Finite Group Databasebeta

← C11×#10503 #14587696

Subgroups — C11×#10503 #14587696

Order 2816.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic
2C11×#1988C211yesmaximal, characteristic, complemented
3C11×#1980C211yesmaximal, characteristic
4C11×#1966C211yesmaximal, characteristic, complemented
5C11×#1565C211yesmaximal, characteristic, complemented
6C11×#1547C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#500—21no—
11C11×#486—21no—
12C11×#480—22no—
13C11×#474—21no—
14C11×#474—21no—
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#104—21no—
19C2×C11×#104—21no—
20C2×C11×#101—21no—
21C2×C11×#101—21no—
22C4×C11×M16C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C11×#340—22no—
25C11×#335—21no—
26C11×#334—21no—
27C11×#332—21no—
28C11×#331—21no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C2×C11×M16—21no—
32C2×C11×M16D411yescharacteristic
33C2×C11×M16D411yescharacteristic
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D412yes—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C11×#107—22no—
52C11×#107—22no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×#104—42no—
60C11×#104—42no—
61C11×#102—22no—
62C11×#102—22no—
63C11×#101—42no—
64C11×#101—42no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C11×#95—21no—
70#10503C1111yesmaximal, characteristic, direct product factor, Sylow
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11—21no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×M16—21no—
93C11×M16—21no—
94C11×M16—21no—
95C11×M16—41no—
96C11×M16—41no—
97C11×M16D812yes—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—21no—
102C2×C8×C11—42no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—22no—
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×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11#4111yescharacteristic
121#3226C2×C1111yescharacteristic
122#1988C2×C1111yescharacteristic, complemented
123#1980C2×C1111yescharacteristic
124#1966C2×C1111yescharacteristic, complemented
125#1565C2×C1111yescharacteristic, complemented
126#1547C2×C1111yescharacteristic
127#1303C2×C1111yescharacteristic, complemented
128C23×C11—41no—
129C23×C11#12111yescharacteristic
130Q8×C11—41no—
131Q8×C11—41no—
132Q8×C11—81no—
133Q8×C11—81no—
134Q8×C11—81no—
135Q8×C11—81no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—41no—
139D4×C11—41no—
140D4×C11—81no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×C4×C11#12411yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C8×C11—22no—
166C8×C11—41no—
167C8×C11—41no—
168C8×C11—41no—
169C8×C11—81no—
170C8×C11—81no—
171#532C22×C1111yescharacteristic
172C2×C4⋊Q8C22×C1111yescharacteristic
173#500—21no—
174#486—21no—
175#480—22no—
176#474—21no—
177#474—21no—
178#431C22×C1111yescharacteristic
179#423C22×C1111yescharacteristic
180C2×C4⋊C8C22×C1111yescharacteristic
181C2×#104—21no—
182C2×#104—21no—
183C2×#101—21no—
184C2×#101—21no—
185C4×M16C22×C1111yescharacteristic
186C4×C4⋊C4C22×C1111yescharacteristic
187#340—22no—
188#335—21no—
189#334—21no—
190#332—21no—
191#331—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39411yescharacteristic
198C22×C11#45911yescharacteristic
199C22×C11#46311yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11#45411yescharacteristic
207C4×C11#45611yescharacteristic
208C4×C11#45911yescharacteristic
209C4×C11#46311yescharacteristic
210C4×C11#46611yescharacteristic
211C4×C11#46911yescharacteristic
212C2×#41—21no—
213C22×Q8—21no—
214C2×M16—21no—
215C2×M16D4×C1111yescharacteristic
216C2×M16D4×C1111yescharacteristic
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8D4×C1111yescharacteristic
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×C4⋊C4D4×C1112yes—
232C2×C42—21no—
233C2×C42C23×C1111yescharacteristic
234#107—22no—
235#107—22no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C1111yescharacteristic
241C4⋊C8D4×C1111yescharacteristic
242#104—42no—
243#104—42no—
244#102—22no—
245#102—22no—
246#101—42no—
247#101—42no—
248C22⋊C8—21no—
249#97—21no—
250C4×C8—21no—
251C4×C8—21no—
252#95—21no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—161no—
256C2×C11#203811yescharacteristic
257C2×C11#204911yescharacteristic
258C2×C11#205411yescharacteristic
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263C2×Q8—21no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C2×D4×C1111yescharacteristic
279C22×C4C11×#4111yescharacteristic
280M16—21no—
281M16—21no—
282M16—21no—
283M16—41no—
284M16—41no—
285M16C11×D812yes—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—42no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42—41no—
305C42C2×D4×C1111yescharacteristic
306C42C2×D4×C1111yescharacteristic
307C42C11×#4111yescharacteristic
308C42C11×#4111yescharacteristic
309C11#1050311yescharacteristic, direct product factor, Sylow
310C23—41no—
311C23C11×#12111yescharacteristic
312Q8—41no—
313Q8—41no—
314Q8—81no—
315Q8—81no—
316Q8—81no—
317Q8—81no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C11×#12011yescharacteristic
338C2×C4C11×#12111yescharacteristic
339C2×C4C11×#12111yescharacteristic
340C2×C4C11×#12311yescharacteristic
341C2×C4C11×#12311yescharacteristic
342C2×C4C11×#12411yescharacteristic
343C2×C4C2×C11×D811yescharacteristic
344C2×C4C11×#13511yescharacteristic
345C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
347C8—22no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22C11×#39411yescharacteristic
359C22C11×#45911yescharacteristic
360C22C11×#46311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—82no—
366C4—81no—
367C4C11×#45411yescharacteristic
368C4C11×#45611yescharacteristic
369C4C11×#45911yescharacteristic
370C4C11×#46311yescharacteristic
371C4C11×#46611yescharacteristic
372C4C11×#46911yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2C11×#203811yescharacteristic
377C2C11×#204911yescharacteristic
378C2C11×#205411yescharacteristic
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×#1988C2semidirect
4. C11×#1966C2semidirect
5. C11×#1565C2semidirect
7. C11×#1303C2semidirect
70. #10503C11direct (N × H)
122. #1988C2×C11semidirect
124. #1966C2×C11semidirect
125. #1565C2×C11semidirect
127. #1303C2×C11semidirect
309. C11#10503direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#19882
C11×#19802
C11×#19662
C11×#15652
C11×#15472
C11×#13032
#1050311