Finite Group Databasebeta

← C11×#18373 #14595566

Subgroups — C11×#18373 #14595566

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3234C212yesmaximal, complemented
3C11×#2634C211yesmaximal, characteristic, complemented
4C11×#1616C214yesmaximal, complemented
5C11×#1610C214yesmaximal, complemented
6C11×#1514C212yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#501—22no—
19C11×#490—22no—
20C11×#481C2214yes—
21C11×#480C2214yes—
22C11×#478—24no—
23C11×#432C2212yes—
24C11×#400—21no—
25C11×#400C2212yes—
26C11×#398C2212yes—
27C11×#395—21no—
28C11×#387—22no—
29C11×#383C2211yescharacteristic
30C11×#327C2218yes—
31C11×#324C2214yes—
32C11×2−1+4—48no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×Q8×C11—24no—
37C22×Q8×C11D411yescharacteristic
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8D412yes—
40C11×#127—22no—
41C11×#127D412yes—
42C11×#125—22no—
43C11×#125—22no—
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—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11D412yes—
67C2×C42×C11C2311yescharacteristic
68C11×#107—24no—
69C11×#106—24no—
70C11×C4⋊C8—22no—
71C11×#102—24no—
72C11×#102—24no—
73C11×C22⋊C8C2314yes—
74C11×#97—22no—
75C11×#95—21no—
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95C2312yes—
81#18373C1111yesmaximal, characteristic, direct product factor, Sylow
82C11×#41—48no—
83C11×#41—48no—
84C11×#41—416no—
85C11×#41—48no—
86C2×Q8×C11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—24no—
90C2×Q8×C11—416no—
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11C2×D414yes—
97C22×C4×C11—28no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C2×C8×C11—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—44no—
118C11×C4⋊C4C2×D414yes—
119C11×C22⋊C4—28no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C42×C11—22no—
123C42×C11—22no—
124C42×C11C2×D412yes—
125C42×C11C2×D412yes—
126#3497C2×C1111yescharacteristic
127#3234C2×C1112yescomplemented
128#2634C2×C1111yescharacteristic, complemented
129#1616C2×C1114yescomplemented
130#1610C2×C1114yescomplemented
131#1514C2×C1112yescomplemented
132#1467C2×C1111yescharacteristic, complemented
133C23×C11—24no—
134C23×C11C22×D411yescharacteristic
135Q8×C11—28no—
136Q8×C11—44no—
137Q8×C11—48no—
138D4×C11—44no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—48no—
142D4×C11—48no—
143D4×C11—84no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—48no—
152C2×C4×C11—416no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12012yes—
164C2×C4×C11AGL(1,ℤ/8)14yes—
165C2×C4×C11C22×D412yes—
166C8×C11—44no—
167C2×2−1+4—21no—
168#550—22no—
169D4×Q8—22no—
170#548—24no—
171#537—21no—
172#537C22×C1114yes—
173#532—22no—
174#532C22×C1112yes—
175C2×#125C22×C1111yescharacteristic
176C2×C4×Q8C22×C1111yescharacteristic
177#501—22no—
178#490—22no—
179#481C22×C1114yes—
180#480C22×C1114yes—
181#478—24no—
182#432C22×C1112yes—
183#400—21no—
184#400C22×C1112yes—
185#398C22×C1112yes—
186#395—21no—
187#387—22no—
188#383C22×C1111yescharacteristic
189#327C22×C1118yes—
190#324C22×C1114yes—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—44no—
194C22×C11—44no—
195C22×C11—44no—
196C22×C11C2×#12011yescharacteristic
197C22×C11C2×AGL(1,ℤ/8)12yes—
198C4×C11—22no—
199C4×C11—24no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—44no—
204C4×C11—42no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11—81no—
2082−1+4—48no—
209C2×#41—24no—
210C2×#41—24no—
211C2×#41—22no—
212C22×Q8—24no—
213C22×Q8D4×C1111yescharacteristic
214C4⋊Q8—22no—
215C4⋊Q8D4×C1112yes—
216#127—22no—
217#127D4×C1112yes—
218#125—22no—
219#125—22no—
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—21no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4D4×C1111yescharacteristic
239C2×C4⋊C4C23×C1111yescharacteristic
240C2×C4⋊C4C23×C1111yescharacteristic
241C2×C4⋊C4C23×C1112yes—
242C2×C42D4×C1112yes—
243C2×C42C23×C1111yescharacteristic
244#107—24no—
245#106—24no—
246C4⋊C8—22no—
247#102—24no—
248#102—24no—
249C22⋊C8C23×C1114yes—
250#97—22no—
251#95—21no—
252#95—21no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95C23×C1112yes—
257C2×C11—22no—
258C2×C11—84no—
259C2×C11#300311yescharacteristic
260C2×C11#302011yescharacteristic
261C2×C11#302811yescharacteristic
262#41—48no—
263#41—48no—
264#41—416no—
265#41—48no—
266C2×Q8—24no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—24no—
270C2×Q8—416no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4C2×D4×C1114yes—
277C22×C4—28no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1112yes—
284C22×C4C2×D4×C1112yes—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C24×C1111yescharacteristic
287C2×C8—24no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—44no—
298C4⋊C4C2×D4×C1114yes—
299C22⋊C4—28no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C42—22no—
303C42—22no—
304C42C2×D4×C1112yes—
305C42C2×D4×C1112yes—
306C11#1837311yescharacteristic, direct product factor, Sylow
307C23—24no—
308C23C22×D4×C1111yescharacteristic
309Q8—28no—
310Q8—44no—
311Q8—48no—
312D4—44no—
313D4—44no—
314D4—44no—
315D4—48no—
316D4—48no—
317D4—84no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—48no—
326C2×C4—416no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4C11×#12011yescharacteristic
336C2×C4C11×#12011yescharacteristic
337C2×C4C11×#12012yes—
338C2×C4C11×AGL(1,ℤ/8)14yes—
339C2×C4C22×D4×C1112yes—
340C8—44no—
341C22—21no—
342C22—21no—
343C22—44no—
344C22—44no—
345C22—44no—
346C22C2×C11×#12011yescharacteristic
347C22C2×C11×AGL(1,ℤ/8)12yes—
348C4—22no—
349C4—24no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—44no—
354C4—42no—
355C4—82no—
356C4—81no—
357C4—81no—
358C2—22no—
359C2—84no—
360C2C11×#300311yescharacteristic
361C2C11×#302011yescharacteristic
362C2C11×#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×#3234C2semidirect
3. C11×#2634C2semidirect
4. C11×#1616C2semidirect
5. C11×#1610C2semidirect
6. C11×#1514C2semidirect
7. C11×#1467C2semidirect
81. #18373C11direct (N × H)
127. #3234C2×C11semidirect
128. #2634C2×C11semidirect
129. #1616C2×C11semidirect
130. #1610C2×C11semidirect
131. #1514C2×C11semidirect
132. #1467C2×C11semidirect
306. C11#18373direct (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×#32342
C11×#26342
C11×#16162
C11×#16102
C11×#15142
C11×#14672
#1837311