Finite Group Databasebeta

← C11×#18389 #14595582

Subgroups — C11×#18389 #14595582

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C11×#3208C212yesmaximal, complemented
3C11×#2541C211yesmaximal, characteristic
4C11×#1596C218yesmaximal, complemented
5C11×#1503C212yesmaximal, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#554—22no—
8C11×#554—24no—
9D4×Q8×C11—22no—
10C11×#544—21no—
11C11×#543C2214yes—
12C11×#533C2212yes—
13C2×C11×#127—21no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×C22⋊Q8—22no—
16C2×C11×#121—22no—
17C11×#518—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C11×#492—22no—
20C11×#486—22no—
21C11×#460—24no—
22C11×#450C2218yes—
23C11×#431C2212yes—
24C11×#392C2214yes—
25C11×#390—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#323C2214yes—
29C22×Q8×C11—22no—
30C22×D4×C11—24no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2312yes—
35C23×C4×C11D412yes—
36C2×C11×SD16—28no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8D412yescomplemented
39C11×C4⋊Q8D412yescomplemented
40C11×#127—22no—
41C11×#127—22no—
42C11×#127—44no—
43C11×#125—24no—
44C11×#125—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8C2314yes—
52C11×#121—48no—
53C4×Q8×C11—22no—
54C4×Q8×C11D414yescomplemented
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4C2312yes—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C11×C4⋊C8—22no—
70C11×#102—28no—
71C11×C22⋊C8C2314yes—
72C4×C8×C11—22no—
73C11×#95C2312yes—
74#18389C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—22no—
76C24×C11C2×D412yes—
77C2×Q8×C11—24no—
78C2×Q8×C11—22no—
79C2×Q8×C11—84no—
80C2×Q8×C11C2×D414yes—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—24no—
84C2×D4×C11—44no—
85C2×D4×C11—48no—
86C2×D4×C11—48no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—82no—
93C2×D4×C11—84no—
94C2×D4×C11SD1614yescomplemented
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—44no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C11×SD16—88no—
106C2×C8×C11—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4C2×D414yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—48no—
121C42×C11—24no—
122C42×C11—42no—
123C42×C11C2×D412yes—
124C42×C11C2×D412yes—
125#3501C2×C1111yescharacteristic, complemented
126#3208C2×C1112yescomplemented
127#2541C2×C1111yescharacteristic
128#1596C2×C1118yescomplemented
129#1503C2×C1112yescomplemented
130#1460C2×C1111yescharacteristic, complemented
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—44no—
136C23×C11—44no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11C2×SD1614yes—
141C23×C11C22×D411yescharacteristic
142Q8×C11—44no—
143Q8×C11—44no—
144Q8×C11—84no—
145D4×C11—28no—
146D4×C11—48no—
147D4×C11—82no—
148D4×C11—816no—
149D4×C11—84no—
150D4×C11—82no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—84no—
163C2×C4×C11—84no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12012yes—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11C2×SD1612yes—
168C2×C4×C11#13712yes—
169C2×C4×C11C22×D412yes—
170C8×C11—44no—
171#554—22no—
172#554—24no—
173D4×Q8—22no—
174#544—21no—
175#543C22×C1114yes—
176#533C22×C1112yes—
177C2×#127—21no—
178C2×#127C22×C1111yescharacteristic
179C2×C22⋊Q8—22no—
180C2×#121—22no—
181#518—21no—
182C2×C4×D4C22×C1111yescharacteristic
183#492—22no—
184#486—22no—
185#460—24no—
186#450C22×C1118yes—
187#431C22×C1112yes—
188#392C22×C1114yes—
189#390—21no—
190C4×C4⋊C4C22×C1111yescharacteristic
191#328C22×C1118yes—
192#323C22×C1114yes—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—24no—
196C22×C11—44no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11—82no—
200C22×C11—84no—
201C22×C11—84no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11C2×#12011yescharacteristic
206C22×C11C22×SD1611yescharacteristic
207C22×C11C2×#13711yescharacteristic
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—44no—
211C4×C11—42no—
212C4×C11—44no—
213C4×C11—44no—
214C4×C11#44814yes—
215C4×C11#45312yes—
216C22×Q8—22no—
217C22×D4—24no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4D4×C1111yescharacteristic
221C22×D4C23×C1112yes—
222C23×C4D4×C1112yes—
223C2×SD16—28no—
224C4⋊Q8—24no—
225C4⋊Q8D4×C1112yescomplemented
226C4⋊Q8D4×C1112yescomplemented
227#127—22no—
228#127—22no—
229#127—44no—
230#125—24no—
231#125—22no—
232C22⋊Q8—24no—
233C22⋊Q8—24no—
234C22⋊Q8—28no—
235C22⋊Q8—22no—
236C22⋊Q8—24no—
237C22⋊Q8—28no—
238C22⋊Q8C23×C1114yes—
239#121—48no—
240C4×Q8—22no—
241C4×Q8D4×C1114yescomplemented
242C4×D4—24no—
243C4×D4—24no—
244C4×D4—22no—
245C4×D4—22no—
246#117—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C1111yescharacteristic
251C2×C22⋊C4—24no—
252C2×C22⋊C4—24no—
253C2×C22⋊C4C23×C1112yes—
254C2×C42—21no—
255C2×C42C23×C1111yescharacteristic
256C4⋊C8—22no—
257#102—28no—
258C22⋊C8C23×C1114yes—
259C4×C8—22no—
260#95C23×C1112yes—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—44no—
264C2×C11—162no—
265C2×C11C2×#44811yescharacteristic
266C2×C11C2×#45311yescharacteristic
267C2×C11#302711yescharacteristic
268C24—22no—
269C24C2×D4×C1112yes—
270C2×Q8—24no—
271C2×Q8—22no—
272C2×Q8—84no—
273C2×Q8C2×D4×C1114yes—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—44no—
278C2×D4—48no—
279C2×D4—48no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—82no—
286C2×D4—84no—
287C2×D4C11×SD1614yescomplemented
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—44no—
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C2×D4×C1112yes—
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C24×C1111yescharacteristic
298SD16—88no—
299C2×C8—24no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—28no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—24no—
309C4⋊C4C2×D4×C1114yes—
310C22⋊C4—28no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—48no—
314C42—24no—
315C42—42no—
316C42C2×D4×C1112yes—
317C42C2×D4×C1112yes—
318C11#1838911yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23—44no—
324C23—44no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23C2×C11×SD1614yes—
329C23C22×D4×C1111yescharacteristic
330Q8—44no—
331Q8—44no—
332Q8—84no—
333D4—28no—
334D4—48no—
335D4—82no—
336D4—816no—
337D4—84no—
338D4—82no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—84no—
351C2×C4—84no—
352C2×C4C11×#12011yescharacteristic
353C2×C4C11×#12012yes—
354C2×C4C11×#12011yescharacteristic
355C2×C4C2×C11×SD1612yes—
356C2×C4C11×#13712yes—
357C2×C4C22×D4×C1112yes—
358C8—44no—
359C22—21no—
360C22—21no—
361C22—24no—
362C22—44no—
363C22—42no—
364C22—42no—
365C22—82no—
366C22—84no—
367C22—84no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22C2×C11×#12011yescharacteristic
372C22C22×C11×SD1611yescharacteristic
373C22C2×C11×#13711yescharacteristic
374C4—21no—
375C4—22no—
376C4—44no—
377C4—42no—
378C4—44no—
379C4—44no—
380C4C11×#44814yes—
381C4C11×#45312yes—
382C2—21no—
383C2—21no—
384C2—44no—
385C2—162no—
386C2C2×C11×#44811yescharacteristic
387C2C2×C11×#45311yescharacteristic
388C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2541C2
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
1. C11×#3501C2semidirect
2. C11×#3208C2semidirect
4. C11×#1596C2semidirect
5. C11×#1503C2semidirect
6. C11×#1460C2semidirect
38. C11×C4⋊Q8D4semidirect
39. C11×C4⋊Q8D4semidirect
54. C4×Q8×C11D4semidirect
74. #18389C11direct (N × H)
94. C2×D4×C11SD16semidirect
125. #3501C2×C11semidirect
126. #3208C2×C11semidirect
128. #1596C2×C11semidirect
129. #1503C2×C11semidirect
130. #1460C2×C11semidirect
225. C4⋊Q8D4×C11semidirect
226. C4⋊Q8D4×C11semidirect
241. C4×Q8D4×C11semidirect
287. C2×D4C11×SD16semidirect
318. C11#18389direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#32082
C11×#25412
C11×#15962
C11×#15032
C11×#14602
#1838911