Finite Group Databasebeta

← C11×#13561 #14590754

Subgroups — C11×#13561 #14590754

Order 2816.

550 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#453C211yesmaximal, characteristic
2C2×C11×#353C211yesmaximal, characteristic, complemented
3C11×#1555C211yesmaximal, characteristic, complemented
4C11×#1402C214yesmaximal, complemented
5C2×C11×H(5,𝔽2)C411yescharacteristic, complemented
6C2×C11×AGL(1,ℤ/8)—21no—
7C2×C11×#127C2211yescharacteristic
8C11×#453—21no—
9C11×#453—21no—
10C11×#453C412yescomplemented
11C11×#453C2212yes—
12C11×#432—21no—
13C2×C11×#104—21no—
14C2×C11×#100C411yescharacteristic, complemented
15C2×C11×#99—21no—
16C11×#353—21no—
17C11×#353C2212yescomplemented
18C11×#331—21no—
19C11×#331C2212yescomplemented
20C11×H(5,𝔽2)—21no—
21C11×H(5,𝔽2)—41no—
22C11×H(5,𝔽2)—42no—
23C11×H(5,𝔽2)C2×C412yescomplemented
24C2×C11×#41—21no—
25C2×C11×#41—41no—
26C22×D4×C11—41no—
27C22×D4×C11—41no—
28C22×D4×C11—41no—
29C22×D4×C11C2×C411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C11×AGL(1,ℤ/8)—22no—
32C11×AGL(1,ℤ/8)—22no—
33C11×AGL(1,ℤ/8)—42no—
34C2×C11×SD16—41no—
35C2×C11×D8—41no—
36C2×C11×M16—21no—
37C11×#127—41no—
38C11×#127C2×C411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#127C2311yescharacteristic
42C2×C11×C22⋊C4—41no—
43C2×C42×C11D411yescharacteristic
44C11×C4⋊C8—22no—
45C11×#104—22no—
46C11×#104—22no—
47C11×#100—21no—
48C11×#100C2×C412yescomplemented
49C11×#99—22no—
50C11×#99—41no—
51C11×C22⋊C8—41no—
52C11×#97—41no—
53#13561C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—21no—
55C24×C11—21no—
56C24×C11—41no—
57C11×#41—22no—
58C11×#41—22no—
59C11×#41—41no—
60C11×#41—42no—
61C11×#41—44no—
62C11×#41—41no—
63C11×#41—42no—
64C2×Q8×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—44no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—84no—
86C2×D4×C11C22⋊C411yescharacteristic
87C2×D4×C11C22⋊C411yescharacteristic
88C2×D4×C11C22×C411yescharacteristic
89C2×D4×C11C2×D411yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—81no—
94C22×C4×C11C22⋊C411yescharacteristic
95C11×SD16—42no—
96C11×SD16—42no—
97C11×D8—42no—
98C11×D8—42no—
99C11×M16—22no—
100C11×M16—41no—
101C2×C8×C11—41no—
102C2×C8×C11—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—81no—
105C42×C11—21no—
106C42×C11C22⋊C411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C2×#453C2×C1111yescharacteristic
109C2×#353C2×C1111yescharacteristic, complemented
110#1555C2×C1111yescharacteristic, complemented
111#1402C2×C1114yescomplemented
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—42no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—42no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11—162no—
126C23×C11#9911yescharacteristic
127Q8×C11—22no—
128Q8×C11—41no—
129D4×C11—22no—
130D4×C11—41no—
131D4×C11—41no—
132D4×C11—41no—
133D4×C11—41no—
134D4×C11—41no—
135D4×C11—42no—
136D4×C11—44no—
137D4×C11—44no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—81no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—82no—
156C2×C4×C11—162no—
157C2×C4×C11#9911yescharacteristic
158C2×C4×C11C2×C22⋊C411yescharacteristic
159C8×C11—42no—
160C8×C11—82no—
161C2×H(5,𝔽2)C4×C1111yescharacteristic, complemented
162C2×AGL(1,ℤ/8)—21no—
163C2×#127C22×C1111yescharacteristic
164#453—21no—
165#453—21no—
166#453C4×C1112yescomplemented
167#453C22×C1112yes—
168#432—21no—
169C2×#104—21no—
170C2×#100C4×C1111yescharacteristic, complemented
171C2×#99—21no—
172#353—21no—
173#353C22×C1112yescomplemented
174#331—21no—
175#331C22×C1112yescomplemented
176C22×C11—41no—
177C22×C11—42no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—161no—
190C22×C11—161no—
191C22×C11—162no—
192C22×C11—162no—
193C22×C11AΣL(1,𝔽16)11yescharacteristic
194C22×C11AΣL(1,𝔽16)11yescharacteristic
195C22×C11C2×#9911yescharacteristic
196C4×C11—22no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—41no—
200C4×C11—42no—
201C4×C11—162no—
202H(5,𝔽2)—21no—
203H(5,𝔽2)—41no—
204H(5,𝔽2)—42no—
205H(5,𝔽2)C2×C4×C1112yescomplemented
206C2×#41—21no—
207C2×#41—41no—
208C22×D4—41no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4C2×C4×C1111yescharacteristic
212C22×D4D4×C1111yescharacteristic
213AGL(1,ℤ/8)—22no—
214AGL(1,ℤ/8)—22no—
215AGL(1,ℤ/8)—42no—
216C2×SD16—41no—
217C2×D8—41no—
218C2×M16—21no—
219#127—41no—
220#127C2×C4×C1111yescharacteristic
221#127D4×C1111yescharacteristic
222#127D4×C1111yescharacteristic
223#127C23×C1111yescharacteristic
224C2×C22⋊C4—41no—
225C2×C42D4×C1111yescharacteristic
226C4⋊C8—22no—
227#104—22no—
228#104—22no—
229#100—21no—
230#100C2×C4×C1112yescomplemented
231#99—22no—
232#99—41no—
233C22⋊C8—41no—
234#97—41no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—81no—
239C2×C11—81no—
240C2×C11—81no—
241C2×C11—81no—
242C2×C11—82no—
243C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
244C24—21no—
245C24—21no—
246C24—41no—
247#41—22no—
248#41—22no—
249#41—41no—
250#41—42no—
251#41—44no—
252#41—41no—
253#41—42no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—44no—
271C2×D4—42no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—84no—
276C2×D4C11×C22⋊C411yescharacteristic
277C2×D4C11×C22⋊C411yescharacteristic
278C2×D4C22×C4×C1111yescharacteristic
279C2×D4C2×D4×C1111yescharacteristic
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—81no—
284C22×C4C11×C22⋊C411yescharacteristic
285SD16—42no—
286SD16—42no—
287D8—42no—
288D8—42no—
289M16—22no—
290M16—41no—
291C2×C8—41no—
292C2×C8—42no—
293C22⋊C4—42no—
294C22⋊C4—81no—
295C42—21no—
296C42C11×C22⋊C411yescharacteristic
297C42C2×D4×C1111yescharacteristic
298C11#1356111yescharacteristic, direct product factor, Sylow
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—42no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—42no—
308C23—41no—
309C23—41no—
310C23—82no—
311C23—82no—
312C23—162no—
313C23C11×#9911yescharacteristic
314Q8—22no—
315Q8—41no—
316D4—22no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—44no—
324D4—44no—
325D4—42no—
326D4—42no—
327D4—81no—
328D4—82no—
329D4—82no—
330D4—82no—
331D4—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—162no—
344C2×C4C11×#9911yescharacteristic
345C2×C4C2×C11×C22⋊C411yescharacteristic
346C8—42no—
347C8—82no—
348C22—41no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22—161no—
362C22—161no—
363C22—162no—
364C22—162no—
365C22C11×AΣL(1,𝔽16)11yescharacteristic
366C22C11×AΣL(1,𝔽16)11yescharacteristic
367C22C2×C11×#9911yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—42no—
373C4—162no—
374C2—21no—
375C2—21no—
376C2—21no—
377C2—81no—
378C2—81no—
379C2—81no—
380C2—81no—
381C2—82no—
382C2C2×C11×AΣL(1,𝔽16)11yescharacteristic
subgroupG/H
center, socleC2×C11C2×AΣL(1,𝔽16)
commutatorC2×D4C22×C4×C11
Frattini, cosocle#127C23×C11
prime radicalC2×C11×#453C2
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C23×C11 ◁ C22×C4×C11 ◁ C2×C11×#127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#353C2semidirect
3. C11×#1555C2semidirect
4. C11×#1402C2semidirect
5. C2×C11×H(5,𝔽2)C4semidirect
10. C11×#453C4semidirect
14. C2×C11×#100C4semidirect
17. C11×#353C22semidirect
19. C11×#331C22semidirect
23. C11×H(5,𝔽2)C2×C4semidirect
48. C11×#100C2×C4semidirect
53. #13561C11direct (N × H)
109. C2×#353C2×C11semidirect
110. #1555C2×C11semidirect
111. #1402C2×C11semidirect
161. C2×H(5,𝔽2)C4×C11semidirect
166. #453C4×C11semidirect
170. C2×#100C4×C11semidirect
173. #353C22×C11semidirect
175. #331C22×C11semidirect
205. H(5,𝔽2)C2×C4×C11semidirect
230. #100C2×C4×C11semidirect
298. C11#13561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4532
C2×C11×#3532
C11×#15552
C11×#14022
#1356111