Finite Group Databasebeta

← C11×#21214 #14598407

Subgroups — C11×#21214 #14598407

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C2×C11×#410C214yesmaximal, complemented
3C11×#2316C211yesmaximal, characteristic, complemented
4C11×#2274C211yesmaximal, characteristic, complemented
5C11×#1964C218yesmaximal, complemented
6C22×C11×#41C2212yes—
7C11×#537—24no—
8C11×#537—24no—
9C2×C11×C22⋊Q8C414yescomplemented
10C2×C11×#121C414yescomplemented
11C2×C11×#121C2214yes—
12C2×C11×#117C2212yes—
13C2×C11×#117C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C11×#410—216no—
16C2×C11×#99C22116yes—
17C11×#389—24no—
18C11×#380C2214yes—
19C4×C11×C4⋊C4—24no—
20C4×C11×C22⋊C4C2214yes—
21C2×C11×#41—24no—
22C2×C11×#41—24no—
23C2×C11×#41—28no—
24C2×C11×#41—28no—
25C22×Q8×C11C2×C412yes—
26C22×D4×C11C2×C412yes—
27C22×D4×C11C2×C414yes—
28C22×D4×C11C2314yes—
29C23×C4×C11C2×C414yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C11×C22⋊Q8—216no—
33C11×#121—28no—
34C11×#121—28no—
35C11×#121—216no—
36C11×#117—24no—
37C11×#117—28no—
38C11×#117D418yescomplemented
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4C2×C414yes—
43C2×C11×C4⋊C4C2×C414yes—
44C2×C11×C4⋊C4D414yes—
45C2×C11×C4⋊C4D414yes—
46C2×C11×C22⋊C4C2×C418yes—
47C2×C11×C22⋊C4C2314yes—
48C2×C11×C22⋊C4C2314yes—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11—24no—
52C11×#99—232no—
53C11×#95—24no—
54C11×#95—24no—
55#21214C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11C22×C414yes—
57C24×C11C2411yescharacteristic
58C11×#41—48no—
59C11×#41—48no—
60C11×#41—48no—
61C11×#41—48no—
62C2×Q8×C11—24no—
63C2×Q8×C11—28no—
64C2×D4×C11—28no—
65C2×D4×C11—24no—
66C2×D4×C11—24no—
67C2×D4×C11—28no—
68C2×D4×C11—24no—
69C2×D4×C11—28no—
70C2×D4×C11—28no—
71C2×D4×C11—84no—
72C22×C4×C11—24no—
73C22×C4×C11—28no—
74C22×C4×C11—216no—
75C22×C4×C11—24no—
76C22×C4×C11—82no—
77C22×C4×C11C22×C414yes—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×D414yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D414yes—
85C22×C4×C11#4114yes—
86C11×C4⋊C4—28no—
87C11×C4⋊C4—28no—
88C11×C4⋊C4—44no—
89C11×C4⋊C4—84no—
90C11×C4⋊C4C22⋊C4116yes—
91C11×C22⋊C4—24no—
92C11×C22⋊C4—216no—
93C11×C22⋊C4—28no—
94C11×C22⋊C4C2×D418yes—
95C42×C11—28no—
96C42×C11—44no—
97C42×C11—84no—
98C2×#537C2×C1111yescharacteristic
99C2×#410C2×C1114yescomplemented
100#2316C2×C1111yescharacteristic, complemented
101#2274C2×C1111yescharacteristic, complemented
102#1964C2×C1118yescomplemented
103C23×C11—24no—
104C23×C11—28no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—44no—
108C23×C11—44no—
109C23×C11C23×C411yescharacteristic
110C23×C11C22×D411yescharacteristic
111C23×C11C22×D411yescharacteristic
112C23×C11C22×D412yes—
113C23×C11C2×#4112yes—
114Q8×C11—48no—
115D4×C11—48no—
116D4×C11—44no—
117D4×C11—44no—
118D4×C11—48no—
119D4×C11—88no—
120C2×C4×C11—24no—
121C2×C4×C11—28no—
122C2×C4×C11—28no—
123C2×C4×C11—44no—
124C2×C4×C11—44no—
125C2×C4×C11—44no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—416no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11C2×C22⋊C418yes—
133C2×C4×C11C2×C22⋊C414yes—
134C2×C4×C11C4×D418yes—
135C2×C4×C11#12114yes—
136C2×C4×C11#12114yes—
137C2×C4×C11#12414yes—
138C2×C4×C11#12714yes—
139C22×#41C22×C1112yes—
140#537—24no—
141#537—24no—
142C2×C22⋊Q8C4×C1114yescomplemented
143C2×#121C4×C1114yescomplemented
144C2×#121C22×C1114yes—
145C2×#117C22×C1112yes—
146C2×#117C22×C1112yes—
147C22×C4⋊C4C22×C1111yescharacteristic
148#410—216no—
149C2×#99C22×C11116yes—
150#389—24no—
151#380C22×C1114yes—
152C4×C4⋊C4—24no—
153C4×C22⋊C4C22×C1114yes—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—44no—
163C22×C11—44no—
164C22×C11—44no—
165C22×C11—88no—
166C22×C11C22×C22⋊C411yescharacteristic
167C22×C11C2×C4×D412yes—
168C22×C11C2×#12112yes—
169C22×C11C2×#12411yescharacteristic
170C22×C11C2×#12711yescharacteristic
171C4×C11—28no—
172C4×C11—48no—
173C4×C11—44no—
174C4×C11—84no—
175C4×C11#39018yes—
176C2×#41—24no—
177C2×#41—24no—
178C2×#41—28no—
179C2×#41—28no—
180C22×Q8C2×C4×C1112yes—
181C22×D4C2×C4×C1112yes—
182C22×D4C2×C4×C1114yes—
183C22×D4C23×C1114yes—
184C23×C4C2×C4×C1114yes—
185C23×C4C23×C1112yes—
186C23×C4C23×C1111yescharacteristic
187C22⋊Q8—216no—
188#121—28no—
189#121—28no—
190#121—216no—
191#117—24no—
192#117—28no—
193#117D4×C1118yescomplemented
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4C2×C4×C1114yes—
198C2×C4⋊C4C2×C4×C1114yes—
199C2×C4⋊C4D4×C1114yes—
200C2×C4⋊C4D4×C1114yes—
201C2×C22⋊C4C2×C4×C1118yes—
202C2×C22⋊C4C23×C1114yes—
203C2×C22⋊C4C23×C1114yes—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—24no—
207#99—232no—
208#95—24no—
209#95—24no—
210C2×C11—22no—
211C2×C11—21no—
212C2×C11—22no—
213C2×C11—21no—
214C2×C11—84no—
215C2×C11C2×#39011yescharacteristic
216C2×C11#288311yescharacteristic
217C2×C11#288411yescharacteristic
218C24C22×C4×C1114yes—
219C24C24×C1111yescharacteristic
220#41—48no—
221#41—48no—
222#41—48no—
223#41—48no—
224C2×Q8—24no—
225C2×Q8—28no—
226C2×D4—28no—
227C2×D4—24no—
228C2×D4—24no—
229C2×D4—28no—
230C2×D4—24no—
231C2×D4—28no—
232C2×D4—28no—
233C2×D4—84no—
234C22×C4—24no—
235C22×C4—28no—
236C22×C4—216no—
237C22×C4—24no—
238C22×C4—82no—
239C22×C4C22×C4×C1114yes—
240C22×C4C22×C4×C1114yes—
241C22×C4C22×C4×C1112yes—
242C22×C4C2×D4×C1114yes—
243C22×C4C2×D4×C1114yes—
244C22×C4C2×D4×C1112yes—
245C22×C4C2×D4×C1112yes—
246C22×C4C2×D4×C1114yes—
247C22×C4C11×#4114yes—
248C4⋊C4—28no—
249C4⋊C4—28no—
250C4⋊C4—44no—
251C4⋊C4—84no—
252C4⋊C4C11×C22⋊C4116yes—
253C22⋊C4—24no—
254C22⋊C4—216no—
255C22⋊C4—28no—
256C22⋊C4C2×D4×C1118yes—
257C42—28no—
258C42—44no—
259C42—84no—
260C11#2121411yescharacteristic, direct product factor, Sylow
261C23—24no—
262C23—28no—
263C23—41no—
264C23—41no—
265C23—44no—
266C23—44no—
267C23C23×C4×C1111yescharacteristic
268C23C22×D4×C1111yescharacteristic
269C23C22×D4×C1111yescharacteristic
270C23C22×D4×C1112yes—
271C23C2×C11×#4112yes—
272Q8—48no—
273D4—48no—
274D4—44no—
275D4—44no—
276D4—48no—
277D4—88no—
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—416no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4C2×C11×C22⋊C418yes—
291C2×C4C2×C11×C22⋊C414yes—
292C2×C4C4×D4×C1118yes—
293C2×C4C11×#12114yes—
294C2×C4C11×#12114yes—
295C2×C4C11×#12414yes—
296C2×C4C11×#12714yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—42no—
305C22—44no—
306C22—44no—
307C22—44no—
308C22—88no—
309C22C22×C11×C22⋊C411yescharacteristic
310C22C2×C4×D4×C1112yes—
311C22C2×C11×#12112yes—
312C22C2×C11×#12411yescharacteristic
313C22C2×C11×#12711yescharacteristic
314C4—28no—
315C4—48no—
316C4—44no—
317C4—84no—
318C4C11×#39018yes—
319C2—22no—
320C2—21no—
321C2—22no—
322C2—21no—
323C2—84no—
324C2C2×C11×#39011yescharacteristic
325C2C11×#288311yescharacteristic
326C2C11×#288411yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#537C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C11×#410C2semidirect
3. C11×#2316C2semidirect
4. C11×#2274C2semidirect
5. C11×#1964C2semidirect
9. C2×C11×C22⋊Q8C4semidirect
10. C2×C11×#121C4semidirect
38. C11×#117D4semidirect
55. #21214C11direct (N × H)
99. C2×#410C2×C11semidirect
100. #2316C2×C11semidirect
101. #2274C2×C11semidirect
102. #1964C2×C11semidirect
142. C2×C22⋊Q8C4×C11semidirect
143. C2×#121C4×C11semidirect
193. #117D4×C11semidirect
260. C11#21214direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4102
C11×#23162
C11×#22742
C11×#19642
#2121411