Finite Group Databasebeta

← C11×#19427 #14596620

Subgroups — C11×#19427 #14596620

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C11×#3036C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic, complemented
5C11×#1697C214yesmaximal, complemented
6C11×#1691C214yesmaximal, complemented
7C11×#1571C211yesmaximal, characteristic, complemented
8C11×#1548C211yesmaximal, characteristic, complemented
9C11×#1540C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C11×#532C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C11×#498C2212yescomplemented
15C11×#486C2212yescomplemented
16C11×#481—22no—
17C11×#476—22no—
18C11×#476—22no—
19C11×#476C2214yes—
20C11×#463—22no—
21C11×#461C2212yes—
22C11×#459C2212yes—
23C11×#436—22no—
24C11×#436C2214yes—
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×#106—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#417—21no—
31C2×C11×#102—21no—
32C11×#407—22no—
33C11×#335C2214yescomplemented
34C11×#333C2214yescomplemented
35C11×#332C2212yescomplemented
36C11×#331C2212yescomplemented
37C2×C11×#41—21no—
38C22×Q8×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×SD16—22no—
43C2×C11×D8—22no—
44C2×C11×M16—21no—
45C2×C11×M16—24no—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2311yescharacteristic
51C11×C4⋊Q8C2312yes—
52C11×#127C2311yescharacteristic
53C11×#124—21no—
54C11×#121—21no—
55C11×#121—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#106—24no—
68C11×#106—24no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—22no—
76C11×#102—24no—
77C11×#102—24no—
78C11×#102—22no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8—24no—
81C11×C22⋊C8D412yes—
82C4×C8×C11—21no—
83C4×C8×C11C2312yes—
84#19427C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—21no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×Q8×C11—22no—
90C2×Q8×C11—41no—
91C2×Q8×C11—82no—
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C2×D4×C11C2×D412yes—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—82no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C11×SD16—44no—
110C11×D8—44no—
111C11×M16—42no—
112C11×M16—84no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—42no—
117C2×C8×C11C2×D414yes—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4C2×D412yes—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134#3227C2×C1111yescharacteristic, complemented
135C2×#476C2×C1111yescharacteristic, complemented
136#3036C2×C1111yescharacteristic
137#2975C2×C1111yescharacteristic, complemented
138#1697C2×C1114yescomplemented
139#1691C2×C1114yescomplemented
140#1571C2×C1111yescharacteristic, complemented
141#1548C2×C1111yescharacteristic, complemented
142#1540C2×C1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—82no—
152Q8×C11—82no—
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—81no—
160D4×C11—82no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—44no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—82no—
168C2×C4×C11—81no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11#13712yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C8×C11—24no—
180C8×C11—42no—
181C8×C11—42no—
182C8×C11—42no—
183C2×AGL(1,ℤ/8)—21no—
184#532C22×C1111yescharacteristic
185C2×C4⋊Q8C22×C1111yescharacteristic
186C2×C4×D4C22×C1111yescharacteristic
187#498C22×C1112yescomplemented
188#486C22×C1112yescomplemented
189#481—22no—
190#476—22no—
191#476—22no—
192#476C22×C1114yes—
193#463—22no—
194#461C22×C1112yes—
195#459C22×C1112yes—
196#436—22no—
197#436C22×C1114yes—
198#431C22×C1111yescharacteristic
199#431C22×C1111yescharacteristic
200C2×#106—21no—
201#423C22×C1111yescharacteristic
202C2×C4⋊C8C22×C1111yescharacteristic
203#417—21no—
204C2×#102—21no—
205#407—22no—
206#335C22×C1114yescomplemented
207#333C22×C1114yescomplemented
208#332C22×C1112yescomplemented
209#331C22×C1112yescomplemented
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—84no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#46812yes—
220C22×C11C2×#12111yescharacteristic
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11#46812yes—
228C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C4×C11#57712yes—
231C2×#41—21no—
232C22×Q8—21no—
233C22×D4D4×C1111yescharacteristic
234C23×C4—21no—
235AGL(1,ℤ/8)—44no—
236C2×SD16—22no—
237C2×D8—22no—
238C2×M16—21no—
239C2×M16—24no—
240C22×C8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8C23×C1112yes—
245C4⋊Q8C23×C1111yescharacteristic
246#127C23×C1111yescharacteristic
247#124—21no—
248#121—21no—
249#121—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4D4×C1112yes—
255C4×D4C23×C1112yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C23×C1111yescharacteristic
261#106—24no—
262#106—24no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C1112yes—
266C4⋊C8C23×C1112yes—
267C4⋊C8C23×C1112yes—
268C4⋊C8C23×C1112yes—
269#103—22no—
270#102—24no—
271#102—24no—
272#102—22no—
273C22⋊C8—21no—
274C22⋊C8—24no—
275C22⋊C8D4×C1112yes—
276C4×C8—21no—
277C4×C8C23×C1112yes—
278C2×C11—22no—
279C2×C11—82no—
280C2×C11—161no—
281C2×C11#304211yescharacteristic
282C2×C11C2×#46811yescharacteristic
283C2×C11#306811yescharacteristic
284C24—21no—
285#41—42no—
286#41—42no—
287C2×Q8—21no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—82no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4C2×D4×C1112yes—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C11×#4111yescharacteristic
308SD16—44no—
309D8—44no—
310M16—42no—
311M16—84no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8C2×D4×C1114yes—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C2×D4×C1112yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42C2×D4×C1111yescharacteristic
330C42C2×D4×C1111yescharacteristic
331C42C11×#4111yescharacteristic
332C42C24×C1111yescharacteristic
333C11#1942711yescharacteristic, direct product factor, Sylow
334C23—22no—
335C23—42no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23C11×#12111yescharacteristic
340Q8—41no—
341Q8—41no—
342Q8—82no—
343Q8—82no—
344D4—22no—
345D4—22no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—81no—
351D4—82no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4C11×#12111yescharacteristic
363C2×C4C11×#12111yescharacteristic
364C2×C4C11×#12111yescharacteristic
365C2×C4C11×AGL(1,ℤ/8)12yes—
366C2×C4C11×#13712yes—
367C2×C4C22×D4×C1111yescharacteristic
368C2×C4C22×D4×C1111yescharacteristic
369C2×C4C2×C11×#4111yescharacteristic
370C8—24no—
371C8—42no—
372C8—42no—
373C8—42no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C11×#46812yes—
384C22C2×C11×#12111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—82no—
391C4C11×#46812yes—
392C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
393C4C2×C11×#13711yescharacteristic
394C4C11×#57712yes—
395C2—22no—
396C2—82no—
397C2—161no—
398C2C11×#304211yescharacteristic
399C2C2×C11×#46811yescharacteristic
400C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3036C2
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×#3227C2semidirect
2. C2×C11×#476C2semidirect
4. C11×#2975C2semidirect
5. C11×#1697C2semidirect
6. C11×#1691C2semidirect
7. C11×#1571C2semidirect
8. C11×#1548C2semidirect
9. C11×#1540C2semidirect
14. C11×#498C22semidirect
15. C11×#486C22semidirect
33. C11×#335C22semidirect
34. C11×#333C22semidirect
35. C11×#332C22semidirect
36. C11×#331C22semidirect
84. #19427C11direct (N × H)
134. #3227C2×C11semidirect
135. C2×#476C2×C11semidirect
137. #2975C2×C11semidirect
138. #1697C2×C11semidirect
139. #1691C2×C11semidirect
140. #1571C2×C11semidirect
141. #1548C2×C11semidirect
142. #1540C2×C11semidirect
187. #498C22×C11semidirect
188. #486C22×C11semidirect
206. #335C22×C11semidirect
207. #333C22×C11semidirect
208. #332C22×C11semidirect
209. #331C22×C11semidirect
333. C11#19427direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C2×C11×#4762
C11×#30362
C11×#29752
C11×#16972
C11×#16912
C11×#15712
C11×#15482
C11×#15402
#1942711