Finite Group Databasebeta

← C11×#24077 #14601270

Subgroups — C11×#24077 #14601270

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C2×C11×#382C211yesmaximal, characteristic, complemented
4C11×#2061C212yesmaximal, complemented
5C11×#2040C212yesmaximal, complemented
6C11×#1896C212yesmaximal, complemented
7C11×#1860C214yesmaximal, complemented
8C11×#1821C211yesmaximal, characteristic, complemented
9C11×#554—22no—
10C11×#553—22no—
11C11×#552—22no—
12C11×#547—22no—
13C11×#544C2211yescharacteristic
14C11×#539—22no—
15C11×#537C2211yescharacteristic
16C11×#525—22no—
17C11×#525C2212yes—
18C11×#520C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C11×#484—22no—
23C11×#483—22no—
24C11×#481—22no—
25C11×#480—22no—
26C11×#428C2214yes—
27C2×C11×#104C2214yes—
28C11×#417C2214yes—
29C11×#407C2212yes—
30C11×#382—22no—
31C11×#382C2212yes—
32C11×#382C2212yes—
33C2×C11×#95—22no—
34C11×#343C2212yes—
35C11×#343C2212yes—
36C11×#339C2214yes—
37C2×C11×#41—22no—
38C2×C11×#41C2312yes—
39C23×C4×C11—21no—
40C23×C4×C11—21no—
41C23×C4×C11D412yes—
42C23×C4×C11C2311yescharacteristic
43C2×C11×M16C2314yes—
44C11×C4⋊Q8—22no—
45C11×#126—24no—
46C11×#125—24no—
47C11×#125—22no—
48C11×#123—24no—
49C11×#123—24no—
50C11×#123—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8D412yes—
56C11×C22⋊Q8D412yes—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121D412yes—
61C11×#121D412yes—
62C11×#120—22no—
63C4×Q8×C11—22no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—24no—
84C2×C42×C11C2312yes—
85C11×#107—24no—
86C11×#106—24no—
87C11×#104—28no—
88C11×#103—24no—
89C11×#102—24no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8—22no—
92C11×#95—24no—
93C11×#95—24no—
94#24077C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11C2×D411yescharacteristic
96C11×#41—24no—
97C11×#41—24no—
98C11×#41—84no—
99C2×Q8×C11—22no—
100C2×Q8×C11C2×D412yes—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11C2×D412yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—44no—
118C22×C4×C11—44no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C11×M16—24no—
128C11×M16—24no—
129C2×C8×C11—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4C2×D412yes—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11—24no—
151C42×C11—24no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11#4114yescomplemented
155#3492C2×C1111yescharacteristic
156#3092C2×C1112yescomplemented
157C2×#382C2×C1111yescharacteristic, complemented
158#2061C2×C1112yescomplemented
159#2040C2×C1112yescomplemented
160#1896C2×C1112yescomplemented
161#1860C2×C1114yescomplemented
162#1821C2×C1111yescharacteristic, complemented
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11#12011yescharacteristic
169C23×C11#12011yescharacteristic
170C23×C11C22×D411yescharacteristic
171Q8×C11—24no—
172Q8×C11—82no—
173D4×C11—24no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—44no—
177D4×C11—44no—
178D4×C11—82no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—48no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—82no—
199C2×C4×C11—84no—
200C2×C4×C11—82no—
201C2×C4×C11—82no—
202C2×C4×C11#12012yes—
203C2×C4×C11C22×D412yes—
204C2×C4×C11C2×#4112yes—
205C2×C4×C112−1+412yes—
206C8×C11—44no—
207#554—22no—
208#553—22no—
209#552—22no—
210#547—22no—
211#544C22×C1111yescharacteristic
212#539—22no—
213#537C22×C1111yescharacteristic
214#525—22no—
215#525C22×C1112yes—
216#520C22×C1112yes—
217C22×C4⋊C4C22×C1111yescharacteristic
218C22×C4⋊C4C22×C1111yescharacteristic
219C22×C42C22×C1111yescharacteristic
220#484—22no—
221#483—22no—
222#481—22no—
223#480—22no—
224#428C22×C1114yes—
225C2×#104C22×C1114yes—
226#417C22×C1114yes—
227#407C22×C1112yes—
228#382—22no—
229#382C22×C1112yes—
230#382C22×C1112yes—
231C2×#95—22no—
232#343C22×C1112yes—
233#343C22×C1112yes—
234#339C22×C1114yes—
235C22×C11—24no—
236C22×C11—24no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11#45412yes—
247C22×C11#45512yes—
248C22×C11C2×#12011yescharacteristic
249C22×C11#52511yescharacteristic
250C22×C11#53611yescharacteristic
251C4×C11—22no—
252C4×C11—44no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—82no—
259C4×C11#54714yes—
260C2×#41—22no—
261C2×#41C23×C1112yes—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4D4×C1112yes—
265C23×C4C23×C1111yescharacteristic
266C2×M16C23×C1114yes—
267C4⋊Q8—22no—
268#126—24no—
269#125—24no—
270#125—22no—
271#123—24no—
272#123—24no—
273#123—22no—
274C22⋊Q8—22no—
275C22⋊Q8—24no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8D4×C1112yes—
279C22⋊Q8D4×C1112yes—
280#121—22no—
281#121—22no—
282#121—22no—
283#121D4×C1112yes—
284#121D4×C1112yes—
285#120—22no—
286C4×Q8—22no—
287C4×D4—24no—
288C4×D4—22no—
289C4×D4—24no—
290C4×D4—22no—
291C4×D4—22no—
292#117—22no—
293#117—22no—
294#117C23×C1112yes—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C1112yes—
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C42—21no—
306C2×C42—24no—
307C2×C42C23×C1112yes—
308#107—24no—
309#106—24no—
310#104—28no—
311#103—24no—
312#102—24no—
313C22⋊C8—22no—
314C22⋊C8—22no—
315#95—24no—
316#95—24no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11—22no—
320C2×C11—22no—
321C2×C11—82no—
322C2×C11#240611yescharacteristic
323C2×C11C2×#45511yescharacteristic
324C2×C11C2×#45411yescharacteristic
325C24C2×D4×C1111yescharacteristic
326#41—24no—
327#41—24no—
328#41—84no—
329C2×Q8—22no—
330C2×Q8C2×D4×C1112yes—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4C2×D4×C1112yes—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C2×D4×C1112yes—
356C22×C4C24×C1111yescharacteristic
357M16—24no—
358M16—24no—
359C2×C8—24no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—24no—
370C4⋊C4—42no—
371C4⋊C4C2×D4×C1112yes—
372C4⋊C4C2×D4×C1112yes—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C42—24no—
381C42—24no—
382C42—22no—
383C42—22no—
384C42C11×#4114yescomplemented
385C11#2407711yescharacteristic, direct product factor, Sylow
386C23—21no—
387C23—21no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23C11×#12011yescharacteristic
392C23C11×#12011yescharacteristic
393C23C22×D4×C1111yescharacteristic
394Q8—24no—
395Q8—82no—
396D4—24no—
397D4—42no—
398D4—42no—
399D4—44no—
400D4—44no—
401D4—82no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—48no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—82no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4C11×#12012yes—
426C2×C4C22×D4×C1112yes—
427C2×C4C2×C11×#4112yes—
428C2×C4C11×2−1+412yes—
429C8—44no—
430C22—24no—
431C22—24no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22C11×#45412yes—
442C22C11×#45512yes—
443C22C2×C11×#12011yescharacteristic
444C22C11×#52511yescharacteristic
445C22C11×#53611yescharacteristic
446C4—22no—
447C4—44no—
448C4—42no—
449C4—42no—
450C4—42no—
451C4—42no—
452C4—42no—
453C4—82no—
454C4C11×#54714yes—
455C2—21no—
456C2—21no—
457C2—22no—
458C2—22no—
459C2—82no—
460C2C11×#240611yescharacteristic
461C2C2×C11×#45511yescharacteristic
462C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3492C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C2×C11×#382C2semidirect
4. C11×#2061C2semidirect
5. C11×#2040C2semidirect
6. C11×#1896C2semidirect
7. C11×#1860C2semidirect
8. C11×#1821C2semidirect
94. #24077C11direct (N × H)
154. C42×C11#41semidirect
156. #3092C2×C11semidirect
157. C2×#382C2×C11semidirect
158. #2061C2×C11semidirect
159. #2040C2×C11semidirect
160. #1896C2×C11semidirect
161. #1860C2×C11semidirect
162. #1821C2×C11semidirect
384. C42C11×#41semidirect
385. C11#24077direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#30922
C2×C11×#3822
C11×#20612
C11×#20402
C11×#18962
C11×#18602
C11×#18212
#2407711