Finite Group Databasebeta

← C11×#18396 #14595589

Subgroups — C11×#18396 #14595589

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3229C212yesmaximal, complemented
3C11×#2547C211yesmaximal, characteristic
4C11×#1608C218yesmaximal, complemented
5C11×#1503C212yesmaximal, complemented
6C11×#1460C211yesmaximal, characteristic
7C11×#554—22no—
8C11×#554—24no—
9D4×Q8×C11—22no—
10C11×#544—21no—
11C11×#543C2214yes—
12C11×#533C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#124—21no—
15C2×C11×C22⋊Q8—22no—
16C11×#518—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C11×#498—22no—
19C11×#487—22no—
20C11×#483C2218yes—
21C11×#475—24no—
22C11×#431C2212yes—
23C11×#397C2214yes—
24C11×#391—21no—
25C11×#380—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#328C2218yes—
28C11×#323C2214yes—
29C22×Q8×C11—22no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11D412yes—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D412yes—
38C11×#125—24no—
39C11×#125—22no—
40C11×#124—44no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—22no—
49C4×Q8×C11D414yes—
50C4×D4×C11—24no—
51C4×D4×C11—24no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4C2312yes—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×#106—28no—
67C11×C4⋊C8—22no—
68C11×#103—28no—
69C11×C22⋊C8C2314yes—
70C4×C8×C11—22no—
71C11×#95—24no—
72C11×#95C2312yes—
73#18396C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11C2×D412yes—
75C2×Q8×C11—24no—
76C2×Q8×C11—22no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—84no—
81C2×Q8×C11C2×D414yes—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11SD1614yes—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—44no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C2×C8×C11—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4C2×D414yes—
110C11×C22⋊C4—28no—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—48no—
114C42×C11—24no—
115C42×C11—42no—
116C42×C11C2×D412yes—
117C42×C11C2×D412yes—
118#3501C2×C1111yescharacteristic
119#3229C2×C1112yescomplemented
120#2547C2×C1111yescharacteristic
121#1608C2×C1118yescomplemented
122#1503C2×C1112yescomplemented
123#1460C2×C1111yescharacteristic
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11C2×SD1614yes—
129C23×C11C22×D411yescharacteristic
130Q8×C11—44no—
131Q8×C11—44no—
132Q8×C11—84no—
133Q8×C11—84no—
134D4×C11—28no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—44no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11—84no—
150C2×C4×C11—84no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12012yes—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11C2×SD1612yes—
155C2×C4×C11#13712yes—
156C2×C4×C11C22×D412yes—
157C8×C11—44no—
158#554—22no—
159#554—24no—
160D4×Q8—22no—
161#544—21no—
162#543C22×C1114yes—
163#533C22×C1112yes—
164C2×C4⋊Q8C22×C1111yescharacteristic
165C2×#124—21no—
166C2×C22⋊Q8—22no—
167#518—21no—
168C2×C4×D4C22×C1111yescharacteristic
169#498—22no—
170#487—22no—
171#483C22×C1118yes—
172#475—24no—
173#431C22×C1112yes—
174#397C22×C1114yes—
175#391—21no—
176#380—22no—
177C4×C4⋊C4C22×C1111yescharacteristic
178#328C22×C1118yes—
179#323C22×C1114yes—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—24no—
183C22×C11—44no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—82no—
187C22×C11C2×#12011yescharacteristic
188C22×C11C22×SD1611yescharacteristic
189C22×C11C2×#13711yescharacteristic
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—42no—
193C4×C11—44no—
194C4×C11—44no—
195C4×C11—82no—
196C4×C11—82no—
197C4×C11#44814yes—
198C4×C11#45512yes—
199C22×Q8—22no—
200C22×Q8—21no—
201C22×D4D4×C1111yescharacteristic
202C23×C4D4×C1112yes—
203C4⋊Q8—24no—
204C4⋊Q8—22no—
205C4⋊Q8—22no—
206C4⋊Q8D4×C1112yes—
207C4⋊Q8D4×C1112yes—
208#125—24no—
209#125—22no—
210#124—44no—
211C22⋊Q8—24no—
212C22⋊Q8—24no—
213C22⋊Q8—28no—
214C22⋊Q8—22no—
215C22⋊Q8—24no—
216C22⋊Q8—28no—
217C22⋊Q8C23×C1114yes—
218C4×Q8—22no—
219C4×Q8D4×C1114yes—
220C4×D4—24no—
221C4×D4—24no—
222C4×D4—22no—
223C4×D4—22no—
224#117—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C1111yescharacteristic
230C2×C4⋊C4C23×C1112yes—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4C23×C1112yes—
234C2×C42—21no—
235C2×C42C23×C1111yescharacteristic
236#106—28no—
237C4⋊C8—22no—
238#103—28no—
239C22⋊C8C23×C1114yes—
240C4×C8—22no—
241#95—24no—
242#95C23×C1112yes—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—44no—
246C2×C11C2×#44811yescharacteristic
247C2×C11C2×#45511yescharacteristic
248C2×C11#302811yescharacteristic
249C24C2×D4×C1112yes—
250C2×Q8—24no—
251C2×Q8—22no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—84no—
256C2×Q8C2×D4×C1114yes—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4C11×SD1614yes—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—44no—
267C22×C4C2×D4×C1111yescharacteristic
268C22×C4C2×D4×C1112yes—
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C24×C1111yescharacteristic
271C2×C8—24no—
272C4⋊C4—24no—
273C4⋊C4—28no—
274C4⋊C4—22no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4C2×D4×C1114yes—
285C22⋊C4—28no—
286C22⋊C4—24no—
287C22⋊C4—24no—
288C22⋊C4—48no—
289C42—24no—
290C42—42no—
291C42C2×D4×C1112yes—
292C42C2×D4×C1112yes—
293C11#1839611yescharacteristic, direct product factor, Sylow
294C23—22no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23C2×C11×SD1614yes—
299C23C22×D4×C1111yescharacteristic
300Q8—44no—
301Q8—44no—
302Q8—84no—
303Q8—84no—
304D4—28no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—84no—
320C2×C4—84no—
321C2×C4C11×#12011yescharacteristic
322C2×C4C11×#12012yes—
323C2×C4C11×#12011yescharacteristic
324C2×C4C2×C11×SD1612yes—
325C2×C4C11×#13712yes—
326C2×C4C22×D4×C1112yes—
327C8—44no—
328C22—21no—
329C22—21no—
330C22—24no—
331C22—44no—
332C22—42no—
333C22—42no—
334C22—82no—
335C22C2×C11×#12011yescharacteristic
336C22C22×C11×SD1611yescharacteristic
337C22C2×C11×#13711yescharacteristic
338C4—21no—
339C4—22no—
340C4—42no—
341C4—44no—
342C4—44no—
343C4—82no—
344C4—82no—
345C4C11×#44814yes—
346C4C11×#45512yes—
347C2—21no—
348C2—21no—
349C2—44no—
350C2C2×C11×#44811yescharacteristic
351C2C2×C11×#45511yescharacteristic
352C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
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×#3229C2semidirect
4. C11×#1608C2semidirect
5. C11×#1503C2semidirect
73. #18396C11direct (N × H)
119. #3229C2×C11semidirect
121. #1608C2×C11semidirect
122. #1503C2×C11semidirect
293. C11#18396direct (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×#32292
C11×#25472
C11×#16082
C11×#15032
C11×#14602
#1839611