Finite Group Databasebeta

← C11×#24483 #14601676

Subgroups — C11×#24483 #14601676

Order 2816.

984 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×#481C211yesmaximal, characteristic
2C22×C11×#103C211yesmaximal, characteristic, complemented
3C11×#2436C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic, complemented
5C11×#2066C212yesmaximal, complemented
6C11×#2042C212yesmaximal, complemented
7C11×#1983C212yesmaximal, complemented
8C11×#1927C212yesmaximal, complemented
9C11×#1893C211yesmaximal, characteristic
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#124C2212yes—
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#481—24no—
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C11×#103—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—22no—
31C11×#391C2212yes—
32C11×#389C2212yes—
33C11×#387—22no—
34C11×#386—21no—
35C11×#386—21no—
36C11×#380—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C22⋊C4—21no—
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×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C8×C11—22no—
55C22×C8×C11—42no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C11×#124—24no—
60C11×#124—42no—
61C11×#121—22no—
62C11×#121—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D414yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11—22no—
78C2×C42×C11C2312yes—
79C11×#106—22no—
80C11×#106—22no—
81C11×C4⋊C8—42no—
82C11×#103—24no—
83C11×#103—24no—
84C11×#103—24no—
85C11×#103—42no—
86C11×#102—22no—
87C11×#102—22no—
88C11×#102—42no—
89C11×C22⋊C8—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95D412yes—
96#24483C1111yesmaximal, 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—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11—42no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—44no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—82no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—82no—
161C2×#481C2×C1111yescharacteristic
162C22×#103C2×C1111yescharacteristic, complemented
163#2436C2×C1111yescharacteristic
164#2345C2×C1111yescharacteristic, complemented
165#2066C2×C1112yescomplemented
166#2042C2×C1112yescomplemented
167#1983C2×C1112yescomplemented
168#1927C2×C1112yescomplemented
169#1893C2×C1111yescharacteristic
170#1850C2×C1111yescharacteristic, complemented
171#1787C2×C1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—42no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—42no—
179C23×C11#12112yes—
180C23×C11#13512yes—
181C23×C11#13712yes—
182C23×C11C22×D411yescharacteristic
183Q8×C11—24no—
184Q8×C11—24no—
185Q8×C11—48no—
186Q8×C11—42no—
187Q8×C11—42no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—42no—
191D4×C11—84no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—48no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—84no—
217C2×C4×C11#12112yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)12yes—
222C8×C11—41no—
223C8×C11—41no—
224C8×C11—42no—
225C23×Q8C22×C1111yescharacteristic
226C23×C8C22×C1111yescharacteristic
227C2×#124C22×C1112yes—
228C2×#121C22×C1111yescharacteristic
229C22×C4⋊C4C22×C1111yescharacteristic
230#481—24no—
231C2×#106C22×C1111yescharacteristic
232C2×#106C22×C1111yescharacteristic
233C2×C4⋊C8C22×C1112yes—
234C2×#103—24no—
235C2×#103C22×C1112yes—
236C2×#103C22×C1112yes—
237C2×#103C22×C1112yes—
238C2×#103C22×C1112yes—
239C2×#102C22×C1111yescharacteristic
240C2×#102C22×C1111yescharacteristic
241C2×#102C22×C1112yes—
242C2×C22⋊C8C22×C1111yescharacteristic
243#393—22no—
244#391C22×C1112yes—
245#389C22×C1112yes—
246#387—22no—
247#386—21no—
248#386—21no—
249#380—21no—
250#380C22×C1111yescharacteristic
251C4×C4⋊C4C22×C1112yes—
252C4×C22⋊C4—21no—
253C4×C22⋊C4C22×C1111yescharacteristic
254#340C22×C1112yes—
255#336C22×C1112yes—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11#46414yes—
266C22×C11C2×#12111yescharacteristic
267C22×C11#54612yes—
268C22×C11C2×#13511yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11#57712yes—
271C4×C11—22no—
272C4×C11—44no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—81no—
278C4×C11—82no—
279C4×C11#52511yescharacteristic
280C4×C11#53511yescharacteristic
281C4×C11#55112yes—
282C22×Q8—21no—
283C22×Q8—24no—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—42no—
287C22×Q8C23×C1112yes—
288C22×D4—21no—
289C22×D4C23×C1111yescharacteristic
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C23×C1111yescharacteristic
293C22×C8—22no—
294C22×C8—42no—
295C22×C8C23×C1112yes—
296C22×C8C23×C1111yescharacteristic
297C22×C8C23×C1111yescharacteristic
298#124—24no—
299#124—42no—
300#121—22no—
301#121—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4D4×C1114yes—
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C4⋊C4C23×C1112yes—
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C4⋊C4C23×C1111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4D4×C1111yescharacteristic
315C2×C22⋊C4D4×C1111yescharacteristic
316C2×C42—22no—
317C2×C42C23×C1112yes—
318#106—22no—
319#106—22no—
320C4⋊C8—42no—
321#103—24no—
322#103—24no—
323#103—24no—
324#103—42no—
325#102—22no—
326#102—22no—
327#102—42no—
328C22⋊C8—22no—
329#95—22no—
330#95—22no—
331#95—21no—
332#95—22no—
333#95—22no—
334#95D4×C1112yes—
335C2×C11—24no—
336C2×C11—161no—
337C2×C11#241111yescharacteristic
338C2×C11C2×#46411yescharacteristic
339C2×C11#304211yescharacteristic
340C2×C11#330112yes—
341C2×C11#331612yes—
342C24—21no—
343C24C2×D4×C1111yescharacteristic
344C2×Q8—22no—
345C2×Q8—28no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—44no—
351C2×Q8—48no—
352C2×Q8—44no—
353C2×Q8—42no—
354C2×Q8C11×#4114yes—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—44no—
371C22×C4—42no—
372C22×C4—82no—
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1112yes—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1112yes—
377C22×C4C11×#4112yes—
378C22×C4C24×C1111yescharacteristic
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—44no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—82no—
395C4⋊C4C2×D4×C1112yes—
396C4⋊C4C2×D4×C1112yes—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—44no—
400C22⋊C4—44no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C42—22no—
404C42—22no—
405C42—82no—
406C11#2448311yescharacteristic, direct product factor, Sylow
407C23—22no—
408C23—22no—
409C23—41no—
410C23—42no—
411C23—41no—
412C23—41no—
413C23—42no—
414C23C11×#12112yes—
415C23C11×#13512yes—
416C23C11×#13712yes—
417C23C22×D4×C1111yescharacteristic
418Q8—24no—
419Q8—24no—
420Q8—48no—
421Q8—42no—
422Q8—42no—
423D4—41no—
424D4—41no—
425D4—42no—
426D4—84no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—84no—
452C2×C4C11×#12112yes—
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C2×C11×#4112yes—
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C11×H(5,𝔽2)12yes—
457C8—41no—
458C8—42no—
459C8—41no—
460C22—22no—
461C22—22no—
462C22—24no—
463C22—24no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—82no—
468C22—82no—
469C22C11×#46414yes—
470C22C2×C11×#12111yescharacteristic
471C22C11×#54612yes—
472C22C2×C11×#13511yescharacteristic
473C22C2×C11×#13711yescharacteristic
474C22C11×#57712yes—
475C4—22no—
476C4—44no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—81no—
482C4—82no—
483C4C11×#52511yescharacteristic
484C4C11×#53511yescharacteristic
485C4C11×#55112yes—
486C2—24no—
487C2—161no—
488C2C11×#241111yescharacteristic
489C2C2×C11×#46411yescharacteristic
490C2C11×#304211yescharacteristic
491C2C11×#330112yes—
492C2C11×#331612yes—
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. C22×C11×#103C2semidirect
4. C11×#2345C2semidirect
5. C11×#2066C2semidirect
6. C11×#2042C2semidirect
7. C11×#1983C2semidirect
8. C11×#1927C2semidirect
10. C11×#1850C2semidirect
11. C11×#1787C2semidirect
96. #24483C11direct (N × H)
162. C22×#103C2×C11semidirect
164. #2345C2×C11semidirect
165. #2066C2×C11semidirect
166. #2042C2×C11semidirect
167. #1983C2×C11semidirect
168. #1927C2×C11semidirect
170. #1850C2×C11semidirect
171. #1787C2×C11semidirect
406. C11#24483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4812
C22×C11×#1032
C11×#24362
C11×#23452
C11×#20662
C11×#20422
C11×#19832
C11×#19272
C11×#18932
C11×#18502
C11×#17872
#2448311