Finite Group Databasebeta

← C11×#10582 #14587775

Subgroups — C11×#10582 #14587775

Order 2816.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2552C211yesmaximal, characteristic
2C11×#1948C211yesmaximal, characteristic
3C11×#1948C211yesmaximal, characteristic
4C11×#1834C211yesmaximal, characteristic
5C11×#1296C211yesmaximal, characteristic
6C11×#1279C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×#125—21no—
9C2×C11×#106—21no—
10C2×C11×#106—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C11×#398—22no—
15C11×#389—21no—
16C11×#389—21no—
17C11×#384—21no—
18C11×#384C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—22no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C11×#125—42no—
29C11×#125—42no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D412yes—
43C2×C42×C11—21no—
44C2×C42×C11—21no—
45C2×C42×C11C2311yescharacteristic
46C11×#106—42no—
47C11×#106—42no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8Q812yes—
51C11×C4⋊C8Q812yes—
52C4×C8×C11—21no—
53C4×C8×C11Q812yes—
54C11×#95—22no—
55C11×#95—21no—
56C11×#95—21no—
57#10582C1111yesmaximal, characteristic, direct product factor, Sylow
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—44no—
83C11×C4⋊C4—44no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—82no—
95C11×C4⋊C4SD1612yes—
96C11×C4⋊C4SD1612yes—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11—41no—
101C42×C11C2×Q811yescharacteristic
102C42×C11C2×Q811yescharacteristic
103C42×C11C2×Q811yescharacteristic
104C42×C11#4111yescharacteristic
105#2552C2×C1111yescharacteristic
106#1948C2×C1111yescharacteristic
107#1948C2×C1111yescharacteristic
108#1834C2×C1111yescharacteristic
109#1296C2×C1111yescharacteristic
110#1279C2×C1111yescharacteristic
111#1279C2×C1111yescharacteristic
112C23×C11#12011yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11C22⋊Q811yescharacteristic
136C2×C4×C11C4⋊Q811yescharacteristic
137C2×C4×C11C4⋊Q811yescharacteristic
138C2×C4×C11C4⋊Q811yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C8×C11—42no—
148C8×C11—42no—
149C8×C11—42no—
150C2×#125—21no—
151C2×#106—21no—
152C2×#106—21no—
153C2×C4⋊C8C22×C1111yescharacteristic
154C2×C4⋊C8C22×C1111yescharacteristic
155C2×C4×C8C22×C1111yescharacteristic
156#398—22no—
157#389—21no—
158#389—21no—
159#384—21no—
160#384C22×C1111yescharacteristic
161#384C22×C1111yescharacteristic
162C4×C4⋊C4C22×C1111yescharacteristic
163C4×C4⋊C4C22×C1111yescharacteristic
164#340—22no—
165#340—21no—
166#340—21no—
167C22×C11#39511yescharacteristic
168C22×C11#44811yescharacteristic
169C22×C11#44911yescharacteristic
170C22×C11#45011yescharacteristic
171C22×C11#45211yescharacteristic
172C22×C11#45411yescharacteristic
173C22×C11#45511yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—82no—
181C4×C11—161no—
182C4×C11#47511yescharacteristic
183C4×C11#47611yescharacteristic
184C4×C11#47811yescharacteristic
185C4×C11#47911yescharacteristic
186C4×C11#49811yescharacteristic
187C4×C11#49911yescharacteristic
188C4×C11#50111yescharacteristic
189C4×C11#50111yescharacteristic
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193#125—42no—
194#125—42no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4D4×C1111yescharacteristic
204C2×C4⋊C4D4×C1111yescharacteristic
205C2×C4⋊C4D4×C1111yescharacteristic
206C2×C4⋊C4D4×C1111yescharacteristic
207C2×C4⋊C4D4×C1112yes—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C23×C1111yescharacteristic
211#106—42no—
212#106—42no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8Q8×C1112yes—
216C4⋊C8Q8×C1112yes—
217C4×C8—21no—
218C4×C8Q8×C1112yes—
219#95—22no—
220#95—21no—
221#95—21no—
222C2×C11#162611yescharacteristic
223C2×C11#163511yescharacteristic
224C2×C11#164211yescharacteristic
225C2×C11#164311yescharacteristic
226C2×C11#205811yescharacteristic
227C2×C11#205911yescharacteristic
228C2×C11#206111yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4C2×D4×C1111yescharacteristic
236C22×C4C2×D4×C1111yescharacteristic
237C22×C4C2×D4×C1111yescharacteristic
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—44no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—82no—
266C4⋊C4C11×SD1612yes—
267C4⋊C4C11×SD1612yes—
268C42—41no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42C2×Q8×C1111yescharacteristic
273C42C2×Q8×C1111yescharacteristic
274C42C2×Q8×C1111yescharacteristic
275C42C11×#4111yescharacteristic
276C11#1058211yescharacteristic, direct product factor, Sylow
277C23C11×#12011yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4C11×C22⋊Q811yescharacteristic
299C2×C4C11×C22⋊Q811yescharacteristic
300C2×C4C11×C22⋊Q811yescharacteristic
301C2×C4C11×C4⋊Q811yescharacteristic
302C2×C4C11×C4⋊Q811yescharacteristic
303C2×C4C11×C4⋊Q811yescharacteristic
304C2×C4C2×C11×SD1611yescharacteristic
305C2×C4C2×C11×SD1611yescharacteristic
306C2×C4C11×#13511yescharacteristic
307C2×C4C11×#13511yescharacteristic
308C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
309C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
310C2×C4C11×#13711yescharacteristic
311C2×C4C11×#13711yescharacteristic
312C8—42no—
313C8—42no—
314C8—42no—
315C22C11×#39511yescharacteristic
316C22C11×#44811yescharacteristic
317C22C11×#44911yescharacteristic
318C22C11×#45011yescharacteristic
319C22C11×#45211yescharacteristic
320C22C11×#45411yescharacteristic
321C22C11×#45511yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4—82no—
329C4—161no—
330C4C11×#47511yescharacteristic
331C4C11×#47611yescharacteristic
332C4C11×#47811yescharacteristic
333C4C11×#47911yescharacteristic
334C4C11×#49811yescharacteristic
335C4C11×#49911yescharacteristic
336C4C11×#50111yescharacteristic
337C4C11×#50111yescharacteristic
338C2C11×#162611yescharacteristic
339C2C11×#163511yescharacteristic
340C2C11×#164211yescharacteristic
341C2C11×#164311yescharacteristic
342C2C11×#205811yescharacteristic
343C2C11×#205911yescharacteristic
344C2C11×#206111yescharacteristic
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
57. #10582C11direct (N × H)
276. C11#10582direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25522
C11×#19482
C11×#18342
C11×#12962
C11×#12792
#1058211