Finite Group Databasebeta

← C11×#10504 #14587697

Subgroups — C11×#10504 #14587697

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic
2C11×#1986C211yesmaximal, characteristic, complemented
3C11×#1982C211yesmaximal, characteristic
4C11×#1965C211yesmaximal, characteristic
5C11×#1565C211yesmaximal, characteristic, complemented
6C11×#1550C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C11×#492—21no—
11C11×#486—21no—
12C11×#460—21no—
13C11×#460—21no—
14C11×#450—22no—
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—22no—
19C2×C11×#100—21no—
20C2×C11×#100—21no—
21C4×C11×M16C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C11×#339—21no—
24C11×#339—21no—
25C11×#335—21no—
26C11×#334—21no—
27C11×#333—21no—
28C11×#332—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C2×C11×SD16—22no—
33C2×C11×SD16—22no—
34C2×C11×M16—21no—
35C2×C11×M16D411yescharacteristic
36C2×C11×M16D411yescharacteristic
37C22×C8×C11—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C11×#117—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×#102—22no—
60C11×#102—22no—
61C11×#102—44no—
62C11×#100—42no—
63C11×#100—42no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C11×#95—21no—
69#10504C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—22no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—82no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C11×SD16—82no—
91C11×SD16—82no—
92C11×M16—21no—
93C11×M16—21no—
94C11×M16—21no—
95C11×M16—41no—
96C11×M16—41no—
97C11×M16SD1612yescomplemented
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—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11#4111yescharacteristic
121#3208C2×C1111yescharacteristic
122#1986C2×C1111yescharacteristic, complemented
123#1982C2×C1111yescharacteristic
124#1965C2×C1111yescharacteristic
125#1565C2×C1111yescharacteristic, complemented
126#1550C2×C1111yescharacteristic, complemented
127#1303C2×C1111yescharacteristic, complemented
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—82no—
132C23×C11—82no—
133C23×C11#12111yescharacteristic
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—81no—
137D4×C11—44no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—81no—
143D4×C11—81no—
144D4×C11—81no—
145D4×C11—81no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12311yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#12411yescharacteristic
160C2×C4×C11C2×SD1611yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C8×C11—22no—
165C8×C11—41no—
166C8×C11—41no—
167C8×C11—41no—
168C8×C11—81no—
169C8×C11—81no—
170#533C22×C1111yescharacteristic
171C2×#127C22×C1111yescharacteristic
172#492—21no—
173#486—21no—
174#460—21no—
175#460—21no—
176#450—22no—
177#431C22×C1111yescharacteristic
178#423C22×C1111yescharacteristic
179C2×C4⋊C8C22×C1111yescharacteristic
180C2×#102—22no—
181C2×#100—21no—
182C2×#100—21no—
183C4×M16C22×C1111yescharacteristic
184C4×C4⋊C4C22×C1111yescharacteristic
185#339—21no—
186#339—21no—
187#335—21no—
188#334—21no—
189#333—21no—
190#332—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—162no—
197C22×C11—162no—
198C22×C11#39411yescharacteristic
199C22×C11#46111yescharacteristic
200C22×C11#46311yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11#45311yescharacteristic
208C4×C11#45511yescharacteristic
209C4×C11#46011yescharacteristic
210C4×C11#46411yescharacteristic
211C4×C11#46511yescharacteristic
212C4×C11#46811yescharacteristic
213C22×D4—21no—
214C22×D4—21no—
215C22×D4D4×C1112yes—
216C2×SD16—22no—
217C2×SD16—22no—
218C2×M16—21no—
219C2×M16D4×C1111yescharacteristic
220C2×M16D4×C1111yescharacteristic
221C22×C8—21no—
222C4⋊Q8D4×C1111yescharacteristic
223C4⋊Q8D4×C1111yescharacteristic
224#127—21no—
225#127—21no—
226#127—21no—
227#127—21no—
228#125—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C42—21no—
236C2×C42C23×C1111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8D4×C1111yescharacteristic
242C4⋊C8D4×C1111yescharacteristic
243#102—22no—
244#102—22no—
245#102—44no—
246#100—42no—
247#100—42no—
248C22⋊C8—21no—
249#97—21no—
250C4×C8—21no—
251C4×C8—21no—
252#95—21no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—162no—
256C2×C11#203711yescharacteristic
257C2×C11#204811yescharacteristic
258C2×C11#205511yescharacteristic
259C24—22no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—82no—
275C22×C4—41no—
276C22×C4C2×D4×C1111yescharacteristic
277C22×C4C2×D4×C1111yescharacteristic
278C22×C4C11×#4111yescharacteristic
279SD16—82no—
280SD16—82no—
281M16—21no—
282M16—21no—
283M16—21no—
284M16—41no—
285M16—41no—
286M16C11×SD1612yescomplemented
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—42no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C42C11×#4111yescharacteristic
309C42C11×#4111yescharacteristic
310C11#1050411yescharacteristic, direct product factor, Sylow
311C23—42no—
312C23—42no—
313C23—42no—
314C23—82no—
315C23—82no—
316C23C11×#12111yescharacteristic
317Q8—41no—
318Q8—41no—
319Q8—81no—
320D4—44no—
321D4—42no—
322D4—42no—
323D4—82no—
324D4—82no—
325D4—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
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×SD1611yescharacteristic
344C2×C4C11×#13511yescharacteristic
345C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C11×#13711yescharacteristic
347C8—22no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—162no—
359C22—162no—
360C22C11×#39411yescharacteristic
361C22C11×#46111yescharacteristic
362C22C11×#46311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4C11×#45311yescharacteristic
370C4C11×#45511yescharacteristic
371C4C11×#46011yescharacteristic
372C4C11×#46411yescharacteristic
373C4C11×#46511yescharacteristic
374C4C11×#46811yescharacteristic
375C2—21no—
376C2—21no—
377C2—162no—
378C2C11×#203711yescharacteristic
379C2C11×#204811yescharacteristic
380C2C11×#205511yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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×#1986C2semidirect
5. C11×#1565C2semidirect
6. C11×#1550C2semidirect
7. C11×#1303C2semidirect
69. #10504C11direct (N × H)
97. C11×M16SD16semidirect
122. #1986C2×C11semidirect
125. #1565C2×C11semidirect
126. #1550C2×C11semidirect
127. #1303C2×C11semidirect
286. M16C11×SD16semidirect
310. C11#10504direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C11×#19862
C11×#19822
C11×#19652
C11×#15652
C11×#15502
C11×#13032
#1050411