Finite Group Databasebeta

← C11×#19426 #14596619

Subgroups — C11×#19426 #14596619

Order 2816.

650 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×#3229C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic
5C11×#1699C214yesmaximal, complemented
6C11×#1691C214yesmaximal, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C11×#1546C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C11×#533C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C11×#498C2212yescomplemented
15C11×#487C2212yescomplemented
16C11×#483—22no—
17C11×#478—22no—
18C11×#476C2212yes—
19C11×#475—22no—
20C11×#474C2212yes—
21C11×#461—22no—
22C11×#461C2214yes—
23C11×#436—22no—
24C11×#436C2214yes—
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C11×#428—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#418—21no—
31C2×C11×#103—21no—
32C11×#407—22no—
33C11×#335C2214yescomplemented
34C11×#333C2212yescomplemented
35C11×#332C2214yescomplemented
36C11×#332C2212yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×C11×SD16—24no—
41C2×C11×SD16—44no—
42C2×C11×M16—21no—
43C2×C11×M16—24no—
44C22×C8×C11—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C11×C4⋊Q8C2311yescharacteristic
50C11×C4⋊Q8C2311yescharacteristic
51C11×#125—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D412yes—
59C4×D4×C11C2312yes—
60C11×#117—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C11×#107—22no—
67C11×#106—24no—
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—24no—
76C11×#103—24no—
77C11×#102—22no—
78C11×#102—22no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8—24no—
81C11×C22⋊C8D412yes—
82C4×C8×C11—21no—
83C4×C8×C11C2312yes—
84#19426C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—21no—
89C2×Q8×C11—41no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11C2×D412yes—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—41no—
100C22×C4×C11—82no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C11×SD16—48no—
105C11×M16—42no—
106C11×M16—84no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C2×C8×C11C2×D414yes—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4C2×D412yes—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—22no—
126C11×C22⋊C4—41no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132#3229C2×C1111yescharacteristic, complemented
133#3077C2×C1111yescharacteristic
134C2×#461C2×C1111yescharacteristic
135#2975C2×C1111yescharacteristic
136#1699C2×C1114yescomplemented
137#1691C2×C1114yescomplemented
138#1571C2×C1111yescharacteristic, complemented
139#1546C2×C1111yescharacteristic, complemented
140#1542C2×C1111yescharacteristic, complemented
141C23×C11—22no—
142C23×C11—42no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—42no—
149Q8×C11—81no—
150Q8×C11—82no—
151D4×C11—22no—
152D4×C11—22no—
153D4×C11—42no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—44no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—81no—
163C2×C4×C11—82no—
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11#13712yes—
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C8×C11—24no—
173C8×C11—42no—
174C8×C11—42no—
175C8×C11—42no—
176C22×SD16—21no—
177#533C22×C1111yescharacteristic
178C2×C4⋊Q8C22×C1111yescharacteristic
179C2×C4×D4C22×C1111yescharacteristic
180#498C22×C1112yescomplemented
181#487C22×C1112yescomplemented
182#483—22no—
183#478—22no—
184#476C22×C1112yes—
185#475—22no—
186#474C22×C1112yes—
187#461—22no—
188#461C22×C1114yes—
189#436—22no—
190#436C22×C1114yes—
191#431C22×C1111yescharacteristic
192#431C22×C1111yescharacteristic
193#428—21no—
194#423C22×C1111yescharacteristic
195C2×C4⋊C8C22×C1111yescharacteristic
196#418—21no—
197C2×#103—21no—
198#407—22no—
199#335C22×C1114yescomplemented
200#333C22×C1112yescomplemented
201#332C22×C1112yescomplemented
202#332C22×C1114yescomplemented
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—84no—
209C22×C11#46812yes—
210C22×C11C2×#12111yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#46812yes—
219C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
220C4×C11C2×#13711yescharacteristic
221C4×C11#57712yes—
222C22×Q8—21no—
223C22×D4D4×C1111yescharacteristic
224C23×C4—21no—
225C2×SD16—24no—
226C2×SD16—44no—
227C2×M16—21no—
228C2×M16—24no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C23×C1112yes—
234C4⋊Q8C23×C1111yescharacteristic
235C4⋊Q8C23×C1111yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4D4×C1112yes—
244C4×D4C23×C1112yes—
245#117—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42C23×C1111yescharacteristic
251#107—22no—
252#106—24no—
253#106—22no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8D4×C1112yes—
257C4⋊C8C23×C1112yes—
258C4⋊C8C23×C1112yes—
259C4⋊C8C23×C1112yes—
260#103—24no—
261#103—24no—
262#102—22no—
263#102—22no—
264C22⋊C8—21no—
265C22⋊C8—24no—
266C22⋊C8D4×C1112yes—
267C4×C8—21no—
268C4×C8C23×C1112yes—
269C2×C11—22no—
270C2×C11—82no—
271C2×C11#304211yescharacteristic
272C2×C11C2×#46811yescharacteristic
273C2×C11#306911yescharacteristic
274C24—21no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4C2×D4×C1112yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—82no—
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C11×#4111yescharacteristic
293SD16—48no—
294M16—42no—
295M16—84no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8C2×D4×C1114yes—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4C2×D4×C1112yes—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C42—41no—
317C42C2×D4×C1111yescharacteristic
318C42C2×D4×C1111yescharacteristic
319C42C11×#4111yescharacteristic
320C42C24×C1111yescharacteristic
321C11#1942611yescharacteristic, direct product factor, Sylow
322C23—22no—
323C23—42no—
324C23—81no—
325C23—81no—
326C23C11×#12111yescharacteristic
327Q8—42no—
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—82no—
332D4—22no—
333D4—22no—
334D4—42no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12111yescharacteristic
347C2×C4C11×#12111yescharacteristic
348C2×C4C11×AGL(1,ℤ/8)12yes—
349C2×C4C11×#13712yes—
350C2×C4C22×D4×C1111yescharacteristic
351C2×C4C22×D4×C1111yescharacteristic
352C2×C4C2×C11×#4111yescharacteristic
353C8—24no—
354C8—42no—
355C8—42no—
356C8—42no—
357C22—21no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22C11×#46812yes—
364C22C2×C11×#12111yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—81no—
370C4—82no—
371C4—81no—
372C4C11×#46812yes—
373C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
374C4C2×C11×#13711yescharacteristic
375C4C11×#57712yes—
376C2—22no—
377C2—82no—
378C2C11×#304211yescharacteristic
379C2C2×C11×#46811yescharacteristic
380C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3229C2semidirect
5. C11×#1699C2semidirect
6. C11×#1691C2semidirect
7. C11×#1571C2semidirect
8. C11×#1546C2semidirect
9. C11×#1542C2semidirect
14. C11×#498C22semidirect
15. C11×#487C22semidirect
33. C11×#335C22semidirect
34. C11×#333C22semidirect
35. C11×#332C22semidirect
36. C11×#332C22semidirect
84. #19426C11direct (N × H)
132. #3229C2×C11semidirect
136. #1699C2×C11semidirect
137. #1691C2×C11semidirect
138. #1571C2×C11semidirect
139. #1546C2×C11semidirect
140. #1542C2×C11semidirect
180. #498C22×C11semidirect
181. #487C22×C11semidirect
199. #335C22×C11semidirect
200. #333C22×C11semidirect
201. #332C22×C11semidirect
202. #332C22×C11semidirect
321. C11#19426direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#30772
C2×C11×#4612
C11×#29752
C11×#16992
C11×#16912
C11×#15712
C11×#15462
C11×#15422
#1942611