Finite Group Databasebeta

← C11×#10244 #14587437

Subgroups — C11×#10244 #14587437

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic, complemented
4C11×#1548C211yesmaximal, characteristic, complemented
5C11×#1502C211yesmaximal, characteristic
6C11×#1479C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#492—21no—
13C11×#487—21no—
14C11×#464—22no—
15C11×#462—21no—
16C11×#461—22no—
17C11×#460—21no—
18C11×#448—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#417—21no—
23C11×#400—22no—
24C11×#391—22no—
25C11×#391—21no—
26C11×#382—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C11×#333—22no—
29C11×#327—22no—
30C11×Q8⋊C8—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11D412yes—
34C11×#137—42no—
35C11×#137—42no—
36C2×C11×Q16—22no—
37C2×C11×SD16—22no—
38C2×C11×SD16—24no—
39C2×C11×M16—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D411yescharacteristic
45C11×#127D411yescharacteristic
46C11×#124—21no—
47C11×#121—21no—
48C11×#121—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—24no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C4×C8×C11—21no—
73C4×C8×C11—21no—
74C11×#95—24no—
75C11×#95—24no—
76C11×#95D412yes—
77#10244C1111yesmaximal, characteristic, direct product factor, Sylow
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—44no—
91C2×Q8×C11SD1612yescomplemented
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×Q16—44no—
105C11×SD16—44no—
106C11×SD16—84no—
107C11×M16—41no—
108C11×M16—41no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133#3206C2×C1111yescharacteristic
134#3037C2×C1111yescharacteristic
135#2568C2×C1111yescharacteristic, complemented
136#1548C2×C1111yescharacteristic, complemented
137#1502C2×C1111yescharacteristic
138#1479C2×C1111yescharacteristic, complemented
139#1303C2×C1111yescharacteristic, complemented
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142Q8×C11—22no—
143Q8×C11—22no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—44no—
149Q8×C11—82no—
150D4×C11—41no—
151D4×C11—41no—
152D4×C11—42no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—44no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12711yescharacteristic
177C2×C4×C11C2×SD1611yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11#13711yescharacteristic
181C8×C11—42no—
182C8×C11—42no—
183C8×C11—81no—
184C2×#137—21no—
185#532C22×C1111yescharacteristic
186C2×C4⋊Q8C22×C1111yescharacteristic
187C2×C4×Q8C22×C1111yescharacteristic
188#492—21no—
189#487—21no—
190#464—22no—
191#462—21no—
192#461—22no—
193#460—21no—
194#448—22no—
195#431C22×C1111yescharacteristic
196#431C22×C1111yescharacteristic
197#423C22×C1111yescharacteristic
198#417—21no—
199#400—22no—
200#391—22no—
201#391—21no—
202#382—21no—
203C4×C4⋊C4C22×C1111yescharacteristic
204#333—22no—
205#327—22no—
206Q8⋊C8—22no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11#39211yescharacteristic
213C22×C11#44811yescharacteristic
214C22×C11#44911yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—82no—
220C4×C11—81no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11#45011yescharacteristic
224C4×C11#45211yescharacteristic
225C4×C11#45512yes—
226C4×C11#46511yescharacteristic
227C4×C11#46811yescharacteristic
228C2×#41—21no—
229C22×Q8D4×C1111yescharacteristic
230C22×Q8D4×C1112yes—
231#137—42no—
232#137—42no—
233C2×Q16—22no—
234C2×SD16—22no—
235C2×SD16—24no—
236C2×M16—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C1111yescharacteristic
242#127D4×C1111yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C1111yescharacteristic
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C23×C1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C1112yes—
263C4⋊C8D4×C1112yes—
264#103—22no—
265#103—24no—
266#102—22no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C4×C8—21no—
270C4×C8—21no—
271#95—24no—
272#95—24no—
273#95D4×C1112yes—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—161no—
277C2×C11#200011yescharacteristic
278C2×C11#200411yescharacteristic
279C2×C11#200911yescharacteristic
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—22no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—44no—
293C2×Q8C11×SD1612yescomplemented
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306Q16—44no—
307SD16—44no—
308SD16—84no—
309M16—41no—
310M16—41no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42C2×D4×C1111yescharacteristic
332C42C2×D4×C1111yescharacteristic
333C42C2×D4×C1111yescharacteristic
334C42C11×#4111yescharacteristic
335C11#1024411yescharacteristic, direct product factor, Sylow
336C23—41no—
337C23C11×#12011yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—44no—
345Q8—82no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4C11×#12011yescharacteristic
368C2×C4C11×#12011yescharacteristic
369C2×C4C11×#12111yescharacteristic
370C2×C4C11×#12111yescharacteristic
371C2×C4C11×#12111yescharacteristic
372C2×C4C11×#12711yescharacteristic
373C2×C4C2×C11×SD1611yescharacteristic
374C2×C4C11×#13511yescharacteristic
375C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C11×#13711yescharacteristic
377C8—42no—
378C8—42no—
379C8—81no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C11×#39211yescharacteristic
386C22C11×#44811yescharacteristic
387C22C11×#44911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—82no—
393C4—81no—
394C4—82no—
395C4—81no—
396C4C11×#45011yescharacteristic
397C4C11×#45211yescharacteristic
398C4C11×#45512yes—
399C4C11×#46511yescharacteristic
400C4C11×#46811yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2C11×#200011yescharacteristic
405C2C11×#200411yescharacteristic
406C2C11×#200911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
3. C11×#2568C2semidirect
4. C11×#1548C2semidirect
6. C11×#1479C2semidirect
7. C11×#1303C2semidirect
77. #10244C11direct (N × H)
91. C2×Q8×C11SD16semidirect
135. #2568C2×C11semidirect
136. #1548C2×C11semidirect
138. #1479C2×C11semidirect
139. #1303C2×C11semidirect
293. C2×Q8C11×SD16semidirect
335. C11#10244direct (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×#30372
C11×#25682
C11×#15482
C11×#15022
C11×#14792
C11×#13032
#1024411