Finite Group Databasebeta

← C11×#24679 #14601872

Subgroups — C11×#24679 #14601872

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic, complemented
5C11×#2074C212yesmaximal, complemented
6C11×#2055C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1949C212yesmaximal, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1925C212yesmaximal
11C11×#1802C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#477—24no—
17C4×C11×SD16—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#393—22no—
28C11×#391C2212yes—
29C11×#390C2212yes—
30C11×#387—22no—
31C11×#384C2211yescharacteristic
32C11×#382—21no—
33C11×#382C2212yes—
34C11×#380—21no—
35C11×#380—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16—22no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11D414yes—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11—22no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C11×#107—24no—
77C11×#106—22no—
78C11×C4⋊C8—24no—
79C11×C4⋊C8—22no—
80C11×#103—22no—
81C11×#103—24no—
82C11×#102—24no—
83C11×#102—22no—
84C4×C8×C11—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D412yes—
91#24679C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—42no—
99C2×Q8×C11—81no—
100C2×Q8×C11—81no—
101C2×Q8×C11C2×D412yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C11×SD16—28no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4C2×D412yes—
145C11×C22⋊C4—42no—
146C11×C22⋊C4—82no—
147C11×C22⋊C4—82no—
148C42×C11—24no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11—82no—
152C42×C11C2×D412yes—
153C42×C11#4112yes—
154C2×#477C2×C1111yescharacteristic, complemented
155C2×C4×SD16C2×C1111yescharacteristic
156#2563C2×C1111yescharacteristic
157#2355C2×C1111yescharacteristic, complemented
158#2074C2×C1112yescomplemented
159#2055C2×C1112yes—
160#1990C2×C1111yescharacteristic, complemented
161#1949C2×C1112yescomplemented
162#1939C2×C1111yescharacteristic, complemented
163#1925C2×C1112yes—
164#1802C2×C1111yescharacteristic
165C23×C11—22no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—22no—
175Q8×C11—41no—
176Q8×C11—41no—
177Q8×C11—84no—
178D4×C11—22no—
179D4×C11—22no—
180D4×C11—41no—
181D4×C11—41no—
182C2×C4×C11—21no—
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—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—84no—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11#13512yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C8×C11—22no—
217C8×C11—42no—
218C8×C11—41no—
219C22×SD16C22×C1111yescharacteristic
220C2×C4⋊Q8C22×C1111yescharacteristic
221C2×C4×Q8C22×C1111yescharacteristic
222C2×C4×D4C22×C1111yescharacteristic
223#477—24no—
224C4×SD16—24no—
225C2×#107C22×C1112yes—
226C2×#106C22×C1111yescharacteristic
227C2×C4⋊C8C22×C1111yescharacteristic
228C2×C4⋊C8C22×C1112yes—
229C2×#103C22×C1112yes—
230C2×#103C22×C1111yescharacteristic
231C2×#102C22×C1112yes—
232C2×#102C22×C1111yescharacteristic
233C2×C4×C8C22×C1111yescharacteristic
234#393—22no—
235#391C22×C1112yes—
236#390C22×C1112yes—
237#387—22no—
238#384C22×C1111yescharacteristic
239#382—21no—
240#382C22×C1112yes—
241#380—21no—
242#380—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C22×C1112yes—
245C4×C4⋊C4C22×C1111yescharacteristic
246#340C22×C1112yes—
247#340C22×C1112yes—
248#340C22×C1112yes—
249#336C22×C1112yes—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11C2×#12111yescharacteristic
258C22×C11#54711yescharacteristic
259C22×C11#54811yescharacteristic
260C22×C11C2×#13511yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C22×C11#57611yescharacteristic
263C22×C11#57711yescharacteristic
264C4×C11—22no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11—81no—
271C4×C11—82no—
272C4×C11#46414yes—
273C4×C11#52511yescharacteristic
274C4×C11#53611yescharacteristic
275C4×C11#55211yescharacteristic
276C4×C11#55611yescharacteristic
277C22×Q8—21no—
278C22×Q8C23×C1111yescharacteristic
279C22×D4C23×C1111yescharacteristic
280C23×C4—21no—
281C2×SD16—22no—
282C2×SD16—22no—
283C2×SD16—22no—
284C22×C8C23×C1111yescharacteristic
285C22×C8C23×C1112yes—
286C22×C8C23×C1111yescharacteristic
287C4⋊Q8—22no—
288C4⋊Q8—22no—
289C4×Q8—22no—
290C4×Q8D4×C1114yes—
291C4×D4—22no—
292C4×D4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4D4×C1111yescharacteristic
298C2×C4⋊C4D4×C1111yescharacteristic
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C4⋊C4C23×C1112yes—
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C42—21no—
307C2×C42—22no—
308C2×C42C23×C1112yes—
309C2×C42C23×C1111yescharacteristic
310#107—24no—
311#106—22no—
312C4⋊C8—24no—
313C4⋊C8—22no—
314#103—22no—
315#103—24no—
316#102—24no—
317#102—22no—
318C4×C8—22no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95—22no—
324#95D4×C1112yes—
325C2×C11—82no—
326C2×C11#241511yescharacteristic
327C2×C11C2×#46411yescharacteristic
328C2×C11#304511yescharacteristic
329C2×C11#334011yescharacteristic
330C2×C11#335711yescharacteristic
331C2×C11#336111yescharacteristic
332C2×C11#337211yescharacteristic
333C24—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—42no—
340C2×Q8—81no—
341C2×Q8—81no—
342C2×Q8C2×D4×C1112yes—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4C11×#4112yes—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4C2×D4×C1112yes—
358C22×C4C2×D4×C1112yes—
359C22×C4C2×D4×C1111yescharacteristic
360C22×C4C2×D4×C1111yescharacteristic
361C22×C4C24×C1111yescharacteristic
362SD16—28no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8C11×#4112yes—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—81no—
385C4⋊C4C2×D4×C1112yes—
386C22⋊C4—42no—
387C22⋊C4—82no—
388C22⋊C4—82no—
389C42—24no—
390C42—22no—
391C42—22no—
392C42—82no—
393C42C2×D4×C1112yes—
394C42C11×#4112yes—
395C11#2467911yescharacteristic, direct product factor, Sylow
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23C22×D4×C1111yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—84no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—84no—
437C2×C4C11×#12112yes—
438C2×C4C11×#12112yes—
439C2×C4C11×#13512yes—
440C2×C4C11×#13712yes—
441C2×C4C22×D4×C1111yescharacteristic
442C2×C4C2×C11×#4111yescharacteristic
443C2×C4C2×C11×#4111yescharacteristic
444C2×C4C2×C11×#4111yescharacteristic
445C2×C4C11×2−1+411yescharacteristic
446C2×C4C11×2−1+411yescharacteristic
447C8—22no—
448C8—42no—
449C8—41no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C2×C11×#12111yescharacteristic
458C22C11×#54711yescharacteristic
459C22C11×#54811yescharacteristic
460C22C2×C11×#13511yescharacteristic
461C22C2×C11×#13711yescharacteristic
462C22C11×#57611yescharacteristic
463C22C11×#57711yescharacteristic
464C4—22no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—81no—
470C4—82no—
471C4—82no—
472C4C11×#46414yes—
473C4C11×#52511yescharacteristic
474C4C11×#53611yescharacteristic
475C4C11×#55211yescharacteristic
476C4C11×#55611yescharacteristic
477C2—82no—
478C2C11×#241511yescharacteristic
479C2C2×C11×#46411yescharacteristic
480C2C11×#304511yescharacteristic
481C2C11×#334011yescharacteristic
482C2C11×#335711yescharacteristic
483C2C11×#336111yescharacteristic
484C2C11×#337211yescharacteristic
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
1. C2×C11×#477C2semidirect
4. C11×#2355C2semidirect
5. C11×#2074C2semidirect
7. C11×#1990C2semidirect
8. C11×#1949C2semidirect
9. C11×#1939C2semidirect
91. #24679C11direct (N × H)
154. C2×#477C2×C11semidirect
157. #2355C2×C11semidirect
158. #2074C2×C11semidirect
160. #1990C2×C11semidirect
161. #1949C2×C11semidirect
162. #1939C2×C11semidirect
395. C11#24679direct (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×SD162
C11×#25632
C11×#23552
C11×#20742
C11×#20552
C11×#19902
C11×#19492
C11×#19392
C11×#19252
C11×#18022
#2467911