Finite Group Databasebeta

← C11×#10168 #14587361

Subgroups — C11×#10168 #14587361

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3205C211yesmaximal, characteristic
2C11×#3152C211yesmaximal, characteristic, complemented
3C2×C11×#486C211yesmaximal, characteristic, complemented
4C11×#1965C211yesmaximal, characteristic, complemented
5C11×#1546C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C11×#497—22no—
13C11×#494—21no—
14C11×#493—21no—
15C11×#492—21no—
16C11×#486—21no—
17C11×#486—22no—
18C11×#486—22no—
19C11×#459—22no—
20C11×#447—22no—
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#102—22no—
24C2×C11×#100—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C11×#137—44no—
35C11×#137—44no—
36C2×C11×Q16—24no—
37C2×C11×SD16—24no—
38C2×C11×D8—24no—
39C2×C11×M16—21no—
40C2×C11×M16D412yes—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D411yescharacteristic
46C11×C4⋊Q8D412yes—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127D411yescharacteristic
52C11×#124—21no—
53C11×#121—21no—
54C11×#121—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#102—28no—
64C11×#102—24no—
65C11×#100—44no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72#10168C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—22no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—44no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—82no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C11×Q16—48no—
101C11×SD16—48no—
102C11×D8—84no—
103C11×M16—22no—
104C11×M16—42no—
105C11×M16D814yescomplemented
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—42no—
110C2×C8×C11—41no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123#3205C2×C1111yescharacteristic
124#3152C2×C1111yescharacteristic, complemented
125C2×#486C2×C1111yescharacteristic, complemented
126#1965C2×C1111yescharacteristic, complemented
127#1546C2×C1111yescharacteristic, complemented
128#1492C2×C1111yescharacteristic, complemented
129#1278C2×C1111yescharacteristic, complemented
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11#12111yescharacteristic
136Q8×C11—44no—
137Q8×C11—42no—
138Q8×C11—81no—
139Q8×C11—81no—
140D4×C11—44no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—44no—
144D4×C11—42no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—82no—
149D4×C11—81no—
150D4×C11—81no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—82no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×D812yes—
165C2×C4×C11AGL(1,ℤ/8)12yes—
166C8×C11—24no—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—81no—
170C2×#137—22no—
171#532C22×C1111yescharacteristic
172C2×C4⋊Q8C22×C1111yescharacteristic
173C2×#127C22×C1111yescharacteristic
174#497—22no—
175#494—21no—
176#493—21no—
177#492—21no—
178#486—22no—
179#486—21no—
180#486—22no—
181#459—22no—
182#447—22no—
183#431C22×C1111yescharacteristic
184#423C22×C1111yescharacteristic
185C2×#102—22no—
186C2×#100—22no—
187C4×M16C22×C1111yescharacteristic
188C2×C4×C8C22×C1111yescharacteristic
189#332—22no—
190D4⋊C8—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—82no—
199C22×C11—164no—
200C22×C11#39211yescharacteristic
201C22×C11#45912yes—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—82no—
206C4×C11#44712yes—
207C4×C11#45512yes—
208C4×C11#47112yes—
209C4×C11#49311yescharacteristic
210C4×C11#49611yescharacteristic
211C2×#41—21no—
212C22×Q8—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4D4×C1112yes—
216#137—44no—
217#137—44no—
218C2×Q16—24no—
219C2×SD16—24no—
220C2×D8—24no—
221C2×M16—21no—
222C2×M16D4×C1112yes—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8D4×C1112yes—
228C4⋊Q8D4×C1111yescharacteristic
229#127—21no—
230#127—21no—
231#127—21no—
232#127—21no—
233#127D4×C1111yescharacteristic
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42C23×C1111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8D4×C1112yes—
245#102—28no—
246#102—24no—
247#100—44no—
248C22⋊C8—21no—
249#97—21no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8D4×C1112yes—
254C2×C11—22no—
255C2×C11—161no—
256C2×C11—162no—
257C2×C11#200411yescharacteristic
258C2×C11#201111yescharacteristic
259C2×C11#201911yescharacteristic
260C24—22no—
261#41—42no—
262#41—42no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—44no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—82no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C11×#4111yescharacteristic
287Q16—48no—
288SD16—48no—
289D8—84no—
290M16—22no—
291M16—42no—
292M16C11×D814yescomplemented
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—41no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C42C2×D4×C1111yescharacteristic
309C42C2×D4×C1111yescharacteristic
310C11#1016811yescharacteristic, direct product factor, Sylow
311C23—41no—
312C23—42no—
313C23—44no—
314C23—82no—
315C23—82no—
316C23C11×#12111yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—81no—
320Q8—81no—
321D4—44no—
322D4—42no—
323D4—42no—
324D4—44no—
325D4—42no—
326D4—82no—
327D4—82no—
328D4—81no—
329D4—81no—
330D4—82no—
331D4—82no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12011yescharacteristic
341C2×C4C11×#12011yescharacteristic
342C2×C4C11×#12111yescharacteristic
343C2×C4C11×#12111yescharacteristic
344C2×C4C11×#12711yescharacteristic
345C2×C4C2×C11×D812yes—
346C2×C4C11×AGL(1,ℤ/8)12yes—
347C8—24no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—82no—
354C22—81no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—164no—
360C22C11×#39211yescharacteristic
361C22C11×#45912yes—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—82no—
366C4C11×#44712yes—
367C4C11×#45512yes—
368C4C11×#47112yes—
369C4C11×#49311yescharacteristic
370C4C11×#49611yescharacteristic
371C2—22no—
372C2—162no—
373C2—161no—
374C2C11×#200411yescharacteristic
375C2C11×#201111yescharacteristic
376C2C11×#201911yescharacteristic
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
2. C11×#3152C2semidirect
3. C2×C11×#486C2semidirect
4. C11×#1965C2semidirect
5. C11×#1546C2semidirect
6. C11×#1492C2semidirect
7. C11×#1278C2semidirect
72. #10168C11direct (N × H)
105. C11×M16D8semidirect
124. #3152C2×C11semidirect
125. C2×#486C2×C11semidirect
126. #1965C2×C11semidirect
127. #1546C2×C11semidirect
128. #1492C2×C11semidirect
129. #1278C2×C11semidirect
292. M16C11×D8semidirect
310. C11#10168direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#31522
C2×C11×#4862
C11×#19652
C11×#15462
C11×#14922
C11×#12782
#1016811