Finite Group Databasebeta

← C11×#10281 #14587474

Subgroups — C11×#10281 #14587474

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic, complemented
2C11×#3205C211yesmaximal, characteristic
3C11×#2858C211yesmaximal, characteristic, complemented
4C11×#1962C211yesmaximal, characteristic, complemented
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1545C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—22no—
12C11×#493—21no—
13C11×#492—21no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#461—22no—
17C11×#459—22no—
18C11×#448—22no—
19C11×#447—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#104—22no—
24C11×#390—22no—
25C11×#390—22no—
26C43×C11C2211yescharacteristic
27C11×#333—22no—
28C11×#331—22no—
29C2×C11×#41—21no—
30C22×Q8×C11D412yes—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C2×C11×SD16—24no—
35C2×C11×D8—24no—
36C2×C11×M16—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127D411yescharacteristic
47C11×#124—21no—
48C11×#124—48no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C22⋊C4—28no—
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×C42×C11D412yes—
59C2×C42×C11C2311yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#104—44no—
65C11×#103—24no—
66C11×#102—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71#10281C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—22no—
76C2×Q8×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—44no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—22no—
84C2×D4×C11—44no—
85C2×D4×C11—44no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×SD16—84no—
100C11×D8—84no—
101C11×M16—42no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—416no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—24no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—42no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122#3206C2×C1111yescharacteristic, complemented
123#3205C2×C1111yescharacteristic
124#2858C2×C1111yescharacteristic, complemented
125#1962C2×C1111yescharacteristic, complemented
126#1548C2×C1111yescharacteristic, complemented
127#1545C2×C1111yescharacteristic, complemented
128#1276C2×C1111yescharacteristic, complemented
129C23×C11—44no—
130C23×C11—44no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—44no—
134C23×C11#12011yescharacteristic
135Q8×C11—44no—
136Q8×C11—42no—
137Q8×C11—82no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—44no—
141D4×C11—42no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—81no—
148D4×C11—81no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C2×C4×C11#13512yes—
166C2×C4×C11AGL(1,ℤ/8)12yes—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—81no—
170#532C22×C1111yescharacteristic
171C2×C4⋊Q8C22×C1111yescharacteristic
172C2×#127C22×C1111yescharacteristic
173C2×#124—22no—
174#493—21no—
175#492—21no—
176#487—21no—
177#486—21no—
178#461—22no—
179#459—22no—
180#448—22no—
181#447—22no—
182#431C22×C1111yescharacteristic
183#431C22×C1111yescharacteristic
184#423C22×C1111yescharacteristic
185C2×#104—22no—
186#390—22no—
187#390—22no—
188C43C22×C1111yescharacteristic
189#333—22no—
190#331—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—88no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—82no—
200C22×C11#39211yescharacteristic
201C22×C11#44912yes—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—44no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11#45312yes—
208C4×C11#45512yes—
209C4×C11#46312yes—
210C4×C11#49511yescharacteristic
211C4×C11#49611yescharacteristic
212C2×#41—21no—
213C22×Q8D4×C1112yes—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4D4×C1112yes—
217C2×SD16—24no—
218C2×D8—24no—
219C2×M16—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8D4×C1111yescharacteristic
225#127—21no—
226#127—21no—
227#127—21no—
228#127—21no—
229#127D4×C1111yescharacteristic
230#124—21no—
231#124—48no—
232#121—21no—
233#121—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C22⋊C4—28no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42D4×C1112yes—
242C2×C42C23×C1111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C1112yes—
246C4⋊C8D4×C1112yes—
247#104—44no—
248#103—24no—
249#102—24no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C2×C11—22no—
255C2×C11—161no—
256C2×C11—162no—
257C2×C11#200211yescharacteristic
258C2×C11#200411yescharacteristic
259C2×C11#201211yescharacteristic
260C24—22no—
261#41—42no—
262#41—42no—
263C2×Q8—22no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—44no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—42no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287SD16—84no—
288D8—84no—
289M16—42no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—416no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42—24no—
303C42—22no—
304C42—22no—
305C42—42no—
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C42C2×D4×C1111yescharacteristic
309C42C11×#4111yescharacteristic
310C11#1028111yescharacteristic, direct product factor, Sylow
311C23—44no—
312C23—44no—
313C23—41no—
314C23—42no—
315C23—44no—
316C23C11×#12011yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—82no—
320D4—42no—
321D4—42no—
322D4—44no—
323D4—42no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—81no—
328D4—81no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C11×#12011yescharacteristic
342C2×C4C11×#12011yescharacteristic
343C2×C4C11×#12111yescharacteristic
344C2×C4C11×#12111yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12711yescharacteristic
347C2×C4C11×#13512yes—
348C2×C4C11×AGL(1,ℤ/8)12yes—
349C8—42no—
350C8—42no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—81no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22—82no—
361C22C11×#39211yescharacteristic
362C22C11×#44912yes—
363C4—21no—
364C4—21no—
365C4—44no—
366C4—82no—
367C4—81no—
368C4C11×#45312yes—
369C4C11×#45512yes—
370C4C11×#46312yes—
371C4C11×#49511yescharacteristic
372C4C11×#49611yescharacteristic
373C2—22no—
374C2—162no—
375C2—161no—
376C2C11×#200211yescharacteristic
377C2C11×#200411yescharacteristic
378C2C11×#201211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3205C2
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×#2858C2semidirect
4. C11×#1962C2semidirect
5. C11×#1548C2semidirect
6. C11×#1545C2semidirect
7. C11×#1276C2semidirect
71. #10281C11direct (N × H)
122. #3206C2×C11semidirect
124. #2858C2×C11semidirect
125. #1962C2×C11semidirect
126. #1548C2×C11semidirect
127. #1545C2×C11semidirect
128. #1276C2×C11semidirect
310. C11#10281direct (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×#32052
C11×#28582
C11×#19622
C11×#15482
C11×#15452
C11×#12762
#1028111