Finite Group Databasebeta

← C11×#24683 #14601876

Subgroups — C11×#24683 #14601876

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#475C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic
5C11×#2074C212yesmaximal
6C11×#2056C212yesmaximal
7C11×#1990C211yesmaximal, characteristic
8C11×#1949C212yesmaximal
9C11×#1939C211yesmaximal, characteristic
10C11×#1927C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C11×#475—24no—
17C4×C11×Q16—24no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#400—22no—
28C11×#391—21no—
29C11×#391—21no—
30C11×#391C2212yes—
31C11×#391C2212yes—
32C11×#387—22no—
33C11×#384C2211yescharacteristic
34C11×#382—21no—
35C11×#382C2212yes—
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×Q8×C11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D414yes—
58C2×C11×C4⋊C4—21no—
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×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11—22no—
72C2×C42×C11C2312yes—
73C2×C42×C11C2311yescharacteristic
74C11×#107—22no—
75C11×#106—24no—
76C11×C4⋊C8—24no—
77C11×C4⋊C8—22no—
78C11×#103—22no—
79C11×#103—24no—
80C11×#103—24no—
81C11×#103—22no—
82C4×C8×C11—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95D412yes—
91#24683C1111yesmaximal, characteristic, direct product factor, Sylow
92C2×Q8×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—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C2×Q8×C11—42no—
105C2×Q8×C11C2×D412yes—
106C2×Q8×C11#4112yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C11×Q16—28no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11#4112yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—81no—
142C11×C4⋊C4C2×D412yes—
143C42×C11—24no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11—42no—
147C42×C11—82no—
148C42×C11C2×D412yes—
149C42×C11#4112yes—
150C2×#475C2×C1111yescharacteristic
151C2×C4×Q16C2×C1111yescharacteristic
152#2568C2×C1111yescharacteristic
153#2355C2×C1111yescharacteristic
154#2074C2×C1112yes—
155#2056C2×C1112yes—
156#1990C2×C1111yescharacteristic
157#1949C2×C1112yes—
158#1939C2×C1111yescharacteristic
159#1927C2×C1112yes—
160#1803C2×C1111yescharacteristic
161C23×C11C22×D411yescharacteristic
162Q8×C11—22no—
163Q8×C11—22no—
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11—41no—
167Q8×C11—41no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11—84no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#13512yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C8×C11—22no—
208C8×C11—42no—
209C8×C11—41no—
210C22×Q16C22×C1111yescharacteristic
211C2×C4⋊Q8C22×C1111yescharacteristic
212C2×C4×Q8C22×C1111yescharacteristic
213C2×C4×Q8C22×C1111yescharacteristic
214#475—24no—
215C4×Q16—24no—
216C2×#107C22×C1111yescharacteristic
217C2×#106C22×C1112yes—
218C2×C4⋊C8C22×C1111yescharacteristic
219C2×C4⋊C8C22×C1112yes—
220C2×#103C22×C1112yes—
221C2×#103C22×C1112yes—
222C2×#103C22×C1111yescharacteristic
223C2×#103C22×C1111yescharacteristic
224C2×C4×C8C22×C1111yescharacteristic
225#400—22no—
226#391—21no—
227#391—21no—
228#391C22×C1112yes—
229#391C22×C1112yes—
230#387—22no—
231#384C22×C1111yescharacteristic
232#382—21no—
233#382C22×C1112yes—
234C4×C4⋊C4—21no—
235C4×C4⋊C4C22×C1112yes—
236C4×C4⋊C4C22×C1111yescharacteristic
237#340C22×C1112yes—
238#340C22×C1112yes—
239#340C22×C1112yes—
240#336C22×C1112yes—
241C22×C11C2×#12111yescharacteristic
242C22×C11#54711yescharacteristic
243C22×C11#54811yescharacteristic
244C22×C11C2×#13511yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C22×C11#57711yescharacteristic
247C22×C11#57811yescharacteristic
248C4×C11—22no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11—82no—
256C4×C11—81no—
257C4×C11#46414yes—
258C4×C11#52511yescharacteristic
259C4×C11#53611yescharacteristic
260C4×C11#55211yescharacteristic
261C4×C11#55611yescharacteristic
262C22×Q8—21no—
263C22×Q8C23×C1111yescharacteristic
264C22×Q8C23×C1111yescharacteristic
265C2×Q16—22no—
266C2×Q16—22no—
267C2×Q16—22no—
268C22×C8C23×C1111yescharacteristic
269C22×C8C23×C1112yes—
270C22×C8C23×C1111yescharacteristic
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4×Q8—22no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8D4×C1114yes—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4D4×C1111yescharacteristic
283C2×C4⋊C4D4×C1111yescharacteristic
284C2×C4⋊C4C23×C1111yescharacteristic
285C2×C4⋊C4C23×C1112yes—
286C2×C4⋊C4C23×C1112yes—
287C2×C4⋊C4C23×C1111yescharacteristic
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—22no—
291C2×C42C23×C1112yes—
292C2×C42C23×C1111yescharacteristic
293#107—22no—
294#106—24no—
295C4⋊C8—24no—
296C4⋊C8—22no—
297#103—22no—
298#103—24no—
299#103—24no—
300#103—22no—
301C4×C8—22no—
302#95—22no—
303#95—22no—
304#95—22no—
305#95—22no—
306#95—22no—
307#95—22no—
308#95—22no—
309#95D4×C1112yes—
310C2×C11#241511yescharacteristic
311C2×C11C2×#46411yescharacteristic
312C2×C11#304611yescharacteristic
313C2×C11#334211yescharacteristic
314C2×C11#335611yescharacteristic
315C2×C11#336511yescharacteristic
316C2×C11#337411yescharacteristic
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8C2×D4×C1112yes—
331C2×Q8C11×#4112yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4C2×D4×C1112yes—
339C22×C4C2×D4×C1112yes—
340C22×C4C2×D4×C1111yescharacteristic
341C22×C4C2×D4×C1111yescharacteristic
342C22×C4C24×C1111yescharacteristic
343Q16—28no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8C11×#4112yes—
353C4⋊C4—24no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—81no—
367C4⋊C4C2×D4×C1112yes—
368C42—24no—
369C42—22no—
370C42—22no—
371C42—42no—
372C42—82no—
373C42C2×D4×C1112yes—
374C42C11×#4112yes—
375C11#2468311yescharacteristic, direct product factor, Sylow
376C23C22×D4×C1111yescharacteristic
377Q8—22no—
378Q8—22no—
379Q8—22no—
380Q8—22no—
381Q8—41no—
382Q8—41no—
383Q8—41no—
384Q8—41no—
385Q8—84no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4C11×#12112yes—
413C2×C4C11×#12112yes—
414C2×C4C11×#13512yes—
415C2×C4C11×#13712yes—
416C2×C4C22×D4×C1111yescharacteristic
417C2×C4C2×C11×#4111yescharacteristic
418C2×C4C2×C11×#4111yescharacteristic
419C2×C4C2×C11×#4111yescharacteristic
420C2×C4C11×2−1+411yescharacteristic
421C2×C4C11×2−1+411yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C22C2×C11×#12111yescharacteristic
426C22C11×#54711yescharacteristic
427C22C11×#54811yescharacteristic
428C22C2×C11×#13511yescharacteristic
429C22C2×C11×#13711yescharacteristic
430C22C11×#57711yescharacteristic
431C22C11×#57811yescharacteristic
432C4—22no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—81no—
440C4—82no—
441C4C11×#46414yes—
442C4C11×#52511yescharacteristic
443C4C11×#53611yescharacteristic
444C4C11×#55211yescharacteristic
445C4C11×#55611yescharacteristic
446C2C11×#241511yescharacteristic
447C2C2×C11×#46411yescharacteristic
448C2C11×#304611yescharacteristic
449C2C11×#334211yescharacteristic
450C2C11×#335611yescharacteristic
451C2C11×#336511yescharacteristic
452C2C11×#337411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
91. #24683C11direct (N × H)
375. C11#24683direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4752
C2×C4×C11×Q162
C11×#25682
C11×#23552
C11×#20742
C11×#20562
C11×#19902
C11×#19492
C11×#19392
C11×#19272
C11×#18032
#2468311