Finite Group Databasebeta

← C11×#23516 #14600709

Subgroups — C11×#23516 #14600709

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3449C211yesmaximal, characteristic
2C2×C11×#410C212yesmaximal, complemented
3C11×#2317C211yesmaximal, characteristic, complemented
4C11×#2311C212yesmaximal, complemented
5C11×#2044C218yesmaximal, complemented
6C11×#1740C211yesmaximal, characteristic, complemented
7C22×C11×#41C2212yes—
8C11×#537—21no—
9C11×#537—21no—
10C11×#536—22no—
11C11×#535—22no—
12C11×#534C2214yes—
13C11×#532—22no—
14C11×#525—24no—
15C2×C11×#117C2212yes—
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#410—28no—
20C2×C11×#99C2218yes—
21C11×#391—22no—
22C11×#390—22no—
23C11×#389—22no—
24C11×#386C2218yes—
25C11×#385C2214yes—
26C11×#384—21no—
27C11×#382—21no—
28C11×#380—24no—
29C11×#342C2214yes—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—22no—
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—24no—
37C2×C11×#41—24no—
38C22×Q8×C11D412yes—
39C22×D4×C11D412yes—
40C22×D4×C11C2314yes—
41C23×C4×C11D414yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C11×C4⋊Q8—22no—
45C11×#127—22no—
46C11×#124—24no—
47C11×#123—28no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×#121—24no—
51C11×#121—24no—
52C11×#121—24no—
53C11×#121—24no—
54C11×#120—28no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117—24no—
61C11×#117—24no—
62C11×#117D414yescomplemented
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4—28no—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2312yes—
75C2×C11×C22⋊C4C2312yes—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11D412yes—
79C11×#99—216no—
80C11×#95—28no—
81C11×#95—24no—
82#23516C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11C2×D414yes—
84C24×C11C2411yescharacteristic
85C11×#41—44no—
86C11×#41—44no—
87C11×#41—44no—
88C11×#41—44no—
89C11×#41—44no—
90C11×#41—44no—
91C11×#41—44no—
92C11×#41—44no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—28no—
113C22×C4×C11—28no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—82no—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4114yes—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—84no—
138C11×C22⋊C4—28no—
139C11×C22⋊C4—28no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—88no—
145C11×C22⋊C4C2×D414yes—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—24no—
149C42×C11—44no—
150#3449C2×C1111yescharacteristic
151C2×#410C2×C1112yescomplemented
152#2317C2×C1111yescharacteristic, complemented
153#2311C2×C1112yescomplemented
154#2044C2×C1118yescomplemented
155#1740C2×C1111yescharacteristic, complemented
156C23×C11—24no—
157C23×C11—24no—
158C23×C11—24no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—44no—
162C23×C11—44no—
163C23×C11C22×D412yes—
164C23×C11C22×D411yescharacteristic
165C23×C11C22×D411yescharacteristic
166C23×C11C2×#4111yescharacteristic
167C23×C11C2×#4112yes—
168Q8×C11—44no—
169Q8×C11—44no—
170D4×C11—44no—
171D4×C11—44no—
172D4×C11—44no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—44no—
176D4×C11—84no—
177D4×C11—84no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—48no—
187C2×C4×C11—48no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—48no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11—42no—
195C2×C4×C11—44no—
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12012yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#12114yes—
201C2×C4×C11#12112yes—
202C2×C4×C11#12114yes—
203C2×C4×C11#12314yes—
204C2×C4×C11#12314yes—
205C2×C4×C11#12412yes—
206C2×C4×C11#12412yes—
207C22×#41C22×C1112yes—
208#537—21no—
209#537—21no—
210#536—22no—
211#535—22no—
212#534C22×C1114yes—
213#532—22no—
214#525—24no—
215C2×#117C22×C1112yes—
216C2×#117C22×C1111yescharacteristic
217C2×#117C22×C1111yescharacteristic
218C22×C4⋊C4C22×C1111yescharacteristic
219#410—28no—
220C2×#99C22×C1118yes—
221#391—22no—
222#390—22no—
223#389—22no—
224#386C22×C1118yes—
225#385C22×C1114yes—
226#384—21no—
227#382—21no—
228#380—24no—
229#342C22×C1114yes—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—42no—
237C22×C11—48no—
238C22×C11—44no—
239C22×C11—44no—
240C22×C11—44no—
241C22×C11—84no—
242C22×C11C2×#12011yescharacteristic
243C22×C11C2×#12111yescharacteristic
244C22×C11C2×#12112yes—
245C22×C11C2×#12312yes—
246C22×C11C2×#12411yescharacteristic
247C4×C11—44no—
248C4×C11—44no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—84no—
252C4×C11—82no—
253C4×C11#39412yes—
254C4×C11#39414yes—
255C4×C11#39412yes—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—24no—
261C2×#41—24no—
262C2×#41—24no—
263C2×#41—24no—
264C22×Q8D4×C1112yes—
265C22×D4D4×C1112yes—
266C22×D4C23×C1114yes—
267C23×C4D4×C1114yes—
268C23×C4C23×C1112yes—
269C23×C4C23×C1111yescharacteristic
270C4⋊Q8—22no—
271#127—22no—
272#124—24no—
273#123—28no—
274C22⋊Q8—24no—
275C22⋊Q8—24no—
276#121—24no—
277#121—24no—
278#121—24no—
279#121—24no—
280#120—28no—
281C4×D4—24no—
282C4×D4—24no—
283#117—22no—
284#117—22no—
285#117—22no—
286#117—24no—
287#117—24no—
288#117D4×C1114yescomplemented
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4D4×C1111yescharacteristic
297C2×C4⋊C4D4×C1111yescharacteristic
298C2×C22⋊C4—28no—
299C2×C22⋊C4C23×C1114yes—
300C2×C22⋊C4C23×C1112yes—
301C2×C22⋊C4C23×C1112yes—
302C2×C42—21no—
303C2×C42—22no—
304C2×C42D4×C1112yes—
305#99—216no—
306#95—28no—
307#95—24no—
308C2×C11—21no—
309C2×C11—22no—
310C2×C11—22no—
311C2×C11—21no—
312C2×C11—84no—
313C2×C11C2×#39411yescharacteristic
314C2×C11#302711yescharacteristic
315C2×C11#302811yescharacteristic
316C24C2×D4×C1114yes—
317C24C24×C1111yescharacteristic
318#41—44no—
319#41—44no—
320#41—44no—
321#41—44no—
322#41—44no—
323#41—44no—
324#41—44no—
325#41—44no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—24no—
329C2×Q8—24no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—24no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4—24no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—28no—
346C22×C4—28no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—82no—
351C22×C4C2×D4×C1114yes—
352C22×C4C2×D4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C2×D4×C1112yes—
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C2×D4×C1111yescharacteristic
358C22×C4C2×D4×C1112yes—
359C22×C4C11×#4112yes—
360C22×C4C11×#4114yes—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—42no—
369C4⋊C4—44no—
370C4⋊C4—84no—
371C22⋊C4—28no—
372C22⋊C4—28no—
373C22⋊C4—24no—
374C22⋊C4—22no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—88no—
378C22⋊C4C2×D4×C1114yes—
379C42—22no—
380C42—22no—
381C42—24no—
382C42—44no—
383C11#2351611yescharacteristic, direct product factor, Sylow
384C23—24no—
385C23—24no—
386C23—24no—
387C23—41no—
388C23—41no—
389C23—44no—
390C23—44no—
391C23C22×D4×C1112yes—
392C23C22×D4×C1111yescharacteristic
393C23C22×D4×C1111yescharacteristic
394C23C2×C11×#4111yescharacteristic
395C23C2×C11×#4112yes—
396Q8—44no—
397Q8—44no—
398D4—44no—
399D4—44no—
400D4—44no—
401D4—44no—
402D4—44no—
403D4—44no—
404D4—84no—
405D4—84no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—48no—
415C2×C4—48no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4C11×#12011yescharacteristic
425C2×C4C11×#12011yescharacteristic
426C2×C4C11×#12012yes—
427C2×C4C11×#12112yes—
428C2×C4C11×#12114yes—
429C2×C4C11×#12112yes—
430C2×C4C11×#12114yes—
431C2×C4C11×#12314yes—
432C2×C4C11×#12314yes—
433C2×C4C11×#12412yes—
434C2×C4C11×#12412yes—
435C22—21no—
436C22—22no—
437C22—21no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—42no—
442C22—48no—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—84no—
447C22C2×C11×#12011yescharacteristic
448C22C2×C11×#12111yescharacteristic
449C22C2×C11×#12112yes—
450C22C2×C11×#12312yes—
451C22C2×C11×#12411yescharacteristic
452C4—44no—
453C4—44no—
454C4—42no—
455C4—42no—
456C4—84no—
457C4—82no—
458C4C11×#39412yes—
459C4C11×#39414yes—
460C4C11×#39412yes—
461C2—21no—
462C2—22no—
463C2—22no—
464C2—21no—
465C2—84no—
466C2C2×C11×#39411yescharacteristic
467C2C11×#302711yescharacteristic
468C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC11×#3449C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#410C2semidirect
3. C11×#2317C2semidirect
4. C11×#2311C2semidirect
5. C11×#2044C2semidirect
6. C11×#1740C2semidirect
62. C11×#117D4semidirect
82. #23516C11direct (N × H)
151. C2×#410C2×C11semidirect
152. #2317C2×C11semidirect
153. #2311C2×C11semidirect
154. #2044C2×C11semidirect
155. #1740C2×C11semidirect
288. #117D4×C11semidirect
383. C11#23516direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34492
C2×C11×#4102
C11×#23172
C11×#23112
C11×#20442
C11×#17402
#2351611