊C411yescharacteristic
114C22×C4×C11C4⋊C411yescharacteristic
115C22×C4×C11C4⋊C411yescharacteristic
116C22×C4×C11C4⋊C411yescharacteristic
117C22×C4×C11C4⋊C411yescharacteristic
118C22×C4×C11C4⋊C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×Q811yescharacteristic
125C11×M16—44no—
126C11×M16—44no—
127C2×C8×C11—24no—
128C2×C8×C11—44no—
129C11×C4⋊C4—44no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—44no—
132C11×C22⋊C4—44no—
133C11×C22⋊C4—44no—
134C11×C22⋊C4—44no—
135C42×C11—44no—
136C2×#407C2×C1111yescharacteristic
137#2280C2×C1111yescharacteristic
138C2×#381C2×C1111yescharacteristic
139#1284C2×C1114yescomplemented
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—416no—
161C23×C11#9511yescharacteristic
162C23×C11#9511yescharacteristic
163C23×C11#9511yescharacteristic
164C23×C11#9511yescharacteristic
165C23×C11#9914yes—
166C23×C11C2×C22⋊C411yescharacteristic
167C23×C11C2×C22⋊C411yescharacteristic
168C23×C11C2×C4⋊C411yescharacteristic
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—88no—
204C2×C4×C11#9511yescharacteristic
205C2×C4×C11#9511yescharacteristic
206C2×C4×C11#9511yescharacteristic
207C2×C4×C11#9511yescharacteristic
208C2×C4×C11C2×C4211yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C4⋊C411yescharacteristic
211C2×C4×C11C2×C4⋊C411yescharacteristic
212C8×C11—44no—
213C24×C4C22×C1111yescharacteristic
214C22×M16—21no—
215C2×#117C4×C1112yescomplemented
216C22×C22⋊C4—21no—
217#407—21no—
218#407—21no—
219#407C4×C1112yescomplemented
220#407C22×C1112yes—
221C2×C22⋊C8—21no—
222C2×C22⋊C8C4×C1112yescomplemented
223#381—21no—
224#381—21no—
225#381—21no—
226#381C4×C1112yescomplemented
227#381C22×C1112yes—
228#380—21no—
229#380—21no—
230#379—21no—
231C4×C22⋊C4C4×C1112yescomplemented
232C4×C22⋊C4C22×C1112yes—
233C2×#95—21no—
234C2×#95C4×C1112yescomplemented
235C22×C11—28no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—44no—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—44no—
258C22×C11H(3,ℤ/4)12yes—
259C22×C11#34212yes—
260C22×C11#34212yes—
261C22×C11C2×#9511yescharacteristic
262C22×C11C2×#9912yes—
263C22×C11#42112yes—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—84no—
273C4×C11—84no—
274C25D4×C1111yescharacteristic
275C23×C4—22no—
276C23×C4—44no—
277C23×C4C2×C4×C1111yescharacteristic
278C23×C4C2×C4×C1111yescharacteristic
279C23×C4C2×C4×C1111yescharacteristic
280C23×C4C2×C4×C1111yescharacteristic
281C23×C4C2×C4×C1111yescharacteristic
282C23×C4C2×C4×C1111yescharacteristic
283C23×C4D4×C1111yescharacteristic
284C23×C4D4×C1111yescharacteristic
285C23×C4D4×C1111yescharacteristic
286C23×C4D4×C1111yescharacteristic
287C23×C4D4×C1111yescharacteristic
288C23×C4Q8×C1111yescharacteristic
289C23×C4Q8×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—44no—
294C22×C8—22no—
295#117—44no—
296C2×C4⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—44no—
303C2×C42C2×C4×C1114yescomplemented
304C22⋊C8—22no—
305C22⋊C8—22no—
306C22⋊C8—22no—
307C22⋊C8C2×C4×C1114yescomplemented
308#95—22no—
309#95—22no—
310#95—22no—
311#95—22no—
312#95—22no—
313#95C2×C4×C1114yes—
314C2×C11—22no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—22no—
318C2×C11—22no—
319C2×C11—41no—
320C2×C11—41no—
321C2×C11C2×H(3,ℤ/4)11yescharacteristic
322C2×C11#173311yescharacteristic
323C2×C11C2×#34211yescharacteristic
324C24—24no—
325C24—42no—
326C24—42no—
327C24C11×C22⋊C411yescharacteristic
328C24C11×C22⋊C411yescharacteristic
329C24C11×C22⋊C411yescharacteristic
330C24C11×C22⋊C411yescharacteristic
331C24C11×C4⋊C411yescharacteristic
332C24C11×C4⋊C411yescharacteristic
333C24C2×D4×C1111yescharacteristic
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4—44no—
353C22×C4C42×C1111yescharacteristic
354C22×C4C42×C1111yescharacteristic
355C22×C4C42×C1111yescharacteristic
356C22×C4C42×C1111yescharacteristic
357C22×C4C11×C22⋊C411yescharacteristic
358C22×C4C11×C22⋊C411yescharacteristic
359C22×C4C11×C22⋊C411yescharacteristic
360C22×C4C11×C22⋊C411yescharacteristic
361C22×C4C11×C22⋊C411yescharacteristic
362C22×C4C11×C22⋊C411yescharacteristic
363C22×C4C11×C22⋊C411yescharacteristic
364C22×C4C11×C22⋊C411yescharacteristic
365C22×C4C11×C4⋊C411yescharacteristic
366C22×C4C11×C4⋊C411yescharacteristic
367C22×C4C11×C4⋊C411yescharacteristic
368C22×C4C11×C4⋊C411yescharacteristic
369C22×C4C11×C4⋊C411yescharacteristic
370C22×C4C11×C4⋊C411yescharacteristic
371C22×C4C11×C4⋊C411yescharacteristic
372C22×C4C11×C4⋊C411yescharacteristic
373C22×C4C11×C4⋊C411yescharacteristic
374C22×C4C11×C4⋊C411yescharacteristic
375C22×C4C22×C4×C1111yescharacteristic
376C22×C4C22×C4×C1111yescharacteristic
377C22×C4C22×C4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×Q8×C1111yescharacteristic
381M16—44no—
382M16—44no—
383C2×C8—24no—
384C2×C8—44no—
385C4⋊C4—44no—
386C22⋊C4—44no—
387C22⋊C4—44no—
388C22⋊C4—44no—
389C22⋊C4—44no—
390C22⋊C4—44no—
391C42—44no—
392C11#794311yescharacteristic, direct product factor, Sylow
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—416no—
414C23C11×#9511yescharacteristic
415C23C11×#9511yescharacteristic
416C23C11×#9511yescharacteristic
417C23C11×#9511yescharacteristic
418C23C11×#9914yes—
419C23C2×C11×C22⋊C411yescharacteristic
420C23C2×C11×C22⋊C411yescharacteristic
421C23C2×C11×C4⋊C411yescharacteristic
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—88no—
457C2×C4C11×#9511yescharacteristic
458C2×C4C11×#9511yescharacteristic
459C2×C4C11×#9511yescharacteristic
460C2×C4C11×#9511yescharacteristic
461C2×C4C2×C42×C1111yescharacteristic
462C2×C4C2×C11×C22⋊C411yescharacteristic
463C2×C4C2×C11×C4⋊C411yescharacteristic
464C2×C4C2×C11×C4⋊C411yescharacteristic
465C8—44no—
466C22—28no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22C11×H(3,ℤ/4)12yes—
490C22C11×#34212yes—
491C22C11×#34212yes—
492C22C2×C11×#9511yescharacteristic
493C22C2×C11×#9912yes—
494C22C11×#42112yes—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—84no—
504C4—84no—
505C2—22no—
506C2—22no—
507C2—22no—
508C2—22no—
509C2—22no—
510C2—41no—
511C2—41no—
512C2C2×C11×H(3,ℤ/4)11yescharacteristic
513C2C11×#173311yescharacteristic
514C2C2×C11×#34211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#95
commutatorC2×C4C2×C42×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1284C2semidirect
7. C2×C11×#117C4semidirect
11. C11×#407C4semidirect
14. C2×C11×C22⋊C8C4semidirect
18. C11×#381C4semidirect
23. C4×C11×C22⋊C4C4semidirect
26. C2×C11×#95C4semidirect
56. C2×C42×C11C2×C4semidirect
60. C11×C22⋊C8C2×C4semidirect
67. #7943C11direct (N × H)
139. #1284C2×C11semidirect
215. C2×#117C4×C11semidirect
219. #407C4×C11semidirect
222. C2×C22⋊C8C4×C11semidirect
226. #381C4×C11semidirect
231. C4×C22⋊C4C4×C11semidirect
234. C2×#95C4×C11semidirect
303. C2×C42C2×C4×C11semidirect
307. C22⋊C8C2×C4×C11semidirect
392. C11#7943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4072
C11×#22802
C2×C11×#3812
C11×#12842
#794311