Finite Group Databasebeta

← C11×#23094 #14600287

Subgroups — C11×#23094 #14600287

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic
2C11×#2365C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic
4C11×#1968C212yesmaximal
5C11×#1956C211yesmaximal, characteristic, complemented
6C11×#1948C211yesmaximal, characteristic, complemented
7C11×#1927C212yesmaximal, complemented
8C11×#1880C212yesmaximal
9C8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
10C4×C11×#103C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#117—21no—
17C11×#461C418yescomplemented
18C2×C11×#106C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×C4×C8×C11C2212yes—
27C11×#391C2212yes—
28C11×#390C2212yes—
29C11×#389—21no—
30C11×#388—22no—
31C11×#387—22no—
32C11×#384C2211yescharacteristic
33C11×#380—21no—
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#336C2212yes—
42C22×Q8×C11C2312yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C2×C11×SD16—42no—
46C2×C11×SD16—42no—
47C2×C11×SD16C2×C418yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C4×Q8×C11—24no—
54C4×Q8×C11—42no—
55C4×D4×C11—22no—
56C4×D4×C11C2×C414yes—
57C11×#117—44no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—22no—
73C2×C42×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C11×#106—42no—
78C11×C4⋊C8C2×C414yes—
79C11×#103—24no—
80C11×#103—42no—
81C11×#103C2×C418yes—
82C11×#102—22no—
83C11×#102—22no—
84C4×C8×C11—22no—
85C4×C8×C11—42no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95D412yes—
91#23094C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22×C414yes—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11C22×C412yes—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—24no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C11×SD16—48no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11C22×C414yes—
127C2×C8×C11#4112yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—81no—
140C11×C4⋊C4SD1614yescomplemented
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4#4112yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—82no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—44no—
149C42×C11—44no—
150C42×C11—42no—
151C42×C11C22×C412yes—
152C42×C11#4112yes—
153C2×#461C2×C1111yescharacteristic
154#2365C2×C1111yescharacteristic, complemented
155#2354C2×C1111yescharacteristic
156#1968C2×C1112yes—
157#1956C2×C1111yescharacteristic, complemented
158#1948C2×C1111yescharacteristic, complemented
159#1927C2×C1112yescomplemented
160#1880C2×C1112yes—
161C8×C4⋊C4C2×C1111yescharacteristic, complemented
162C4×#103C2×C1112yescomplemented
163C4×#102C2×C1111yescharacteristic
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C22×D411yescharacteristic
172Q8×C11—24no—
173Q8×C11—24no—
174Q8×C11—42no—
175Q8×C11—42no—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—41no—
179D4×C11—41no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—48no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11C4×D412yes—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C2×SD1614yes—
206C2×C4×C11C2×SD1612yes—
207C2×C4×C11#13512yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C8×C11—24no—
215C8×C11—22no—
216C8×C11—41no—
217C22×SD16C22×C1112yes—
218C2×C4⋊Q8C22×C1111yescharacteristic
219C2×C4×Q8C22×C1112yes—
220C2×C4×D4C22×C1111yescharacteristic
221C2×#117—21no—
222#461C4×C1118yescomplemented
223C2×#106C22×C1112yes—
224C2×C4⋊C8C22×C1111yescharacteristic
225C2×#103C22×C1112yes—
226C2×#103C22×C1112yes—
227C2×#103C22×C1112yes—
228C2×#102C22×C1111yescharacteristic
229C2×#102C22×C1111yescharacteristic
230C2×C4×C8C22×C1111yescharacteristic
231C2×C4×C8C22×C1112yes—
232#391C22×C1112yes—
233#390C22×C1112yes—
234#389—21no—
235#388—22no—
236#387—22no—
237#384C22×C1111yescharacteristic
238#380—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4C22×C1112yes—
241C4×C4⋊C4C22×C1111yescharacteristic
242C4×C4⋊C4C22×C1111yescharacteristic
243#340C22×C1112yes—
244#340C22×C1111yescharacteristic
245#340C22×C1111yescharacteristic
246#336C22×C1112yes—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11C2×C4×D411yescharacteristic
255C22×C11#54611yescharacteristic
256C22×C11#55011yescharacteristic
257C22×C11C22×SD1611yescharacteristic
258C22×C11C2×#13511yescharacteristic
259C22×C11#57711yescharacteristic
260C22×C11#57811yescharacteristic
261C4×C11—22no—
262C4×C11—24no—
263C4×C11—44no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11C4×SD1614yes—
270C4×C11C4×#4111yescharacteristic
271C4×C11#51811yescharacteristic
272C4×C11#55311yescharacteristic
273C4×C11#55511yescharacteristic
274C22×Q8C23×C1112yes—
275C22×D4C23×C1111yescharacteristic
276C23×C4—21no—
277C2×SD16—42no—
278C2×SD16—42no—
279C2×SD16C2×C4×C1118yes—
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1112yes—
282C22×C8C23×C1111yescharacteristic
283C4⋊Q8—22no—
284C4⋊Q8C2×C4×C1114yes—
285C4×Q8—24no—
286C4×Q8—42no—
287C4×D4—22no—
288C4×D4C2×C4×C1114yes—
289#117—44no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4D4×C1111yescharacteristic
296C2×C4⋊C4D4×C1111yescharacteristic
297C2×C4⋊C4C23×C1112yes—
298C2×C4⋊C4C23×C1111yescharacteristic
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C4⋊C4C23×C1111yescharacteristic
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—21no—
307C2×C42C23×C1112yes—
308C2×C42C23×C1111yescharacteristic
309#106—42no—
310C4⋊C8C2×C4×C1114yes—
311#103—24no—
312#103—42no—
313#103C2×C4×C1118yes—
314#102—22no—
315#102—22no—
316C4×C8—22no—
317C4×C8—42no—
318#95—22no—
319#95—22no—
320#95—21no—
321#95—22no—
322#95D4×C1112yes—
323C2×C11—82no—
324C2×C11#236311yescharacteristic
325C2×C11C2×C4×SD1611yescharacteristic
326C2×C11#294711yescharacteristic
327C2×C11#329811yescharacteristic
328C2×C11#330311yescharacteristic
329C2×C11#339211yescharacteristic
330C2×C11#339311yescharacteristic
331C24—21no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8C22×C4×C1114yes—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4C22×C4×C1112yes—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C2×D4×C1112yes—
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C24×C1111yescharacteristic
357SD16—48no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8C22×C4×C1114yes—
366C2×C8C11×#4112yes—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—44no—
377C4⋊C4—42no—
378C4⋊C4—81no—
379C4⋊C4C11×SD1614yescomplemented
380C4⋊C4C22×C4×C1112yes—
381C4⋊C4C11×#4112yes—
382C22⋊C4—24no—
383C22⋊C4—44no—
384C22⋊C4—82no—
385C42—22no—
386C42—22no—
387C42—44no—
388C42—44no—
389C42—42no—
390C42C22×C4×C1112yes—
391C42C11×#4112yes—
392C11#2309411yescharacteristic, direct product factor, Sylow
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23C22×D4×C1111yescharacteristic
401Q8—24no—
402Q8—24no—
403Q8—42no—
404Q8—42no—
405D4—22no—
406D4—22no—
407D4—41no—
408D4—41no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—48no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4C4×D4×C1112yes—
433C2×C4C4×D4×C1112yes—
434C2×C4C2×C11×SD1614yes—
435C2×C4C2×C11×SD1612yes—
436C2×C4C11×#13512yes—
437C2×C4C23×C4×C1111yescharacteristic
438C2×C4C2×C11×#4111yescharacteristic
439C2×C4C2×C11×#4111yescharacteristic
440C2×C4C2×C11×#4111yescharacteristic
441C2×C4C11×H(5,𝔽2)11yescharacteristic
442C2×C4C11×H(5,𝔽2)11yescharacteristic
443C8—24no—
444C8—22no—
445C8—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22C2×C4×D4×C1111yescharacteristic
454C22C11×#54611yescharacteristic
455C22C11×#55011yescharacteristic
456C22C22×C11×SD1611yescharacteristic
457C22C2×C11×#13511yescharacteristic
458C22C11×#57711yescharacteristic
459C22C11×#57811yescharacteristic
460C4—22no—
461C4—24no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—44no—
466C4—82no—
467C4—81no—
468C4C4×C11×SD1614yes—
469C4C4×C11×#4111yescharacteristic
470C4C11×#51811yescharacteristic
471C4C11×#55311yescharacteristic
472C4C11×#55511yescharacteristic
473C2—82no—
474C2C11×#236311yescharacteristic
475C2C2×C4×C11×SD1611yescharacteristic
476C2C11×#294711yescharacteristic
477C2C11×#329811yescharacteristic
478C2C11×#330311yescharacteristic
479C2C11×#339211yescharacteristic
480C2C11×#339311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2365C2semidirect
5. C11×#1956C2semidirect
6. C11×#1948C2semidirect
7. C11×#1927C2semidirect
9. C8×C11×C4⋊C4C2semidirect
10. C4×C11×#103C2semidirect
17. C11×#461C4semidirect
91. #23094C11direct (N × H)
140. C11×C4⋊C4SD16semidirect
154. #2365C2×C11semidirect
157. #1956C2×C11semidirect
158. #1948C2×C11semidirect
159. #1927C2×C11semidirect
161. C8×C4⋊C4C2×C11semidirect
162. C4×#103C2×C11semidirect
222. #461C4×C11semidirect
379. C4⋊C4C11×SD16semidirect
392. C11#23094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C11×#23652
C11×#23542
C11×#19682
C11×#19562
C11×#19482
C11×#19272
C11×#18802
C8×C11×C4⋊C42
C4×C11×#1032
C4×C11×#1022
#2309411