Finite Group Databasebeta

← C11×#10284 #14587477

Subgroups — C11×#10284 #14587477

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic, complemented
2C11×#3205C211yesmaximal, characteristic
3C11×#2858C211yesmaximal, characteristic, complemented
4C11×#1962C211yesmaximal, characteristic, complemented
5C11×#1546C211yesmaximal, characteristic, complemented
6C11×#1545C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—22no—
12C11×#500—21no—
13C11×#493—21no—
14C11×#486—21no—
15C11×#486—21no—
16C11×#480—22no—
17C11×#474—22no—
18C11×#459—22no—
19C11×#447—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#104—22no—
24C11×#390—22no—
25C11×#390—22no—
26C43×C11C2211yescharacteristic
27C11×#332—22no—
28C11×#331—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C2×C11×D8—24no—
35C2×C11×M16—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127D411yescharacteristic
46C11×#124—21no—
47C11×#124—44no—
48C11×#124—44no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—28no—
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×C42×C11D412yes—
59C2×C42×C11C2311yescharacteristic
60C11×#107—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×C4⋊C8D412yes—
65C11×#104—44no—
66C11×#102—24no—
67C11×#102—24no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C4×C8×C11—21no—
71C4×C8×C11—21no—
72#10284C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—22no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—44no—
87C2×D4×C11—44no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C11×D8—84no—
102C11×M16—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—416no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—22no—
116C42×C11—42no—
117C42×C11—42no—
118C42×C11D814yescomplemented
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123#3226C2×C1111yescharacteristic, complemented
124#3205C2×C1111yescharacteristic
125#2858C2×C1111yescharacteristic, complemented
126#1962C2×C1111yescharacteristic, complemented
127#1546C2×C1111yescharacteristic, complemented
128#1545C2×C1111yescharacteristic, complemented
129#1276C2×C1111yescharacteristic, complemented
130C23×C11—44no—
131C23×C11—44no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—44no—
135C23×C11#12011yescharacteristic
136Q8×C11—42no—
137Q8×C11—82no—
138Q8×C11—81no—
139Q8×C11—81no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—44no—
143D4×C11—42no—
144D4×C11—82no—
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—24no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—44no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×D812yes—
168C2×C4×C11AGL(1,ℤ/8)12yes—
169C8×C11—42no—
170C8×C11—42no—
171C8×C11—81no—
172#532C22×C1111yescharacteristic
173C2×C4⋊Q8C22×C1111yescharacteristic
174C2×#127C22×C1111yescharacteristic
175C2×#124—22no—
176#500—21no—
177#493—21no—
178#486—21no—
179#486—21no—
180#480—22no—
181#474—22no—
182#459—22no—
183#447—22no—
184#431C22×C1111yescharacteristic
185#431C22×C1111yescharacteristic
186#423C22×C1111yescharacteristic
187C2×#104—22no—
188#390—22no—
189#390—22no—
190C43C22×C1111yescharacteristic
191#332—22no—
192#331—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—88no—
196C22×C11—81no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—82no—
202C22×C11#39211yescharacteristic
203C22×C11#44712yes—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—44no—
207C4×C11—82no—
208C4×C11—81no—
209C4×C11#45412yes—
210C4×C11#45512yes—
211C4×C11#45912yes—
212C4×C11#49311yescharacteristic
213C4×C11#49611yescharacteristic
214C2×#41—21no—
215C22×Q8—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4D4×C1112yes—
219C2×D8—24no—
220C2×M16—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8D4×C1111yescharacteristic
226#127—21no—
227#127—21no—
228#127—21no—
229#127—21no—
230#127D4×C1111yescharacteristic
231#124—21no—
232#124—44no—
233#124—44no—
234#121—21no—
235#121—21no—
236C4×D4—21no—
237C4×D4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C1112yes—
240C2×C22⋊C4—28no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42D4×C1112yes—
244C2×C42C23×C1111yescharacteristic
245#107—24no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C1112yes—
249C4⋊C8D4×C1112yes—
250#104—44no—
251#102—24no—
252#102—24no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C4×C8—21no—
256C4×C8—21no—
257C2×C11—22no—
258C2×C11—161no—
259C2×C11—162no—
260C2×C11#200311yescharacteristic
261C2×C11#200411yescharacteristic
262C2×C11#201111yescharacteristic
263C24—22no—
264#41—42no—
265#41—42no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×D4—21no—
272C2×D4—22no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—42no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291D8—84no—
292M16—42no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—416no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—22no—
306C42—42no—
307C42—42no—
308C42C11×D814yescomplemented
309C42C2×D4×C1111yescharacteristic
310C42C2×D4×C1111yescharacteristic
311C42C2×D4×C1111yescharacteristic
312C42C11×#4111yescharacteristic
313C11#1028411yescharacteristic, direct product factor, Sylow
314C23—44no—
315C23—44no—
316C23—41no—
317C23—42no—
318C23—44no—
319C23C11×#12011yescharacteristic
320Q8—42no—
321Q8—81no—
322Q8—81no—
323Q8—82no—
324D4—42no—
325D4—42no—
326D4—44no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331D4—81no—
332D4—81no—
333D4—82no—
334D4—82no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4C11×#12011yescharacteristic
346C2×C4C11×#12011yescharacteristic
347C2×C4C11×#12111yescharacteristic
348C2×C4C11×#12111yescharacteristic
349C2×C4C11×#12111yescharacteristic
350C2×C4C11×#12711yescharacteristic
351C2×C4C2×C11×D812yes—
352C2×C4C11×AGL(1,ℤ/8)12yes—
353C8—42no—
354C8—42no—
355C8—81no—
356C22—21no—
357C22—21no—
358C22—88no—
359C22—81no—
360C22—82no—
361C22—82no—
362C22—81no—
363C22—81no—
364C22—82no—
365C22C11×#39211yescharacteristic
366C22C11×#44712yes—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—82no—
371C4—81no—
372C4C11×#45412yes—
373C4C11×#45512yes—
374C4C11×#45912yes—
375C4C11×#49311yescharacteristic
376C4C11×#49611yescharacteristic
377C2—22no—
378C2—162no—
379C2—161no—
380C2C11×#200311yescharacteristic
381C2C11×#200411yescharacteristic
382C2C11×#201111yescharacteristic
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×#3226C2semidirect
3. C11×#2858C2semidirect
4. C11×#1962C2semidirect
5. C11×#1546C2semidirect
6. C11×#1545C2semidirect
7. C11×#1276C2semidirect
72. #10284C11direct (N × H)
118. C42×C11D8semidirect
123. #3226C2×C11semidirect
125. #2858C2×C11semidirect
126. #1962C2×C11semidirect
127. #1546C2×C11semidirect
128. #1545C2×C11semidirect
129. #1276C2×C11semidirect
308. C42C11×D8semidirect
313. C11#10284direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#32052
C11×#28582
C11×#19622
C11×#15462
C11×#15452
C11×#12762
#1028411