Finite Group Databasebeta

← C11×#10046 #14587239

Subgroups — C11×#10046 #14587239

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#493C211yesmaximal, characteristic, complemented
2C2×C11×#459C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic, complemented
4C11×#1982C211yesmaximal, characteristic, complemented
5C2×C11×#331C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C22×C11×D8—22no—
10C2×C11×#127—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C11×#121—22no—
14C2×C4×D4×C11C2211yescharacteristic
15C11×#493—22no—
16C11×#493—22no—
17C11×#459—22no—
18C11×#459—22no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102—21no—
22C2×C11×#102—22no—
23C2×C4×C8×C11C2211yescharacteristic
24C11×#392—22no—
25C11×#390—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#331—22no—
28C11×D4⋊C8—22no—
29C22×D4×C11—24no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11D411yescharacteristic
36C22×D4×C11D412yes—
37C23×C4×C11—21no—
38C2×C11×D8—28no—
39C2×C11×D8—24no—
40C2×C11×D8—48no—
41C2×C11×D8—42no—
42C2×C11×D8—42no—
43C22×C8×C11—21no—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127—42no—
54C11×#127—42no—
55C11×#127D412yescomplemented
56C11×#121—44no—
57C11×#121—44no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4D412yes—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yescomplemented
72C11×#102—24no—
73C11×#102—44no—
74C4×C8×C11—21no—
75C4×C8×C11D412yescomplemented
76C11×#95—21no—
77#10046C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C24×C11—22no—
80C24×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—44no—
92C2×D4×C11—44no—
93C2×D4×C11—48no—
94C2×D4×C11—48no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—84no—
115C2×D4×C11D812yescomplemented
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C11×D8—48no—
126C11×D8—416no—
127C2×C8×C11—24no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C2×C8×C11—42no—
133C2×C8×C11—41no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4D814yescomplemented
138C11×C22⋊C4—48no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C42×C11—41no—
142C42×C11—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C2×#493C2×C1111yescharacteristic, complemented
148C2×#459C2×C1111yescharacteristic, complemented
149#2541C2×C1111yescharacteristic, complemented
150#1982C2×C1111yescharacteristic, complemented
151C2×#331C2×C1111yescharacteristic, complemented
152C2×D4⋊C8C2×C1111yescharacteristic, complemented
153#1279C2×C1111yescharacteristic, complemented
154C23×C11—22no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—44no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—44no—
165C23×C11—81no—
166C23×C11—82no—
167C23×C11—81no—
168C23×C11—82no—
169C23×C11#12011yescharacteristic
170D4×C11—22no—
171D4×C11—22no—
172D4×C11—44no—
173D4×C11—44no—
174D4×C11—42no—
175D4×C11—41no—
176D4×C11—42no—
177D4×C11—44no—
178D4×C11—41no—
179D4×C11—82no—
180D4×C11—82no—
181D4×C11—816no—
182D4×C11—81no—
183D4×C11—81no—
184D4×C11—82no—
185D4×C11—81no—
186D4×C11—81no—
187D4×C11—81no—
188D4×C11—81no—
189D4×C11—81no—
190D4×C11—81no—
191D4×C11—81no—
192D4×C11—81no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11—81no—
201C2×C4×C11—81no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12711yescharacteristic
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D812yes—
210C2×C4×C11#13511yescharacteristic
211C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C8×C11—24no—
215C8×C11—42no—
216C8×C11—81no—
217C22×D8—22no—
218C22×D8—21no—
219C2×#127—21no—
220C2×#127C22×C1111yescharacteristic
221C2×#127C22×C1111yescharacteristic
222C2×#121—22no—
223C2×C4×D4C22×C1111yescharacteristic
224#493—22no—
225#493—22no—
226#459—22no—
227#459—22no—
228C2×C4⋊C8C22×C1111yescharacteristic
229C2×C4⋊C8C22×C1111yescharacteristic
230C2×#102—21no—
231C2×#102—22no—
232C2×C4×C8C22×C1111yescharacteristic
233#392—22no—
234#390—21no—
235C4×C4⋊C4C22×C1111yescharacteristic
236#331—22no—
237D4⋊C8—22no—
238C22×C11—44no—
239C22×C11—42no—
240C22×C11—82no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—84no—
244C22×C11—84no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—162no—
252C22×C11—162no—
253C22×C11#39211yescharacteristic
254C22×C11#44711yescharacteristic
255C22×C11#44712yes—
256C22×C11#44911yescharacteristic
257C22×C11#45312yes—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—44no—
261C4×C11—81no—
262C4×C11#44711yescharacteristic
263C4×C11#44911yescharacteristic
264C4×C11#45912yes—
265C4×C11#46611yescharacteristic
266C4×C11#46911yescharacteristic
267C4×C11#49311yescharacteristic
268C4×C11#49611yescharacteristic
269C22×D4—24no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4D4×C1111yescharacteristic
276C22×D4D4×C1112yes—
277C23×C4—21no—
278C2×D8—24no—
279C2×D8—28no—
280C2×D8—48no—
281C2×D8—42no—
282C2×D8—42no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286#127—21no—
287#127—21no—
288#127—21no—
289#127—21no—
290#127—21no—
291#127—21no—
292#127—21no—
293#127—42no—
294#127—42no—
295#127D4×C1112yescomplemented
296#121—44no—
297#121—44no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C2×C4⋊C4D4×C1111yescharacteristic
303C2×C4⋊C4D4×C1112yes—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—21no—
306C2×C42—21no—
307C2×C42C23×C1111yescharacteristic
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8—21no—
311C4⋊C8D4×C1112yescomplemented
312#102—24no—
313#102—44no—
314C4×C8—21no—
315C4×C8D4×C1112yescomplemented
316#95—21no—
317C2×C11—82no—
318C2×C11—162no—
319C2×C11—162no—
320C2×C11#161912yes—
321C2×C11#162112yes—
322C2×C11#199911yescharacteristic
323C2×C11#200211yescharacteristic
324C2×C11#201111yescharacteristic
325C24—21no—
326C24—22no—
327C24—41no—
328C2×D4—21no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—48no—
341C2×D4—48no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—42no—
350C2×D4—41no—
351C2×D4—42no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—42no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—84no—
362C2×D4C11×D812yescomplemented
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372D8—416no—
373D8—48no—
374C2×C8—24no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—42no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4C11×D814yescomplemented
385C22⋊C4—48no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C42—41no—
389C42—41no—
390C42C2×D4×C1111yescharacteristic
391C42C2×D4×C1111yescharacteristic
392C42C2×D4×C1111yescharacteristic
393C42C11×#4111yescharacteristic
394C11#1004611yescharacteristic, direct product factor, Sylow
395C23—22no—
396C23—41no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—44no—
403C23—42no—
404C23—42no—
405C23—44no—
406C23—81no—
407C23—82no—
408C23—81no—
409C23—82no—
410C23C11×#12011yescharacteristic
411D4—22no—
412D4—22no—
413D4—44no—
414D4—44no—
415D4—42no—
416D4—41no—
417D4—42no—
418D4—44no—
419D4—41no—
420D4—82no—
421D4—82no—
422D4—816no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—82no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—81no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4C11×#12011yescharacteristic
444C2×C4C11×#12011yescharacteristic
445C2×C4C11×#12111yescharacteristic
446C2×C4C11×#12111yescharacteristic
447C2×C4C11×#12111yescharacteristic
448C2×C4C11×#12711yescharacteristic
449C2×C4C2×C11×D812yes—
450C2×C4C2×C11×D811yescharacteristic
451C2×C4C11×#13511yescharacteristic
452C2×C4C11×AGL(1,ℤ/8)12yes—
453C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
454C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
455C8—24no—
456C8—42no—
457C8—81no—
458C22—44no—
459C22—42no—
460C22—82no—
461C22—81no—
462C22—81no—
463C22—84no—
464C22—84no—
465C22—82no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—162no—
472C22—162no—
473C22C11×#39211yescharacteristic
474C22C11×#44711yescharacteristic
475C22C11×#44712yes—
476C22C11×#44911yescharacteristic
477C22C11×#45312yes—
478C4—21no—
479C4—21no—
480C4—44no—
481C4—81no—
482C4C11×#44711yescharacteristic
483C4C11×#44911yescharacteristic
484C4C11×#45912yes—
485C4C11×#46611yescharacteristic
486C4C11×#46911yescharacteristic
487C4C11×#49311yescharacteristic
488C4C11×#49611yescharacteristic
489C2—82no—
490C2—162no—
491C2—162no—
492C2C11×#161912yes—
493C2C11×#162112yes—
494C2C11×#199911yescharacteristic
495C2C11×#200211yescharacteristic
496C2C11×#201111yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#493C2semidirect
2. C2×C11×#459C2semidirect
3. C11×#2541C2semidirect
4. C11×#1982C2semidirect
5. C2×C11×#331C2semidirect
6. C2×C11×D4⋊C8C2semidirect
7. C11×#1279C2semidirect
55. C11×#127D4semidirect
71. C11×C4⋊C8D4semidirect
75. C4×C8×C11D4semidirect
77. #10046C11direct (N × H)
115. C2×D4×C11D8semidirect
137. C11×C4⋊C4D8semidirect
147. C2×#493C2×C11semidirect
148. C2×#459C2×C11semidirect
149. #2541C2×C11semidirect
150. #1982C2×C11semidirect
151. C2×#331C2×C11semidirect
152. C2×D4⋊C8C2×C11semidirect
153. #1279C2×C11semidirect
295. #127D4×C11semidirect
311. C4⋊C8D4×C11semidirect
315. C4×C8D4×C11semidirect
362. C2×D4C11×D8semidirect
384. C4⋊C4C11×D8semidirect
394. C11#10046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4932
C2×C11×#4592
C11×#25412
C11×#19822
C2×C11×#3312
C2×C11×D4⋊C82
C11×#12792
#1004611