Finite Group Databasebeta

← C11×#24817 #14602010

Subgroups — C11×#24817 #14602010

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic
3C11×#2567C211yesmaximal, characteristic
4Q8×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#2083C212yesmaximal
6C11×#2068C212yesmaximal
7C11×#1990C211yesmaximal, characteristic
8C11×#1939C211yesmaximal, characteristic
9C11×#1878C212yesmaximal
10C11×#1803C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C11×#477—24no—
18C4×C11×Q16—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#395—22no—
29C11×#391C2212yes—
30C11×#389—21no—
31C11×#389—21no—
32C11×#389—22no—
33C11×#389C2212yes—
34C11×#384—21no—
35C11×#384C2211yescharacteristic
36C11×#384C2212yes—
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16Q814yescomplemented
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—24no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—42no—
59C4×Q8×C11D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C42×C11—21no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#107—22no—
81C11×#107—24no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C11×#103—22no—
85C11×#103—24no—
86C11×#103—22no—
87C11×#103—42no—
88C4×C8×C11—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95D412yes—
93#24817C1111yesmaximal, characteristic, direct product factor, Sylow
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—42no—
103C2×Q8×C11—81no—
104C2×Q8×C11—81no—
105C2×Q8×C11C2×D412yes—
106C2×Q8×C11C2×Q812yes—
107C2×Q8×C11C2×Q812yes—
108C2×Q8×C11#4112yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C11×Q16—28no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11C2×Q812yes—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4—82no—
145C11×C4⋊C4—82no—
146C11×C4⋊C4—82no—
147C11×C4⋊C4Q1614yescomplemented
148C11×C4⋊C4C2×D412yes—
149C42×C11—24no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—44no—
153C42×C11—42no—
154C42×C11C2×D412yes—
155C42×C11#4112yes—
156C2×#477C2×C1111yescharacteristic
157C2×C4×Q16C2×C1111yescharacteristic
158#2567C2×C1111yescharacteristic
159Q8×C4⋊C4C2×C1111yescharacteristic
160#2083C2×C1112yes—
161#2068C2×C1112yes—
162#1990C2×C1111yescharacteristic
163#1939C2×C1111yescharacteristic
164#1878C2×C1112yes—
165#1803C2×C1111yescharacteristic
166#1803C2×C1112yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—22no—
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—41no—
174Q8×C11—41no—
175Q8×C11—84no—
176Q8×C11C22⋊Q814yes—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11C2×Q1614yes—
205C2×C4×C11C2×Q1612yes—
206C2×C4×C11#13712yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×Q811yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×C4×C112−1+411yescharacteristic
213C8×C11—22no—
214C8×C11—41no—
215C8×C11—42no—
216C22×Q16C22×C1111yescharacteristic
217C2×C4⋊Q8C22×C1111yescharacteristic
218C2×C4×Q8C22×C1111yescharacteristic
219C2×C4×Q8C22×C1112yes—
220C2×C4×Q8C22×C1111yescharacteristic
221#477—24no—
222C4×Q16—24no—
223C2×#107C22×C1112yes—
224C2×#107C22×C1111yescharacteristic
225C2×C4⋊C8C22×C1111yescharacteristic
226C2×C4⋊C8C22×C1112yes—
227C2×#103C22×C1112yes—
228C2×#103C22×C1111yescharacteristic
229C2×#103C22×C1111yescharacteristic
230C2×#103C22×C1112yes—
231C2×C4×C8C22×C1111yescharacteristic
232#395—22no—
233#391C22×C1112yes—
234#389—21no—
235#389—21no—
236#389—22no—
237#389C22×C1112yes—
238#384—21no—
239#384C22×C1112yes—
240#384C22×C1111yescharacteristic
241C4×C4⋊C4—21no—
242C4×C4⋊C4C22×C1111yescharacteristic
243#340C22×C1112yes—
244#340C22×C1112yes—
245#340C22×C1112yes—
246#336C22×C1112yes—
247C22×C11C2×#12111yescharacteristic
248C22×C11#54611yescharacteristic
249C22×C11D4×Q811yescharacteristic
250C22×C11C22×Q1611yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11#57611yescharacteristic
253C22×C11#57711yescharacteristic
254C4×C11—24no—
255C4×C11—24no—
256C4×C11—22no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—82no—
261C4×C11—81no—
262C4×C11—82no—
263C4×C11#46214yes—
264C4×C11C2×C22⋊Q811yescharacteristic
265C4×C11#53711yescharacteristic
266C4×C11#55211yescharacteristic
267C4×C11#55411yescharacteristic
268C22×Q8—21no—
269C22×Q8C23×C1111yescharacteristic
270C22×Q8C23×C1111yescharacteristic
271C2×Q16—22no—
272C2×Q16—22no—
273C2×Q16Q8×C1114yescomplemented
274C22×C8C23×C1112yes—
275C22×C8C23×C1111yescharacteristic
276C22×C8C23×C1111yescharacteristic
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4×Q8—22no—
280C4×Q8—24no—
281C4×Q8—22no—
282C4×Q8—22no—
283C4×Q8—42no—
284C4×Q8D4×C1114yes—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4D4×C1111yescharacteristic
295C2×C4⋊C4D4×C1111yescharacteristic
296C2×C4⋊C4C23×C1112yes—
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C42—21no—
301C2×C42—22no—
302C2×C42—21no—
303C2×C42C23×C1112yes—
304C2×C42C23×C1111yescharacteristic
305#107—22no—
306#107—24no—
307C4⋊C8—22no—
308C4⋊C8—42no—
309#103—22no—
310#103—24no—
311#103—22no—
312#103—42no—
313C4×C8—22no—
314#95—22no—
315#95—22no—
316#95—22no—
317#95D4×C1112yes—
318C2×C11#241711yescharacteristic
319C2×C11C2×#46211yescharacteristic
320C2×C11#304511yescharacteristic
321C2×C11#329911yescharacteristic
322C2×C11#333311yescharacteristic
323C2×C11Q8×Q1611yescharacteristic
324C2×C11#338711yescharacteristic
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—42no—
334C2×Q8—81no—
335C2×Q8—81no—
336C2×Q8C2×D4×C1112yes—
337C2×Q8C2×Q8×C1112yes—
338C2×Q8C2×Q8×C1112yes—
339C2×Q8C11×#4112yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4C2×D4×C1112yes—
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C24×C1111yescharacteristic
351Q16—28no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8C2×Q8×C1112yes—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—44no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—81no—
375C4⋊C4—82no—
376C4⋊C4—82no—
377C4⋊C4—82no—
378C4⋊C4C11×Q1614yescomplemented
379C4⋊C4C2×D4×C1112yes—
380C42—24no—
381C42—22no—
382C42—22no—
383C42—44no—
384C42—42no—
385C42C2×D4×C1112yes—
386C42C11×#4112yes—
387C11#2481711yescharacteristic, direct product factor, Sylow
388C23C22×D4×C1111yescharacteristic
389Q8—22no—
390Q8—22no—
391Q8—22no—
392Q8—22no—
393Q8—22no—
394Q8—41no—
395Q8—41no—
396Q8—84no—
397Q8C11×C22⋊Q814yes—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4C11×#12112yes—
424C2×C4C11×#12112yes—
425C2×C4C2×C11×Q1614yes—
426C2×C4C2×C11×Q1612yes—
427C2×C4C11×#13712yes—
428C2×C4C22×D4×C1111yescharacteristic
429C2×C4C22×Q8×C1111yescharacteristic
430C2×C4C2×C11×#4111yescharacteristic
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C11×H(5,𝔽2)11yescharacteristic
433C2×C4C11×2−1+411yescharacteristic
434C8—22no—
435C8—41no—
436C8—42no—
437C22C2×C11×#12111yescharacteristic
438C22C11×#54611yescharacteristic
439C22D4×Q8×C1111yescharacteristic
440C22C22×C11×Q1611yescharacteristic
441C22C2×C11×#13711yescharacteristic
442C22C11×#57611yescharacteristic
443C22C11×#57711yescharacteristic
444C4—24no—
445C4—24no—
446C4—22no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—82no—
453C4C11×#46214yes—
454C4C2×C11×C22⋊Q811yescharacteristic
455C4C11×#53711yescharacteristic
456C4C11×#55211yescharacteristic
457C4C11×#55411yescharacteristic
458C2C11×#241711yescharacteristic
459C2C2×C11×#46211yescharacteristic
460C2C11×#304511yescharacteristic
461C2C11×#329911yescharacteristic
462C2C11×#333311yescharacteristic
463C2Q8×C11×Q1611yescharacteristic
464C2C11×#338711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×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
48. C2×C11×Q16Q8semidirect
93. #24817C11direct (N × H)
147. C11×C4⋊C4Q16semidirect
273. C2×Q16Q8×C11semidirect
378. C4⋊C4C11×Q16semidirect
387. C11#24817direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C2×C4×C11×Q162
C11×#25672
Q8×C11×C4⋊C42
C11×#20832
C11×#20682
C11×#19902
C11×#19392
C11×#18782
C11×#18032
#2481711