Finite Group Databasebeta

← C11×#24497 #14601690

Subgroups — C11×#24497 #14601690

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic, complemented
3C11×#2436C211yesmaximal, characteristic
4C11×#2347C211yesmaximal, characteristic, complemented
5C11×#2068C212yesmaximal, complemented
6C11×#2042C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1927C212yesmaximal, complemented
9C11×#1895C211yesmaximal, characteristic
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#121C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#482—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C11×#419—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#393—21no—
31C11×#393—21no—
32C11×#391C2212yes—
33C11×#389C2212yes—
34C11×#388—22no—
35C11×#386—22no—
36C11×#383—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C22⋊C4C2211yescharacteristic
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11—24no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2312yes—
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C2×C11×M16—22no—
54C2×C11×M16—42no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×#124—24no—
59C11×#124—42no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#117—22no—
63C11×#117D414yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C42×C11C2312yes—
78C11×#107—22no—
79C11×#106—22no—
80C11×C4⋊C8—42no—
81C11×#103—24no—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103—42no—
85C11×#102—22no—
86C11×#102—22no—
87C11×#102—42no—
88C11×C22⋊C8—22no—
89C11×#95—21no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95D411yescharacteristic
95C11×#95D411yescharacteristic
96#24497C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—22no—
100C2×Q8×C11—28no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—44no—
106C2×Q8×C11—48no—
107C2×Q8×C11—44no—
108C2×Q8×C11—42no—
109C2×Q8×C11#4114yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—44no—
115C2×D4×C11—42no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—44no—
124C22×C4×C11—42no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C11×M16—44no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4C2×D412yes—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—42no—
153C11×C22⋊C4—81no—
154C42×C11—24no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—82no—
158C2×#482C2×C1111yescharacteristic
159C2×#419C2×C1111yescharacteristic, complemented
160#2436C2×C1111yescharacteristic
161#2347C2×C1111yescharacteristic, complemented
162#2068C2×C1112yescomplemented
163#2042C2×C1112yescomplemented
164#1983C2×C1112yescomplemented
165#1927C2×C1112yescomplemented
166#1895C2×C1111yescharacteristic
167#1851C2×C1111yescharacteristic, complemented
168#1787C2×C1111yescharacteristic, complemented
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11#12112yes—
179C23×C11C22×D411yescharacteristic
180Q8×C11—24no—
181Q8×C11—24no—
182Q8×C11—48no—
183Q8×C11—42no—
184Q8×C11—42no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—42no—
188D4×C11—84no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—48no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11#12112yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4112yes—
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C8×C11—41no—
219C8×C11—41no—
220C8×C11—42no—
221C23×Q8C22×C1111yescharacteristic
222C22×M16C22×C1111yescharacteristic
223C2×#124C22×C1112yes—
224C2×#121C22×C1111yescharacteristic
225C2×#117C22×C1111yescharacteristic
226#482—24no—
227C2×#107C22×C1111yescharacteristic
228C2×#106C22×C1111yescharacteristic
229C2×C4⋊C8C22×C1112yes—
230#419—24no—
231C2×#103C22×C1112yes—
232C2×#103C22×C1112yes—
233C2×#103C22×C1112yes—
234C2×#103C22×C1112yes—
235C2×#102C22×C1111yescharacteristic
236C2×#102C22×C1111yescharacteristic
237C2×#102C22×C1112yes—
238C2×C22⋊C8C22×C1111yescharacteristic
239#393—21no—
240#393—21no—
241#391C22×C1112yes—
242#389C22×C1112yes—
243#388—22no—
244#386—22no—
245#383—21no—
246#380C22×C1111yescharacteristic
247C4×C4⋊C4—21no—
248C4×C4⋊C4C22×C1112yes—
249C4×C22⋊C4C22×C1111yescharacteristic
250#340C22×C1112yes—
251#336C22×C1112yes—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11C2×#12111yescharacteristic
263C22×C11#54612yes—
264C22×C11#57512yes—
265C22×C11#57711yescharacteristic
266C22×C11#57811yescharacteristic
267C4×C11—22no—
268C4×C11—44no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11—82no—
275C4×C11#52511yescharacteristic
276C4×C11#53511yescharacteristic
277C4×C11#55112yes—
278C22×Q8—21no—
279C22×Q8—24no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—42no—
283C22×Q8C23×C1112yes—
284C22×D4—21no—
285C22×D4C23×C1111yescharacteristic
286C23×C4—21no—
287C23×C4C23×C1111yescharacteristic
288C2×M16—22no—
289C2×M16—42no—
290C22×C8C23×C1112yes—
291C22×C8C23×C1111yescharacteristic
292C22×C8C23×C1111yescharacteristic
293#124—24no—
294#124—42no—
295#121—22no—
296#121—22no—
297#117—22no—
298#117D4×C1114yes—
299C2×C4⋊C4—22no—
300C2×C4⋊C4C23×C1111yescharacteristic
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1111yescharacteristic
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4D4×C1112yes—
310C2×C42—21no—
311C2×C42—22no—
312C2×C42C23×C1112yes—
313#107—22no—
314#106—22no—
315C4⋊C8—42no—
316#103—24no—
317#103—24no—
318#103—24no—
319#103—42no—
320#102—22no—
321#102—22no—
322#102—42no—
323C22⋊C8—22no—
324#95—21no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—22no—
329#95D4×C1111yescharacteristic
330#95D4×C1111yescharacteristic
331C2×C11—42no—
332C2×C11—161no—
333C2×C11#241111yescharacteristic
334C2×C11#304011yescharacteristic
335C2×C11#304611yescharacteristic
336C2×C11#331312yes—
337C2×C11#332612yes—
338C24—21no—
339C24C2×D4×C1111yescharacteristic
340C2×Q8—22no—
341C2×Q8—28no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—44no—
347C2×Q8—48no—
348C2×Q8—44no—
349C2×Q8—42no—
350C2×Q8C11×#4114yes—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—44no—
356C2×D4—42no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4C2×D4×C1112yes—
367C22×C4C2×D4×C1112yes—
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1112yes—
370C22×C4C11×#4112yes—
371C22×C4C24×C1111yescharacteristic
372M16—44no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—44no—
387C4⋊C4C2×D4×C1112yes—
388C4⋊C4C2×D4×C1112yes—
389C22⋊C4—24no—
390C22⋊C4—42no—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—42no—
394C22⋊C4—81no—
395C42—24no—
396C42—22no—
397C42—22no—
398C42—82no—
399C11#2449711yescharacteristic, direct product factor, Sylow
400C23—22no—
401C23—22no—
402C23—21no—
403C23—21no—
404C23—41no—
405C23—42no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23C11×#12112yes—
410C23C22×D4×C1111yescharacteristic
411Q8—24no—
412Q8—24no—
413Q8—48no—
414Q8—42no—
415Q8—42no—
416D4—41no—
417D4—41no—
418D4—42no—
419D4—84no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4C11×#12112yes—
445C2×C4C22×D4×C1111yescharacteristic
446C2×C4C2×C11×#4112yes—
447C2×C4C2×C11×#4111yescharacteristic
448C2×C4C11×H(5,𝔽2)12yes—
449C8—41no—
450C8—42no—
451C8—41no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—82no—
461C22—82no—
462C22C2×C11×#12111yescharacteristic
463C22C11×#54612yes—
464C22C11×#57512yes—
465C22C11×#57711yescharacteristic
466C22C11×#57811yescharacteristic
467C4—22no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—82no—
475C4C11×#52511yescharacteristic
476C4C11×#53511yescharacteristic
477C4C11×#55112yes—
478C2—42no—
479C2—161no—
480C2C11×#241111yescharacteristic
481C2C11×#304011yescharacteristic
482C2C11×#304611yescharacteristic
483C2C11×#331312yes—
484C2C11×#332612yes—
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. C2×C11×#419C2semidirect
4. C11×#2347C2semidirect
5. C11×#2068C2semidirect
6. C11×#2042C2semidirect
7. C11×#1983C2semidirect
8. C11×#1927C2semidirect
10. C11×#1851C2semidirect
11. C11×#1787C2semidirect
96. #24497C11direct (N × H)
159. C2×#419C2×C11semidirect
161. #2347C2×C11semidirect
162. #2068C2×C11semidirect
163. #2042C2×C11semidirect
164. #1983C2×C11semidirect
165. #1927C2×C11semidirect
167. #1851C2×C11semidirect
168. #1787C2×C11semidirect
399. C11#24497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C2×C11×#4192
C11×#24362
C11×#23472
C11×#20682
C11×#20422
C11×#19832
C11×#19272
C11×#18952
C11×#18512
C11×#17872
#2449711