Finite Group Databasebeta

← C11×#24649 #14601842

Subgroups — C11×#24649 #14601842

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C11×#2548C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic, complemented
5C11×#2055C212yesmaximal, complemented
6C11×#2015C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1926C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#460—24no—
19C11×#441—24no—
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#97C2211yescharacteristic
30C11×#394—21no—
31C11×#394—21no—
32C11×#391C2212yes—
33C11×#390—22no—
34C11×#390C2212yes—
35C11×#387—22no—
36C11×#383—21no—
37C11×#382C2211yescharacteristic
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C11×#376—21no—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C2×C11×Q16—22no—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×SD16—24no—
52C2×C11×SD16—42no—
53C2×C11×SD16—42no—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#127—22no—
58C11×#127—22no—
59C11×#124—24no—
60C11×#124—42no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11D414yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C42×C11—21no—
78C2×C42×C11C2312yes—
79C2×C42×C11C2311yescharacteristic
80C11×#106—22no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—42no—
83C11×#103—22no—
84C11×#103—22no—
85C11×#103—42no—
86C11×#102—24no—
87C11×#102—24no—
88C11×#102—42no—
89C11×#97—22no—
90C11×#95—21no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—21no—
94C11×#95—22no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24649C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—22no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4112yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—44no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—82no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C11×Q16—28no—
132C11×SD16—48no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11#4112yes—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—82no—
154C11×C22⋊C4—82no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—44no—
159C42×C11—42no—
160C42×C11C2×D412yes—
161C42×C11#4112yes—
162C2×#460C2×C1111yescharacteristic
163C2×#441C2×C1111yescharacteristic, complemented
164#2548C2×C1111yescharacteristic
165#2356C2×C1111yescharacteristic, complemented
166#2055C2×C1112yescomplemented
167#2015C2×C1112yescomplemented
168#1983C2×C1112yescomplemented
169#1961C2×C1111yescharacteristic
170#1940C2×C1111yescharacteristic, complemented
171#1926C2×C1112yescomplemented
172#1805C2×C1111yescharacteristic, complemented
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—22no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—41no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—84no—
194D4×C11—84no—
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—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C8×C11—22no—
225C8×C11—41no—
226C8×C11—42no—
227C22×Q16C22×C1111yescharacteristic
228C22×SD16C22×C1112yes—
229C2×#127C22×C1111yescharacteristic
230C2×#124C22×C1112yes—
231C2×C4×Q8C22×C1111yescharacteristic
232C2×C4×Q8C22×C1111yescharacteristic
233#460—24no—
234#441—24no—
235C2×#106C22×C1111yescharacteristic
236C2×C4⋊C8C22×C1111yescharacteristic
237C2×C4⋊C8C22×C1112yes—
238C2×#103C22×C1111yescharacteristic
239C2×#103C22×C1111yescharacteristic
240C2×#103C22×C1112yes—
241C2×#102C22×C1112yes—
242C2×#102C22×C1112yes—
243C2×#102C22×C1112yes—
244C2×#97C22×C1111yescharacteristic
245#394—21no—
246#394—21no—
247#391C22×C1112yes—
248#390—22no—
249#390C22×C1112yes—
250#387—22no—
251#383—21no—
252#382C22×C1111yescharacteristic
253C4×C4⋊C4C22×C1112yes—
254C4×C4⋊C4C22×C1111yescharacteristic
255#376—21no—
256#340C22×C1112yes—
257#336C22×C1112yes—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11#55011yescharacteristic
268C22×C11#57512yes—
269C22×C11#57712yes—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11#52511yescharacteristic
280C4×C11#53511yescharacteristic
281C4×C11#55311yescharacteristic
282C4×C11#55511yescharacteristic
283C22×Q8C23×C1111yescharacteristic
284C22×Q8C23×C1111yescharacteristic
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C23×C1112yes—
288C2×Q16—22no—
289C2×Q16—22no—
290C2×Q16—22no—
291C2×SD16—24no—
292C2×SD16—42no—
293C2×SD16—42no—
294C22×C8C23×C1112yes—
295C22×C8C23×C1111yescharacteristic
296C22×C8C23×C1111yescharacteristic
297#127—22no—
298#127—22no—
299#124—24no—
300#124—42no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8D4×C1114yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4D4×C1112yes—
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C4⋊C4C23×C1112yes—
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42C23×C1112yes—
319C2×C42C23×C1111yescharacteristic
320#106—22no—
321C4⋊C8—22no—
322C4⋊C8—42no—
323#103—22no—
324#103—22no—
325#103—42no—
326#102—24no—
327#102—24no—
328#102—42no—
329#97—22no—
330#95—21no—
331#95—22no—
332#95—22no—
333#95—21no—
334#95—22no—
335#95D4×C1111yescharacteristic
336#95D4×C1111yescharacteristic
337C2×C11—162no—
338C2×C11#241411yescharacteristic
339C2×C11#304011yescharacteristic
340C2×C11#304311yescharacteristic
341C2×C11#331712yes—
342C2×C11#340112yes—
343C24—22no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8C2×D4×C1112yes—
355C2×Q8C11×#4112yes—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—44no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—82no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1112yes—
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C24×C1111yescharacteristic
376Q16—28no—
377SD16—48no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8C11×#4112yes—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4C2×D4×C1112yes—
396C22⋊C4—44no—
397C22⋊C4—44no—
398C22⋊C4—82no—
399C22⋊C4—82no—
400C42—24no—
401C42—22no—
402C42—22no—
403C42—44no—
404C42—42no—
405C42C2×D4×C1112yes—
406C42C11×#4112yes—
407C11#2464911yescharacteristic, direct product factor, Sylow
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23C22×D4×C1111yescharacteristic
416Q8—22no—
417Q8—22no—
418Q8—22no—
419Q8—22no—
420Q8—41no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—84no—
429D4—84no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4C11×#12112yes—
452C2×C4C11×#12112yes—
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C2×C11×#4111yescharacteristic
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C2×C11×#4111yescharacteristic
457C2×C4C11×H(5,𝔽2)11yescharacteristic
458C2×C4C11×H(5,𝔽2)11yescharacteristic
459C8—22no—
460C8—42no—
461C8—41no—
462C22—82no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22C2×C11×#12111yescharacteristic
470C22C11×#54611yescharacteristic
471C22C11×#55011yescharacteristic
472C22C11×#57512yes—
473C22C11×#57712yes—
474C4—22no—
475C4—22no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—81no—
482C4—82no—
483C4C11×#52511yescharacteristic
484C4C11×#53511yescharacteristic
485C4C11×#55311yescharacteristic
486C4C11×#55511yescharacteristic
487C2—162no—
488C2C11×#241411yescharacteristic
489C2C11×#304011yescharacteristic
490C2C11×#304311yescharacteristic
491C2C11×#331712yes—
492C2C11×#340112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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×#441C2semidirect
4. C11×#2356C2semidirect
5. C11×#2055C2semidirect
6. C11×#2015C2semidirect
7. C11×#1983C2semidirect
9. C11×#1940C2semidirect
10. C11×#1926C2semidirect
11. C11×#1805C2semidirect
97. #24649C11direct (N × H)
163. C2×#441C2×C11semidirect
165. #2356C2×C11semidirect
166. #2055C2×C11semidirect
167. #2015C2×C11semidirect
168. #1983C2×C11semidirect
170. #1940C2×C11semidirect
171. #1926C2×C11semidirect
172. #1805C2×C11semidirect
407. C11#24649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C11×#4412
C11×#25482
C11×#23562
C11×#20552
C11×#20152
C11×#19832
C11×#19612
C11×#19402
C11×#19262
C11×#18052
#2464911