Finite Group Databasebeta

← C11×#21909 #14599102

Subgroups — C11×#21909 #14599102

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2297C211yesmaximal, characteristic
2C11×#1924C214yesmaximal, complemented
3C11×#1923C214yesmaximal, complemented
4C11×#1797C212yesmaximal, complemented
5C11×#1780C212yesmaximal
6C11×#1750C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C2×C11×C4⋊C8C2212yes—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C22⋊C8C2214yes—
13C2×C11×C22⋊C8C2212yes—
14C2×C11×C22⋊C8C2214yes—
15C2×C11×C22⋊C8C2212yes—
16C2×C11×#97C2212yes—
17C2×C4×C8×C11C2212yes—
18C11×#391C411yescharacteristic
19C11×#391C411yescharacteristic
20C11×#390C411yescharacteristic
21C11×#390C411yescharacteristic
22C11×#386C414yes—
23C4×C11×C22⋊C4C2214yes—
24C11×#336C2214yes—
25C11×#336C2214yes—
26C2×C11×#41—24no—
27C2×C11×#41—42no—
28C2×C11×#41—41no—
29C2×C11×#41—41no—
30C22×Q8×C11C2×C411yescharacteristic
31C22×D4×C11C2×C412yes—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C22×C8×C11C2314yes—
37C22×C8×C11C2314yes—
38C11×#117—41no—
39C11×#117—41no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4C2×C414yes—
43C2×C11×C22⋊C4C2×C412yes—
44C2×C11×C22⋊C4C2×C414yes—
45C2×C42×C11—42no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2312yes—
49C2×C42×C11C2312yes—
50C11×C4⋊C8—42no—
51C11×C4⋊C8—42no—
52C11×C22⋊C8—28no—
53C11×C22⋊C8—42no—
54C11×C22⋊C8—42no—
55C11×C22⋊C8—44no—
56C11×#97—42no—
57C4×C8×C11—42no—
58C11×#95C2×C414yes—
59C11×#95C2×C414yes—
60#21909C1111yesmaximal, characteristic, direct product factor, Sylow
61C24×C11C22×C412yes—
62C24×C11C22×C411yescharacteristic
63C11×#41—48no—
64C11×#41—48no—
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×D4×C11—24no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C412yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C412yes—
90C22×C4×C11#4114yes—
91C22×C4×C11C2411yescharacteristic
92C2×C8×C11—24no—
93C2×C8×C11—24no—
94C2×C8×C11—24no—
95C2×C8×C11—24no—
96C2×C8×C11—24no—
97C2×C8×C11—24no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—28no—
101C11×C22⋊C4—44no—
102C11×C22⋊C4—42no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—41no—
108C42×C11—41no—
109#2297C2×C1111yescharacteristic
110#1924C2×C1114yescomplemented
111#1923C2×C1114yescomplemented
112#1797C2×C1112yescomplemented
113#1780C2×C1112yes—
114#1750C2×C1112yescomplemented
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—24no—
123C23×C11—24no—
124C23×C11#11712yes—
125C23×C11C23×C411yescharacteristic
126Q8×C11—44no—
127D4×C11—44no—
128D4×C11—48no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—48no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11#11712yes—
149C2×C4×C11#13114yes—
150C2×C4×C11C2×#4112yes—
151C2×C4×C11H(5,𝔽2)12yes—
152C2×C4×C11H(5,𝔽2)11yescharacteristic
153C2×C4×C11H(5,𝔽2)11yescharacteristic
154C8×C11—44no—
155C8×C11—44no—
156C22×#41C22×C1111yescharacteristic
157C2×#117C22×C1111yescharacteristic
158C22×C42C22×C1111yescharacteristic
159C2×C4⋊C8C22×C1112yes—
160C2×C4⋊C8C22×C1112yes—
161C2×C22⋊C8C22×C1114yes—
162C2×C22⋊C8C22×C1112yes—
163C2×C22⋊C8C22×C1114yes—
164C2×C22⋊C8C22×C1112yes—
165C2×#97C22×C1112yes—
166C2×C4×C8C22×C1112yes—
167#391C4×C1111yescharacteristic
168#391C4×C1111yescharacteristic
169#390C4×C1111yescharacteristic
170#390C4×C1111yescharacteristic
171#386C4×C1114yes—
172C4×C22⋊C4C22×C1114yes—
173#336C22×C1114yes—
174#336C22×C1114yes—
175C22×C11—22no—
176C22×C11—24no—
177C22×C11—42no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—42no—
181C22×C11—44no—
182C22×C11—44no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11C2×#11711yescharacteristic
186C22×C11#51811yescharacteristic
187C22×C11#51811yescharacteristic
188C22×C11C2×#13112yes—
189C22×C11#56812yes—
190C4×C11—22no—
191C4×C11—24no—
192C4×C11—42no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11—42no—
196C4×C11#53812yes—
197C4×C11#53812yes—
198C2×#41—24no—
199C2×#41—42no—
200C2×#41—41no—
201C2×#41—41no—
202C22×Q8C2×C4×C1111yescharacteristic
203C22×D4C2×C4×C1112yes—
204C22×D4C2×C4×C1111yescharacteristic
205C23×C4C2×C4×C1112yes—
206C23×C4C23×C1112yes—
207C23×C4C23×C1111yescharacteristic
208C22×C8C23×C1114yes—
209C22×C8C23×C1114yes—
210#117—41no—
211#117—41no—
212C2×C4⋊C4C2×C4×C1111yescharacteristic
213C2×C4⋊C4C2×C4×C1111yescharacteristic
214C2×C22⋊C4C2×C4×C1114yes—
215C2×C22⋊C4C2×C4×C1112yes—
216C2×C22⋊C4C2×C4×C1114yes—
217C2×C42—42no—
218C2×C42C2×C4×C1111yescharacteristic
219C2×C42C2×C4×C1111yescharacteristic
220C2×C42C23×C1112yes—
221C2×C42C23×C1112yes—
222C4⋊C8—42no—
223C4⋊C8—42no—
224C22⋊C8—28no—
225C22⋊C8—42no—
226C22⋊C8—42no—
227C22⋊C8—44no—
228#97—42no—
229C4×C8—42no—
230#95C2×C4×C1114yes—
231#95C2×C4×C1114yes—
232C2×C11—42no—
233C2×C11—82no—
234C2×C11#231211yescharacteristic
235C2×C11#292512yes—
236C2×C11#297612yes—
237C2×C11#297911yescharacteristic
238C2×C11#298011yescharacteristic
239C24C22×C4×C1112yes—
240C24C22×C4×C1111yescharacteristic
241#41—48no—
242#41—48no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—24no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4C22×C4×C1112yes—
263C22×C4C22×C4×C1112yes—
264C22×C4C22×C4×C1112yes—
265C22×C4C22×C4×C1112yes—
266C22×C4C22×C4×C1111yescharacteristic
267C22×C4C22×C4×C1112yes—
268C22×C4C11×#4114yes—
269C22×C4C24×C1111yescharacteristic
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—24no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C22⋊C4—28no—
279C22⋊C4—42no—
280C22⋊C4—44no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—41no—
286C42—41no—
287C11#2190911yescharacteristic, direct product factor, Sylow
288C23—21no—
289C23—21no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—24no—
296C23—24no—
297C23C11×#11712yes—
298C23C23×C4×C1111yescharacteristic
299Q8—44no—
300D4—44no—
301D4—48no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—48no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4C11×#11712yes—
322C2×C4C11×#13114yes—
323C2×C4C2×C11×#4112yes—
324C2×C4C11×H(5,𝔽2)12yes—
325C2×C4C11×H(5,𝔽2)11yescharacteristic
326C2×C4C11×H(5,𝔽2)11yescharacteristic
327C8—44no—
328C8—44no—
329C22—24no—
330C22—22no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—44no—
335C22—44no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22C2×C11×#11711yescharacteristic
340C22C11×#51811yescharacteristic
341C22C11×#51811yescharacteristic
342C22C2×C11×#13112yes—
343C22C11×#56812yes—
344C4—24no—
345C4—22no—
346C4—42no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4C11×#53812yes—
351C4C11×#53812yes—
352C2—42no—
353C2—82no—
354C2C11×#231211yescharacteristic
355C2C11×#292512yes—
356C2C11×#297612yes—
357C2C11×#297911yescharacteristic
358C2C11×#298011yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×C11×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1924C2semidirect
3. C11×#1923C2semidirect
4. C11×#1797C2semidirect
6. C11×#1750C2semidirect
60. #21909C11direct (N × H)
110. #1924C2×C11semidirect
111. #1923C2×C11semidirect
112. #1797C2×C11semidirect
114. #1750C2×C11semidirect
287. C11#21909direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22972
C11×#19242
C11×#19232
C11×#17972
C11×#17802
C11×#17502
#2190911