Finite Group Databasebeta

← C11×#10466 #14587659

Subgroups — C11×#10466 #14587659

Order 2816.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3037C211yesmaximal, characteristic
2C11×#1805C211yesmaximal, characteristic, complemented
3C11×#1571C211yesmaximal, characteristic, complemented
4C11×#1540C211yesmaximal, characteristic
5C11×#1517C211yesmaximal, characteristic
6C11×#1461C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#464—22no—
12C11×#462—21no—
13C11×#460—21no—
14C11×#431C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C11×#417—21no—
19C2×C11×#103—21no—
20C11×#382C2211yescharacteristic
21C11×#340—21no—
22C11×#335—22no—
23C11×#332—21no—
24C11×#331—21no—
25C11×#327—22no—
26C11×#324—22no—
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C11×#137—42no—
30C11×#137—42no—
31C2×C11×Q16—22no—
32C2×C11×SD16—22no—
33C2×C11×M16—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57C11×#103—22no—
58C11×#103—42no—
59C11×#102—22no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8D412yes—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64C11×#95—21no—
65C11×#95—21no—
66#10466C1111yesmaximal, characteristic, direct product factor, Sylow
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11D812yes—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C11×Q16—44no—
90C11×SD16—44no—
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11#4111yescharacteristic
115#3037C2×C1111yescharacteristic
116#1805C2×C1111yescharacteristic, complemented
117#1571C2×C1111yescharacteristic, complemented
118#1540C2×C1111yescharacteristic
119#1517C2×C1111yescharacteristic
120#1461C2×C1111yescharacteristic, complemented
121#1286C2×C1111yescharacteristic, complemented
122C23×C11—41no—
123C23×C11#12111yescharacteristic
124Q8×C11—22no—
125Q8×C11—22no—
126Q8×C11—41no—
127Q8×C11—41no—
128Q8×C11—41no—
129Q8×C11—41no—
130D4×C11—41no—
131D4×C11—41no—
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11#12411yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C8×C11—42no—
160C8×C11—42no—
161C8×C11—81no—
162C8×C11—81no—
163C2×#137—21no—
164#532C22×C1111yescharacteristic
165C2×C4×Q8C22×C1111yescharacteristic
166#464—22no—
167#462—21no—
168#460—21no—
169#431C22×C1111yescharacteristic
170#431C22×C1111yescharacteristic
171#423C22×C1111yescharacteristic
172C2×C4⋊C8C22×C1111yescharacteristic
173#417—21no—
174C2×#103—21no—
175#382C22×C1111yescharacteristic
176#340—21no—
177#335—22no—
178#332—21no—
179#331—21no—
180#327—22no—
181#324—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#39411yescharacteristic
188C22×C11#46611yescharacteristic
189C22×C11#46811yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—161no—
198C4×C11#44711yescharacteristic
199C4×C11#45211yescharacteristic
200C4×C11#48011yescharacteristic
201C4×C11#48211yescharacteristic
202C2×#41—21no—
203C22×Q8D4×C1111yescharacteristic
204#137—42no—
205#137—42no—
206C2×Q16—22no—
207C2×SD16—22no—
208C2×M16—21no—
209C22×C8—21no—
210C4⋊Q8D4×C1111yescharacteristic
211#127D4×C1111yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×D4—21no—
220C4×D4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C1111yescharacteristic
224C2×C42—21no—
225C2×C42C23×C1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8D4×C1112yes—
232#103—22no—
233#103—42no—
234#102—22no—
235C22⋊C8—21no—
236C22⋊C8D4×C1112yes—
237C4×C8—21no—
238C4×C8—21no—
239#95—21no—
240#95—21no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—161no—
244C2×C11#203311yescharacteristic
245C2×C11#204911yescharacteristic
246C2×C11#205311yescharacteristic
247#41—41no—
248#41—41no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8C11×D812yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C2×D4×C1111yescharacteristic
268C22×C4C11×#4111yescharacteristic
269Q16—44no—
270SD16—44no—
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C42—41no—
290C42—41no—
291C42C2×D4×C1111yescharacteristic
292C42C2×D4×C1111yescharacteristic
293C42C11×#4111yescharacteristic
294C42C11×#4111yescharacteristic
295C11#1046611yescharacteristic, direct product factor, Sylow
296C23—41no—
297C23C11×#12111yescharacteristic
298Q8—22no—
299Q8—22no—
300Q8—41no—
301Q8—41no—
302Q8—41no—
303Q8—41no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C11×#12011yescharacteristic
324C2×C4C11×#12111yescharacteristic
325C2×C4C11×#12111yescharacteristic
326C2×C4C11×#12311yescharacteristic
327C2×C4C11×#12311yescharacteristic
328C2×C4C11×#12411yescharacteristic
329C2×C4C2×C11×D811yescharacteristic
330C2×C4C11×#13511yescharacteristic
331C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C11×#13711yescharacteristic
333C8—42no—
334C8—42no—
335C8—81no—
336C8—81no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C11×#39411yescharacteristic
343C22C11×#46611yescharacteristic
344C22C11×#46811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—161no—
353C4C11×#44711yescharacteristic
354C4C11×#45211yescharacteristic
355C4C11×#48011yescharacteristic
356C4C11×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C11×#203311yescharacteristic
361C2C11×#204911yescharacteristic
362C2C11×#205311yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
2. C11×#1805C2semidirect
3. C11×#1571C2semidirect
6. C11×#1461C2semidirect
7. C11×#1286C2semidirect
66. #10466C11direct (N × H)
116. #1805C2×C11semidirect
117. #1571C2×C11semidirect
120. #1461C2×C11semidirect
121. #1286C2×C11semidirect
295. C11#10466direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30372
C11×#18052
C11×#15712
C11×#15402
C11×#15172
C11×#14612
C11×#12862
#1046611