Finite Group Databasebeta

← C11×#24743 #14601936

Subgroups — C11×#24743 #14601936

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C212yesmaximal
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2547C211yesmaximal, characteristic
5C11×#2351C211yesmaximal, characteristic, complemented
6C11×#2068C212yesmaximal, complemented
7C11×#2042C212yesmaximal
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1878C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#464—28no—
20C11×#462—24no—
21C11×#440—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2212yes—
31C2×C11×#97C2211yescharacteristic
32C11×#397—21no—
33C11×#397—21no—
34C11×#391C2212yes—
35C11×#389—22no—
36C11×#389C2212yes—
37C11×#382—21no—
38C11×#382C2211yescharacteristic
39C11×#380—22no—
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C2×C11×Q16—24no—
49C2×C11×Q16—24no—
50C2×C11×Q16—24no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16D414yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×#124—24no—
60C11×#124—42no—
61C4×Q8×C11—22no—
62C4×Q8×C11—24no—
63C4×Q8×C11—42no—
64C4×Q8×C11D414yes—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11—21no—
80C2×C42×C11—22no—
81C2×C42×C11C2312yes—
82C2×C42×C11C2311yescharacteristic
83C11×#107—22no—
84C11×C4⋊C8—24no—
85C11×C4⋊C8—22no—
86C11×#103—22no—
87C11×#103—24no—
88C11×#103—24no—
89C11×#103—42no—
90C11×#102—24no—
91C11×#102—22no—
92C11×#97—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—21no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100#24743C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D412yes—
112C2×Q8×C11C2×D412yes—
113C2×Q8×C11#4112yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C11×Q16—48no—
133C11×SD16—28no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—44no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4C2×D412yes—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—42no—
158C42×C11—24no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—44no—
162C42×C11C2×D412yes—
163C42×C11#4112yes—
164C2×#464C2×C1112yes—
165C2×#462C2×C1111yescharacteristic, complemented
166C2×#440C2×C1111yescharacteristic
167#2547C2×C1111yescharacteristic
168#2351C2×C1111yescharacteristic, complemented
169#2068C2×C1112yescomplemented
170#2042C2×C1112yes—
171#1960C2×C1111yescharacteristic, complemented
172#1940C2×C1111yescharacteristic, complemented
173#1878C2×C1112yescomplemented
174#1804C2×C1111yescharacteristic
175C23×C11—22no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11#12114yes—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
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—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—84no—
215C2×C4×C11#12112yes—
216C2×C4×C11#12112yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C112−1+411yescharacteristic
223C8×C11—22no—
224C8×C11—42no—
225C8×C11—41no—
226C22×Q16C22×C1112yes—
227C22×SD16C22×C1111yescharacteristic
228C2×C4⋊Q8C22×C1111yescharacteristic
229C2×#124C22×C1112yes—
230C2×C4×Q8C22×C1112yes—
231C2×C4×Q8C22×C1111yescharacteristic
232C2×C4×D4C22×C1111yescharacteristic
233#464—28no—
234#462—24no—
235#440—24no—
236C2×#107C22×C1111yescharacteristic
237C2×C4⋊C8C22×C1111yescharacteristic
238C2×C4⋊C8C22×C1112yes—
239C2×#103C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×#103C22×C1111yescharacteristic
242C2×#103C22×C1112yes—
243C2×#102C22×C1112yes—
244C2×#102C22×C1111yescharacteristic
245C2×#97C22×C1111yescharacteristic
246#397—21no—
247#397—21no—
248#391C22×C1112yes—
249#389—22no—
250#389C22×C1112yes—
251#382—21no—
252#382C22×C1111yescharacteristic
253#380—22no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4C22×C1111yescharacteristic
256#340C22×C1112yes—
257#336C22×C1112yes—
258C22×C11—42no—
259C22×C11—44no—
260C22×C11—82no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11C2×#12111yescharacteristic
264C22×C11D4211yescharacteristic
265C22×C11#54811yescharacteristic
266C22×C11#57512yes—
267C22×C11#57812yes—
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11C2×#12111yescharacteristic
278C4×C11#53711yescharacteristic
279C4×C11#54711yescharacteristic
280C4×C11#55311yescharacteristic
281C22×Q8C23×C1112yes—
282C22×Q8C23×C1111yescharacteristic
283C22×D4C23×C1111yescharacteristic
284C23×C4—21no—
285C2×Q16—24no—
286C2×Q16—24no—
287C2×Q16—24no—
288C2×SD16—22no—
289C2×SD16—22no—
290C2×SD16D4×C1114yes—
291C22×C8C23×C1112yes—
292C22×C8C23×C1111yescharacteristic
293C22×C8C23×C1111yescharacteristic
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296#124—24no—
297#124—42no—
298C4×Q8—22no—
299C4×Q8—24no—
300C4×Q8—42no—
301C4×Q8D4×C1114yes—
302C4×D4—22no—
303C4×D4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4D4×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C4⋊C4C23×C1112yes—
312C2×C4⋊C4C23×C1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42C23×C1112yes—
319C2×C42C23×C1111yescharacteristic
320#107—22no—
321C4⋊C8—24no—
322C4⋊C8—22no—
323#103—22no—
324#103—24no—
325#103—24no—
326#103—42no—
327#102—24no—
328#102—22no—
329#97—22no—
330#95—21no—
331#95—22no—
332#95—22no—
333#95—22no—
334#95—21no—
335#95D4×C1111yescharacteristic
336#95D4×C1111yescharacteristic
337C2×C11—82no—
338C2×C11#241611yescharacteristic
339C2×C11#304011yescharacteristic
340C2×C11#304411yescharacteristic
341C2×C11#326912yes—
342C2×C11#337712yes—
343C24—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8C2×D4×C1112yes—
354C2×Q8C2×D4×C1112yes—
355C2×Q8C11×#4112yes—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4C2×D4×C1112yes—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1112yes—
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C24×C1111yescharacteristic
374Q16—48no—
375SD16—28no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8C2×D4×C1112yes—
385C4⋊C4—24no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—42no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4C2×D4×C1112yes—
397C22⋊C4—44no—
398C22⋊C4—44no—
399C22⋊C4—42no—
400C42—24no—
401C42—22no—
402C42—22no—
403C42—44no—
404C42C2×D4×C1112yes—
405C42C11×#4112yes—
406C11#2474311yescharacteristic, direct product factor, Sylow
407C23—22no—
408C23—41no—
409C23—41no—
410C23—42no—
411C23—42no—
412C23C22×D4×C1111yescharacteristic
413Q8—22no—
414Q8—22no—
415Q8—22no—
416Q8—42no—
417Q8—42no—
418Q8—42no—
419Q8—42no—
420Q8C11×#12114yes—
421D4—22no—
422D4—22no—
423D4—41no—
424D4—41no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—84no—
447C2×C4C11×#12112yes—
448C2×C4C11×#12112yes—
449C2×C4C22×D4×C1111yescharacteristic
450C2×C4C22×D4×C1111yescharacteristic
451C2×C4C2×C11×#4111yescharacteristic
452C2×C4C2×C11×#4111yescharacteristic
453C2×C4C11×H(5,𝔽2)11yescharacteristic
454C2×C4C11×2−1+411yescharacteristic
455C8—22no—
456C8—42no—
457C8—41no—
458C22—42no—
459C22—44no—
460C22—81no—
461C22—81no—
462C22—82no—
463C22C2×C11×#12111yescharacteristic
464C22D42×C1111yescharacteristic
465C22C11×#54811yescharacteristic
466C22C11×#57512yes—
467C22C11×#57812yes—
468C4—24no—
469C4—22no—
470C4—22no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—82no—
475C4—82no—
476C4—81no—
477C4C2×C11×#12111yescharacteristic
478C4C11×#53711yescharacteristic
479C4C11×#54711yescharacteristic
480C4C11×#55311yescharacteristic
481C2—82no—
482C2C11×#241611yescharacteristic
483C2C11×#304011yescharacteristic
484C2C11×#304411yescharacteristic
485C2C11×#326912yes—
486C2C11×#337712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
2. C2×C11×#462C2semidirect
5. C11×#2351C2semidirect
6. C11×#2068C2semidirect
8. C11×#1960C2semidirect
9. C11×#1940C2semidirect
10. C11×#1878C2semidirect
100. #24743C11direct (N × H)
165. C2×#462C2×C11semidirect
168. #2351C2×C11semidirect
169. #2068C2×C11semidirect
171. #1960C2×C11semidirect
172. #1940C2×C11semidirect
173. #1878C2×C11semidirect
406. C11#24743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4642
C2×C11×#4622
C2×C11×#4402
C11×#25472
C11×#23512
C11×#20682
C11×#20422
C11×#19602
C11×#19402
C11×#18782
C11×#18042
#2474311