Finite Group Databasebeta

← C11×#21962 #14599155

Subgroups — C11×#21962 #14599155

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊C8C211yesmaximal, characteristic
2C11×#2285C211yesmaximal, characteristic
3C11×#2283C211yesmaximal, characteristic
4C11×#1949C214yesmaximal, complemented
5C11×#1948C212yesmaximal, complemented
6C11×#1947C212yesmaximal, complemented
7C11×#1808C212yesmaximal
8C11×#1807C212yesmaximal
9C23×C8×C11C2212yes—
10C2×C11×#117—21no—
11C22×C42×C11C2211yescharacteristic
12C2×C11×#107C2214yes—
13C2×C11×#106C2214yes—
14C2×C11×C4⋊C8C418yescomplemented
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2212yes—
18C11×#384C2212yes—
19C11×#383—21no—
20C11×#382—21no—
21C11×#382C2212yes—
22C11×#381—21no—
23C11×#380—21no—
24C11×#380C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C11×#380C2212yes—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2212yes—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—21no—
31C11×#376—21no—
32C11×#340C2214yes—
33C11×#340C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—44no—
38C22×C8×C11C2×C418yes—
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C11×#117—44no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C4⋊C4C2314yes—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11C2×C414yes—
53C2×C42×C11D411yescharacteristic
54C2×C42×C11D411yescharacteristic
55C2×C42×C11Q814yes—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C11×#107—44no—
59C11×#106—44no—
60C11×C4⋊C8C2×C414yes—
61C11×C4⋊C8C2×C414yes—
62C11×C4⋊C8C2×C418yes—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—22no—
66C11×#95—22no—
67C11×#95—22no—
68C11×#95—22no—
69C11×#95—22no—
70#21962C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—24no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11C4⋊C414yes—
81C22×C4×C11C4⋊C414yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×Q812yes—
89C22×C4×C11C2411yescharacteristic
90C2×C8×C11—24no—
91C2×C8×C11—24no—
92C2×C8×C11—48no—
93C2×C8×C11C22×C414yes—
94C2×C8×C11C22×C414yes—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—44no—
102C11×C4⋊C4—44no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—44no—
105C11×C22⋊C4—42no—
106C42×C11—44no—
107C42×C11—44no—
108C42×C11C4⋊C414yes—
109C42×C11C4⋊C414yes—
110C42×C11C22×C412yes—
111C42×C11C22×C412yes—
112C42×C11C2×Q812yes—
113C42×C11C2×Q812yes—
114C22×C4⋊C8C2×C1111yescharacteristic
115#2285C2×C1111yescharacteristic
116#2283C2×C1111yescharacteristic
117#1949C2×C1114yescomplemented
118#1948C2×C1112yescomplemented
119#1947C2×C1112yescomplemented
120#1808C2×C1112yes—
121#1807C2×C1112yes—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11C2×C4⋊C412yes—
125C23×C11AGL(1,ℤ/8)12yes—
126C23×C11#13712yes—
127C23×C11C22×D411yescharacteristic
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—28no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—28no—
139C2×C4×C11—44no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11C2×C4⋊C412yes—
149C2×C4×C11C2×C4⋊C412yes—
150C2×C4×C11C2×C4⋊C412yes—
151C2×C4×C11C2×C4⋊C412yes—
152C2×C4×C11C2×C4⋊C412yes—
153C2×C4×C11#13514yes—
154C2×C4×C11C23×C411yescharacteristic
155C2×C4×C11C22×Q811yescharacteristic
156C2×C4×C11H(5,𝔽2)12yes—
157C2×C4×C112−1+412yes—
158C8×C11—24no—
159C8×C11—24no—
160C23×C8C22×C1112yes—
161C2×#117—21no—
162C22×C42C22×C1111yescharacteristic
163C2×#107C22×C1114yes—
164C2×#106C22×C1114yes—
165C2×C4⋊C8C4×C1118yescomplemented
166C2×C4⋊C8C22×C1111yescharacteristic
167C2×C4⋊C8C22×C1111yescharacteristic
168C2×C4⋊C8C22×C1112yes—
169#384C22×C1112yes—
170#383—21no—
171#382—21no—
172#382C22×C1112yes—
173#381—21no—
174#380—21no—
175#380C22×C1111yescharacteristic
176#380C22×C1112yes—
177#380C22×C1111yescharacteristic
178C4×C4⋊C4—21no—
179C4×C4⋊C4C22×C1112yes—
180C4×C4⋊C4C22×C1112yes—
181C4×C22⋊C4—21no—
182#376—21no—
183#340C22×C1114yes—
184#340C22×C1114yes—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—24no—
188C22×C11—24no—
189C22×C11#42814yes—
190C22×C11C22×C4⋊C411yescharacteristic
191C22×C11#53712yes—
192C22×C11C2×#13512yes—
193C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
194C22×C11C2×#13711yescharacteristic
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—82no—
200C4×C11—84no—
201C4×C11—82no—
202C4×C11#42714yes—
203C4×C11#51811yescharacteristic
204C4×C11#51911yescharacteristic
205C4×C11#54412yes—
206C23×C4D4×C1111yescharacteristic
207C23×C4D4×C1111yescharacteristic
208C23×C4C23×C1111yescharacteristic
209C22×C8—44no—
210C22×C8C2×C4×C1118yes—
211C22×C8C23×C1112yes—
212C22×C8C23×C1112yes—
213#117—44no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4C23×C1112yes—
217C2×C4⋊C4C23×C1112yes—
218C2×C4⋊C4C23×C1114yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42C2×C4×C1114yes—
225C2×C42D4×C1111yescharacteristic
226C2×C42D4×C1111yescharacteristic
227C2×C42Q8×C1114yes—
228C2×C42C23×C1111yescharacteristic
229C2×C42C23×C1111yescharacteristic
230#107—44no—
231#106—44no—
232C4⋊C8C2×C4×C1114yes—
233C4⋊C8C2×C4×C1114yes—
234C4⋊C8C2×C4×C1118yes—
235#95—21no—
236#95—21no—
237#95—22no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95—22no—
242C2×C11—24no—
243C2×C11#231611yescharacteristic
244C2×C11C2×#42711yescharacteristic
245C2×C11C2×#42811yescharacteristic
246C2×C11#324712yes—
247C2×C11#324812yes—
248C24C2×D4×C1111yescharacteristic
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4C11×C4⋊C414yes—
258C22×C4C11×C4⋊C414yes—
259C22×C4C22×C4×C1112yes—
260C22×C4C2×D4×C1111yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265C22×C4C2×Q8×C1112yes—
266C22×C4C24×C1111yescharacteristic
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—48no—
270C2×C8C22×C4×C1114yes—
271C2×C8C22×C4×C1114yes—
272C4⋊C4—22no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4—44no—
279C4⋊C4—44no—
280C22⋊C4—44no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—44no—
284C42—44no—
285C42C11×C4⋊C414yes—
286C42C11×C4⋊C414yes—
287C42C22×C4×C1112yes—
288C42C22×C4×C1112yes—
289C42C2×Q8×C1112yes—
290C42C2×Q8×C1112yes—
291C11#2196211yescharacteristic, direct product factor, Sylow
292C23—22no—
293C23—22no—
294C23C2×C11×C4⋊C412yes—
295C23C11×AGL(1,ℤ/8)12yes—
296C23C11×#13712yes—
297C23C22×D4×C1111yescharacteristic
298C2×C4—22no—
299C2×C4—28no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4C2×C11×C4⋊C412yes—
319C2×C4C2×C11×C4⋊C412yes—
320C2×C4C2×C11×C4⋊C412yes—
321C2×C4C2×C11×C4⋊C412yes—
322C2×C4C2×C11×C4⋊C412yes—
323C2×C4C11×#13514yes—
324C2×C4C23×C4×C1111yescharacteristic
325C2×C4C22×Q8×C1111yescharacteristic
326C2×C4C11×H(5,𝔽2)12yes—
327C2×C4C11×2−1+412yes—
328C8—24no—
329C8—24no—
330C22—22no—
331C22—24no—
332C22—24no—
333C22—22no—
334C22C11×#42814yes—
335C22C22×C11×C4⋊C411yescharacteristic
336C22C11×#53712yes—
337C22C2×C11×#13512yes—
338C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
339C22C2×C11×#13711yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—22no—
344C4—82no—
345C4—84no—
346C4—82no—
347C4C11×#42714yes—
348C4C11×#51811yescharacteristic
349C4C11×#51911yescharacteristic
350C4C11×#54412yes—
351C2—24no—
352C2C11×#231611yescharacteristic
353C2C2×C11×#42711yescharacteristic
354C2C2×C11×#42811yescharacteristic
355C2C11×#324712yes—
356C2C11×#324812yes—
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×#1949C2semidirect
5. C11×#1948C2semidirect
6. C11×#1947C2semidirect
14. C2×C11×C4⋊C8C4semidirect
70. #21962C11direct (N × H)
117. #1949C2×C11semidirect
118. #1948C2×C11semidirect
119. #1947C2×C11semidirect
165. C2×C4⋊C8C4×C11semidirect
291. C11#21962direct (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⋊C82
C11×#22852
C11×#22832
C11×#19492
C11×#19482
C11×#19472
C11×#18082
C11×#18072
#2196211