Finite Group Databasebeta

← C11×#24080 #14601273

Subgroups — C11×#24080 #14601273

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C11×#2317C211yesmaximal, characteristic, complemented
4C11×#2060C212yesmaximal, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1860C214yesmaximal, complemented
8C11×#1822C211yesmaximal, characteristic, complemented
9C11×#556—22no—
10C11×#555—22no—
11C11×#553—22no—
12C11×#552—22no—
13C11×#544C2211yescharacteristic
14C11×#538—22no—
15C11×#537C2211yescharacteristic
16C11×#529—22no—
17C11×#525C2212yes—
18C11×#520C2212yes—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C11×#484—22no—
23C11×#483—22no—
24C11×#481—22no—
25C11×#480—22no—
26C11×#428C2214yes—
27C2×C11×#104C2214yes—
28C11×#417C2214yes—
29C11×#407C2212yes—
30C11×#389—22no—
31C11×#385—22no—
32C11×#384C2212yes—
33C11×#382C2212yes—
34C11×#343C2212yes—
35C11×#343C2212yes—
36C11×#339C2214yes—
37C2×C11×#41C2312yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C2×C11×M16C2314yes—
41C11×C4⋊Q8—22no—
42C11×#126—24no—
43C11×#126—24no—
44C11×#125—22no—
45C11×#125—22no—
46C11×#124—22no—
47C11×#124—24no—
48C11×#123—24no—
49C11×#123—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8D412yes—
53C11×C22⋊Q8D412yes—
54C11×#121—24no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#121D412yes—
58C11×#121D412yes—
59C11×#120—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C11×#117—24no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—24no—
72C11×#117C2312yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4D412yes—
84C2×C42×C11D412yes—
85C2×C42×C11C2312yes—
86C11×#107—24no—
87C11×#106—24no—
88C11×#104—28no—
89C11×#103—24no—
90C11×#102—24no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8—22no—
93C11×#95—24no—
94#24080C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11C2×D411yescharacteristic
96C11×#41—24no—
97C11×#41—24no—
98C2×Q8×C11—22no—
99C2×Q8×C11C2×D412yes—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11C2×D412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—42no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2411yescharacteristic
119C11×M16—24no—
120C11×M16—24no—
121C2×C8×C11—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—84no—
135C11×C4⋊C4C2×D412yes—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11—24no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11#4114yes—
152#3493C2×C1111yescharacteristic
153#3092C2×C1112yescomplemented
154#2317C2×C1111yescharacteristic, complemented
155#2060C2×C1112yescomplemented
156#2039C2×C1112yescomplemented
157#1897C2×C1112yescomplemented
158#1860C2×C1114yescomplemented
159#1822C2×C1111yescharacteristic, complemented
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—22no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12012yes—
166C23×C11C22×D411yescharacteristic
167Q8×C11—24no—
168Q8×C11—82no—
169D4×C11—24no—
170D4×C11—42no—
171D4×C11—42no—
172D4×C11—82no—
173D4×C11—82no—
174D4×C11—82no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—44no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—84no—
193C2×C4×C11—84no—
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11C22×D412yes—
197C2×C4×C11C2×#4112yes—
198C2×C4×C112−1+412yes—
199C8×C11—44no—
200#556—22no—
201#555—22no—
202#553—22no—
203#552—22no—
204#544C22×C1111yescharacteristic
205#538—22no—
206#537C22×C1111yescharacteristic
207#529—22no—
208#525C22×C1112yes—
209#520C22×C1112yes—
210C2×#117C22×C1111yescharacteristic
211C2×#117C22×C1111yescharacteristic
212C22×C4⋊C4C22×C1111yescharacteristic
213#484—22no—
214#483—22no—
215#481—22no—
216#480—22no—
217#428C22×C1114yes—
218C2×#104C22×C1114yes—
219#417C22×C1114yes—
220#407C22×C1112yes—
221#389—22no—
222#385—22no—
223#384C22×C1112yes—
224#382C22×C1112yes—
225#343C22×C1112yes—
226#343C22×C1112yes—
227#339C22×C1114yes—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11C2×#12011yescharacteristic
239C22×C11#52511yescharacteristic
240C22×C11#53611yescharacteristic
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—44no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—82no—
250C4×C11#54714yes—
251C2×#41C23×C1112yes—
252C23×C4—21no—
253C23×C4C23×C1111yescharacteristic
254C2×M16C23×C1114yes—
255C4⋊Q8—22no—
256#126—24no—
257#126—24no—
258#125—22no—
259#125—22no—
260#124—22no—
261#124—24no—
262#123—24no—
263#123—22no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C22⋊Q8D4×C1112yes—
267C22⋊Q8D4×C1112yes—
268#121—24no—
269#121—22no—
270#121—22no—
271#121D4×C1112yes—
272#121D4×C1112yes—
273#120—22no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×D4—22no—
277C4×D4—22no—
278C4×D4—24no—
279C4×D4—22no—
280C4×D4—22no—
281#117—24no—
282#117—22no—
283#117—22no—
284#117—22no—
285#117—24no—
286#117C23×C1112yes—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4C23×C1112yes—
294C2×C4⋊C4C23×C1111yescharacteristic
295C2×C4⋊C4C23×C1111yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4D4×C1112yes—
298C2×C42D4×C1112yes—
299C2×C42C23×C1112yes—
300#107—24no—
301#106—24no—
302#104—28no—
303#103—24no—
304#102—24no—
305C22⋊C8—22no—
306C22⋊C8—22no—
307#95—24no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—42no—
311C2×C11—82no—
312C2×C11#240611yescharacteristic
313C2×C11#302111yescharacteristic
314C2×C11#302211yescharacteristic
315C24C2×D4×C1111yescharacteristic
316#41—24no—
317#41—24no—
318C2×Q8—22no—
319C2×Q8C2×D4×C1112yes—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4C2×D4×C1112yes—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—42no—
332C22×C4—82no—
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C2×D4×C1112yes—
335C22×C4C2×D4×C1112yes—
336C22×C4C2×D4×C1112yes—
337C22×C4C2×D4×C1112yes—
338C22×C4C24×C1111yescharacteristic
339M16—24no—
340M16—24no—
341C2×C8—24no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—84no—
355C4⋊C4C2×D4×C1112yes—
356C4⋊C4C2×D4×C1112yes—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C42—24no—
367C42—22no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42C11×#4114yes—
372C11#2408011yescharacteristic, direct product factor, Sylow
373C23—21no—
374C23—21no—
375C23—22no—
376C23—41no—
377C23—41no—
378C23C11×#12012yes—
379C23C22×D4×C1111yescharacteristic
380Q8—24no—
381Q8—82no—
382D4—24no—
383D4—42no—
384D4—42no—
385D4—82no—
386D4—82no—
387D4—82no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—84no—
406C2×C4—84no—
407C2×C4C11×#12011yescharacteristic
408C2×C4C11×#12011yescharacteristic
409C2×C4C22×D4×C1112yes—
410C2×C4C2×C11×#4112yes—
411C2×C4C11×2−1+412yes—
412C8—44no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22C2×C11×#12011yescharacteristic
424C22C11×#52511yescharacteristic
425C22C11×#53611yescharacteristic
426C4—21no—
427C4—21no—
428C4—44no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—82no—
435C4C11×#54714yes—
436C2—21no—
437C2—21no—
438C2—42no—
439C2—82no—
440C2C11×#240611yescharacteristic
441C2C11×#302111yescharacteristic
442C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3493C2
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. C11×#2317C2semidirect
4. C11×#2060C2semidirect
5. C11×#2039C2semidirect
6. C11×#1897C2semidirect
7. C11×#1860C2semidirect
8. C11×#1822C2semidirect
94. #24080C11direct (N × H)
153. #3092C2×C11semidirect
154. #2317C2×C11semidirect
155. #2060C2×C11semidirect
156. #2039C2×C11semidirect
157. #1897C2×C11semidirect
158. #1860C2×C11semidirect
159. #1822C2×C11semidirect
372. C11#24080direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#30922
C11×#23172
C11×#20602
C11×#20392
C11×#18972
C11×#18602
C11×#18222
#2408011