Finite Group Databasebeta

← C11×#10146 #14587339

Subgroups — C11×#10146 #14587339

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic, complemented
2C11×#3151C211yesmaximal, characteristic
3C2×C11×#492C211yesmaximal, characteristic, complemented
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—22no—
9C22×C11×SD16—22no—
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C11×#496—22no—
14C11×#493—21no—
15C11×#492—21no—
16C11×#492—21no—
17C11×#492—22no—
18C11×#492—22no—
19C11×#487—21no—
20C11×#461—22no—
21C11×#448—22no—
22C11×#431C2211yescharacteristic
23C11×#423C2211yescharacteristic
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#331—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11D412yes—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C11×AGL(1,ℤ/8)—44no—
35C11×AGL(1,ℤ/8)—44no—
36C2×C11×SD16—28no—
37C2×C11×SD16—24no—
38C2×C11×SD16—24no—
39C2×C11×SD16—48no—
40C2×C11×D8—24no—
41C2×C11×M16—21no—
42C2×C11×M16D412yes—
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8D411yescharacteristic
49C11×#127—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127D411yescharacteristic
53C11×#127D412yes—
54C11×#124—21no—
55C11×#121—21no—
56C11×#121—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72#10146C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—41no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—44no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—22no—
86C2×D4×C11—44no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—82no—
94C22×C4×C11—22no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C11×SD16—416no—
100C11×SD16—48no—
101C11×SD16—84no—
102C11×D8—48no—
103C11×M16—22no—
104C11×M16—42no—
105C11×M16SD1614yescomplemented
106C2×C8×C11—24no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123#3206C2×C1111yescharacteristic, complemented
124#3151C2×C1111yescharacteristic
125C2×#492C2×C1111yescharacteristic, complemented
126#1997C2×C1111yescharacteristic, complemented
127#1545C2×C1111yescharacteristic, complemented
128#1492C2×C1111yescharacteristic, complemented
129#1278C2×C1111yescharacteristic, complemented
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11#12111yescharacteristic
136Q8×C11—44no—
137Q8×C11—42no—
138Q8×C11—44no—
139D4×C11—44no—
140D4×C11—42no—
141D4×C11—44no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—81no—
149D4×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×C4×C11C2×SD1612yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C8×C11—24no—
166C8×C11—24no—
167C8×C11—42no—
168C8×C11—81no—
169C2×AGL(1,ℤ/8)—22no—
170C22×SD16—22no—
171#532C22×C1111yescharacteristic
172C2×C4⋊Q8C22×C1111yescharacteristic
173C2×#127C22×C1111yescharacteristic
174#496—22no—
175#493—21no—
176#492—21no—
177#492—22no—
178#492—21no—
179#492—22no—
180#487—21no—
181#461—22no—
182#448—22no—
183#431C22×C1111yescharacteristic
184#423C22×C1111yescharacteristic
185C4×M16C22×C1111yescharacteristic
186C2×C4×C8C22×C1111yescharacteristic
187#343—22no—
188#331—22no—
189D4⋊C8—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—81no—
197C22×C11—82no—
198C22×C11—164no—
199C22×C11#39211yescharacteristic
200C22×C11#46012yes—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11—81no—
205C4×C11#45012yes—
206C4×C11#45312yes—
207C4×C11#47112yes—
208C4×C11#49211yescharacteristic
209C4×C11#49611yescharacteristic
210C2×#41—21no—
211C22×Q8D4×C1112yes—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215AGL(1,ℤ/8)—44no—
216AGL(1,ℤ/8)—44no—
217C2×SD16—28no—
218C2×SD16—24no—
219C2×SD16—24no—
220C2×SD16—48no—
221C2×D8—24no—
222C2×M16—21no—
223C2×M16D4×C1112yes—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C1111yescharacteristic
230#127—21no—
231#127—21no—
232#127—21no—
233#127D4×C1112yes—
234#127D4×C1111yescharacteristic
235#124—21no—
236#121—21no—
237#121—21no—
238C4×D4—21no—
239C4×D4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C42C23×C1111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C1112yes—
246#103—24no—
247C22⋊C8—21no—
248#97—21no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8D4×C1112yes—
253C2×C11—22no—
254C2×C11—161no—
255C2×C11—162no—
256C2×C11#200211yescharacteristic
257C2×C11#201411yescharacteristic
258C2×C11#201911yescharacteristic
259C24—41no—
260#41—42no—
261#41—42no—
262C2×Q8—22no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—44no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—44no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—82no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C11×#4111yescharacteristic
285SD16—416no—
286SD16—48no—
287SD16—84no—
288D8—48no—
289M16—22no—
290M16—42no—
291M16C11×SD1614yescomplemented
292C2×C8—24no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42C2×D4×C1111yescharacteristic
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C42C2×D4×C1111yescharacteristic
309C11#1014611yescharacteristic, direct product factor, Sylow
310C23—41no—
311C23—42no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23C11×#12111yescharacteristic
316Q8—44no—
317Q8—42no—
318Q8—44no—
319D4—44no—
320D4—42no—
321D4—44no—
322D4—42no—
323D4—42no—
324D4—82no—
325D4—82no—
326D4—81no—
327D4—81no—
328D4—82no—
329D4—82no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#12011yescharacteristic
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#12711yescharacteristic
343C2×C4C2×C11×SD1612yes—
344C2×C4C11×AGL(1,ℤ/8)12yes—
345C8—24no—
346C8—24no—
347C8—42no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22—81no—
356C22—82no—
357C22—164no—
358C22C11×#39211yescharacteristic
359C22C11×#46012yes—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4C11×#45012yes—
365C4C11×#45312yes—
366C4C11×#47112yes—
367C4C11×#49211yescharacteristic
368C4C11×#49611yescharacteristic
369C2—22no—
370C2—162no—
371C2—161no—
372C2C11×#200211yescharacteristic
373C2C11×#201411yescharacteristic
374C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3206C2semidirect
3. C2×C11×#492C2semidirect
4. C11×#1997C2semidirect
5. C11×#1545C2semidirect
6. C11×#1492C2semidirect
7. C11×#1278C2semidirect
72. #10146C11direct (N × H)
105. C11×M16SD16semidirect
123. #3206C2×C11semidirect
125. C2×#492C2×C11semidirect
126. #1997C2×C11semidirect
127. #1545C2×C11semidirect
128. #1492C2×C11semidirect
129. #1278C2×C11semidirect
291. M16C11×SD16semidirect
309. C11#10146direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C11×#31512
C2×C11×#4922
C11×#19972
C11×#15452
C11×#14922
C11×#12782
#1014611