Finite Group Databasebeta

← C11×#24526 #14601719

Subgroups — C11×#24526 #14601719

Order 2816.

1280 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#447C211yesmaximal, characteristic
2C22×C11×#102C211yesmaximal, characteristic, complemented
3C11×#2501C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2071C212yesmaximal, complemented
6C11×#2054C212yesmaximal, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1802C212yesmaximal, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4—21no—
22C11×#447—24no—
23C2×C11×C4⋊C8C2212yescomplemented
24C2×C11×#102—24no—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2212yescomplemented
30C2×C11×C22⋊C8C2211yescharacteristic
31C11×#399—22no—
32C11×#390C2212yes—
33C11×#390C2212yescomplemented
34C11×#386—22no—
35C11×#384C2212yescomplemented
36C11×#380C2211yescharacteristic
37C11×#379—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yescomplemented
40C11×#340C2212yescomplemented
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×D4×C11—24no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11D414yes—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—22no—
55C23×C4×C11C2311yescharacteristic
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×D8—24no—
59C2×C11×D8—42no—
60C22×C8×C11—22no—
61C22×C8×C11—42no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2312yes—
64C22×C8×C11C2311yescharacteristic
65C11×#123—44no—
66C11×#123—44no—
67C11×#121—22no—
68C11×#121—22no—
69C4×D4×C11—24no—
70C4×D4×C11—42no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—44no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11C2312yes—
90C11×C4⋊C8—42no—
91C11×#102—24no—
92C11×#102—24no—
93C11×#102—22no—
94C11×#102—22no—
95C11×#102—42no—
96C11×C22⋊C8—22no—
97C11×#95—21no—
98C11×#95D412yes—
99#24526C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C24×C11—21no—
102C24×C11—24no—
103C24×C11—21no—
104C24×C11—44no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—82no—
108C24×C11C2×D411yescharacteristic
109C2×D4×C11—28no—
110C2×D4×C11—24no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—44no—
121C2×D4×C11—48no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11C2×D412yes—
127C2×D4×C11C2×D412yes—
128C2×D4×C11#4114yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—44no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—44no—
139C22×C4×C11—82no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C11×D8—44no—
147C11×D8—44no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—44no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—44no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—82no—
173C11×C22⋊C4D814yescomplemented
174C42×C11—22no—
175C42×C11—22no—
176C2×#447C2×C1111yescharacteristic
177C22×#102C2×C1111yescharacteristic, complemented
178#2501C2×C1111yescharacteristic, complemented
179D4×C22⋊C4C2×C1111yescharacteristic, complemented
180#2071C2×C1112yescomplemented
181#2054C2×C1112yescomplemented
182#1893C2×C1111yescharacteristic, complemented
183#1879C2×C1112yescomplemented
184#1850C2×C1111yescharacteristic, complemented
185#1823C2×C1111yescharacteristic, complemented
186#1802C2×C1112yescomplemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—48no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—42no—
200C23×C11—48no—
201C23×C11—41no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11—84no—
207C23×C11—88no—
208C23×C11—88no—
209C23×C11#12112yes—
210C23×C11C2×D812yes—
211C23×C11AGL(1,ℤ/8)12yes—
212C23×C11C22×D411yescharacteristic
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—24no—
217D4×C11—48no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—84no—
223D4×C11#12314yescomplemented
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—88no—
243C2×C4×C11—84no—
244C2×C4×C11#12112yes—
245C2×C4×C11C2×D814yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4112yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)12yes—
250C8×C11—41no—
251C8×C11—42no—
252C8×C11—41no—
253C23×D4C22×C1111yescharacteristic
254C22×D8C22×C1111yescharacteristic
255C22×D8C22×C1111yescharacteristic
256C23×C8C22×C1111yescharacteristic
257C2×#123—21no—
258C2×#123—21no—
259C2×#121C22×C1111yescharacteristic
260C2×C4×D4C22×C1112yes—
261C22×C4⋊C4C22×C1111yescharacteristic
262C22×C22⋊C4—21no—
263#447—24no—
264C2×C4⋊C8C22×C1112yescomplemented
265C2×#102—24no—
266C2×#102C22×C1112yes—
267C2×#102C22×C1111yescharacteristic
268C2×#102C22×C1112yes—
269C2×#102C22×C1111yescharacteristic
270C2×#102C22×C1112yescomplemented
271C2×C22⋊C8C22×C1111yescharacteristic
272#399—22no—
273#390C22×C1112yes—
274#390C22×C1112yescomplemented
275#386—22no—
276#384C22×C1112yescomplemented
277#380C22×C1111yescharacteristic
278#379—21no—
279C4×C22⋊C4C22×C1111yescharacteristic
280#340C22×C1112yescomplemented
281#340C22×C1112yescomplemented
282#340C22×C1112yescomplemented
283#336C22×C1112yescomplemented
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—816no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—82no—
302C22×C11—81no—
303C22×C11—82no—
304C22×C11#45914yes—
305C22×C11C2×#12111yescharacteristic
306C22×C11#54612yes—
307C22×C11C22×D811yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C11#57712yes—
310C4×C11—22no—
311C4×C11—24no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11—81no—
315C4×C11—82no—
316C4×C11C2×#12311yescharacteristic
317C4×C11#53411yescharacteristic
318C4×C11#55112yes—
319C25—21no—
320C22×D4—24no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—22no—
324C22×D4—42no—
325C22×D4D4×C1114yes—
326C22×D4C23×C1111yescharacteristic
327C22×D4C23×C1111yescharacteristic
328C22×D4C23×C1111yescharacteristic
329C23×C4—21no—
330C23×C4—22no—
331C23×C4C23×C1111yescharacteristic
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—24no—
335C2×D8—42no—
336C22×C8—22no—
337C22×C8—42no—
338C22×C8C23×C1112yes—
339C22×C8C23×C1111yescharacteristic
340C22×C8C23×C1111yescharacteristic
341#123—44no—
342#123—44no—
343#121—22no—
344#121—22no—
345C4×D4—24no—
346C4×D4—42no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4D4×C1111yescharacteristic
364C2×C22⋊C4D4×C1111yescharacteristic
365C2×C42C23×C1112yes—
366C4⋊C8—42no—
367#102—24no—
368#102—24no—
369#102—22no—
370#102—22no—
371#102—42no—
372C22⋊C8—22no—
373#95—21no—
374#95D4×C1112yes—
375C2×C11—24no—
376C2×C11—44no—
377C2×C11—82no—
378C2×C11—161no—
379C2×C11#241211yescharacteristic
380C2×C11C2×#45911yescharacteristic
381C2×C11#304211yescharacteristic
382C2×C11#329412yes—
383C2×C11#330612yes—
384C24—21no—
385C24—21no—
386C24—24no—
387C24—21no—
388C24—44no—
389C24—42no—
390C24—42no—
391C24—82no—
392C24C2×D4×C1111yescharacteristic
393C2×D4—28no—
394C2×D4—24no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—44no—
405C2×D4—48no—
406C2×D4—44no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4C2×D4×C1112yes—
411C2×D4C2×D4×C1112yes—
412C2×D4C11×#4114yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—44no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—44no—
423C22×C4—82no—
424C22×C4C2×D4×C1112yes—
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1112yes—
427C22×C4C2×D4×C1112yes—
428C22×C4C11×#4112yes—
429C22×C4C24×C1111yescharacteristic
430D8—44no—
431D8—44no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—44no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—44no—
447C4⋊C4—42no—
448C4⋊C4—44no—
449C22⋊C4—22no—
450C22⋊C4—44no—
451C22⋊C4—44no—
452C22⋊C4—42no—
453C22⋊C4—42no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—82no—
457C22⋊C4C11×D814yescomplemented
458C42—22no—
459C42—22no—
460C11#2452611yescharacteristic, direct product factor, Sylow
461C23—22no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—22no—
466C23—48no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—48no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—84no—
481C23—88no—
482C23—88no—
483C23C11×#12112yes—
484C23C2×C11×D812yes—
485C23C11×AGL(1,ℤ/8)12yes—
486C23C22×D4×C1111yescharacteristic
487D4—22no—
488D4—22no—
489D4—22no—
490D4—24no—
491D4—48no—
492D4—41no—
493D4—41no—
494D4—42no—
495D4—42no—
496D4—84no—
497D4C11×#12314yescomplemented
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—88no—
517C2×C4—84no—
518C2×C4C11×#12112yes—
519C2×C4C2×C11×D814yes—
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C2×C11×#4112yes—
522C2×C4C2×C11×#4111yescharacteristic
523C2×C4C11×H(5,𝔽2)12yes—
524C8—41no—
525C8—42no—
526C8—41no—
527C22—22no—
528C22—24no—
529C22—22no—
530C22—24no—
531C22—24no—
532C22—42no—
533C22—44no—
534C22—42no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—816no—
540C22—82no—
541C22—82no—
542C22—81no—
543C22—81no—
544C22—82no—
545C22—81no—
546C22—82no—
547C22C11×#45914yes—
548C22C2×C11×#12111yescharacteristic
549C22C11×#54612yes—
550C22C22×C11×D811yescharacteristic
551C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
552C22C11×#57712yes—
553C4—22no—
554C4—24no—
555C4—42no—
556C4—82no—
557C4—81no—
558C4—82no—
559C4C2×C11×#12311yescharacteristic
560C4C11×#53411yescharacteristic
561C4C11×#55112yes—
562C2—24no—
563C2—44no—
564C2—82no—
565C2—161no—
566C2C11×#241211yescharacteristic
567C2C2×C11×#45911yescharacteristic
568C2C11×#304211yescharacteristic
569C2C11×#329412yes—
570C2C11×#330612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#102C2semidirect
3. C11×#2501C2semidirect
4. D4×C11×C22⋊C4C2semidirect
5. C11×#2071C2semidirect
6. C11×#2054C2semidirect
7. C11×#1893C2semidirect
8. C11×#1879C2semidirect
9. C11×#1850C2semidirect
10. C11×#1823C2semidirect
11. C11×#1802C2semidirect
23. C2×C11×C4⋊C8C22semidirect
29. C2×C11×#102C22semidirect
33. C11×#390C22semidirect
35. C11×#384C22semidirect
39. C11×#340C22semidirect
40. C11×#340C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
99. #24526C11direct (N × H)
173. C11×C22⋊C4D8semidirect
177. C22×#102C2×C11semidirect
178. #2501C2×C11semidirect
179. D4×C22⋊C4C2×C11semidirect
180. #2071C2×C11semidirect
181. #2054C2×C11semidirect
182. #1893C2×C11semidirect
183. #1879C2×C11semidirect
184. #1850C2×C11semidirect
185. #1823C2×C11semidirect
186. #1802C2×C11semidirect
223. D4×C11#123semidirect
264. C2×C4⋊C8C22×C11semidirect
270. C2×#102C22×C11semidirect
274. #390C22×C11semidirect
276. #384C22×C11semidirect
280. #340C22×C11semidirect
281. #340C22×C11semidirect
282. #340C22×C11semidirect
283. #336C22×C11semidirect
457. C22⋊C4C11×D8semidirect
460. C11#24526direct (N × H)
497. D4C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4472
C22×C11×#1022
C11×#25012
D4×C11×C22⋊C42
C11×#20712
C11×#20542
C11×#18932
C11×#18792
C11×#18502
C11×#18232
C11×#18022
#2452611