Finite Group Databasebeta

← C11×#22047 #14599240

Subgroups — C11×#22047 #14599240

Order 2816.

1080 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C4×C11×#121C211yesmaximal, characteristic
3C2×C11×#391C211yesmaximal, characteristic, complemented
4C11×#1973C212yesmaximal, complemented
5C11×#1935C212yesmaximal, complemented
6C11×#1928C212yesmaximal, complemented
7C11×#1877C212yesmaximal, complemented
8C11×#1874C211yesmaximal, characteristic
9C11×#1852C211yesmaximal, characteristic, complemented
10C11×#1787C211yesmaximal, characteristic, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#121C2211yescharacteristic
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#448C418yescomplemented
20C2×C11×#107C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2212yes—
28C11×#391—21no—
29C11×#391—21no—
30C11×#391C2212yes—
31C11×#391C2212yes—
32C11×#390C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#388—21no—
35C11×#386—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C2×C11×#95—21no—
40C2×C11×#95—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yescomplemented
49C22×Q8×C11C2312yes—
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×SD16—42no—
59C2×C11×SD16—42no—
60C2×C11×SD16C2×C418yescomplemented
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#121—22no—
64C11×#121C2×C414yes—
65C4×D4×C11—42no—
66C4×D4×C11—44no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—42no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11—42no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×#107—42no—
86C11×#103—42no—
87C11×#103—42no—
88C11×#103C2×C418yescomplemented
89C11×#102—42no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8C2×C414yescomplemented
92C11×#97—42no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100#22047C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—48no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11—48no—
113C2×Q8×C11C22×C414yes—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11C22×C412yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—41no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C11×SD16—48no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11C22×C414yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C22×C412yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—41no—
174C42×C11—41no—
175C42×C11—42no—
176C2×#448C2×C1111yescharacteristic
177C4×#121C2×C1111yescharacteristic
178C2×#391C2×C1111yescharacteristic, complemented
179#1973C2×C1112yescomplemented
180#1935C2×C1112yescomplemented
181#1928C2×C1112yescomplemented
182#1877C2×C1112yescomplemented
183#1874C2×C1111yescharacteristic
184#1852C2×C1111yescharacteristic, complemented
185#1787C2×C1111yescharacteristic, complemented
186#1749C2×C1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C4×D412yes—
199C23×C11AGL(1,ℤ/8)12yes—
200C23×C11#13712yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—24no—
203Q8×C11—24no—
204Q8×C11—48no—
205Q8×C11—42no—
206Q8×C11—42no—
207D4×C11—24no—
208D4×C11—48no—
209D4×C11—42no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—48no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—84no—
244C2×C4×C11—84no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11#13712yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)12yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C8×C11—24no—
252C8×C11—42no—
253C23×Q8C22×C1111yescharacteristic
254C22×SD16C22×C1112yes—
255C2×#121C22×C1111yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C22×C1111yescharacteristic
258C22×C4⋊C4C22×C1111yescharacteristic
259C22×C42C22×C1111yescharacteristic
260#448C4×C1118yescomplemented
261C2×#107C22×C1112yes—
262C2×#103C22×C1112yes—
263C2×#103C22×C1112yes—
264C2×#103C22×C1112yes—
265C2×#102C22×C1112yes—
266C2×C22⋊C8C22×C1111yescharacteristic
267C2×C22⋊C8C22×C1111yescharacteristic
268C2×#97C22×C1112yes—
269#391—21no—
270#391—21no—
271#391C22×C1112yes—
272#391C22×C1112yes—
273#390C22×C1111yescharacteristic
274#389C22×C1111yescharacteristic
275#388—21no—
276#386—21no—
277#380C22×C1111yescharacteristic
278C4×C4⋊C4C22×C1111yescharacteristic
279C4×C22⋊C4—21no—
280C2×#95—21no—
281C2×#95—21no—
282#340C22×C1112yes—
283#340C22×C1112yes—
284#336C22×C1112yes—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11#44014yes—
299C22×C11C2×C4×D411yescharacteristic
300C22×C11#53411yescharacteristic
301C22×C11#53511yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57511yescharacteristic
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11—41no—
312C4×C11—41no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11—82no—
316C4×C11#51812yes—
317C4×C11#53812yes—
318C22×Q8—21no—
319C22×Q8—22no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8C2×C4×C1114yescomplemented
323C22×Q8C23×C1112yes—
324C22×D4—21no—
325C22×D4C23×C1111yescharacteristic
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4D4×C1111yescharacteristic
330C23×C4D4×C1111yescharacteristic
331C23×C4C23×C1111yescharacteristic
332C2×SD16—42no—
333C2×SD16—42no—
334C2×SD16C2×C4×C1118yescomplemented
335C22×C8C23×C1112yes—
336C22×C8C23×C1112yes—
337#121—22no—
338#121C2×C4×C1114yes—
339C4×D4—42no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4C23×C1112yes—
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C42—21no—
354C2×C42—42no—
355C2×C42D4×C1111yescharacteristic
356C2×C42D4×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358C2×C42C23×C1111yescharacteristic
359#107—42no—
360#103—42no—
361#103—42no—
362#103C2×C4×C1118yescomplemented
363#102—42no—
364C22⋊C8—22no—
365C22⋊C8C2×C4×C1114yescomplemented
366#97—42no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—21no—
372#95—21no—
373#95—21no—
374C2×C11—24no—
375C2×C11—82no—
376C2×C11#232111yescharacteristic
377C2×C11C2×#44011yescharacteristic
378C2×C11C4×#13711yescharacteristic
379C2×C11#319311yescharacteristic
380C2×C11#319611yescharacteristic
381C2×C11#321311yescharacteristic
382C2×C11#321811yescharacteristic
383C24—21no—
384C24C2×D4×C1111yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—48no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—48no—
395C2×Q8C22×C4×C1114yes—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4C22×C4×C1112yes—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4C22×C4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C11×#4112yes—
432C22×C4C24×C1111yescharacteristic
433SD16—48no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8C22×C4×C1114yes—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4C22×C4×C1112yes—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C42—22no—
454C42—22no—
455C42—41no—
456C42—41no—
457C42—42no—
458C11#2204711yescharacteristic, direct product factor, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23C4×D4×C1112yes—
471C23C11×AGL(1,ℤ/8)12yes—
472C23C11×#13712yes—
473C23C22×D4×C1111yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479D4—24no—
480D4—48no—
481D4—42no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4—84no—
517C2×C4C4×D4×C1112yes—
518C2×C4C11×#13712yes—
519C2×C4C23×C4×C1111yescharacteristic
520C2×C4C2×C11×#4111yescharacteristic
521C2×C4C11×H(5,𝔽2)12yes—
522C2×C4C11×H(5,𝔽2)12yes—
523C8—24no—
524C8—42no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22C11×#44014yes—
539C22C2×C4×D4×C1111yescharacteristic
540C22C11×#53411yescharacteristic
541C22C11×#53511yescharacteristic
542C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
543C22C2×C11×#13711yescharacteristic
544C22C2×C11×#13711yescharacteristic
545C22C11×#57511yescharacteristic
546C4—22no—
547C4—22no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—41no—
552C4—44no—
553C4—81no—
554C4—82no—
555C4—81no—
556C4C11×#51812yes—
557C4C11×#53812yes—
558C2—24no—
559C2—82no—
560C2C11×#232111yescharacteristic
561C2C2×C11×#44011yescharacteristic
562C2C4×C11×#13711yescharacteristic
563C2C11×#319311yescharacteristic
564C2C11×#319611yescharacteristic
565C2C11×#321311yescharacteristic
566C2C11×#321811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#391C2semidirect
4. C11×#1973C2semidirect
5. C11×#1935C2semidirect
6. C11×#1928C2semidirect
7. C11×#1877C2semidirect
9. C11×#1852C2semidirect
10. C11×#1787C2semidirect
11. C11×#1749C2semidirect
19. C11×#448C4semidirect
48. C22×Q8×C11C2×C4semidirect
60. C2×C11×SD16C2×C4semidirect
88. C11×#103C2×C4semidirect
91. C11×C22⋊C8C2×C4semidirect
100. #22047C11direct (N × H)
178. C2×#391C2×C11semidirect
179. #1973C2×C11semidirect
180. #1935C2×C11semidirect
181. #1928C2×C11semidirect
182. #1877C2×C11semidirect
184. #1852C2×C11semidirect
185. #1787C2×C11semidirect
186. #1749C2×C11semidirect
260. #448C4×C11semidirect
322. C22×Q8C2×C4×C11semidirect
334. C2×SD16C2×C4×C11semidirect
362. #103C2×C4×C11semidirect
365. C22⋊C8C2×C4×C11semidirect
458. C11#22047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C4×C11×#1212
C2×C11×#3912
C11×#19732
C11×#19352
C11×#19282
C11×#18772
C11×#18742
C11×#18522
C11×#17872
C11×#17492
#2204711