Finite Group Databasebeta

← C11×#24076 #14601269

Subgroups — C11×#24076 #14601269

Order 2816.

1174 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×#3492C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C2×C11×#384C211yesmaximal, characteristic, complemented
4C11×#2060C212yesmaximal, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#1896C212yesmaximal, complemented
7C11×#1859C214yesmaximal, 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⋊C4—22no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#484—22no—
24C11×#483—22no—
25C11×#481—22no—
26C11×#480—22no—
27C11×#428C2214yes—
28C2×C11×#104C2214yes—
29C11×#417C2214yes—
30C11×#407C2212yes—
31C11×#384—22no—
32C11×#384C2212yes—
33C11×#384C2212yes—
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—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—48no—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11—24no—
87C2×C42×C11C2312yes—
88C11×#107—24no—
89C11×#106—24no—
90C11×#104—28no—
91C11×#103—24no—
92C11×#102—24no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8—22no—
95#24076C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11C2×D411yescharacteristic
97C11×#41—24no—
98C11×#41—24no—
99C11×#41—84no—
100C2×Q8×C11—22no—
101C2×Q8×C11C2×D412yes—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11C2×D412yes—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C11×M16—24no—
129C11×M16—24no—
130C2×C8×C11—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—48no—
142C11×C4⋊C4—48no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4C2×D412yes—
145C11×C4⋊C4C2×D412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C42×C11—24no—
154C42×C11—24no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11#4114yescomplemented
158#3492C2×C1111yescharacteristic
159#3092C2×C1112yescomplemented
160C2×#384C2×C1111yescharacteristic, complemented
161#2060C2×C1112yescomplemented
162#2039C2×C1112yescomplemented
163#1896C2×C1112yescomplemented
164#1859C2×C1114yescomplemented
165#1821C2×C1111yescharacteristic, complemented
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11#12011yescharacteristic
172C23×C11#12011yescharacteristic
173C23×C11C22×D411yescharacteristic
174Q8×C11—24no—
175Q8×C11—82no—
176D4×C11—24no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—44no—
180D4×C11—44no—
181D4×C11—82no—
182C2×C4×C11—24no—
183C2×C4×C11—216no—
184C2×C4×C11—24no—
185C2×C4×C11—21no—
186C2×C4×C11—24no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11—84no—
203C2×C4×C11—82no—
204C2×C4×C11—82no—
205C2×C4×C11#12012yes—
206C2×C4×C11C22×D412yes—
207C2×C4×C11C2×#4112yes—
208C2×C4×C112−1+412yes—
209C8×C11—44no—
210#554—22no—
211#553—22no—
212#552—22no—
213#547—22no—
214#544C22×C1111yescharacteristic
215#539—22no—
216#537C22×C1111yescharacteristic
217#525—22no—
218#525C22×C1112yes—
219#520C22×C1112yes—
220C22×C4⋊C4—22no—
221C22×C4⋊C4C22×C1111yescharacteristic
222C22×C4⋊C4C22×C1111yescharacteristic
223C22×C42C22×C1111yescharacteristic
224#484—22no—
225#483—22no—
226#481—22no—
227#480—22no—
228#428C22×C1114yes—
229C2×#104C22×C1114yes—
230#417C22×C1114yes—
231#407C22×C1112yes—
232#384—22no—
233#384C22×C1112yes—
234#384C22×C1112yes—
235#343C22×C1112yes—
236#343C22×C1112yes—
237#339C22×C1114yes—
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11#45312yes—
250C22×C11#45612yes—
251C22×C11C2×#12011yescharacteristic
252C22×C11#52511yescharacteristic
253C22×C11#53611yescharacteristic
254C4×C11—28no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—82no—
262C4×C11#54714yes—
263C2×#41—22no—
264C2×#41C23×C1112yes—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4D4×C1112yes—
268C23×C4C23×C1111yescharacteristic
269C2×M16C23×C1114yes—
270C4⋊Q8—22no—
271#126—24no—
272#125—24no—
273#125—22no—
274#123—24no—
275#123—24no—
276#123—22no—
277C22⋊Q8—22no—
278C22⋊Q8—24no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8D4×C1112yes—
282C22⋊Q8D4×C1112yes—
283#121—22no—
284#121—22no—
285#121—22no—
286#121D4×C1112yes—
287#121D4×C1112yes—
288#120—22no—
289C4×Q8—22no—
290C4×D4—24no—
291C4×D4—22no—
292C4×D4—24no—
293C4×D4—22no—
294C4×D4—22no—
295#117—22no—
296#117—22no—
297#117C23×C1112yes—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4D4×C1112yes—
308C2×C4⋊C4C23×C1112yes—
309C2×C4⋊C4C23×C1111yescharacteristic
310C2×C4⋊C4C23×C1111yescharacteristic
311C2×C42—21no—
312C2×C42—24no—
313C2×C42C23×C1112yes—
314#107—24no—
315#106—24no—
316#104—28no—
317#103—24no—
318#102—24no—
319C22⋊C8—22no—
320C22⋊C8—22no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—22no—
324C2×C11—22no—
325C2×C11—82no—
326C2×C11#240611yescharacteristic
327C2×C11C2×#45311yescharacteristic
328C2×C11C2×#45611yescharacteristic
329C24C2×D4×C1111yescharacteristic
330#41—24no—
331#41—24no—
332#41—84no—
333C2×Q8—22no—
334C2×Q8C2×D4×C1112yes—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4C2×D4×C1112yes—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—44no—
352C22×C4—44no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1112yes—
357C22×C4C2×D4×C1112yes—
358C22×C4C2×D4×C1112yes—
359C22×C4C2×D4×C1112yes—
360C22×C4C24×C1111yescharacteristic
361M16—24no—
362M16—24no—
363C2×C8—24no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—48no—
375C4⋊C4—48no—
376C4⋊C4—42no—
377C4⋊C4C2×D4×C1112yes—
378C4⋊C4C2×D4×C1112yes—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C42—24no—
387C42—24no—
388C42—22no—
389C42—22no—
390C42C11×#4114yescomplemented
391C11#2407611yescharacteristic, direct product factor, Sylow
392C23—21no—
393C23—21no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23C11×#12011yescharacteristic
398C23C11×#12011yescharacteristic
399C23C22×D4×C1111yescharacteristic
400Q8—24no—
401Q8—82no—
402D4—24no—
403D4—42no—
404D4—42no—
405D4—44no—
406D4—44no—
407D4—82no—
408C2×C4—24no—
409C2×C4—216no—
410C2×C4—24no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—82no—
428C2×C4—84no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4C11×#12012yes—
432C2×C4C22×D4×C1112yes—
433C2×C4C2×C11×#4112yes—
434C2×C4C11×2−1+412yes—
435C8—44no—
436C22—24no—
437C22—24no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22C11×#45312yes—
448C22C11×#45612yes—
449C22C2×C11×#12011yescharacteristic
450C22C11×#52511yescharacteristic
451C22C11×#53611yescharacteristic
452C4—28no—
453C4—22no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4C11×#54714yes—
461C2—21no—
462C2—21no—
463C2—22no—
464C2—22no—
465C2—82no—
466C2C11×#240611yescharacteristic
467C2C2×C11×#45311yescharacteristic
468C2C2×C11×#45611yescharacteristic
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×#384C2semidirect
4. C11×#2060C2semidirect
5. C11×#2039C2semidirect
6. C11×#1896C2semidirect
7. C11×#1859C2semidirect
8. C11×#1821C2semidirect
95. #24076C11direct (N × H)
157. C42×C11#41semidirect
159. #3092C2×C11semidirect
160. C2×#384C2×C11semidirect
161. #2060C2×C11semidirect
162. #2039C2×C11semidirect
163. #1896C2×C11semidirect
164. #1859C2×C11semidirect
165. #1821C2×C11semidirect
390. C42C11×#41semidirect
391. C11#24076direct (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×#3842
C11×#20602
C11×#20392
C11×#18962
C11×#18592
C11×#18212
#2407611