Finite Group Databasebeta

← C11×#24648 #14601841

Subgroups — C11×#24648 #14601841

Order 2816.

816 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#462C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic
5C11×#2056C212yesmaximal
6C11×#2016C212yesmaximal
7C11×#1981C212yesmaximal
8C11×#1960C211yesmaximal, characteristic
9C11×#1940C211yesmaximal, characteristic
10C11×#1927C212yesmaximal
11C11×#1805C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#462—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×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#97C2211yescharacteristic
30C11×#398—21no—
31C11×#398—21no—
32C11×#391C2212yes—
33C11×#391C2212yes—
34C11×#389—22no—
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×C11C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16—24no—
49C2×C11×Q16—22no—
50C2×C11×Q16—42no—
51C2×C11×Q16—42no—
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—42no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11—21no—
76C2×C42×C11C2312yes—
77C2×C42×C11C2311yescharacteristic
78C11×#106—22no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—42no—
81C11×#103—22no—
82C11×#103—24no—
83C11×#103—22no—
84C11×#103—24no—
85C11×#103—42no—
86C11×#103—42no—
87C11×#97—22no—
88C11×#95—21no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24648C1111yesmaximal, characteristic, direct product factor, Sylow
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C11×Q16—28no—
128C11×Q16—48no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11#4112yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C2×D412yes—
151C42×C11—24no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11—42no—
155C42×C11—44no—
156C42×C11C2×D412yes—
157C42×C11#4112yes—
158C2×#462C2×C1111yescharacteristic
159C2×#441C2×C1111yescharacteristic
160#2546C2×C1111yescharacteristic
161#2356C2×C1111yescharacteristic
162#2056C2×C1112yes—
163#2016C2×C1112yes—
164#1981C2×C1112yes—
165#1960C2×C1111yescharacteristic
166#1940C2×C1111yescharacteristic
167#1927C2×C1112yes—
168#1805C2×C1111yescharacteristic
169C23×C11C22×D411yescharacteristic
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11—41no—
175Q8×C11—41no—
176Q8×C11—41no—
177Q8×C11—41no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—42no—
181Q8×C11—42no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
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—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11#12112yes—
206C2×C4×C11#12112yes—
207C2×C4×C11#13714yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C8×C11—22no—
215C8×C11—41no—
216C8×C11—42no—
217C22×Q16C22×C1111yescharacteristic
218C22×Q16C22×C1112yes—
219C2×C4⋊Q8C22×C1111yescharacteristic
220C2×C4⋊Q8C22×C1112yes—
221C2×C4×Q8C22×C1111yescharacteristic
222C2×C4×Q8C22×C1111yescharacteristic
223#462—24no—
224#441—24no—
225C2×#106C22×C1111yescharacteristic
226C2×C4⋊C8C22×C1111yescharacteristic
227C2×C4⋊C8C22×C1112yes—
228C2×#103C22×C1111yescharacteristic
229C2×#103C22×C1111yescharacteristic
230C2×#103C22×C1112yes—
231C2×#103C22×C1112yes—
232C2×#103C22×C1112yes—
233C2×#103C22×C1112yes—
234C2×#97C22×C1111yescharacteristic
235#398—21no—
236#398—21no—
237#391C22×C1112yes—
238#391C22×C1112yes—
239#389—22no—
240#387—22no—
241#383—21no—
242#382C22×C1111yescharacteristic
243C4×C4⋊C4C22×C1112yes—
244C4×C4⋊C4C22×C1111yescharacteristic
245#376—21no—
246#340C22×C1112yes—
247#336C22×C1112yes—
248C22×C11C2×#12111yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11#55011yescharacteristic
251C22×C11C2×#13712yes—
252C22×C11#57812yes—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—24no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—82no—
261C4×C11—82no—
262C4×C11—81no—
263C4×C11#52511yescharacteristic
264C4×C11#53511yescharacteristic
265C4×C11#55311yescharacteristic
266C4×C11#55511yescharacteristic
267C22×Q8C23×C1112yes—
268C22×Q8C23×C1111yescharacteristic
269C22×Q8C23×C1111yescharacteristic
270C2×Q16—22no—
271C2×Q16—22no—
272C2×Q16—24no—
273C2×Q16—22no—
274C2×Q16—42no—
275C2×Q16—42no—
276C22×C8C23×C1112yes—
277C22×C8C23×C1111yescharacteristic
278C22×C8C23×C1111yescharacteristic
279C4⋊Q8—24no—
280C4⋊Q8—22no—
281C4⋊Q8—22no—
282C4⋊Q8—42no—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×Q8—22no—
286C4×Q8D4×C1114yes—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4D4×C1112yes—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C4⋊C4C23×C1112yes—
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—22no—
300C2×C42C23×C1112yes—
301C2×C42C23×C1111yescharacteristic
302#106—22no—
303C4⋊C8—22no—
304C4⋊C8—42no—
305#103—22no—
306#103—24no—
307#103—22no—
308#103—24no—
309#103—42no—
310#103—42no—
311#97—22no—
312#95—21no—
313#95—22no—
314#95—22no—
315#95—21no—
316#95—22no—
317#95—22no—
318#95—22no—
319#95D4×C1111yescharacteristic
320#95D4×C1111yescharacteristic
321C2×C11#241411yescharacteristic
322C2×C11#303911yescharacteristic
323C2×C11#304411yescharacteristic
324C2×C11#331212yes—
325C2×C11#339812yes—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—22no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8C2×D4×C1112yes—
343C2×Q8C11×#4112yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4C2×D4×C1112yes—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1112yes—
354C22×C4C24×C1111yescharacteristic
355Q16—28no—
356Q16—48no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—21no—
362C2×C8—22no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8C11×#4112yes—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—44no—
374C4⋊C4—44no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4C2×D4×C1112yes—
379C42—24no—
380C42—22no—
381C42—22no—
382C42—42no—
383C42—44no—
384C42C2×D4×C1112yes—
385C42C11×#4112yes—
386C11#2464811yescharacteristic, direct product factor, Sylow
387C23C22×D4×C1111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—22no—
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395Q8—41no—
396Q8—42no—
397Q8—42no—
398Q8—42no—
399Q8—42no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4C11×#12112yes—
424C2×C4C11×#12112yes—
425C2×C4C11×#13714yes—
426C2×C4C22×D4×C1111yescharacteristic
427C2×C4C2×C11×#4111yescharacteristic
428C2×C4C2×C11×#4111yescharacteristic
429C2×C4C2×C11×#4111yescharacteristic
430C2×C4C11×H(5,𝔽2)11yescharacteristic
431C2×C4C11×H(5,𝔽2)11yescharacteristic
432C8—22no—
433C8—42no—
434C8—41no—
435C22C2×C11×#12111yescharacteristic
436C22C11×#54611yescharacteristic
437C22C11×#55011yescharacteristic
438C22C2×C11×#13712yes—
439C22C11×#57812yes—
440C4—22no—
441C4—22no—
442C4—24no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—82no—
448C4—81no—
449C4—82no—
450C4C11×#52511yescharacteristic
451C4C11×#53511yescharacteristic
452C4C11×#55311yescharacteristic
453C4C11×#55511yescharacteristic
454C2C11×#241411yescharacteristic
455C2C11×#303911yescharacteristic
456C2C11×#304411yescharacteristic
457C2C11×#331212yes—
458C2C11×#339812yes—
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
97. #24648C11direct (N × H)
386. C11#24648direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4622
C2×C11×#4412
C11×#25462
C11×#23562
C11×#20562
C11×#20162
C11×#19812
C11×#19602
C11×#19402
C11×#19272
C11×#18052
#2464811