Finite Group Databasebeta

← C11×#24529 #14601722

Subgroups — C11×#24529 #14601722

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#451C211yesmaximal, characteristic
2C22×C11×#103C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic
4Q8×C11×C22⋊C4C211yesmaximal, characteristic
5C11×#2074C212yesmaximal, complemented
6C11×#2056C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic
8C11×#1878C212yesmaximal, complemented
9C11×#1850C211yesmaximal, characteristic
10C11×#1823C211yesmaximal, characteristic
11C11×#1805C212yesmaximal, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#451—24no—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×#103—24no—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#400—22no—
29C11×#391—22no—
30C11×#391C2212yes—
31C11×#391C2212yes—
32C11×#382C2212yes—
33C11×#381—21no—
34C11×#381—21no—
35C11×#380—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11—24no—
46C22×Q8×C11—42no—
47C22×Q8×C11D414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×Q8×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C2×C11×Q16—22no—
55C2×C11×Q16—22no—
56C2×C11×Q16—24no—
57C2×C11×Q16—42no—
58C22×C8×C11—22no—
59C22×C8×C11—42no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C4×Q8×C11—24no—
66C4×Q8×C11—42no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C42×C11—22no—
80C2×C42×C11C2312yes—
81C11×C4⋊C8—42no—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103—22no—
85C11×#103—22no—
86C11×#103—42no—
87C11×C22⋊C8—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—21no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95D412yes—
96#24529C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C2×D411yescharacteristic
98C2×Q8×C11—24no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—28no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×Q8×C11—48no—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11#4114yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C11×Q16—44no—
135C11×Q16—44no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—44no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—44no—
160C2×#451C2×C1111yescharacteristic
161C22×#103C2×C1111yescharacteristic
162#2503C2×C1111yescharacteristic
163Q8×C22⋊C4C2×C1111yescharacteristic
164#2074C2×C1112yescomplemented
165#2056C2×C1112yescomplemented
166#1892C2×C1111yescharacteristic
167#1878C2×C1112yescomplemented
168#1850C2×C1111yescharacteristic
169#1823C2×C1111yescharacteristic
170#1805C2×C1112yescomplemented
171C23×C11—22no—
172C23×C11—22no—
173C23×C11#12112yes—
174C23×C11#13512yes—
175C23×C11#13712yes—
176C23×C11C22×D411yescharacteristic
177Q8×C11—22no—
178Q8×C11—24no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—48no—
182Q8×C11—42no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—42no—
186Q8×C11#12314yes—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
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—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—48no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—84no—
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—42no—
220C8×C11—41no—
221C23×Q8C22×C1111yescharacteristic
222C22×Q16C22×C1111yescharacteristic
223C22×Q16C22×C1111yescharacteristic
224C23×C8C22×C1111yescharacteristic
225C2×C22⋊Q8C22×C1111yescharacteristic
226C2×C4×Q8C22×C1112yes—
227C22×C4⋊C4C22×C1111yescharacteristic
228#451—24no—
229C2×C4⋊C8C22×C1112yes—
230C2×#103—24no—
231C2×#103C22×C1112yes—
232C2×#103C22×C1111yescharacteristic
233C2×#103C22×C1112yes—
234C2×#103C22×C1111yescharacteristic
235C2×#103C22×C1112yes—
236C2×C22⋊C8C22×C1111yescharacteristic
237#400—22no—
238#391—22no—
239#391C22×C1112yes—
240#391C22×C1112yes—
241#382C22×C1112yes—
242#381—21no—
243#381—21no—
244#380—21no—
245#380C22×C1111yescharacteristic
246C4×C22⋊C4—21no—
247C4×C22⋊C4C22×C1111yescharacteristic
248#340C22×C1112yes—
249#340C22×C1112yes—
250#340C22×C1112yes—
251#336C22×C1112yes—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11#46414yes—
257C22×C11C2×#12111yescharacteristic
258C22×C11#54612yes—
259C22×C11C2×#13511yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C22×C11#57812yes—
262C4×C11—22no—
263C4×C11—24no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—81no—
268C4×C11—82no—
269C4×C11—81no—
270C4×C11—82no—
271C4×C11C2×#12311yescharacteristic
272C4×C11#53411yescharacteristic
273C4×C11#55112yes—
274C22×Q8—21no—
275C22×Q8—22no—
276C22×Q8—24no—
277C22×Q8—42no—
278C22×Q8D4×C1114yes—
279C22×Q8C23×C1111yescharacteristic
280C22×Q8C23×C1111yescharacteristic
281C22×Q8C23×C1111yescharacteristic
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C23×C1111yescharacteristic
285C2×Q16—22no—
286C2×Q16—22no—
287C2×Q16—24no—
288C2×Q16—42no—
289C22×C8—22no—
290C22×C8—42no—
291C22×C8C23×C1112yes—
292C22×C8C23×C1111yescharacteristic
293C22×C8C23×C1111yescharacteristic
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C4×Q8—24no—
297C4×Q8—42no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4C23×C1112yes—
304C2×C4⋊C4C23×C1112yes—
305C2×C4⋊C4C23×C1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4D4×C1111yescharacteristic
309C2×C22⋊C4D4×C1111yescharacteristic
310C2×C42—22no—
311C2×C42C23×C1112yes—
312C4⋊C8—42no—
313#103—24no—
314#103—24no—
315#103—22no—
316#103—22no—
317#103—42no—
318C22⋊C8—22no—
319#95—22no—
320#95—22no—
321#95—21no—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95D4×C1112yes—
327C2×C11—24no—
328C2×C11#241211yescharacteristic
329C2×C11C2×#46411yescharacteristic
330C2×C11#304411yescharacteristic
331C2×C11#330012yes—
332C2×C11#331212yes—
333C24C2×D4×C1111yescharacteristic
334C2×Q8—24no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8—28no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×Q8—48no—
348C2×Q8C2×D4×C1112yes—
349C2×Q8C2×D4×C1112yes—
350C2×Q8C11×#4114yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—44no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4C2×D4×C1112yes—
365C22×C4C2×D4×C1112yes—
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C2×D4×C1112yes—
368C22×C4C11×#4112yes—
369C22×C4C24×C1111yescharacteristic
370Q16—44no—
371Q16—44no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—44no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—44no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—42no—
392C22⋊C4—42no—
393C42—22no—
394C42—22no—
395C42—44no—
396C11#2452911yescharacteristic, direct product factor, Sylow
397C23—22no—
398C23—22no—
399C23C11×#12112yes—
400C23C11×#13512yes—
401C23C11×#13712yes—
402C23C22×D4×C1111yescharacteristic
403Q8—22no—
404Q8—24no—
405Q8—22no—
406Q8—22no—
407Q8—48no—
408Q8—42no—
409Q8—41no—
410Q8—41no—
411Q8—42no—
412Q8C11×#12314yes—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—48no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—84no—
439C2×C4C11×#12112yes—
440C2×C4C22×D4×C1111yescharacteristic
441C2×C4C2×C11×#4112yes—
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C11×H(5,𝔽2)12yes—
444C8—41no—
445C8—42no—
446C8—41no—
447C22—22no—
448C22—22no—
449C22—24no—
450C22—24no—
451C22C11×#46414yes—
452C22C2×C11×#12111yescharacteristic
453C22C11×#54612yes—
454C22C2×C11×#13511yescharacteristic
455C22C2×C11×#13711yescharacteristic
456C22C11×#57812yes—
457C4—22no—
458C4—24no—
459C4—42no—
460C4—42no—
461C4—42no—
462C4—81no—
463C4—82no—
464C4—81no—
465C4—82no—
466C4C2×C11×#12311yescharacteristic
467C4C11×#53411yescharacteristic
468C4C11×#55112yes—
469C2—24no—
470C2C11×#241211yescharacteristic
471C2C2×C11×#46411yescharacteristic
472C2C11×#304411yescharacteristic
473C2C11×#330012yes—
474C2C11×#331212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
5. C11×#2074C2semidirect
6. C11×#2056C2semidirect
8. C11×#1878C2semidirect
11. C11×#1805C2semidirect
96. #24529C11direct (N × H)
164. #2074C2×C11semidirect
165. #2056C2×C11semidirect
167. #1878C2×C11semidirect
170. #1805C2×C11semidirect
396. C11#24529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4512
C22×C11×#1032
C11×#25032
Q8×C11×C22⋊C42
C11×#20742
C11×#20562
C11×#18922
C11×#18782
C11×#18502
C11×#18232
C11×#18052
#2452911