Finite Group Databasebeta

← C11×#22029 #14599222

Subgroups — C11×#22029 #14599222

Order 2816.

1062 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D4×C11C211yesmaximal, characteristic, complemented
2C2×C11×#408C211yesmaximal, characteristic, complemented
3C11×#2388C211yesmaximal, characteristic
4C11×#1954C212yesmaximal, complemented
5C11×#1923C212yesmaximal, complemented
6C11×#1923C212yesmaximal, complemented
7C11×#1870C211yesmaximal, characteristic, complemented
8C11×#1869C212yesmaximal, complemented
9C11×#1851C211yesmaximal, characteristic, complemented
10C11×#1780C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C8×D4×C11—24no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C11×#408—24no—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C2×C4×C8×C11C2212yes—
32C11×#395C411yescharacteristic
33C11×#394C412yes—
34C11×#394C411yescharacteristic
35C11×#393C411yescharacteristic
36C11×#392C411yescharacteristic
37C11×#392C412yes—
38C4×C11×C22⋊C4C2212yes—
39C4×C11×C22⋊C4C2211yescharacteristic
40C11×#336C2212yes—
41C11×#336C2212yes—
42C11×#336C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—42no—
46C2×C11×#41—42no—
47C22×Q8×C11C2×C411yescharacteristic
48C22×D4×C11C2×C411yescharacteristic
49C22×D4×C11C2×C412yes—
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C411yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×C11×M16—22no—
56C2×C11×M16—42no—
57C22×C8×C11—22no—
58C22×C8×C11—42no—
59C22×C8×C11—42no—
60C22×C8×C11D414yescomplemented
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2312yes—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—42no—
70C4×D4×C11—42no—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C412yes—
73C2×C11×C22⋊C4C2×C412yes—
74C2×C11×C22⋊C4C2×C412yes—
75C2×C11×C22⋊C4C2×C412yes—
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C412yes—
79C2×C11×C22⋊C4C2×C412yes—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2312yes—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C11×C22⋊C8—22no—
85C11×C22⋊C8—22no—
86C11×C22⋊C8—24no—
87C11×C22⋊C8—24no—
88C11×C22⋊C8—22no—
89C11×C22⋊C8—42no—
90C11×C22⋊C8—42no—
91C11×C22⋊C8—42no—
92C4×C8×C11—22no—
93C4×C8×C11—42no—
94C11×#95C2×C412yes—
95C11×#95C2×C411yescharacteristic
96C11×#95C2×C412yes—
97C11×#95C2×C411yescharacteristic
98#22029C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C22×C412yes—
100C24×C11C22×C411yescharacteristic
101C24×C11C22×C411yescharacteristic
102C11×#41—44no—
103C11×#41—44no—
104C11×#41—48no—
105C2×Q8×C11—22no—
106C2×Q8×C11—42no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—24no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C11×M16—44no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—44no—
154C2×C8×C11—44no—
155C2×C8×C11C2×D412yes—
156C2×C8×C11C2×D412yes—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—42no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—22no—
169C42×C11—22no—
170C2×C8×D4C2×C1111yescharacteristic, complemented
171C2×#408C2×C1111yescharacteristic, complemented
172#2388C2×C1111yescharacteristic
173#1954C2×C1112yescomplemented
174#1923C2×C1112yescomplemented
175#1923C2×C1112yescomplemented
176#1870C2×C1111yescharacteristic, complemented
177#1869C2×C1112yescomplemented
178#1851C2×C1111yescharacteristic, complemented
179#1780C2×C1111yescharacteristic, complemented
180C8×C22⋊C4C2×C1111yescharacteristic, complemented
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11C4×D412yes—
197C23×C11#13112yes—
198C23×C11C23×C411yescharacteristic
199Q8×C11—44no—
200D4×C11—28no—
201D4×C11—48no—
202D4×C11—44no—
203D4×C11—48no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11C4×D412yes—
230C2×C4×C11#13112yes—
231C2×C4×C11#13114yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)12yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C8×C11—22no—
237C8×C11—22no—
238C8×C11—41no—
239C8×C11—41no—
240C8×C11—42no—
241C8×C11—42no—
242C22×#41C22×C1111yescharacteristic
243C22×M16C22×C1111yescharacteristic
244C23×C8C22×C1111yescharacteristic
245C23×C8C22×C1111yescharacteristic
246C2×C4×D4C22×C1111yescharacteristic
247C2×C4×D4C22×C1112yes—
248C8×D4—24no—
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×C4⋊C8C22×C1112yes—
251#408—24no—
252C2×C22⋊C8C22×C1111yescharacteristic
253C2×C22⋊C8C22×C1112yes—
254C2×C22⋊C8C22×C1112yes—
255C2×C22⋊C8C22×C1111yescharacteristic
256C2×C22⋊C8C22×C1111yescharacteristic
257C2×C22⋊C8C22×C1112yes—
258C2×C22⋊C8C22×C1112yes—
259C2×C22⋊C8C22×C1112yes—
260C2×C4×C8C22×C1111yescharacteristic
261C2×C4×C8C22×C1112yes—
262#395C4×C1111yescharacteristic
263#394C4×C1112yes—
264#394C4×C1111yescharacteristic
265#393C4×C1111yescharacteristic
266#392C4×C1111yescharacteristic
267#392C4×C1112yes—
268C4×C22⋊C4C22×C1111yescharacteristic
269C4×C22⋊C4C22×C1112yes—
270#336C22×C1112yes—
271#336C22×C1112yes—
272#336C22×C1112yes—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—24no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11C2×C4×D411yescharacteristic
291C22×C11#51812yes—
292C22×C11C2×#13111yescharacteristic
293C22×C11C2×#13111yescharacteristic
294C22×C11C2×#13112yes—
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—24no—
298C4×C11—41no—
299C4×C11—42no—
300C4×C11—41no—
301C4×C11—42no—
302C4×C11#53411yescharacteristic
303C4×C11#53511yescharacteristic
304C4×C11#53812yes—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—42no—
308C2×#41—42no—
309C22×Q8C2×C4×C1111yescharacteristic
310C22×D4C2×C4×C1111yescharacteristic
311C22×D4C2×C4×C1112yes—
312C22×D4C2×C4×C1112yes—
313C22×D4C2×C4×C1111yescharacteristic
314C23×C4C23×C1111yescharacteristic
315C23×C4C23×C1112yes—
316C23×C4C23×C1111yescharacteristic
317C2×M16—22no—
318C2×M16—42no—
319C22×C8—22no—
320C22×C8—42no—
321C22×C8—42no—
322C22×C8D4×C1114yescomplemented
323C22×C8C23×C1111yescharacteristic
324C22×C8C23×C1112yes—
325C22×C8C23×C1112yes—
326C22×C8C23×C1111yescharacteristic
327C22×C8C23×C1111yescharacteristic
328C22×C8C23×C1111yescharacteristic
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—42no—
332C4×D4—42no—
333C2×C4⋊C4C2×C4×C1111yescharacteristic
334C2×C4⋊C4C2×C4×C1112yes—
335C2×C22⋊C4C2×C4×C1111yescharacteristic
336C2×C22⋊C4C2×C4×C1111yescharacteristic
337C2×C22⋊C4C2×C4×C1112yes—
338C2×C22⋊C4C2×C4×C1112yes—
339C2×C22⋊C4C2×C4×C1112yes—
340C2×C22⋊C4C2×C4×C1112yes—
341C2×C22⋊C4C2×C4×C1112yes—
342C2×C42C23×C1111yescharacteristic
343C2×C42C23×C1112yes—
344C4⋊C8—22no—
345C4⋊C8—42no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348C22⋊C8—24no—
349C22⋊C8—24no—
350C22⋊C8—22no—
351C22⋊C8—42no—
352C22⋊C8—42no—
353C22⋊C8—42no—
354C4×C8—22no—
355C4×C8—42no—
356#95C2×C4×C1112yes—
357#95C2×C4×C1111yescharacteristic
358#95C2×C4×C1112yes—
359#95C2×C4×C1111yescharacteristic
360C2×C11—42no—
361C2×C11—42no—
362C2×C11—82no—
363C2×C11#232111yescharacteristic
364C2×C11#292911yescharacteristic
365C2×C11#293111yescharacteristic
366C2×C11#297712yes—
367C2×C11#297912yes—
368C24C22×C4×C1112yes—
369C24C22×C4×C1111yescharacteristic
370C24C22×C4×C1111yescharacteristic
371#41—44no—
372#41—44no—
373#41—48no—
374C2×Q8—22no—
375C2×Q8—42no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—24no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4C22×C4×C1111yescharacteristic
400C22×C4C22×C4×C1112yes—
401C22×C4C22×C4×C1112yes—
402C22×C4C22×C4×C1111yescharacteristic
403C22×C4C22×C4×C1111yescharacteristic
404C22×C4C22×C4×C1111yescharacteristic
405C22×C4C22×C4×C1112yes—
406C22×C4C2×D4×C1112yes—
407C22×C4C11×#4112yes—
408C22×C4C24×C1111yescharacteristic
409M16—44no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—21no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—44no—
423C2×C8—44no—
424C2×C8C2×D4×C1112yes—
425C2×C8C2×D4×C1112yes—
426C4⋊C4—22no—
427C4⋊C4—42no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C42—21no—
436C42—21no—
437C42—22no—
438C42—22no—
439C11#2202911yescharacteristic, direct product factor, Sylow
440C23—21no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23C4×D4×C1112yes—
456C23C11×#13112yes—
457C23C23×C4×C1111yescharacteristic
458Q8—44no—
459D4—28no—
460D4—48no—
461D4—44no—
462D4—48no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4C4×D4×C1112yes—
489C2×C4C11×#13112yes—
490C2×C4C11×#13114yes—
491C2×C4C22×D4×C1111yescharacteristic
492C2×C4C2×C11×#4111yescharacteristic
493C2×C4C11×H(5,𝔽2)12yes—
494C2×C4C11×H(5,𝔽2)12yes—
495C8—22no—
496C8—22no—
497C8—41no—
498C8—42no—
499C8—41no—
500C8—42no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—24no—
505C22—22no—
506C22—41no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—41no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22C2×C4×D4×C1111yescharacteristic
519C22C11×#51812yes—
520C22C2×C11×#13111yescharacteristic
521C22C2×C11×#13111yescharacteristic
522C22C2×C11×#13112yes—
523C4—22no—
524C4—24no—
525C4—22no—
526C4—41no—
527C4—42no—
528C4—42no—
529C4—41no—
530C4C11×#53411yescharacteristic
531C4C11×#53511yescharacteristic
532C4C11×#53812yes—
533C2—42no—
534C2—42no—
535C2—82no—
536C2C11×#232111yescharacteristic
537C2C11×#292911yescharacteristic
538C2C11×#293111yescharacteristic
539C2C11×#297712yes—
540C2C11×#297912yes—
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C8×D4×C11C2semidirect
2. C2×C11×#408C2semidirect
4. C11×#1954C2semidirect
5. C11×#1923C2semidirect
6. C11×#1923C2semidirect
7. C11×#1870C2semidirect
8. C11×#1869C2semidirect
9. C11×#1851C2semidirect
10. C11×#1780C2semidirect
11. C8×C11×C22⋊C4C2semidirect
60. C22×C8×C11D4semidirect
98. #22029C11direct (N × H)
170. C2×C8×D4C2×C11semidirect
171. C2×#408C2×C11semidirect
173. #1954C2×C11semidirect
174. #1923C2×C11semidirect
175. #1923C2×C11semidirect
176. #1870C2×C11semidirect
177. #1869C2×C11semidirect
178. #1851C2×C11semidirect
179. #1780C2×C11semidirect
180. C8×C22⋊C4C2×C11semidirect
322. C22×C8D4×C11semidirect
439. C11#22029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×D4×C112
C2×C11×#4082
C11×#23882
C11×#19542
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#17802
C8×C11×C22⋊C42
#2202911