Finite Group Databasebeta

← C11×#19431 #14596624

Subgroups — C11×#19431 #14596624

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3231C211yesmaximal, characteristic, complemented
2C11×#3110C211yesmaximal, characteristic
3C11×#3101C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic
5C11×#1703C212yesmaximal, complemented
6C11×#1699C212yesmaximal, complemented
7C11×#1693C212yesmaximal, complemented
8C11×#1691C212yesmaximal, complemented
9C11×#1572C211yesmaximal, characteristic, complemented
10C11×#1554C211yesmaximal, characteristic, complemented
11C11×#1544C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C11×#500C2211yescharacteristic, complemented
16C11×#498C2211yescharacteristic, complemented
17C11×#487C2211yescharacteristic, complemented
18C11×#487C2211yescharacteristic, complemented
19C11×#485—22no—
20C11×#484—21no—
21C11×#483—21no—
22C11×#479—22no—
23C11×#476C2212yes—
24C11×#474C2212yes—
25C11×#461C2212yes—
26C11×#461C2212yes—
27C11×#450—21no—
28C11×#450—21no—
29C11×#440—22no—
30C4×C11×SD16—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×#332C2212yescomplemented
44C11×#332C2212yescomplemented
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C11×C4⋊Q8C2311yescharacteristic
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×#125—21no—
56C11×#125—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11D412yes—
68C4×D4×C11C2312yes—
69C11×#117—21no—
70C11×#117—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C11×#107—22no—
75C11×#107—22no—
76C11×#106—22no—
77C11×#106—22no—
78C11×C4⋊C8D412yes—
79C11×C4⋊C8C2312yes—
80C11×C4⋊C8C2312yes—
81C11×C4⋊C8C2312yes—
82C11×#103—22no—
83C11×#103—22no—
84C11×#103—22no—
85C11×#103—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#19431C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—42no—
107C2×D4×C11C2×D412yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—82no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C11×SD16—44no—
116C11×SD16—44no—
117C11×M16—82no—
118C11×M16—82no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D412yes—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11—41no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148#3231C2×C1111yescharacteristic, complemented
149#3110C2×C1111yescharacteristic
150#3101C2×C1111yescharacteristic
151#2975C2×C1111yescharacteristic
152#1703C2×C1112yescomplemented
153#1699C2×C1112yescomplemented
154#1693C2×C1112yescomplemented
155#1691C2×C1112yescomplemented
156#1572C2×C1111yescharacteristic, complemented
157#1554C2×C1111yescharacteristic, complemented
158#1544C2×C1111yescharacteristic, complemented
159C23×C11—22no—
160C23×C11—42no—
161C23×C11—81no—
162C23×C11—81no—
163C23×C11#12111yescharacteristic
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—42no—
167Q8×C11—81no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—42no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—82no—
182C2×C4×C11—81no—
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C8×C11—22no—
190C8×C11—22no—
191C8×C11—42no—
192C8×C11—42no—
193C8×C11—42no—
194#533C22×C1111yescharacteristic
195#533C22×C1111yescharacteristic
196C2×C4×D4C22×C1111yescharacteristic
197#500C22×C1111yescharacteristic, complemented
198#498C22×C1111yescharacteristic, complemented
199#487C22×C1111yescharacteristic, complemented
200#487C22×C1111yescharacteristic, complemented
201#485—22no—
202#484—21no—
203#483—21no—
204#479—22no—
205#476C22×C1112yes—
206#474C22×C1112yes—
207#461C22×C1112yes—
208#461C22×C1112yes—
209#450—21no—
210#450—21no—
211#440—22no—
212C4×SD16—22no—
213#436—22no—
214#436C22×C1112yes—
215#436C22×C1112yes—
216#432C22×C1111yescharacteristic
217#431C22×C1111yescharacteristic
218#431C22×C1111yescharacteristic
219#431C22×C1111yescharacteristic
220#407—22no—
221#335C22×C1112yescomplemented
222#334C22×C1112yescomplemented
223#333C22×C1112yescomplemented
224#332C22×C1112yescomplemented
225#332C22×C1112yescomplemented
226#332C22×C1112yescomplemented
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—84no—
234C22×C11C2×#12111yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—42no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11#57512yes—
245C4×C11#57712yes—
246C22×D4D4×C1111yescharacteristic
247C23×C4—21no—
248C2×SD16—22no—
249C2×SD16—22no—
250C2×M16—22no—
251C2×M16—22no—
252C4⋊Q8C23×C1111yescharacteristic
253C4⋊Q8C23×C1111yescharacteristic
254C4⋊Q8C23×C1111yescharacteristic
255C4⋊Q8C23×C1111yescharacteristic
256#125—21no—
257#125—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4D4×C1112yes—
269C4×D4C23×C1112yes—
270#117—21no—
271#117—21no—
272C2×C4⋊C4D4×C1111yescharacteristic
273C2×C22⋊C4—21no—
274C2×C42C23×C1111yescharacteristic
275#107—22no—
276#107—22no—
277#106—22no—
278#106—22no—
279C4⋊C8D4×C1112yes—
280C4⋊C8C23×C1112yes—
281C4⋊C8C23×C1112yes—
282C4⋊C8C23×C1112yes—
283#103—22no—
284#103—22no—
285#103—22no—
286#103—22no—
287#102—22no—
288#102—22no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—22no—
293C22⋊C8—22no—
294C22⋊C8D4×C1112yes—
295#97—21no—
296C4×C8—21no—
297C4×C8—21no—
298C4×C8C23×C1111yescharacteristic
299C4×C8C23×C1111yescharacteristic
300C2×C11—41no—
301C2×C11—82no—
302C2×C11#304211yescharacteristic
303C2×C11#305411yescharacteristic
304C2×C11#306911yescharacteristic
305C24—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4C2×D4×C1112yes—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—82no—
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C11×#4111yescharacteristic
320SD16—44no—
321SD16—44no—
322M16—82no—
323M16—82no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8C2×D4×C1112yes—
328C2×C8C2×D4×C1112yes—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4C2×D4×C1112yes—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—41no—
348C42—41no—
349C42C2×D4×C1111yescharacteristic
350C42C2×D4×C1111yescharacteristic
351C42C11×#4111yescharacteristic
352C42C24×C1111yescharacteristic
353C11#1943111yescharacteristic, direct product factor, Sylow
354C23—22no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23C11×#12111yescharacteristic
359Q8—42no—
360Q8—42no—
361Q8—42no—
362Q8—81no—
363D4—22no—
364D4—22no—
365D4—42no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4C11×#12111yescharacteristic
379C2×C4C11×#12111yescharacteristic
380C2×C4C11×#12111yescharacteristic
381C2×C4C22×D4×C1111yescharacteristic
382C2×C4C22×D4×C1111yescharacteristic
383C2×C4C2×C11×#4111yescharacteristic
384C8—22no—
385C8—22no—
386C8—42no—
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—84no—
396C22C2×C11×#12111yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C4C11×#57512yes—
407C4C11×#57712yes—
408C2—41no—
409C2—82no—
410C2C11×#304211yescharacteristic
411C2C11×#305411yescharacteristic
412C2C11×#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×#3231C2semidirect
5. C11×#1703C2semidirect
6. C11×#1699C2semidirect
7. C11×#1693C2semidirect
8. C11×#1691C2semidirect
9. C11×#1572C2semidirect
10. C11×#1554C2semidirect
11. C11×#1544C2semidirect
15. C11×#500C22semidirect
16. C11×#498C22semidirect
17. C11×#487C22semidirect
18. C11×#487C22semidirect
39. C11×#335C22semidirect
40. C11×#334C22semidirect
41. C11×#333C22semidirect
42. C11×#332C22semidirect
43. C11×#332C22semidirect
44. C11×#332C22semidirect
99. #19431C11direct (N × H)
148. #3231C2×C11semidirect
152. #1703C2×C11semidirect
153. #1699C2×C11semidirect
154. #1693C2×C11semidirect
155. #1691C2×C11semidirect
156. #1572C2×C11semidirect
157. #1554C2×C11semidirect
158. #1544C2×C11semidirect
197. #500C22×C11semidirect
198. #498C22×C11semidirect
199. #487C22×C11semidirect
200. #487C22×C11semidirect
221. #335C22×C11semidirect
222. #334C22×C11semidirect
223. #333C22×C11semidirect
224. #332C22×C11semidirect
225. #332C22×C11semidirect
226. #332C22×C11semidirect
353. C11#19431direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32312
C11×#31102
C11×#31012
C11×#29752
C11×#17032
C11×#16992
C11×#16932
C11×#16912
C11×#15722
C11×#15542
C11×#15442
#1943111