Finite Group Databasebeta

← C11×#23760 #14600953

Subgroups — C11×#23760 #14600953

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#121C211yesmaximal, characteristic
2C11×#2285C211yesmaximal, characteristic, complemented
3C11×#2100C211yesmaximal, characteristic, complemented
4C11×#2094C211yesmaximal, characteristic, complemented
5C11×#2083C211yesmaximal, characteristic, complemented
6C11×#2077C212yesmaximal, complemented
7C11×#2071C211yesmaximal, characteristic, complemented
8C11×#2033C212yesmaximal
9C11×#1776C212yesmaximal, complemented
10C11×#1762C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C2×C11×#121C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C22×C42×C11C2211yescharacteristic
17C2×C11×#107C2212yes—
18C2×C11×#106C2212yes—
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×#97C2212yes—
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#386—21no—
27C11×#384C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C11×#382—21no—
30C11×#380—21no—
31C11×#380C2212yes—
32C11×#380C2211yescharacteristic
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4—21no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2211yescharacteristic
42C11×#336C2211yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C22×C8×C11C2312yes—
51C11×#121—22no—
52C11×#121—22no—
53C4×D4×C11—24no—
54C4×D4×C11—44no—
55C11×#117—44no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—24no—
73C2×C42×C11—22no—
74C2×C42×C11—21no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—24no—
80C11×#106—24no—
81C11×#102—24no—
82C11×#102—24no—
83C11×C22⋊C8—24no—
84C11×#97—24no—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—21no—
90#23760C1111yesmaximal, characteristic, direct product factor, Sylow
91C24×C11—21no—
92C24×C11C2×D411yescharacteristic
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—21no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11#4112yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—41no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11#4114yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4#4112yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—42no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—44no—
153C42×C11—42no—
154C42×C11#4114yes—
155C4×#121C2×C1111yescharacteristic
156#2285C2×C1111yescharacteristic, complemented
157#2100C2×C1111yescharacteristic, complemented
158#2094C2×C1111yescharacteristic, complemented
159#2083C2×C1111yescharacteristic, complemented
160#2077C2×C1112yescomplemented
161#2071C2×C1111yescharacteristic, complemented
162#2033C2×C1112yes—
163#1776C2×C1112yescomplemented
164#1762C2×C1112yescomplemented
165#1749C2×C1111yescharacteristic, complemented
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—22no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11AGL(1,ℤ/8)12yes—
180C23×C11C22×D411yescharacteristic
181D4×C11—24no—
182D4×C11—48no—
183D4×C11—42no—
184C2×C4×C11—28no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—44no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—84no—
215C2×C4×C11#12312yes—
216C2×C4×C11#12312yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C2×#4112yes—
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4112yes—
223C8×C11—24no—
224C8×C11—42no—
225C2×#121C22×C1111yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C22×C1111yescharacteristic
228C2×#117—21no—
229C22×C42C22×C1111yescharacteristic
230C2×#107C22×C1112yes—
231C2×#106C22×C1112yes—
232C2×#102C22×C1112yes—
233C2×#102C22×C1112yes—
234C2×C22⋊C8C22×C1112yes—
235C2×#97C22×C1112yes—
236#390C22×C1111yescharacteristic
237#389C22×C1111yescharacteristic
238#388—21no—
239#386—21no—
240#384C22×C1111yescharacteristic
241#384C22×C1111yescharacteristic
242#382—21no—
243#380—21no—
244#380C22×C1111yescharacteristic
245#380C22×C1112yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C22×C1112yes—
248C4×C4⋊C4C22×C1111yescharacteristic
249C4×C22⋊C4—21no—
250#340C22×C1112yes—
251#340C22×C1112yes—
252#340C22×C1112yes—
253#340C22×C1112yes—
254#336C22×C1111yescharacteristic
255#336C22×C1111yescharacteristic
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C2×#12311yescharacteristic
271C22×C11#52511yescharacteristic
272C22×C11#53211yescharacteristic
273C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57511yescharacteristic
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—42no—
282C4×C11—41no—
283C4×C11—81no—
284C4×C11—82no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11#52912yes—
288C4×C11#52912yes—
289C22×D4—21no—
290C22×D4C23×C1111yescharacteristic
291C23×C4—21no—
292C23×C4D4×C1111yescharacteristic
293C23×C4D4×C1111yescharacteristic
294C23×C4C23×C1111yescharacteristic
295C22×C8C23×C1112yes—
296C22×C8C23×C1112yes—
297#121—22no—
298#121—22no—
299C4×D4—24no—
300C4×D4—44no—
301#117—44no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4C23×C1111yescharacteristic
308C2×C4⋊C4C23×C1112yes—
309C2×C4⋊C4C23×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C4⋊C4C23×C1111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C42—24no—
319C2×C42—22no—
320C2×C42—21no—
321C2×C42D4×C1111yescharacteristic
322C2×C42D4×C1111yescharacteristic
323C2×C42C23×C1111yescharacteristic
324C2×C42C23×C1111yescharacteristic
325#107—24no—
326#106—24no—
327#102—24no—
328#102—24no—
329C22⋊C8—24no—
330#97—24no—
331#95—21no—
332#95—21no—
333#95—22no—
334#95—22no—
335#95—21no—
336C2×C11—42no—
337C2×C11—82no—
338C2×C11#239511yescharacteristic
339C2×C11#309211yescharacteristic
340C2×C11#309411yescharacteristic
341C2×C11#310911yescharacteristic
342C2×C11#311611yescharacteristic
343C2×C11#318011yescharacteristic
344C2×C11#318211yescharacteristic
345C24—21no—
346C24C2×D4×C1111yescharacteristic
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4C11×#4112yes—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C24×C1111yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8C11×#4114yes—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4C11×#4112yes—
397C22⋊C4—24no—
398C22⋊C4—42no—
399C22⋊C4—44no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—44no—
407C42—42no—
408C42C11×#4114yes—
409C11#2376011yescharacteristic, direct product factor, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23C11×AGL(1,ℤ/8)12yes—
424C23C22×D4×C1111yescharacteristic
425D4—24no—
426D4—48no—
427D4—42no—
428C2×C4—28no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—84no—
459C2×C4C11×#12312yes—
460C2×C4C11×#12312yes—
461C2×C4C11×AGL(1,ℤ/8)12yes—
462C2×C4C11×#13712yes—
463C2×C4C2×C11×#4112yes—
464C2×C4C2×C11×#4111yescharacteristic
465C2×C4C2×C11×#4111yescharacteristic
466C2×C4C2×C11×#4112yes—
467C8—24no—
468C8—42no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×C11×#12311yescharacteristic
484C22C11×#52511yescharacteristic
485C22C11×#53211yescharacteristic
486C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
487C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
488C22C2×C11×#13711yescharacteristic
489C22C11×#57511yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—22no—
494C4—41no—
495C4—42no—
496C4—82no—
497C4—81no—
498C4—81no—
499C4—82no—
500C4C11×#52912yes—
501C4C11×#52912yes—
502C2—42no—
503C2—82no—
504C2C11×#239511yescharacteristic
505C2C11×#309211yescharacteristic
506C2C11×#309411yescharacteristic
507C2C11×#310911yescharacteristic
508C2C11×#311611yescharacteristic
509C2C11×#318011yescharacteristic
510C2C11×#318211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2285C2semidirect
3. C11×#2100C2semidirect
4. C11×#2094C2semidirect
5. C11×#2083C2semidirect
6. C11×#2077C2semidirect
7. C11×#2071C2semidirect
9. C11×#1776C2semidirect
10. C11×#1762C2semidirect
11. C11×#1749C2semidirect
90. #23760C11direct (N × H)
156. #2285C2×C11semidirect
157. #2100C2×C11semidirect
158. #2094C2×C11semidirect
159. #2083C2×C11semidirect
160. #2077C2×C11semidirect
161. #2071C2×C11semidirect
163. #1776C2×C11semidirect
164. #1762C2×C11semidirect
165. #1749C2×C11semidirect
409. C11#23760direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1212
C11×#22852
C11×#21002
C11×#20942
C11×#20832
C11×#20772
C11×#20712
C11×#20332
C11×#17762
C11×#17622
C11×#17492
#2376011