Finite Group Databasebeta

← C11×#24576 #14601769

Subgroups — C11×#24576 #14601769

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic
2C22×C11×#107C211yesmaximal, characteristic, complemented
3C11×#2501C211yesmaximal, characteristic
4C11×#2344C211yesmaximal, characteristic, complemented
5C11×#2083C212yesmaximal, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#1947C212yesmaximal, complemented
8C11×#1925C212yesmaximal, complemented
9C11×#1893C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×C11×#123—21no—
14C2×C11×#123—21no—
15C2×C11×#121C2211yescharacteristic
16C2×C11×#117—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#480—24no—
20C2×C11×#107—24no—
21C2×C11×#107C2212yes—
22C2×C11×#107C2212yes—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#399—22no—
31C11×#390C2212yes—
32C11×#389C2212yes—
33C11×#387—22no—
34C11×#384C2212yes—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C8×C11—22no—
49C22×C8×C11—24no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×#123—44no—
54C11×#123—44no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#117—44no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D414yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11—22no—
79C2×C42×C11C2312yes—
80C11×#107—24no—
81C11×#107—24no—
82C11×#107—22no—
83C11×#107—22no—
84C11×C4⋊C8—24no—
85C11×#102—24no—
86C11×#102—22no—
87C11×#102—22no—
88C11×C22⋊C8—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95—22no—
92C11×#95D412yes—
93#24576C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11C2×D411yescharacteristic
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—22no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C2×C8×C11—28no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11#4114yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4C2×D412yes—
144C11×C4⋊C4C2×D412yes—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4D814yes—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—44no—
154C2×#480C2×C1111yescharacteristic
155C22×#107C2×C1111yescharacteristic, complemented
156#2501C2×C1111yescharacteristic
157#2344C2×C1111yescharacteristic, complemented
158#2083C2×C1112yescomplemented
159#2067C2×C1112yescomplemented
160#1947C2×C1112yescomplemented
161#1925C2×C1112yescomplemented
162#1893C2×C1111yescharacteristic
163#1850C2×C1111yescharacteristic, complemented
164#1823C2×C1111yescharacteristic, complemented
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—41no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—42no—
172C23×C11#12112yes—
173C23×C11C2×D812yes—
174C23×C11AGL(1,ℤ/8)12yes—
175C23×C11C22×D411yescharacteristic
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—42no—
179D4×C11—84no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
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—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—48no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—84no—
206C2×C4×C11#12112yes—
207C2×C4×C11C2×D814yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C112−1+412yes—
212C8×C11—24no—
213C8×C11—41no—
214C8×C11—41no—
215C23×C8C22×C1111yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#121C22×C1111yescharacteristic
219C2×#117—21no—
220C22×C4⋊C4C22×C1111yescharacteristic
221C22×C4⋊C4C22×C1111yescharacteristic
222#480—24no—
223C2×#107—24no—
224C2×#107C22×C1111yescharacteristic
225C2×#107C22×C1111yescharacteristic
226C2×#107C22×C1112yes—
227C2×#107C22×C1112yes—
228C2×C4⋊C8C22×C1112yes—
229C2×#102C22×C1111yescharacteristic
230C2×#102C22×C1111yescharacteristic
231C2×#102C22×C1112yes—
232C2×C22⋊C8C22×C1111yescharacteristic
233#399—22no—
234#390C22×C1112yes—
235#389C22×C1112yes—
236#387—22no—
237#384C22×C1112yes—
238#381—21no—
239#380C22×C1111yescharacteristic
240C4×C4⋊C4C22×C1112yes—
241C4×C22⋊C4C22×C1111yescharacteristic
242#340C22×C1112yes—
243#340C22×C1112yes—
244#340C22×C1112yes—
245#336C22×C1112yes—
246C22×C11—24no—
247C22×C11—24no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#45914yes—
256C22×C11C2×#12111yescharacteristic
257C22×C11#54712yes—
258C22×C11C22×D811yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11#57812yes—
261C4×C11—24no—
262C4×C11—22no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—82no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11#52511yescharacteristic
270C4×C11#53611yescharacteristic
271C4×C11#55212yes—
272C22×D4—21no—
273C22×D4C23×C1111yescharacteristic
274C23×C4—21no—
275C23×C4—21no—
276C23×C4C23×C1111yescharacteristic
277C22×C8—22no—
278C22×C8—24no—
279C22×C8C23×C1111yescharacteristic
280C22×C8C23×C1111yescharacteristic
281C22×C8C23×C1112yes—
282#123—44no—
283#123—44no—
284#121—22no—
285#121—22no—
286#117—44no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4D4×C1114yes—
296C2×C4⋊C4C23×C1112yes—
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C4⋊C4C23×C1111yescharacteristic
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4D4×C1111yescharacteristic
306C2×C22⋊C4D4×C1111yescharacteristic
307C2×C42—22no—
308C2×C42C23×C1112yes—
309#107—24no—
310#107—24no—
311#107—22no—
312#107—22no—
313C4⋊C8—24no—
314#102—24no—
315#102—22no—
316#102—22no—
317C22⋊C8—22no—
318#95—22no—
319#95—21no—
320#95—22no—
321#95D4×C1112yes—
322C2×C11—24no—
323C2×C11—161no—
324C2×C11#241311yescharacteristic
325C2×C11C2×#45911yescharacteristic
326C2×C11#304411yescharacteristic
327C2×C11#333412yes—
328C2×C11#334312yes—
329C24—21no—
330C24C2×D4×C1111yescharacteristic
331C2×D4—21no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—22no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—42no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4C2×D4×C1112yes—
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C11×#4112yes—
356C22×C4C24×C1111yescharacteristic
357C2×C8—28no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8C11×#4114yes—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—44no—
375C4⋊C4—42no—
376C4⋊C4—44no—
377C4⋊C4—44no—
378C4⋊C4C2×D4×C1112yes—
379C4⋊C4C2×D4×C1112yes—
380C22⋊C4—22no—
381C22⋊C4—44no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—44no—
385C22⋊C4C11×D814yes—
386C42—22no—
387C42—22no—
388C42—44no—
389C11#2457611yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23—41no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23—42no—
397C23C11×#12112yes—
398C23C2×C11×D812yes—
399C23C11×AGL(1,ℤ/8)12yes—
400C23C22×D4×C1111yescharacteristic
401D4—41no—
402D4—41no—
403D4—42no—
404D4—84no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—48no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—84no—
431C2×C4C11×#12112yes—
432C2×C4C2×C11×D814yes—
433C2×C4C22×D4×C1111yescharacteristic
434C2×C4C2×C11×#4112yes—
435C2×C4C2×C11×#4111yescharacteristic
436C2×C4C11×2−1+412yes—
437C8—24no—
438C8—41no—
439C8—41no—
440C22—22no—
441C22—22no—
442C22—24no—
443C22—24no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—82no—
448C22—82no—
449C22C11×#45914yes—
450C22C2×C11×#12111yescharacteristic
451C22C11×#54712yes—
452C22C22×C11×D811yescharacteristic
453C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
454C22C11×#57812yes—
455C4—22no—
456C4—24no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4—81no—
462C4—82no—
463C4C11×#52511yescharacteristic
464C4C11×#53611yescharacteristic
465C4C11×#55212yes—
466C2—24no—
467C2—161no—
468C2C11×#241311yescharacteristic
469C2C2×C11×#45911yescharacteristic
470C2C11×#304411yescharacteristic
471C2C11×#333412yes—
472C2C11×#334312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#107C2semidirect
4. C11×#2344C2semidirect
5. C11×#2083C2semidirect
6. C11×#2067C2semidirect
7. C11×#1947C2semidirect
8. C11×#1925C2semidirect
10. C11×#1850C2semidirect
11. C11×#1823C2semidirect
93. #24576C11direct (N × H)
155. C22×#107C2×C11semidirect
157. #2344C2×C11semidirect
158. #2083C2×C11semidirect
159. #2067C2×C11semidirect
160. #1947C2×C11semidirect
161. #1925C2×C11semidirect
163. #1850C2×C11semidirect
164. #1823C2×C11semidirect
389. C11#24576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C22×C11×#1072
C11×#25012
C11×#23442
C11×#20832
C11×#20672
C11×#19472
C11×#19252
C11×#18932
C11×#18502
C11×#18232
#2457611