Finite Group Databasebeta

← C11×#18408 #14595601

Subgroups — C11×#18408 #14595601

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3226C212yesmaximal, complemented
3C11×#2546C211yesmaximal, characteristic, complemented
4C11×#1610C218yesmaximal, complemented
5C11×#1502C212yesmaximal, complemented
6C11×#1461C211yesmaximal, characteristic, complemented
7C2×C11×2−1+4—21no—
8C11×#550—22no—
9D4×Q8×C11—22no—
10C11×#548—24no—
11C11×#537—21no—
12C11×#537C2214yes—
13C11×#532—22no—
14C11×#532C2212yes—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#500—22no—
19C11×#486—22no—
20C11×#480C2218yes—
21C11×#474—24no—
22C11×#431C2212yes—
23C11×#398C2214yes—
24C11×#391—21no—
25C11×#389—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#327C2218yes—
28C11×#324C2214yes—
29C11×2−1+4—44no—
30C11×2−1+4—44no—
31C2×C11×#41—24no—
32C2×C11×#41—24no—
33C2×C11×#41—22no—
34C22×Q8×C11—24no—
35C22×Q8×C11—21no—
36C22×Q8×C11D411yescharacteristic
37C11×C4⋊Q8—22no—
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—44no—
41C11×C4⋊Q8D412yes—
42C11×#127—22no—
43C11×#127D412yes—
44C11×#124—24no—
45C11×#124—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×#121—24no—
49C11×#121—28no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11—21no—
66C2×C42×C11D412yes—
67C2×C42×C11C2311yescharacteristic
68C11×#107—28no—
69C11×C4⋊C8—22no—
70C11×#102—28no—
71C11×C22⋊C8C2314yes—
72C4×C8×C11—22no—
73C11×#95—24no—
74C11×#95C2312yes—
75#18408C1111yesmaximal, characteristic, direct product factor, Sylow
76C11×#41—48no—
77C11×#41—416no—
78C11×#41—48no—
79C11×#41—44no—
80C11×#41—44no—
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—416no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11D814yes—
90C2×D4×C11—24no—
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11C2×D414yes—
96C22×C4×C11—28no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C2×C8×C11—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—48no—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—42no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#3497C2×C1111yescharacteristic
125#3226C2×C1112yescomplemented
126#2546C2×C1111yescharacteristic, complemented
127#1610C2×C1118yescomplemented
128#1502C2×C1112yescomplemented
129#1461C2×C1111yescharacteristic, complemented
130C23×C11—24no—
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—48no—
134Q8×C11—44no—
135Q8×C11—84no—
136D4×C11—44no—
137D4×C11—48no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—44no—
142D4×C11—84no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—41no—
150C2×C4×C11—416no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—48no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12012yes—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11C2×D814yes—
162C2×C4×C11C2×D812yes—
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11C22×D412yes—
165C8×C11—44no—
166C2×2−1+4—21no—
167#550—22no—
168D4×Q8—22no—
169#548—24no—
170#537—21no—
171#537C22×C1114yes—
172#532—22no—
173#532C22×C1112yes—
174C2×C4⋊Q8—21no—
175C2×C4⋊Q8C22×C1111yescharacteristic
176C2×C4×Q8C22×C1111yescharacteristic
177#500—22no—
178#486—22no—
179#480C22×C1118yes—
180#474—24no—
181#431C22×C1112yes—
182#398C22×C1114yes—
183#391—21no—
184#389—22no—
185C4×C4⋊C4C22×C1111yescharacteristic
186#327C22×C1118yes—
187#324C22×C1114yes—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—44no—
191C22×C11—44no—
192C22×C11—44no—
193C22×C11C2×#12011yescharacteristic
194C22×C11C22×D811yescharacteristic
195C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
196C4×C11—24no—
197C4×C11—21no—
198C4×C11—22no—
199C4×C11—44no—
200C4×C11—44no—
201C4×C11—42no—
202C4×C11—82no—
203C4×C11#44714yes—
204C4×C11#45612yes—
2052−1+4—44no—
2062−1+4—44no—
207C2×#41—24no—
208C2×#41—24no—
209C2×#41—22no—
210C22×Q8—24no—
211C22×Q8—21no—
212C22×Q8D4×C1111yescharacteristic
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C4⋊Q8—22no—
216C4⋊Q8—44no—
217C4⋊Q8D4×C1112yes—
218#127—22no—
219#127D4×C1112yes—
220#124—24no—
221#124—22no—
222C22⋊Q8—24no—
223C22⋊Q8—28no—
224#121—24no—
225#121—28no—
226#121—22no—
227#121—24no—
228#121C23×C1114yes—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×D4—24no—
232C4×D4—24no—
233C4×D4—22no—
234C4×D4D4×C1114yes—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C1111yescharacteristic
239C2×C4⋊C4C23×C1112yes—
240C2×C4⋊C4C23×C1112yes—
241C2×C42—21no—
242C2×C42D4×C1112yes—
243C2×C42C23×C1111yescharacteristic
244#107—28no—
245C4⋊C8—22no—
246#102—28no—
247C22⋊C8C23×C1114yes—
248C4×C8—22no—
249#95—24no—
250#95C23×C1112yes—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—84no—
254C2×C11C2×#44711yescharacteristic
255C2×C11C2×#45611yescharacteristic
256C2×C11#302811yescharacteristic
257#41—48no—
258#41—416no—
259#41—48no—
260#41—44no—
261#41—44no—
262C2×Q8—24no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—416no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8C11×D814yes—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4C2×D4×C1114yes—
277C22×C4—28no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4C2×D4×C1111yescharacteristic
282C22×C4C2×D4×C1112yes—
283C22×C4C2×D4×C1112yes—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C24×C1111yescharacteristic
286C2×C8—24no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—48no—
296C4⋊C4C2×D4×C1114yes—
297C22⋊C4—28no—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C42—22no—
301C42—22no—
302C42—42no—
303C42C2×D4×C1112yes—
304C42C2×D4×C1112yes—
305C11#1840811yescharacteristic, direct product factor, Sylow
306C23—24no—
307C23C22×D4×C1111yescharacteristic
308Q8—28no—
309Q8—48no—
310Q8—44no—
311Q8—84no—
312D4—44no—
313D4—48no—
314D4—44no—
315D4—44no—
316D4—44no—
317D4—44no—
318D4—84no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—41no—
326C2×C4—416no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—48no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4C11×#12011yescharacteristic
335C2×C4C11×#12012yes—
336C2×C4C11×#12011yescharacteristic
337C2×C4C2×C11×D814yes—
338C2×C4C2×C11×D812yes—
339C2×C4C11×AGL(1,ℤ/8)12yes—
340C2×C4C22×D4×C1112yes—
341C8—44no—
342C22—21no—
343C22—21no—
344C22—44no—
345C22—44no—
346C22—44no—
347C22C2×C11×#12011yescharacteristic
348C22C22×C11×D811yescharacteristic
349C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
350C4—24no—
351C4—21no—
352C4—22no—
353C4—44no—
354C4—44no—
355C4—42no—
356C4—82no—
357C4C11×#44714yes—
358C4C11×#45612yes—
359C2—21no—
360C2—21no—
361C2—84no—
362C2C2×C11×#44711yescharacteristic
363C2C2×C11×#45611yescharacteristic
364C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3497C2
LCSG ▷ C22×C4 ▷ 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×#3226C2semidirect
3. C11×#2546C2semidirect
4. C11×#1610C2semidirect
5. C11×#1502C2semidirect
6. C11×#1461C2semidirect
75. #18408C11direct (N × H)
125. #3226C2×C11semidirect
126. #2546C2×C11semidirect
127. #1610C2×C11semidirect
128. #1502C2×C11semidirect
129. #1461C2×C11semidirect
305. C11#18408direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34972
C11×#32262
C11×#25462
C11×#16102
C11×#15022
C11×#14612
#1840811