Finite Group Databasebeta

← C11×#21313 #14598506

Subgroups — C11×#21313 #14598506

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic
3C4×C11×#117C211yesmaximal, characteristic
4C11×#1988C214yesmaximal, complemented
5C11×#1987C214yesmaximal, complemented
6C11×#1736C214yesmaximal
7C23×Q8×C11—21no—
8C22×C11×M16C2212yes—
9C2×C11×C4⋊Q8—21no—
10C2×C11×C4⋊Q8—21no—
11C2×C11×C4⋊Q8—24no—
12C2×C11×C4⋊Q8C418yescomplemented
13C2×C11×C4⋊Q8C2212yes—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C11×#423—24no—
20C2×C11×C4⋊C8C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C4×C11×C4⋊C4C2212yes—
23C4×C11×C4⋊C4C2212yes—
24C4×C11×C22⋊C4—21no—
25C4×C11×C22⋊C4—21no—
26C11×#376—21no—
27C43×C11—21no—
28C11×#340C22116yes—
29C22×Q8×C11—28no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—48no—
33C23×C4×C11—22no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C2×C11×M16—24no—
38C2×C11×M16—28no—
39C22×C8×C11C2314yes—
40C11×C4⋊Q8—28no—
41C11×C4⋊Q8—28no—
42C11×C4⋊Q8—24no—
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8C2×C418yes—
45C11×C4⋊Q8C2×C418yes—
46C11×#117—24no—
47C11×#117Q818yescomplemented
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4C2×C418yes—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11C2×C414yes—
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D414yes—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C11×C4⋊C8—24no—
67C11×C4⋊C8—24no—
68C11×#95—22no—
69C11×#95—22no—
70#21313C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—28no—
73C2×Q8×C11—28no—
74C2×Q8×C11—48no—
75C2×Q8×C11—432no—
76C2×Q8×C11—48no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—28no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—48no—
83C22×C4×C11C22⋊C414yes—
84C22×C4×C11C22⋊C414yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×Q814yes—
93C22×C4×C11#4114yes—
94C22×C4×C11C2411yescharacteristic
95C11×M16—48no—
96C2×C8×C11—24no—
97C2×C8×C11—28no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4C22×C418yes—
104C11×C4⋊C4C2×Q818yescomplemented
105C11×C22⋊C4—28no—
106C42×C11—28no—
107C42×C11—44no—
108C42×C11—44no—
109C42×C11C22⋊C414yes—
110C42×C11C22⋊C414yes—
111C42×C11C22×C412yes—
112C42×C11C22×C412yes—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115C22×C4⋊Q8C2×C1111yescharacteristic
116C2×#423C2×C1111yescharacteristic
117C4×#117C2×C1111yescharacteristic
118#1988C2×C1114yescomplemented
119#1987C2×C1114yescomplemented
120#1736C2×C1114yes—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11C2×C22⋊C412yes—
124C23×C11C22⋊Q814yes—
125C23×C11C22×D411yescharacteristic
126Q8×C11—416no—
127Q8×C11—416no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—28no—
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—28no—
134C2×C4×C11—416no—
135C2×C4×C11—44no—
136C2×C4×C11—48no—
137C2×C4×C11—44no—
138C2×C4×C11C2×C22⋊C412yes—
139C2×C4×C11C2×C22⋊C412yes—
140C2×C4×C11C2×C22⋊C412yes—
141C2×C4×C11C2×C22⋊C412yes—
142C2×C4×C11C2×C22⋊C412yes—
143C2×C4×C11C4×Q818yes—
144C2×C4×C11C22⋊Q814yes—
145C2×C4×C11#12414yes—
146C2×C4×C11C4⋊Q814yes—
147C2×C4×C11AGL(1,ℤ/8)14yes—
148C2×C4×C11#13714yes—
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×Q812yes—
152C2×C4×C11C2×#4112yes—
153C8×C11—44no—
154C23×Q8—21no—
155C22×M16C22×C1112yes—
156C2×C4⋊Q8—21no—
157C2×C4⋊Q8—21no—
158C2×C4⋊Q8—24no—
159C2×C4⋊Q8C4×C1118yescomplemented
160C2×C4⋊Q8C22×C1112yes—
161C2×C4⋊Q8C22×C1112yes—
162C2×#117C22×C1112yes—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C22×C1112yes—
165C22×C42C22×C1111yescharacteristic
166#423—24no—
167C2×C4⋊C8C22×C1112yes—
168C2×C4⋊C8C22×C1112yes—
169C4×C4⋊C4C22×C1112yes—
170C4×C4⋊C4C22×C1112yes—
171C4×C22⋊C4—21no—
172C4×C22⋊C4—21no—
173#376—21no—
174C43—21no—
175#340C22×C11116yes—
176C22×C11—28no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11#39114yes—
180C22×C11C22×C22⋊C411yescharacteristic
181C22×C11C2×C22⋊Q812yes—
182C22×C11C2×AGL(1,ℤ/8)12yes—
183C22×C11C2×#13712yes—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—48no—
187C4×C11—48no—
188C4×C11#39114yes—
189C4×C11#41814yes—
190C4×C11#41914yes—
191C4×C11C2×C4×Q812yes—
192C4×C11C2×#12411yescharacteristic
193C4×C11C2×C4⋊Q811yescharacteristic
194C22×Q8—28no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—48no—
198C23×C4—22no—
199C23×C4D4×C1111yescharacteristic
200C23×C4D4×C1111yescharacteristic
201C23×C4C23×C1111yescharacteristic
202C2×M16—24no—
203C2×M16—28no—
204C22×C8C23×C1114yes—
205C4⋊Q8—28no—
206C4⋊Q8—28no—
207C4⋊Q8—24no—
208C4⋊Q8—24no—
209C4⋊Q8C2×C4×C1118yes—
210C4⋊Q8C2×C4×C1118yes—
211#117—24no—
212#117Q8×C1118yescomplemented
213C2×C4⋊C4—28no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4C2×C4×C1118yes—
219C2×C4⋊C4C23×C1114yes—
220C2×C4⋊C4C23×C1114yes—
221C2×C22⋊C4—22no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42C2×C4×C1114yes—
226C2×C42D4×C1111yescharacteristic
227C2×C42D4×C1111yescharacteristic
228C2×C42D4×C1114yes—
229C2×C42C23×C1111yescharacteristic
230C2×C42C23×C1111yescharacteristic
231C4⋊C8—24no—
232C4⋊C8—24no—
233#95—22no—
234#95—22no—
235C2×C11—24no—
236C2×C11C2×#39111yescharacteristic
237C2×C11C2×#41811yescharacteristic
238C2×C11C2×#41911yescharacteristic
239C2×C11#307914yes—
240C24C2×D4×C1111yescharacteristic
241C2×Q8—28no—
242C2×Q8—28no—
243C2×Q8—48no—
244C2×Q8—432no—
245C2×Q8—48no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—28no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—48no—
252C22×C4C11×C22⋊C414yes—
253C22×C4C11×C22⋊C414yes—
254C22×C4C22×C4×C1112yes—
255C22×C4C2×D4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×D4×C1111yescharacteristic
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×D4×C1112yes—
261C22×C4C2×Q8×C1114yes—
262C22×C4C11×#4114yes—
263C22×C4C24×C1111yescharacteristic
264M16—48no—
265C2×C8—24no—
266C2×C8—28no—
267C4⋊C4—28no—
268C4⋊C4—28no—
269C4⋊C4—28no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4C22×C4×C1118yes—
273C4⋊C4C2×Q8×C1118yescomplemented
274C22⋊C4—28no—
275C42—28no—
276C42—44no—
277C42—44no—
278C42C11×C22⋊C414yes—
279C42C11×C22⋊C414yes—
280C42C22×C4×C1112yes—
281C42C22×C4×C1112yes—
282C42C2×D4×C1112yes—
283C42C2×D4×C1112yes—
284C11#2131311yescharacteristic, direct product factor, Sylow
285C23—22no—
286C23—22no—
287C23C2×C11×C22⋊C412yes—
288C23C11×C22⋊Q814yes—
289C23C22×D4×C1111yescharacteristic
290Q8—416no—
291Q8—416no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—28no—
297C2×C4—28no—
298C2×C4—416no—
299C2×C4—44no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4C2×C11×C22⋊C412yes—
303C2×C4C2×C11×C22⋊C412yes—
304C2×C4C2×C11×C22⋊C412yes—
305C2×C4C2×C11×C22⋊C412yes—
306C2×C4C2×C11×C22⋊C412yes—
307C2×C4C4×Q8×C1118yes—
308C2×C4C11×C22⋊Q814yes—
309C2×C4C11×#12414yes—
310C2×C4C11×C4⋊Q814yes—
311C2×C4C11×AGL(1,ℤ/8)14yes—
312C2×C4C11×#13714yes—
313C2×C4C23×C4×C1111yescharacteristic
314C2×C4C22×D4×C1111yescharacteristic
315C2×C4C22×Q8×C1112yes—
316C2×C4C2×C11×#4112yes—
317C8—44no—
318C22—22no—
319C22—22no—
320C22—28no—
321C22C11×#39114yes—
322C22C22×C11×C22⋊C411yescharacteristic
323C22C2×C11×C22⋊Q812yes—
324C22C2×C11×AGL(1,ℤ/8)12yes—
325C22C2×C11×#13712yes—
326C4—22no—
327C4—22no—
328C4—48no—
329C4—48no—
330C4C11×#39114yes—
331C4C11×#41814yes—
332C4C11×#41914yes—
333C4C2×C4×Q8×C1112yes—
334C4C2×C11×#12411yescharacteristic
335C4C2×C11×C4⋊Q811yescharacteristic
336C2—24no—
337C2C2×C11×#39111yescharacteristic
338C2C2×C11×#41811yescharacteristic
339C2C2×C11×#41911yescharacteristic
340C2C11×#307914yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1988C2semidirect
5. C11×#1987C2semidirect
12. C2×C11×C4⋊Q8C4semidirect
47. C11×#117Q8semidirect
70. #21313C11direct (N × H)
104. C11×C4⋊C4C2×Q8semidirect
118. #1988C2×C11semidirect
119. #1987C2×C11semidirect
159. C2×C4⋊Q8C4×C11semidirect
212. #117Q8×C11semidirect
273. C4⋊C4C2×Q8×C11semidirect
284. C11#21313direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#4232
C4×C11×#1172
C11×#19882
C11×#19872
C11×#17362
#2131311