Finite Group Databasebeta

← C11×#10438 #14587631

Subgroups — C11×#10438 #14587631

Order 2816.

462 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2582C211yesmaximal, characteristic
2C11×#1834C211yesmaximal, characteristic
3C11×#1803C211yesmaximal, characteristic
4C11×#1803C211yesmaximal, characteristic
5C2×C11×Q8⋊C8C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C2×C11×#103—21no—
14C2×C4×C8×C11C2211yescharacteristic
15C11×#398—22no—
16C11×#391—21no—
17C11×#391—21no—
18C11×#389—21no—
19C11×#389—21no—
20C11×#384C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—22no—
25C11×Q8⋊C8—22no—
26C11×Q8⋊C8—22no—
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D412yes—
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×#103—42no—
59C11×#103—42no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62C11×#95—22no—
63C11×#95—22no—
64C11×#95—22no—
65#10438C1111yesmaximal, characteristic, direct product factor, Sylow
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11SD1612yes—
77C2×Q8×C11Q1612yes—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—82no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11#4111yescharacteristic
123#2582C2×C1111yescharacteristic
124#1834C2×C1111yescharacteristic
125#1803C2×C1111yescharacteristic
126#1803C2×C1111yescharacteristic
127C2×Q8⋊C8C2×C1111yescharacteristic
128C2×Q8⋊C8C2×C1111yescharacteristic
129#1296C2×C1111yescharacteristic
130C23×C11#12011yescharacteristic
131Q8×C11—22no—
132Q8×C11—22no—
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—41no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C2×C4×C11#12311yescharacteristic
164C2×C4×C11#12411yescharacteristic
165C2×C4×C11C2×SD1611yescharacteristic
166C2×C4×C11C2×Q1611yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C11#13711yescharacteristic
171C2×C4×C11#13711yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C8×C11—42no—
174C8×C11—81no—
175C8×C11—81no—
176C2×C4×Q8C22×C1111yescharacteristic
177C2×C4×Q8C22×C1111yescharacteristic
178C2×C4⋊C8C22×C1111yescharacteristic
179C2×C4⋊C8C22×C1111yescharacteristic
180C2×#103—21no—
181C2×#103—21no—
182C2×C4×C8C22×C1111yescharacteristic
183#398—22no—
184#391—21no—
185#391—21no—
186#389—21no—
187#389—21no—
188#384C22×C1111yescharacteristic
189#384C22×C1111yescharacteristic
190#340—21no—
191#340—21no—
192#340—22no—
193Q8⋊C8—22no—
194Q8⋊C8—22no—
195C22×C11#39411yescharacteristic
196C22×C11#44811yescharacteristic
197C22×C11#44911yescharacteristic
198C22×C11#45111yescharacteristic
199C22×C11#45211yescharacteristic
200C22×C11#45411yescharacteristic
201C22×C11#45511yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—42no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—161no—
210C4×C11#46511yescharacteristic
211C4×C11#46711yescharacteristic
212C4×C11#46811yescharacteristic
213C4×C11#47011yescharacteristic
214C4×C11#48311yescharacteristic
215C4×C11#48411yescharacteristic
216C4×C11#48511yescharacteristic
217C4×C11#48511yescharacteristic
218C22×Q8D4×C1111yescharacteristic
219C22×Q8D4×C1111yescharacteristic
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4D4×C1111yescharacteristic
240C2×C4⋊C4D4×C1111yescharacteristic
241C2×C4⋊C4D4×C1112yes—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42C23×C1111yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249#103—42no—
250#103—42no—
251C4×C8—21no—
252C4×C8D4×C1112yes—
253#95—22no—
254#95—22no—
255#95—22no—
256C2×C11#162611yescharacteristic
257C2×C11#163611yescharacteristic
258C2×C11#164011yescharacteristic
259C2×C11#164511yescharacteristic
260C2×C11#203511yescharacteristic
261C2×C11#203611yescharacteristic
262C2×C11#204011yescharacteristic
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8C11×SD1612yes—
274C2×Q8C11×Q1612yes—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4C2×D4×C1111yescharacteristic
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1111yescharacteristic
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—82no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42C2×D4×C1111yescharacteristic
317C42C11×#4111yescharacteristic
318C42C11×#4111yescharacteristic
319C42C11×#4111yescharacteristic
320C11#1043811yescharacteristic, direct product factor, Sylow
321C23C11×#12011yescharacteristic
322Q8—22no—
323Q8—22no—
324Q8—22no—
325Q8—22no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4C11×#12111yescharacteristic
351C2×C4C11×#12111yescharacteristic
352C2×C4C11×#12111yescharacteristic
353C2×C4C11×#12311yescharacteristic
354C2×C4C11×#12311yescharacteristic
355C2×C4C11×#12411yescharacteristic
356C2×C4C2×C11×SD1611yescharacteristic
357C2×C4C2×C11×Q1611yescharacteristic
358C2×C4C11×#13511yescharacteristic
359C2×C4C11×#13511yescharacteristic
360C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
361C2×C4C11×#13711yescharacteristic
362C2×C4C11×#13711yescharacteristic
363C2×C4C11×#13711yescharacteristic
364C8—42no—
365C8—81no—
366C8—81no—
367C22C11×#39411yescharacteristic
368C22C11×#44811yescharacteristic
369C22C11×#44911yescharacteristic
370C22C11×#45111yescharacteristic
371C22C11×#45211yescharacteristic
372C22C11×#45411yescharacteristic
373C22C11×#45511yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—81no—
380C4—81no—
381C4—161no—
382C4C11×#46511yescharacteristic
383C4C11×#46711yescharacteristic
384C4C11×#46811yescharacteristic
385C4C11×#47011yescharacteristic
386C4C11×#48311yescharacteristic
387C4C11×#48411yescharacteristic
388C4C11×#48511yescharacteristic
389C4C11×#48511yescharacteristic
390C2C11×#162611yescharacteristic
391C2C11×#163611yescharacteristic
392C2C11×#164011yescharacteristic
393C2C11×#164511yescharacteristic
394C2C11×#203511yescharacteristic
395C2C11×#203611yescharacteristic
396C2C11×#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
65. #10438C11direct (N × H)
320. C11#10438direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25822
C11×#18342
C11×#18032
C2×C11×Q8⋊C82
C11×#12962
#1043811