Finite Group Databasebeta

← C11×#10240 #14587433

Subgroups — C11×#10240 #14587433

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic, complemented
4C11×#1548C211yesmaximal, characteristic, complemented
5C11×#1502C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C22⋊Q8—22no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#492—21no—
14C11×#487—21no—
15C11×#463—22no—
16C11×#461—21no—
17C11×#461—22no—
18C11×#459—21no—
19C11×#448—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#417—21no—
24C11×#399—22no—
25C11×#390—21no—
26C11×#384—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#333—22no—
29C11×#327—22no—
30C11×D4⋊C8—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D412yes—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×SD16—24no—
39C2×C11×D8—22no—
40C2×C11×M16—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D411yescharacteristic
46C11×#127D411yescharacteristic
47C11×#124—21no—
48C11×C22⋊Q8—48no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8D412yes—
70C11×#103—22no—
71C11×#103—24no—
72C11×#102—22no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77C11×#95D412yes—
78#10240C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—21no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—44no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C2×D4×C11SD1612yescomplemented
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—44no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C11×SD16—44no—
109C11×SD16—84no—
110C11×D8—44no—
111C11×M16—41no—
112C11×M16—41no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—48no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—48no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137#3206C2×C1111yescharacteristic, complemented
138#3036C2×C1111yescharacteristic
139#2542C2×C1111yescharacteristic, complemented
140#1548C2×C1111yescharacteristic, complemented
141#1502C2×C1111yescharacteristic, complemented
142#1478C2×C1111yescharacteristic, complemented
143#1303C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151Q8×C11—41no—
152Q8×C11—41no—
153Q8×C11—44no—
154Q8×C11—82no—
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—42no—
161D4×C11—41no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12711yescharacteristic
185C2×C4×C11C2×SD1611yescharacteristic
186C2×C4×C11#13511yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C11#13711yescharacteristic
189C8×C11—42no—
190C8×C11—42no—
191C8×C11—81no—
192C2×AGL(1,ℤ/8)—21no—
193#532C22×C1111yescharacteristic
194C2×C4⋊Q8C22×C1111yescharacteristic
195C2×C22⋊Q8—22no—
196C2×C4×D4C22×C1111yescharacteristic
197#492—21no—
198#487—21no—
199#463—22no—
200#461—21no—
201#461—22no—
202#459—21no—
203#448—22no—
204#431C22×C1111yescharacteristic
205#431C22×C1111yescharacteristic
206#423C22×C1111yescharacteristic
207#417—21no—
208#399—22no—
209#390—21no—
210#384—21no—
211C4×C4⋊C4C22×C1111yescharacteristic
212#333—22no—
213#327—22no—
214D4⋊C8—22no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39211yescharacteristic
226C22×C11#44811yescharacteristic
227C22×C11#44911yescharacteristic
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—44no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—82no—
235C4×C11#45011yescharacteristic
236C4×C11#45211yescharacteristic
237C4×C11#45312yes—
238C4×C11#46511yescharacteristic
239C4×C11#46811yescharacteristic
240C2×#41—21no—
241C22×Q8D4×C1112yes—
242C22×D4D4×C1111yescharacteristic
243C23×C4—21no—
244AGL(1,ℤ/8)—42no—
245AGL(1,ℤ/8)—42no—
246C2×SD16—22no—
247C2×SD16—24no—
248C2×D8—22no—
249C2×M16—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8D4×C1111yescharacteristic
255#127D4×C1111yescharacteristic
256#124—21no—
257C22⋊Q8—48no—
258#121—21no—
259#121—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4D4×C1111yescharacteristic
271C2×C22⋊C4—24no—
272C2×C22⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C1111yescharacteristic
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8D4×C1112yes—
278C4⋊C8D4×C1112yes—
279#103—22no—
280#103—24no—
281#102—22no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C4×C8—21no—
285C4×C8—21no—
286#95D4×C1112yes—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—82no—
290C2×C11—161no—
291C2×C11#200011yescharacteristic
292C2×C11#200211yescharacteristic
293C2×C11#200911yescharacteristic
294C24—21no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—44no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4C11×SD1612yescomplemented
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—44no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C2×D4×C1111yescharacteristic
323SD16—44no—
324SD16—84no—
325D8—44no—
326M16—41no—
327M16—41no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—41no—
331C4⋊C4—24no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—48no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C22⋊C4—48no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—41no—
347C42—41no—
348C42C2×D4×C1111yescharacteristic
349C42C2×D4×C1111yescharacteristic
350C42C2×D4×C1111yescharacteristic
351C42C11×#4111yescharacteristic
352C11#1024011yescharacteristic, direct product factor, Sylow
353C23—22no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23C11×#12011yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—44no—
363Q8—82no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—81no—
372D4—81no—
373D4—81no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4C11×#12011yescharacteristic
389C2×C4C11×#12011yescharacteristic
390C2×C4C11×#12111yescharacteristic
391C2×C4C11×#12111yescharacteristic
392C2×C4C11×#12111yescharacteristic
393C2×C4C11×#12711yescharacteristic
394C2×C4C2×C11×SD1611yescharacteristic
395C2×C4C11×#13511yescharacteristic
396C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
397C2×C4C11×#13711yescharacteristic
398C8—42no—
399C8—42no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—44no—
404C22—42no—
405C22—82no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22C11×#39211yescharacteristic
412C22C11×#44811yescharacteristic
413C22C11×#44911yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—44no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4C11×#45011yescharacteristic
422C4C11×#45211yescharacteristic
423C4C11×#45312yes—
424C4C11×#46511yescharacteristic
425C4C11×#46811yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—161no—
430C2C11×#200011yescharacteristic
431C2C11×#200211yescharacteristic
432C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3206C2semidirect
3. C11×#2542C2semidirect
4. C11×#1548C2semidirect
5. C11×#1502C2semidirect
6. C11×#1478C2semidirect
7. C11×#1303C2semidirect
78. #10240C11direct (N × H)
97. C2×D4×C11SD16semidirect
137. #3206C2×C11semidirect
139. #2542C2×C11semidirect
140. #1548C2×C11semidirect
141. #1502C2×C11semidirect
142. #1478C2×C11semidirect
143. #1303C2×C11semidirect
312. C2×D4C11×SD16semidirect
352. C11#10240direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C11×#30362
C11×#25422
C11×#15482
C11×#15022
C11×#14782
C11×#13032
#1024011