Finite Group Databasebeta

← C11×#24327 #14601520

Subgroups — C11×#24327 #14601520

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic, complemented
5C11×#2059C212yesmaximal, complemented
6C11×#2025C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1984C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1864C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#554—24no—
14C11×#554—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4—21no—
25C11×#476—24no—
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#396—22no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#384C2211yescharacteristic
39C11×#380—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C2×C11×D8Q814yescomplemented
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yes—
60C11×#125—24no—
61C11×#125—24no—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—216no—
64C11×C22⋊Q8—44no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11D414yes—
73C2×C11×C4⋊C4—28no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C42×C11C2312yes—
92C2×C42×C11C2311yescharacteristic
93C11×#107—22no—
94C11×#106—24no—
95C11×C4⋊C8—22no—
96C11×#102—22no—
97C11×#102—24no—
98C11×#102—22no—
99C11×#102—24no—
100C4×C8×C11—22no—
101C11×#95—22no—
102#24327C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—81no—
110C2×Q8×C11—81no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C2×D4×C11C2×Q812yes—
121C2×D4×C11C2×Q812yes—
122C2×D4×C11#4112yes—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—28no—
126C22×C4×C11—24no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—82no—
135C22×C4×C11—82no—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C11×D8—28no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11C2×Q812yes—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—82no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176C2×#554C2×C1111yescharacteristic, complemented
177C2×#476C2×C1111yescharacteristic, complemented
178C2×C4×D8C2×C1111yescharacteristic
179#2538C2×C1111yescharacteristic, complemented
180#2059C2×C1112yescomplemented
181#2025C2×C1112yescomplemented
182#1990C2×C1111yescharacteristic, complemented
183#1984C2×C1111yescharacteristic, complemented
184#1879C2×C1112yes—
185#1864C2×C1112yescomplemented
186#1802C2×C1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11C22×D411yescharacteristic
202Q8×C11—44no—
203Q8×C11—84no—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11C22⋊Q814yescomplemented
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—48no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—88no—
234C2×C4×C11—84no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11#13512yes—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×Q811yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C8×C11—22no—
246C8×C11—41no—
247C8×C11—42no—
248C22×D8C22×C1111yescharacteristic
249#554—24no—
250#554—24no—
251C2×C4⋊Q8C22×C1111yescharacteristic
252C2×#125C22×C1112yes—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—22no—
256C2×C4×Q8C22×C1111yescharacteristic
257C2×C4×D4C22×C1112yes—
258C2×C4×D4C22×C1111yescharacteristic
259C2×C4×D4C22×C1111yescharacteristic
260C22×C4⋊C4—21no—
261#476—24no—
262C4×D8—24no—
263C2×#107C22×C1111yescharacteristic
264C2×#106C22×C1112yes—
265C2×C4⋊C8C22×C1111yescharacteristic
266C2×#102C22×C1112yes—
267C2×#102C22×C1111yescharacteristic
268C2×#102C22×C1112yes—
269C2×#102C22×C1111yescharacteristic
270C2×C4×C8C22×C1111yescharacteristic
271#396—22no—
272#390C22×C1112yes—
273#389C22×C1112yes—
274#384C22×C1111yescharacteristic
275#380—21no—
276#340C22×C1112yes—
277#340C22×C1112yes—
278#340C22×C1112yes—
279#336C22×C1112yes—
280#336C22×C1112yes—
281C22×C11—24no—
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×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C2×#12011yescharacteristic
296C22×C11#54811yescharacteristic
297C22×C11D4×Q811yescharacteristic
298C22×C11C2×#13511yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57611yescharacteristic
301C22×C11#57711yescharacteristic
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11—82no—
308C4×C11—81no—
309C4×C11#44914yes—
310C4×C11C2×C22⋊Q811yescharacteristic
311C4×C11#53611yescharacteristic
312C4×C11#54811yescharacteristic
313C4×C11D4×Q811yescharacteristic
314C22×Q8—21no—
315C22×Q8D4×C1111yescharacteristic
316C22×D4C23×C1111yescharacteristic
317C22×D4C23×C1111yescharacteristic
318C23×C4—21no—
319C23×C4—22no—
320C23×C4—21no—
321C2×D8—22no—
322C2×D8—22no—
323C2×D8Q8×C1114yescomplemented
324C22×C8C23×C1111yescharacteristic
325C22×C8C23×C1112yes—
326C22×C8C23×C1111yescharacteristic
327C4⋊Q8—22no—
328C4⋊Q8D4×C1114yes—
329#125—24no—
330#125—24no—
331C22⋊Q8—28no—
332C22⋊Q8—216no—
333C22⋊Q8—44no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C1114yes—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4D4×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C42C23×C1112yes—
361C2×C42C23×C1111yescharacteristic
362#107—22no—
363#106—24no—
364C4⋊C8—22no—
365#102—22no—
366#102—24no—
367#102—22no—
368#102—24no—
369C4×C8—22no—
370#95—22no—
371C2×C11—44no—
372C2×C11—82no—
373C2×C11#240911yescharacteristic
374C2×C11C2×#44911yescharacteristic
375C2×C11#301211yescharacteristic
376C2×C11#336011yescharacteristic
377C2×C11#336611yescharacteristic
378C2×C11#338011yescharacteristic
379C2×C11#338411yescharacteristic
380C24—21no—
381C24—21no—
382C2×Q8—22no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—81no—
387C2×Q8—81no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4C2×D4×C1112yes—
397C2×D4C2×Q8×C1112yes—
398C2×D4C2×Q8×C1112yes—
399C2×D4C11×#4112yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—28no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—82no—
412C22×C4—82no—
413C22×C4C2×D4×C1112yes—
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C24×C1111yescharacteristic
418D8—28no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8C2×Q8×C1112yes—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—22no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—44no—
440C4⋊C4—42no—
441C4⋊C4—81no—
442C4⋊C4C2×D4×C1114yes—
443C4⋊C4C2×D4×C1112yes—
444C22⋊C4—28no—
445C22⋊C4—24no—
446C22⋊C4—44no—
447C22⋊C4—42no—
448C22⋊C4—82no—
449C42—22no—
450C42—22no—
451C42C2×D4×C1112yes—
452C42C2×D4×C1112yes—
453C11#2432711yescharacteristic, direct product factor, Sylow
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23C22×D4×C1111yescharacteristic
469Q8—44no—
470Q8—84no—
471D4—22no—
472D4—22no—
473D4—22no—
474D4—22no—
475D4—22no—
476D4—41no—
477D4—41no—
478D4C11×C22⋊Q814yescomplemented
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—48no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—88no—
501C2×C4—84no—
502C2×C4C11×#12012yes—
503C2×C4C11×#12012yes—
504C2×C4C11×#13512yes—
505C2×C4C11×AGL(1,ℤ/8)12yes—
506C2×C4C22×D4×C1111yescharacteristic
507C2×C4C22×D4×C1111yescharacteristic
508C2×C4C22×Q8×C1111yescharacteristic
509C2×C4C2×C11×#4111yescharacteristic
510C2×C4C11×2−1+411yescharacteristic
511C2×C4C11×2−1+411yescharacteristic
512C8—22no—
513C8—41no—
514C8—42no—
515C22—24no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22C2×C11×#12011yescharacteristic
530C22C11×#54811yescharacteristic
531C22D4×Q8×C1111yescharacteristic
532C22C2×C11×#13511yescharacteristic
533C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
534C22C11×#57611yescharacteristic
535C22C11×#57711yescharacteristic
536C4—22no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—44no—
541C4—81no—
542C4—82no—
543C4C11×#44914yes—
544C4C2×C11×C22⋊Q811yescharacteristic
545C4C11×#53611yescharacteristic
546C4C11×#54811yescharacteristic
547C4D4×Q8×C1111yescharacteristic
548C2—44no—
549C2—82no—
550C2C11×#240911yescharacteristic
551C2C2×C11×#44911yescharacteristic
552C2C11×#301211yescharacteristic
553C2C11×#336011yescharacteristic
554C2C11×#336611yescharacteristic
555C2C11×#338011yescharacteristic
556C2C11×#338411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#554C2semidirect
2. C2×C11×#476C2semidirect
4. C11×#2538C2semidirect
5. C11×#2059C2semidirect
6. C11×#2025C2semidirect
7. C11×#1990C2semidirect
8. C11×#1984C2semidirect
10. C11×#1864C2semidirect
11. C11×#1802C2semidirect
54. C2×C11×D8Q8semidirect
102. #24327C11direct (N × H)
176. C2×#554C2×C11semidirect
177. C2×#476C2×C11semidirect
179. #2538C2×C11semidirect
180. #2059C2×C11semidirect
181. #2025C2×C11semidirect
182. #1990C2×C11semidirect
183. #1984C2×C11semidirect
185. #1864C2×C11semidirect
186. #1802C2×C11semidirect
211. D4×C11C22⋊Q8semidirect
323. C2×D8Q8×C11semidirect
453. C11#24327direct (N × H)
478. D4C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4762
C2×C4×C11×D82
C11×#25382
C11×#20592
C11×#20252
C11×#19902
C11×#19842
C11×#18792
C11×#18642
C11×#18022
#2432711