Finite Group Databasebeta

← C11×#24019 #14601212

Subgroups — C11×#24019 #14601212

Order 2816.

1286 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3486C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C2×C11×#391C211yesmaximal, characteristic, complemented
4C11×#2038C214yesmaximal, complemented
5C11×#1896C212yesmaximal, complemented
6C11×#1857C212yesmaximal, complemented
7C11×#1793C212yesmaximal, complemented
8C11×#1784C211yesmaximal, characteristic, complemented
9C2×C11×2−1+4C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11D4×Q8×C11—22no—
12D4×Q8×C11—22no—
13C11×#548—22no—
14C11×#548—22no—
15C11×#536—22no—
16C11×#536C2212yes—
17C11×#525—22no—
18C11×#525C2212yes—
19C11×#519C2211yescharacteristic
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—
29C2×C11×#101C2212yes—
30C2×C11×#101C2212yes—
31C11×#407C2212yes—
32C11×#391—22no—
33C11×#391C2212yes—
34C11×#391C2212yes—
35C2×C11×#95—22no—
36C11×#339C2214yes—
37C11×2−1+4—24no—
38C11×2−1+4—42no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41C2312yes—
42C22×Q8×C11—22no—
43C22×Q8×C11—24no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11D412yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11D412yes—
53C23×C4×C11C2311yescharacteristic
54C2×C11×M16C2314yes—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×#124—24no—
58C11×#124—22no—
59C11×#123—24no—
60C11×#123—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D412yes—
68C11×C22⋊Q8D412yes—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121D412yes—
72C11×#121D412yes—
73C11×#120—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×D4×C11—24no—
77C4×D4×C11—24no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C11×#117—22no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2312yes—
86C2×C42×C11—21no—
87C2×C42×C11—42no—
88C2×C42×C11C2312yes—
89C11×#107—24no—
90C11×#106—24no—
91C11×#104—44no—
92C11×#103—24no—
93C11×#102—24no—
94C11×#101—24no—
95C11×#101—42no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8—22no—
98C11×#95—24no—
99C11×#95—24no—
100#24019C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11C2×D411yescharacteristic
102C11×#41—24no—
103C11×#41—24no—
104C11×#41—44no—
105C11×#41—48no—
106C11×#41—44no—
107C2×Q8×C11—22no—
108C2×Q8×C11—24no—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—42no—
116C2×Q8×C11—48no—
117C2×Q8×C11—48no—
118C2×Q8×C11—48no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11#4114yes—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—44no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C11×M16—24no—
149C11×M16—24no—
150C2×C8×C11—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C42×C11—24no—
169C42×C11—22no—
170C42×C11—24no—
171C42×C11—42no—
172#3486C2×C1111yescharacteristic
173#3092C2×C1112yescomplemented
174C2×#391C2×C1111yescharacteristic, complemented
175#2038C2×C1114yescomplemented
176#1896C2×C1112yescomplemented
177#1857C2×C1112yescomplemented
178#1793C2×C1112yescomplemented
179#1784C2×C1111yescharacteristic, complemented
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11#12011yescharacteristic
186C23×C11#12011yescharacteristic
187C23×C11C22×D411yescharacteristic
188Q8×C11—28no—
189Q8×C11—24no—
190Q8×C11—48no—
191Q8×C11—44no—
192Q8×C11—44no—
193D4×C11—24no—
194D4×C11—44no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—44no—
198D4×C11—44no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—48no—
215C2×C4×C11—48no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12314yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4112yes—
227C2×C4×C11H(5,𝔽2)12yes—
228C8×C11—44no—
229C2×2−1+4C22×C1111yescharacteristic
230C23×Q8C22×C1111yescharacteristic
231D4×Q8—22no—
232D4×Q8—22no—
233#548—22no—
234#548—22no—
235#536—22no—
236#536C22×C1112yes—
237#525—22no—
238#525C22×C1112yes—
239#519C22×C1111yescharacteristic
240C22×C4⋊C4C22×C1111yescharacteristic
241C22×C42C22×C1111yescharacteristic
242#484—22no—
243#483—22no—
244#481—22no—
245#480—22no—
246#428C22×C1114yes—
247C2×#104C22×C1114yes—
248#417C22×C1114yes—
249C2×#101C22×C1112yes—
250C2×#101C22×C1112yes—
251#407C22×C1112yes—
252#391—22no—
253#391C22×C1112yes—
254#391C22×C1112yes—
255C2×#95—22no—
256#339C22×C1114yes—
257C22×C11—24no—
258C22×C11—24no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11#45412yes—
269C22×C11#45612yes—
270C22×C11C2×#12011yescharacteristic
271C22×C11C2×#12311yescharacteristic
272C22×C11#53411yescharacteristic
273C4×C11—22no—
274C4×C11—24no—
275C4×C11—44no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—82no—
281C4×C11#54614yes—
2822−1+4—24no—
2832−1+4—42no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41C23×C1112yes—
287C22×Q8—22no—
288C22×Q8—24no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—42no—
292C22×Q8D4×C1112yes—
293C22×Q8C23×C1111yescharacteristic
294C22×Q8C23×C1111yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4D4×C1112yes—
298C23×C4C23×C1111yescharacteristic
299C2×M16C23×C1114yes—
300C4⋊Q8—24no—
301C4⋊Q8—22no—
302#124—24no—
303#124—22no—
304#123—24no—
305#123—22no—
306C22⋊Q8—22no—
307C22⋊Q8—22no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8D4×C1112yes—
313C22⋊Q8D4×C1112yes—
314#121—22no—
315#121—22no—
316#121D4×C1112yes—
317#121D4×C1112yes—
318#120—22no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—22no—
324C4×D4—22no—
325#117—22no—
326#117C23×C1112yes—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4C23×C1112yes—
331C2×C42—21no—
332C2×C42—42no—
333C2×C42C23×C1112yes—
334#107—24no—
335#106—24no—
336#104—44no—
337#103—24no—
338#102—24no—
339#101—24no—
340#101—42no—
341C22⋊C8—22no—
342C22⋊C8—22no—
343#95—24no—
344#95—24no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—22no—
348C2×C11—22no—
349C2×C11—82no—
350C2×C11#240511yescharacteristic
351C2×C11C2×#45411yescharacteristic
352C2×C11C2×#45611yescharacteristic
353C24C2×D4×C1111yescharacteristic
354#41—24no—
355#41—24no—
356#41—44no—
357#41—48no—
358#41—44no—
359C2×Q8—22no—
360C2×Q8—24no—
361C2×Q8—24no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—42no—
368C2×Q8—48no—
369C2×Q8—48no—
370C2×Q8—48no—
371C2×Q8C2×D4×C1112yes—
372C2×Q8C11×#4114yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4C2×D4×C1112yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—44no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4C2×D4×C1112yes—
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1112yes—
399C22×C4C24×C1111yescharacteristic
400M16—24no—
401M16—24no—
402C2×C8—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—24no—
410C4⋊C4—42no—
411C4⋊C4C2×D4×C1112yes—
412C4⋊C4C2×D4×C1112yes—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C42—24no—
421C42—22no—
422C42—24no—
423C42—42no—
424C11#2401911yescharacteristic, direct product factor, Sylow
425C23—21no—
426C23—21no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23C11×#12011yescharacteristic
431C23C11×#12011yescharacteristic
432C23C22×D4×C1111yescharacteristic
433Q8—28no—
434Q8—24no—
435Q8—48no—
436Q8—44no—
437Q8—44no—
438D4—24no—
439D4—44no—
440D4—42no—
441D4—42no—
442D4—44no—
443D4—44no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—48no—
460C2×C4—48no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4C11×#12012yes—
469C2×C4C11×#12314yes—
470C2×C4C22×D4×C1112yes—
471C2×C4C2×C11×#4112yes—
472C2×C4C11×H(5,𝔽2)12yes—
473C8—44no—
474C22—24no—
475C22—24no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22C11×#45412yes—
486C22C11×#45612yes—
487C22C2×C11×#12011yescharacteristic
488C22C2×C11×#12311yescharacteristic
489C22C11×#53411yescharacteristic
490C4—22no—
491C4—24no—
492C4—44no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4C11×#54614yes—
499C2—21no—
500C2—21no—
501C2—22no—
502C2—22no—
503C2—82no—
504C2C11×#240511yescharacteristic
505C2C2×C11×#45411yescharacteristic
506C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3486C2
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×#391C2semidirect
4. C11×#2038C2semidirect
5. C11×#1896C2semidirect
6. C11×#1857C2semidirect
7. C11×#1793C2semidirect
8. C11×#1784C2semidirect
100. #24019C11direct (N × H)
173. #3092C2×C11semidirect
174. C2×#391C2×C11semidirect
175. #2038C2×C11semidirect
176. #1896C2×C11semidirect
177. #1857C2×C11semidirect
178. #1793C2×C11semidirect
179. #1784C2×C11semidirect
424. C11#24019direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34862
C11×#30922
C2×C11×#3912
C11×#20382
C11×#18962
C11×#18572
C11×#17932
C11×#17842
#2401911