Finite Group Databasebeta

← C11×#19424 #14596617

Subgroups — C11×#19424 #14596617

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3210C211yesmaximal, characteristic, complemented
2C11×#3110C211yesmaximal, characteristic, complemented
3C11×#3100C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic, complemented
5C11×#1701C212yesmaximal, complemented
6C11×#1699C212yesmaximal, complemented
7C11×#1689C212yesmaximal, complemented
8C11×#1685C212yesmaximal, complemented
9C11×#1572C211yesmaximal, characteristic, complemented
10C11×#1553C211yesmaximal, characteristic, complemented
11C11×#1544C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C11×#494C2211yescharacteristic, complemented
16C11×#492C2211yescharacteristic, complemented
17C11×#487C2211yescharacteristic, complemented
18C11×#486C2211yescharacteristic, complemented
19C11×#484—21no—
20C11×#480—21no—
21C11×#474C2212yes—
22C11×#474C2212yes—
23C11×#464—22no—
24C11×#461C2212yes—
25C11×#459C2212yes—
26C11×#452—22no—
27C11×#450—21no—
28C11×#447—21no—
29C11×#440—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×#332C2212yescomplemented
42C11×#332C2212yescomplemented
43C11×#332C2212yescomplemented
44C11×#331C2212yescomplemented
45C2×C11×#41—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C2×C11×Q16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×D8—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#125—21no—
59C11×#124—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×#121—21no—
63C11×#121—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11D412yes—
71C4×D4×C11C2312yes—
72C11×#117—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C11×#107—22no—
77C11×#107—22no—
78C11×C4⋊C8D412yes—
79C11×C4⋊C8C2312yes—
80C11×C4⋊C8C2312yes—
81C11×C4⋊C8C2312yes—
82C11×#103—22no—
83C11×#103—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#19424C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C11×#41—82no—
102C2×Q8×C11—21no—
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—42no—
110C2×D4×C11—41no—
111C2×D4×C11C2×D412yes—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—41no—
116C22×C4×C11—82no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C11×Q16—82no—
121C11×SD16—44no—
122C11×SD16—82no—
123C11×D8—44no—
124C11×M16—82no—
125C11×M16—82no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C2×D412yes—
130C2×C8×C11C2×D412yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4C2×D412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151#3210C2×C1111yescharacteristic, complemented
152#3110C2×C1111yescharacteristic, complemented
153#3100C2×C1111yescharacteristic
154#2975C2×C1111yescharacteristic, complemented
155#1701C2×C1112yescomplemented
156#1699C2×C1112yescomplemented
157#1689C2×C1112yescomplemented
158#1685C2×C1112yescomplemented
159#1572C2×C1111yescharacteristic, complemented
160#1553C2×C1111yescharacteristic, complemented
161#1544C2×C1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11#12111yescharacteristic
168Q8×C11—42no—
169Q8×C11—42no—
170Q8×C11—42no—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—81no—
177D4×C11—82no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—82no—
188C2×C4×C11—82no—
189C2×C4×C11—81no—
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C8×C11—22no—
197C8×C11—22no—
198C8×C11—42no—
199C8×C11—42no—
200C8×C11—42no—
201#533C22×C1111yescharacteristic
202#532C22×C1111yescharacteristic
203C2×C4×D4C22×C1111yescharacteristic
204#494C22×C1111yescharacteristic, complemented
205#492C22×C1111yescharacteristic, complemented
206#487C22×C1111yescharacteristic, complemented
207#486C22×C1111yescharacteristic, complemented
208#484—21no—
209#480—21no—
210#474C22×C1112yes—
211#474C22×C1112yes—
212#464—22no—
213#461C22×C1112yes—
214#459C22×C1112yes—
215#452—22no—
216#450—21no—
217#447—21no—
218#440—22no—
219C4×D8—22no—
220#436—22no—
221#436C22×C1112yes—
222#436C22×C1112yes—
223#432C22×C1111yescharacteristic
224#431C22×C1111yescharacteristic
225#431C22×C1111yescharacteristic
226#431C22×C1111yescharacteristic
227#407—22no—
228#335C22×C1112yescomplemented
229#334C22×C1112yescomplemented
230#332C22×C1112yescomplemented
231#332C22×C1112yescomplemented
232#332C22×C1112yescomplemented
233#331C22×C1112yescomplemented
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—84no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11C2×#12111yescharacteristic
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—42no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11#57512yes—
254C4×C11#57612yes—
255C2×#41—21no—
256C22×D4D4×C1111yescharacteristic
257C23×C4—21no—
258C2×Q16—22no—
259C2×SD16—22no—
260C2×SD16—22no—
261C2×D8—22no—
262C2×M16—22no—
263C2×M16—22no—
264C4⋊Q8C23×C1111yescharacteristic
265C4⋊Q8C23×C1111yescharacteristic
266C4⋊Q8C23×C1111yescharacteristic
267#127C23×C1111yescharacteristic
268#125—21no—
269#124—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—21no—
273#121—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D4×C1112yes—
281C4×D4C23×C1112yes—
282#117—21no—
283C2×C4⋊C4D4×C1111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C42C23×C1111yescharacteristic
286#107—22no—
287#107—22no—
288C4⋊C8D4×C1112yes—
289C4⋊C8C23×C1112yes—
290C4⋊C8C23×C1112yes—
291C4⋊C8C23×C1112yes—
292#103—22no—
293#103—22no—
294#102—22no—
295#102—22no—
296#102—22no—
297#102—22no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—22no—
302C22⋊C8—22no—
303C22⋊C8D4×C1112yes—
304#97—21no—
305C4×C8—21no—
306C4×C8—21no—
307C4×C8C23×C1111yescharacteristic
308C4×C8C23×C1111yescharacteristic
309C2×C11—41no—
310C2×C11—82no—
311C2×C11—161no—
312C2×C11#304111yescharacteristic
313C2×C11#305411yescharacteristic
314C2×C11#306911yescharacteristic
315C24—21no—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—42no—
325C2×D4—41no—
326C2×D4C2×D4×C1112yes—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—82no—
332C22×C4C2×D4×C1111yescharacteristic
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C11×#4111yescharacteristic
335Q16—82no—
336SD16—44no—
337SD16—82no—
338D8—44no—
339M16—82no—
340M16—82no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8C2×D4×C1112yes—
345C2×C8C2×D4×C1112yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4C2×D4×C1112yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—41no—
362C42C2×D4×C1111yescharacteristic
363C42C2×D4×C1111yescharacteristic
364C42C11×#4111yescharacteristic
365C42C24×C1111yescharacteristic
366C11#1942411yescharacteristic, direct product factor, Sylow
367C23—22no—
368C23—42no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C11×#12111yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—42no—
376D4—22no—
377D4—22no—
378D4—42no—
379D4—42no—
380D4—42no—
381D4—81no—
382D4—82no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4C11×#12111yescharacteristic
396C2×C4C11×#12111yescharacteristic
397C2×C4C11×#12111yescharacteristic
398C2×C4C22×D4×C1111yescharacteristic
399C2×C4C22×D4×C1111yescharacteristic
400C2×C4C2×C11×#4111yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—42no—
405C8—42no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C2×C11×#12111yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4C11×#57512yes—
426C4C11×#57612yes—
427C2—41no—
428C2—82no—
429C2—161no—
430C2C11×#304111yescharacteristic
431C2C11×#305411yescharacteristic
432C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3100C2
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×#3210C2semidirect
2. C11×#3110C2semidirect
4. C11×#2975C2semidirect
5. C11×#1701C2semidirect
6. C11×#1699C2semidirect
7. C11×#1689C2semidirect
8. C11×#1685C2semidirect
9. C11×#1572C2semidirect
10. C11×#1553C2semidirect
11. C11×#1544C2semidirect
15. C11×#494C22semidirect
16. C11×#492C22semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
39. C11×#335C22semidirect
40. C11×#334C22semidirect
41. C11×#332C22semidirect
42. C11×#332C22semidirect
43. C11×#332C22semidirect
44. C11×#331C22semidirect
99. #19424C11direct (N × H)
151. #3210C2×C11semidirect
152. #3110C2×C11semidirect
154. #2975C2×C11semidirect
155. #1701C2×C11semidirect
156. #1699C2×C11semidirect
157. #1689C2×C11semidirect
158. #1685C2×C11semidirect
159. #1572C2×C11semidirect
160. #1553C2×C11semidirect
161. #1544C2×C11semidirect
204. #494C22×C11semidirect
205. #492C22×C11semidirect
206. #487C22×C11semidirect
207. #486C22×C11semidirect
228. #335C22×C11semidirect
229. #334C22×C11semidirect
230. #332C22×C11semidirect
231. #332C22×C11semidirect
232. #332C22×C11semidirect
233. #331C22×C11semidirect
366. C11#19424direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32102
C11×#31102
C11×#31002
C11×#29752
C11×#17012
C11×#16992
C11×#16892
C11×#16852
C11×#15722
C11×#15532
C11×#15442
#1942411