Finite Group Databasebeta

← C11×#21985 #14599178

Subgroups — C11×#21985 #14599178

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#431C211yesmaximal, characteristic
2C11×#2285C211yesmaximal, characteristic
3C11×#2283C211yesmaximal, characteristic
4C11×#1948C212yesmaximal, complemented
5C11×#1947C212yesmaximal, complemented
6C11×#1854C214yesmaximal
7C11×#1846C212yesmaximal, complemented
8C11×#1835C212yesmaximal, complemented
9C2×C11×#117C2212yes—
10C22×C42×C11C2211yescharacteristic
11C11×#431C418yescomplemented
12C2×C11×#107C2214yes—
13C2×C11×#106C2214yes—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C22⋊C8C2212yes—
17C2×C4×C8×C11C2212yes—
18C11×#384C2212yes—
19C11×#383—21no—
20C11×#382C2211yescharacteristic
21C11×#382C2211yescharacteristic
22C11×#382C2212yes—
23C11×#381—21no—
24C11×#380—21no—
25C11×#380—21no—
26C11×#380C2212yes—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4—21no—
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×C11C2312yes—
38C22×C8×C11C2312yes—
39C11×#117—42no—
40C11×#117—42no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C4⋊C4C2314yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C42×C11—22no—
49C2×C42×C11—22no—
50C2×C42×C11C2×C414yes—
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11Q814yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C11×#107—44no—
57C11×#106—44no—
58C11×C4⋊C8C2×C414yes—
59C11×C4⋊C8C2×C414yes—
60C11×C22⋊C8C2×C418yes—
61C4×C8×C11C2×C418yes—
62C11×#95—22no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95—22no—
68C11×#95—22no—
69C11×#95—22no—
70#21985C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—24no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—42no—
81C22×C4×C11C4⋊C414yes—
82C22×C4×C11C4⋊C414yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q812yes—
90C22×C4×C11C2411yescharacteristic
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C22×C414yes—
96C2×C8×C11C22×C414yes—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—44no—
104C11×C4⋊C4—44no—
105C11×C22⋊C4—44no—
106C11×C22⋊C4—44no—
107C42×C11—44no—
108C42×C11—44no—
109C42×C11C4⋊C414yes—
110C42×C11C4⋊C414yes—
111C42×C11C22×C412yes—
112C42×C11C22×C412yes—
113C42×C11C2×Q812yes—
114C42×C11C2×Q812yes—
115C2×#431C2×C1111yescharacteristic
116#2285C2×C1111yescharacteristic
117#2283C2×C1111yescharacteristic
118#1948C2×C1112yescomplemented
119#1947C2×C1112yescomplemented
120#1854C2×C1114yes—
121#1846C2×C1112yescomplemented
122#1835C2×C1112yescomplemented
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11C2×C4⋊C412yes—
128C23×C11C22×D411yescharacteristic
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—28no—
139C2×C4×C11—44no—
140C2×C4×C11—44no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11C2×C4⋊C412yes—
150C2×C4×C11C2×C4⋊C412yes—
151C2×C4×C11C2×C4⋊C412yes—
152C2×C4×C11C2×C4⋊C412yes—
153C2×C4×C11C2×C4⋊C412yes—
154C2×C4×C11#13514yes—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C22×Q811yescharacteristic
157C2×C4×C11H(5,𝔽2)11yescharacteristic
158C2×C4×C11H(5,𝔽2)11yescharacteristic
159C2×C4×C112−1+411yescharacteristic
160C2×C4×C112−1+411yescharacteristic
161C8×C11—24no—
162C8×C11—24no—
163C2×#117C22×C1112yes—
164C22×C42C22×C1111yescharacteristic
165#431C4×C1118yescomplemented
166C2×#107C22×C1114yes—
167C2×#106C22×C1114yes—
168C2×C4⋊C8C22×C1111yescharacteristic
169C2×C4⋊C8C22×C1111yescharacteristic
170C2×C22⋊C8C22×C1112yes—
171C2×C4×C8C22×C1112yes—
172#384C22×C1112yes—
173#383—21no—
174#382C22×C1111yescharacteristic
175#382C22×C1112yes—
176#382C22×C1111yescharacteristic
177#381—21no—
178#380—21no—
179#380—21no—
180#380C22×C1112yes—
181C4×C4⋊C4—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4C22×C1112yes—
184C4×C22⋊C4—21no—
185#376—21no—
186#340C22×C1114yes—
187#340C22×C1114yes—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11C22×C4⋊C411yescharacteristic
194C22×C11#53511yescharacteristic
195C22×C11#53611yescharacteristic
196C22×C11C2×#13512yes—
197C22×C11#57512yes—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—84no—
203C4×C11—82no—
204C4×C11—82no—
205C4×C11#42714yes—
206C4×C11#52011yescharacteristic
207C4×C11#52011yescharacteristic
208C4×C11#54411yescharacteristic
209C4×C11#54411yescharacteristic
210C23×C4D4×C1111yescharacteristic
211C23×C4D4×C1111yescharacteristic
212C23×C4C23×C1111yescharacteristic
213C22×C8C23×C1112yes—
214C22×C8C23×C1112yes—
215#117—42no—
216#117—42no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4C23×C1114yes—
220C2×C4⋊C4C23×C1112yes—
221C2×C4⋊C4C23×C1112yes—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42C2×C4×C1114yes—
227C2×C42D4×C1111yescharacteristic
228C2×C42D4×C1111yescharacteristic
229C2×C42Q8×C1114yes—
230C2×C42C23×C1111yescharacteristic
231C2×C42C23×C1111yescharacteristic
232#107—44no—
233#106—44no—
234C4⋊C8C2×C4×C1114yes—
235C4⋊C8C2×C4×C1114yes—
236C22⋊C8C2×C4×C1118yes—
237C4×C8C2×C4×C1118yes—
238#95—22no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—22no—
244#95—22no—
245#95—22no—
246C2×C11—42no—
247C2×C11#231711yescharacteristic
248C2×C11C2×#42711yescharacteristic
249C2×C11#291111yescharacteristic
250C2×C11#321212yes—
251C2×C11#323312yes—
252C24C2×D4×C1111yescharacteristic
253C22×C4—24no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—42no—
262C22×C4C11×C4⋊C414yes—
263C22×C4C11×C4⋊C414yes—
264C22×C4C22×C4×C1112yes—
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C2×D4×C1111yescharacteristic
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C2×Q8×C1112yes—
271C22×C4C24×C1111yescharacteristic
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8C22×C4×C1114yes—
277C2×C8C22×C4×C1114yes—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—44no—
285C4⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C42—44no—
289C42—44no—
290C42C11×C4⋊C414yes—
291C42C11×C4⋊C414yes—
292C42C22×C4×C1112yes—
293C42C22×C4×C1112yes—
294C42C2×Q8×C1112yes—
295C42C2×Q8×C1112yes—
296C11#2198511yescharacteristic, direct product factor, Sylow
297C23—21no—
298C23—21no—
299C23—22no—
300C23—22no—
301C23C2×C11×C4⋊C412yes—
302C23C22×D4×C1111yescharacteristic
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—28no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4C2×C11×C4⋊C412yes—
324C2×C4C2×C11×C4⋊C412yes—
325C2×C4C2×C11×C4⋊C412yes—
326C2×C4C2×C11×C4⋊C412yes—
327C2×C4C2×C11×C4⋊C412yes—
328C2×C4C11×#13514yes—
329C2×C4C23×C4×C1111yescharacteristic
330C2×C4C22×Q8×C1111yescharacteristic
331C2×C4C11×H(5,𝔽2)11yescharacteristic
332C2×C4C11×H(5,𝔽2)11yescharacteristic
333C2×C4C11×2−1+411yescharacteristic
334C2×C4C11×2−1+411yescharacteristic
335C8—24no—
336C8—24no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22C22×C11×C4⋊C411yescharacteristic
343C22C11×#53511yescharacteristic
344C22C11×#53611yescharacteristic
345C22C2×C11×#13512yes—
346C22C11×#57512yes—
347C4—22no—
348C4—22no—
349C4—22no—
350C4—22no—
351C4—84no—
352C4—82no—
353C4—82no—
354C4C11×#42714yes—
355C4C11×#52011yescharacteristic
356C4C11×#52011yescharacteristic
357C4C11×#54411yescharacteristic
358C4C11×#54411yescharacteristic
359C2—42no—
360C2C11×#231711yescharacteristic
361C2C2×C11×#42711yescharacteristic
362C2C11×#291111yescharacteristic
363C2C11×#321212yes—
364C2C11×#323312yes—
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×#1948C2semidirect
5. C11×#1947C2semidirect
7. C11×#1846C2semidirect
8. C11×#1835C2semidirect
11. C11×#431C4semidirect
70. #21985C11direct (N × H)
118. #1948C2×C11semidirect
119. #1947C2×C11semidirect
121. #1846C2×C11semidirect
122. #1835C2×C11semidirect
165. #431C4×C11semidirect
296. C11#21985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4312
C11×#22852
C11×#22832
C11×#19482
C11×#19472
C11×#18542
C11×#18462
C11×#18352
#2198511