Finite Group Databasebeta

← C11×#10357 #14587550

Subgroups — C11×#10357 #14587550

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2552C211yesmaximal, characteristic
2C11×#1990C211yesmaximal, characteristic
3C11×#1988C211yesmaximal, characteristic
4C11×#1981C211yesmaximal, characteristic
5C11×#1296C211yesmaximal, characteristic
6C11×#1279C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—21no—
13C2×C11×#103—21no—
14C2×C4×C8×C11C2211yescharacteristic
15C11×#398—22no—
16C11×#389—21no—
17C11×#389—21no—
18C11×#384—21no—
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—22no—
25C22×Q8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8Q812yes—
33C11×#125—42no—
34C11×#125—42no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D412yes—
47C2×C42×C11—21no—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×#103—42no—
55C11×#103—42no—
56C4×C8×C11—21no—
57C4×C8×C11—21no—
58C11×#95—22no—
59C11×#95—21no—
60C11×#95—21no—
61#10357C1111yesmaximal, characteristic, direct product factor, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—44no—
95C11×C4⋊C4—44no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—82no—
104C11×C4⋊C4SD1612yes—
105C11×C4⋊C4Q1612yes—
106C42×C11—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11C2×Q811yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114#2552C2×C1111yescharacteristic
115#1990C2×C1111yescharacteristic
116#1988C2×C1111yescharacteristic
117#1981C2×C1111yescharacteristic
118#1296C2×C1111yescharacteristic
119#1279C2×C1111yescharacteristic
120#1279C2×C1111yescharacteristic
121C23×C11#12011yescharacteristic
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—81no—
125Q8×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11C22⋊Q811yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11#12411yescharacteristic
151C2×C4×C11#12411yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11C2×Q1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C8×C11—42no—
161C8×C11—81no—
162C8×C11—81no—
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×#125—21no—
165C2×C4⋊C8C22×C1111yescharacteristic
166C2×C4⋊C8C22×C1111yescharacteristic
167C2×#103—21no—
168C2×#103—21no—
169C2×C4×C8C22×C1111yescharacteristic
170#398—22no—
171#389—21no—
172#389—21no—
173#384—21no—
174#384C22×C1111yescharacteristic
175C4×C4⋊C4C22×C1111yescharacteristic
176C4×C4⋊C4C22×C1111yescharacteristic
177#340—21no—
178#340—21no—
179#340—22no—
180C22×C11#39311yescharacteristic
181C22×C11#44911yescharacteristic
182C22×C11#44911yescharacteristic
183C22×C11#45011yescharacteristic
184C22×C11#45111yescharacteristic
185C22×C11#45511yescharacteristic
186C22×C11#45611yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11—42no—
191C4×C11—81no—
192C4×C11—82no—
193C4×C11—81no—
194C4×C11—82no—
195C4×C11#47511yescharacteristic
196C4×C11#47711yescharacteristic
197C4×C11#47811yescharacteristic
198C4×C11#47811yescharacteristic
199C4×C11#48711yescharacteristic
200C4×C11#48811yescharacteristic
201C4×C11#48911yescharacteristic
202C4×C11#49011yescharacteristic
203C22×Q8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8Q8×C1112yes—
211#125—42no—
212#125—42no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4D4×C1111yescharacteristic
221C2×C4⋊C4D4×C1111yescharacteristic
222C2×C4⋊C4D4×C1111yescharacteristic
223C2×C4⋊C4D4×C1111yescharacteristic
224C2×C4⋊C4D4×C1112yes—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42C23×C1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232#103—42no—
233#103—42no—
234C4×C8—21no—
235C4×C8—21no—
236#95—22no—
237#95—21no—
238#95—21no—
239C2×C11#164211yescharacteristic
240C2×C11#164411yescharacteristic
241C2×C11#164811yescharacteristic
242C2×C11#165411yescharacteristic
243C2×C11#202411yescharacteristic
244C2×C11#202511yescharacteristic
245C2×C11#202811yescharacteristic
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×D4×C1111yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—82no—
288C4⋊C4C11×SD1612yes—
289C4⋊C4C11×Q1612yes—
290C42—41no—
291C42—41no—
292C42—41no—
293C42—41no—
294C42C2×Q8×C1111yescharacteristic
295C42C11×#4111yescharacteristic
296C42C11×#4111yescharacteristic
297C42C11×#4111yescharacteristic
298C11#1035711yescharacteristic, direct product factor, Sylow
299C23C11×#12011yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C11×C22⋊Q811yescharacteristic
325C2×C4C11×C22⋊Q811yescharacteristic
326C2×C4C11×C22⋊Q811yescharacteristic
327C2×C4C11×#12411yescharacteristic
328C2×C4C11×#12411yescharacteristic
329C2×C4C11×#12411yescharacteristic
330C2×C4C2×C11×SD1611yescharacteristic
331C2×C4C2×C11×Q1611yescharacteristic
332C2×C4C11×#13511yescharacteristic
333C2×C4C11×#13511yescharacteristic
334C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
335C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
336C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
337C2×C4C11×#13711yescharacteristic
338C8—42no—
339C8—81no—
340C8—81no—
341C22C11×#39311yescharacteristic
342C22C11×#44911yescharacteristic
343C22C11×#44911yescharacteristic
344C22C11×#45011yescharacteristic
345C22C11×#45111yescharacteristic
346C22C11×#45511yescharacteristic
347C22C11×#45611yescharacteristic
348C4—21no—
349C4—21no—
350C4—42no—
351C4—42no—
352C4—81no—
353C4—82no—
354C4—81no—
355C4—82no—
356C4C11×#47511yescharacteristic
357C4C11×#47711yescharacteristic
358C4C11×#47811yescharacteristic
359C4C11×#47811yescharacteristic
360C4C11×#48711yescharacteristic
361C4C11×#48811yescharacteristic
362C4C11×#48911yescharacteristic
363C4C11×#49011yescharacteristic
364C2C11×#164211yescharacteristic
365C2C11×#164411yescharacteristic
366C2C11×#164811yescharacteristic
367C2C11×#165411yescharacteristic
368C2C11×#202411yescharacteristic
369C2C11×#202511yescharacteristic
370C2C11×#202811yescharacteristic
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
61. #10357C11direct (N × H)
298. C11#10357direct (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×#19902
C11×#19882
C11×#19812
C11×#12962
C11×#12792
#1035711