Finite Group Databasebeta

← C11×#10160 #14587353

Subgroups — C11×#10160 #14587353

Order 2816.

578 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
1C11×#3205C211yesmaximal, characteristic
2C11×#3141C211yesmaximal, characteristic, complemented
3C2×C11×#486C211yesmaximal, characteristic, complemented
4C11×#1965C211yesmaximal, characteristic, complemented
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C11×#493—21no—
12C11×#489—22no—
13C11×#487—21no—
14C11×#486—21no—
15C11×#486—22no—
16C11×#486—21no—
17C11×#486—22no—
18C11×#459—22no—
19C11×#447—22no—
20C11×#431C2211yescharacteristic
21C11×#423C2211yescharacteristic
22C11×#417—22no—
23C2×C11×#102—22no—
24C2×C11×#100—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#333—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D412yes—
34C2×C11×D8—24no—
35C2×C11×M16—21no—
36C2×C11×M16D412yes—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yes—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127D411yescharacteristic
48C11×#124—21no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×#103—24no—
60C11×#102—24no—
61C11×#102—28no—
62C11×#102—24no—
63C11×#100—44no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70#10160C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—22no—
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C2×D4×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—44no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—82no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C11×D8—84no—
98C11×M16—22no—
99C11×M16—22no—
100C11×M16—42no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11—41no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118#3205C2×C1111yescharacteristic
119#3141C2×C1111yescharacteristic, complemented
120C2×#486C2×C1111yescharacteristic, complemented
121#1965C2×C1111yescharacteristic, complemented
122#1548C2×C1111yescharacteristic, complemented
123#1492C2×C1111yescharacteristic, complemented
124#1278C2×C1111yescharacteristic, complemented
125C23×C11—41no—
126C23×C11—42no—
127C23×C11—44no—
128C23×C11—82no—
129C23×C11—82no—
130C23×C11#12111yescharacteristic
131Q8×C11—42no—
132Q8×C11—82no—
133Q8×C11—82no—
134D4×C11—44no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—44no—
138D4×C11—42no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×C4×C11#13512yes—
159C2×C4×C11AGL(1,ℤ/8)12yes—
160C8×C11—42no—
161C8×C11—42no—
162C8×C11—42no—
163C8×C11—81no—
164#532C22×C1111yescharacteristic
165C2×C4⋊Q8C22×C1111yescharacteristic
166C2×#127C22×C1111yescharacteristic
167#493—21no—
168#489—22no—
169#487—21no—
170#486—22no—
171#486—21no—
172#486—21no—
173#486—22no—
174#459—22no—
175#447—22no—
176#431C22×C1111yescharacteristic
177#423C22×C1111yescharacteristic
178#417—22no—
179C2×#102—22no—
180C2×#100—22no—
181C4×M16C22×C1111yescharacteristic
182C2×C4×C8C22×C1111yescharacteristic
183#333—22no—
184D4⋊C8—22no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—82no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—82no—
191C22×C11—81no—
192C22×C11—82no—
193C22×C11—164no—
194C22×C11#39211yescharacteristic
195C22×C11#46312yes—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—81no—
199C4×C11—82no—
200C4×C11#44912yes—
201C4×C11#45512yes—
202C4×C11#47212yes—
203C4×C11#49511yescharacteristic
204C4×C11#49611yescharacteristic
205C2×#41—21no—
206C22×Q8—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4D4×C1112yes—
210C2×D8—24no—
211C2×M16—21no—
212C2×M16D4×C1112yes—
213C22×C8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C1112yes—
218C4⋊Q8D4×C1111yescharacteristic
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#127D4×C1111yescharacteristic
224#124—21no—
225#121—21no—
226#121—21no—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42C23×C1111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8D4×C1112yes—
235#103—24no—
236#102—28no—
237#102—24no—
238#102—24no—
239#100—44no—
240C22⋊C8—21no—
241#97—21no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—21no—
245C4×C8D4×C1112yes—
246C2×C11—22no—
247C2×C11—161no—
248C2×C11—162no—
249C2×C11#200411yescharacteristic
250C2×C11#201211yescharacteristic
251C2×C11#201811yescharacteristic
252C24—22no—
253#41—42no—
254#41—42no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—82no—
259C2×D4—21no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—82no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C2×D4×C1111yescharacteristic
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C11×#4111yescharacteristic
278D8—84no—
279M16—22no—
280M16—22no—
281M16—42no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—41no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42C2×D4×C1111yescharacteristic
296C42C2×D4×C1111yescharacteristic
297C42C2×D4×C1111yescharacteristic
298C42C2×D4×C1111yescharacteristic
299C11#1016011yescharacteristic, direct product factor, Sylow
300C23—41no—
301C23—42no—
302C23—44no—
303C23—82no—
304C23—82no—
305C23C11×#12111yescharacteristic
306Q8—42no—
307Q8—82no—
308Q8—82no—
309D4—44no—
310D4—42no—
311D4—42no—
312D4—44no—
313D4—42no—
314D4—82no—
315D4—82no—
316D4—81no—
317D4—81no—
318D4—82no—
319D4—82no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C11×#12011yescharacteristic
328C2×C4C11×#12011yescharacteristic
329C2×C4C11×#12011yescharacteristic
330C2×C4C11×#12111yescharacteristic
331C2×C4C11×#12111yescharacteristic
332C2×C4C11×#12711yescharacteristic
333C2×C4C11×#13512yes—
334C2×C4C11×AGL(1,ℤ/8)12yes—
335C8—42no—
336C8—42no—
337C8—42no—
338C8—81no—
339C22—21no—
340C22—21no—
341C22—82no—
342C22—81no—
343C22—81no—
344C22—82no—
345C22—81no—
346C22—82no—
347C22—164no—
348C22C11×#39211yescharacteristic
349C22C11×#46312yes—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—82no—
354C4C11×#44912yes—
355C4C11×#45512yes—
356C4C11×#47212yes—
357C4C11×#49511yescharacteristic
358C4C11×#49611yescharacteristic
359C2—22no—
360C2—162no—
361C2—161no—
362C2C11×#200411yescharacteristic
363C2C11×#201211yescharacteristic
364C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3205C2
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×#3141C2semidirect
3. C2×C11×#486C2semidirect
4. C11×#1965C2semidirect
5. C11×#1548C2semidirect
6. C11×#1492C2semidirect
7. C11×#1278C2semidirect
70. #10160C11direct (N × H)
119. #3141C2×C11semidirect
120. C2×#486C2×C11semidirect
121. #1965C2×C11semidirect
122. #1548C2×C11semidirect
123. #1492C2×C11semidirect
124. #1278C2×C11semidirect
299. C11#10160direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#31412
C2×C11×#4862
C11×#19652
C11×#15482
C11×#14922
C11×#12782
#1016011