Finite Group Databasebeta

← C11×#19425 #14596618

Subgroups — C11×#19425 #14596618

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3207C211yesmaximal, characteristic, complemented
2C11×#3109C211yesmaximal, characteristic, complemented
3C11×#3100C211yesmaximal, characteristic, complemented
4C11×#2975C211yesmaximal, characteristic, complemented
5C11×#1703C212yesmaximal, complemented
6C11×#1697C212yesmaximal, complemented
7C11×#1687C212yesmaximal, complemented
8C11×#1685C212yesmaximal, complemented
9C11×#1572C211yesmaximal, characteristic, complemented
10C11×#1553C211yesmaximal, characteristic, complemented
11C11×#1543C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C11×#493C2211yescharacteristic, complemented
16C11×#492C2211yescharacteristic, complemented
17C11×#487C2211yescharacteristic, complemented
18C11×#486C2211yescharacteristic, complemented
19C11×#481—21no—
20C11×#480—21no—
21C11×#476C2212yes—
22C11×#474C2212yes—
23C11×#463—22no—
24C11×#459C2212yes—
25C11×#459C2212yes—
26C11×#449—22no—
27C11×#447—21no—
28C11×#447—21no—
29C11×#442—22no—
30C4×C11×D8—22no—
31C11×#436—22no—
32C11×#436C2212yes—
33C11×#436C2212yes—
34C11×#432C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C11×#431C2211yescharacteristic
38C11×#407—22no—
39C11×#335C2212yescomplemented
40C11×#334C2212yescomplemented
41C11×#333C2212yescomplemented
42C11×#332C2212yescomplemented
43C11×#331C2212yescomplemented
44C11×#331C2212yescomplemented
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C2×C11×SD16—22no—
50C2×C11×D8—22no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#127C2311yescharacteristic
59C11×#124—21no—
60C11×#124—21no—
61C11×#121—21no—
62C11×#121—21no—
63C11×#121—21no—
64C11×#121—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11D412yes—
72C4×D4×C11C2312yes—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C11×#107—22no—
77C11×#106—22no—
78C11×C4⋊C8D412yes—
79C11×C4⋊C8C2312yes—
80C11×C4⋊C8C2312yes—
81C11×C4⋊C8C2312yes—
82C11×#103—22no—
83C11×#102—22no—
84C11×#102—22no—
85C11×#102—22no—
86C11×#102—22no—
87C11×#102—22no—
88C11×C22⋊C8—21no—
89C11×C22⋊C8—21no—
90C11×C22⋊C8—21no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8—22no—
93C11×C22⋊C8D412yes—
94C11×#97—21no—
95C4×C8×C11—21no—
96C4×C8×C11—21no—
97C4×C8×C11C2311yescharacteristic
98C4×C8×C11C2311yescharacteristic
99#19425C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C11×#41—82no—
102C11×#41—82no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—42no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—82no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C11×SD16—82no—
126C11×D8—44no—
127C11×D8—44no—
128C11×D8—82no—
129C11×M16—82no—
130C11×M16—82no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11#4111yescharacteristic
151C42×C11C2411yescharacteristic
152#3207C2×C1111yescharacteristic, complemented
153#3109C2×C1111yescharacteristic, complemented
154#3100C2×C1111yescharacteristic, complemented
155#2975C2×C1111yescharacteristic, complemented
156#1703C2×C1112yescomplemented
157#1697C2×C1112yescomplemented
158#1687C2×C1112yescomplemented
159#1685C2×C1112yescomplemented
160#1572C2×C1111yescharacteristic, complemented
161#1553C2×C1111yescharacteristic, complemented
162#1543C2×C1111yescharacteristic, complemented
163C23×C11—22no—
164C23×C11—42no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11#12111yescharacteristic
170Q8×C11—42no—
171Q8×C11—81no—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—81no—
180D4×C11—81no—
181D4×C11—82no—
182D4×C11—82no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—82no—
192C2×C4×C11—82no—
193C2×C4×C11—82no—
194C2×C4×C11—81no—
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C8×C11—22no—
202C8×C11—22no—
203C8×C11—42no—
204C8×C11—42no—
205C8×C11—42no—
206#532C22×C1111yescharacteristic
207#532C22×C1111yescharacteristic
208C2×C4×D4C22×C1111yescharacteristic
209#493C22×C1111yescharacteristic, complemented
210#492C22×C1111yescharacteristic, complemented
211#487C22×C1111yescharacteristic, complemented
212#486C22×C1111yescharacteristic, complemented
213#481—21no—
214#480—21no—
215#476C22×C1112yes—
216#474C22×C1112yes—
217#463—22no—
218#459C22×C1112yes—
219#459C22×C1112yes—
220#449—22no—
221#447—21no—
222#447—21no—
223#442—22no—
224C4×D8—22no—
225#436—22no—
226#436C22×C1112yes—
227#436C22×C1112yes—
228#432C22×C1111yescharacteristic
229#431C22×C1111yescharacteristic
230#431C22×C1111yescharacteristic
231#431C22×C1111yescharacteristic
232#407—22no—
233#335C22×C1112yescomplemented
234#334C22×C1112yescomplemented
235#333C22×C1112yescomplemented
236#332C22×C1112yescomplemented
237#331C22×C1112yescomplemented
238#331C22×C1112yescomplemented
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—42no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—84no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11C2×#12111yescharacteristic
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—42no—
258C4×C11—81no—
259C4×C11—81no—
260C4×C11#57512yes—
261C4×C11#57612yes—
262C2×#41—21no—
263C2×#41—21no—
264C22×D4D4×C1111yescharacteristic
265C23×C4—21no—
266C2×SD16—22no—
267C2×D8—22no—
268C2×D8—22no—
269C2×D8—22no—
270C2×M16—22no—
271C2×M16—22no—
272C4⋊Q8C23×C1111yescharacteristic
273C4⋊Q8C23×C1111yescharacteristic
274#127C23×C1111yescharacteristic
275#127C23×C1111yescharacteristic
276#124—21no—
277#124—21no—
278#121—21no—
279#121—21no—
280#121—21no—
281#121—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4D4×C1112yes—
289C4×D4C23×C1112yes—
290C2×C4⋊C4D4×C1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C42C23×C1111yescharacteristic
293#107—22no—
294#106—22no—
295C4⋊C8D4×C1112yes—
296C4⋊C8C23×C1112yes—
297C4⋊C8C23×C1112yes—
298C4⋊C8C23×C1112yes—
299#103—22no—
300#102—22no—
301#102—22no—
302#102—22no—
303#102—22no—
304#102—22no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—22no—
309C22⋊C8—22no—
310C22⋊C8D4×C1112yes—
311#97—21no—
312C4×C8—21no—
313C4×C8—21no—
314C4×C8C23×C1111yescharacteristic
315C4×C8C23×C1111yescharacteristic
316C2×C11—41no—
317C2×C11—82no—
318C2×C11—161no—
319C2×C11—161no—
320C2×C11#304111yescharacteristic
321C2×C11#305411yescharacteristic
322C2×C11#306811yescharacteristic
323C24—21no—
324#41—82no—
325#41—82no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4C2×D4×C1112yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—82no—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1111yescharacteristic
347C22×C4C11×#4111yescharacteristic
348SD16—82no—
349D8—44no—
350D8—44no—
351D8—82no—
352M16—82no—
353M16—82no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8C2×D4×C1112yes—
358C2×C8C2×D4×C1112yes—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4C2×D4×C1112yes—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C42C2×D4×C1111yescharacteristic
372C42C2×D4×C1111yescharacteristic
373C42C11×#4111yescharacteristic
374C42C24×C1111yescharacteristic
375C11#1942511yescharacteristic, direct product factor, Sylow
376C23—22no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—81no—
382C23C11×#12111yescharacteristic
383Q8—42no—
384Q8—81no—
385D4—22no—
386D4—22no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—81no—
393D4—81no—
394D4—82no—
395D4—82no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—81no—
408C2×C4C11×#12111yescharacteristic
409C2×C4C11×#12111yescharacteristic
410C2×C4C11×#12111yescharacteristic
411C2×C4C22×D4×C1111yescharacteristic
412C2×C4C22×D4×C1111yescharacteristic
413C2×C4C2×C11×#4111yescharacteristic
414C8—22no—
415C8—22no—
416C8—42no—
417C8—42no—
418C8—42no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—84no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C2×C11×#12111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—81no—
439C4—81no—
440C4C11×#57512yes—
441C4C11×#57612yes—
442C2—41no—
443C2—82no—
444C2—161no—
445C2—161no—
446C2C11×#304111yescharacteristic
447C2C11×#305411yescharacteristic
448C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
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×#3207C2semidirect
2. C11×#3109C2semidirect
3. C11×#3100C2semidirect
4. C11×#2975C2semidirect
5. C11×#1703C2semidirect
6. C11×#1697C2semidirect
7. C11×#1687C2semidirect
8. C11×#1685C2semidirect
9. C11×#1572C2semidirect
10. C11×#1553C2semidirect
11. C11×#1543C2semidirect
15. C11×#493C22semidirect
16. C11×#492C22semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
39. C11×#335C22semidirect
40. C11×#334C22semidirect
41. C11×#333C22semidirect
42. C11×#332C22semidirect
43. C11×#331C22semidirect
44. C11×#331C22semidirect
99. #19425C11direct (N × H)
152. #3207C2×C11semidirect
153. #3109C2×C11semidirect
154. #3100C2×C11semidirect
155. #2975C2×C11semidirect
156. #1703C2×C11semidirect
157. #1697C2×C11semidirect
158. #1687C2×C11semidirect
159. #1685C2×C11semidirect
160. #1572C2×C11semidirect
161. #1553C2×C11semidirect
162. #1543C2×C11semidirect
209. #493C22×C11semidirect
210. #492C22×C11semidirect
211. #487C22×C11semidirect
212. #486C22×C11semidirect
233. #335C22×C11semidirect
234. #334C22×C11semidirect
235. #333C22×C11semidirect
236. #332C22×C11semidirect
237. #331C22×C11semidirect
238. #331C22×C11semidirect
375. C11#19425direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32072
C11×#31092
C11×#31002
C11×#29752
C11×#17032
C11×#16972
C11×#16872
C11×#16852
C11×#15722
C11×#15532
C11×#15432
#1942511