Finite Group Databasebeta

← C11×#24728 #14601921

Subgroups — C11×#24728 #14601921

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C212yesmaximal, complemented
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2541C211yesmaximal, characteristic
5Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#2041C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1880C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×C11×#127C2212yes—
16C2×C11×#121—21no—
17C2×C11×#121—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#460—28no—
22C11×#460—24no—
23C4×C11×SD16—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C2×C4×C8×C11C2211yescharacteristic
34C11×#392—22no—
35C11×#390C2212yes—
36C11×#389—22no—
37C11×#389C2212yes—
38C11×#384—21no—
39C11×#384C2211yescharacteristic
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—24no—
55C2×C11×SD16—24no—
56C2×C11×SD16—24no—
57C2×C11×SD16D414yescomplemented
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C11×#127—24no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#127—42no—
65C11×#121—44no—
66C11×#121—44no—
67C4×Q8×C11—22no—
68C4×Q8×C11—24no—
69C4×Q8×C11—42no—
70C4×Q8×C11D414yescomplemented
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—21no—
87C2×C42×C11—22no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C11×#106—22no—
91C11×C4⋊C8—24no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#102—24no—
95C11×#102—24no—
96C11×#102—22no—
97C11×#102—24no—
98C11×#102—42no—
99C4×C8×C11—22no—
100C11×#95—22no—
101C11×#95D412yes—
102#24728C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C24×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C2×D412yes—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4112yes—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—81no—
131C2×D4×C11—82no—
132C2×D4×C11—81no—
133C2×D4×C11—82no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×SD16—28no—
148C11×SD16—48no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C2×D412yes—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—44no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4—82no—
169C11×C4⋊C4SD1614yescomplemented
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—44no—
174C42×C11—24no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—44no—
178C42×C11C2×D412yes—
179C42×C11#4112yes—
180C2×#460C2×C1112yescomplemented
181C2×#460C2×C1111yescharacteristic, complemented
182C2×C4×SD16C2×C1111yescharacteristic, complemented
183#2541C2×C1111yescharacteristic
184Q8×C4⋊C4C2×C1111yescharacteristic, complemented
185#2065C2×C1112yescomplemented
186#2041C2×C1112yescomplemented
187#1957C2×C1111yescharacteristic, complemented
188#1939C2×C1111yescharacteristic, complemented
189#1880C2×C1112yescomplemented
190#1802C2×C1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11#12114yescomplemented
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—42no—
213D4×C11—41no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—41no—
217D4×C11—42no—
218D4×C11—88no—
219D4×C11—84no—
220D4×C11—88no—
221D4×C11—84no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—84no—
242C2×C4×C11#12112yes—
243C2×C4×C11#12112yes—
244C2×C4×C11C2×SD1614yes—
245C2×C4×C11C2×SD1612yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C8×C11—22no—
254C8×C11—42no—
255C8×C11—41no—
256C22×SD16C22×C1112yes—
257C22×SD16C22×C1111yescharacteristic
258C2×#127C22×C1111yescharacteristic
259C2×#127C22×C1112yes—
260C2×#121—21no—
261C2×#121—21no—
262C2×C4×Q8C22×C1112yes—
263C2×C4×Q8C22×C1111yescharacteristic
264C2×C4×D4C22×C1111yescharacteristic
265#460—28no—
266#460—24no—
267C4×SD16—24no—
268C2×#106C22×C1111yescharacteristic
269C2×C4⋊C8C22×C1111yescharacteristic
270C2×C4⋊C8C22×C1112yes—
271C2×#103C22×C1111yescharacteristic
272C2×#102C22×C1112yes—
273C2×#102C22×C1112yes—
274C2×#102C22×C1112yes—
275C2×#102C22×C1111yescharacteristic
276C2×#102C22×C1112yes—
277C2×C4×C8C22×C1111yescharacteristic
278#392—22no—
279#390C22×C1112yes—
280#389—22no—
281#389C22×C1112yes—
282#384—21no—
283#384C22×C1111yescharacteristic
284C4×C4⋊C4—21no—
285C4×C4⋊C4C22×C1111yescharacteristic
286#340C22×C1112yes—
287#336C22×C1112yes—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11C2×#12111yescharacteristic
303C22×C11D4211yescharacteristic
304C22×C11#54811yescharacteristic
305C22×C11C22×SD1611yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57611yescharacteristic
308C22×C11#57711yescharacteristic
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—82no—
315C4×C11—81no—
316C4×C11#46014yescomplemented
317C4×C11C2×#12111yescharacteristic
318C4×C11#53711yescharacteristic
319C4×C11#54711yescharacteristic
320C4×C11#55311yescharacteristic
321C22×Q8C23×C1111yescharacteristic
322C22×D4—21no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4C23×C1112yes—
327C22×D4C23×C1111yescharacteristic
328C23×C4—21no—
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16—24no—
334C2×SD16D4×C1114yescomplemented
335C22×C8C23×C1112yes—
336C22×C8C23×C1111yescharacteristic
337C22×C8C23×C1111yescharacteristic
338#127—24no—
339#127—22no—
340#127—22no—
341#127—42no—
342#121—44no—
343#121—44no—
344C4×Q8—22no—
345C4×Q8—24no—
346C4×Q8—42no—
347C4×Q8D4×C1114yescomplemented
348C4×D4—22no—
349C4×D4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4D4×C1111yescharacteristic
356C2×C4⋊C4D4×C1111yescharacteristic
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C4⋊C4C23×C1112yes—
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C42—21no—
364C2×C42—22no—
365C2×C42C23×C1112yes—
366C2×C42C23×C1111yescharacteristic
367#106—22no—
368C4⋊C8—24no—
369C4⋊C8—22no—
370#103—22no—
371#102—24no—
372#102—24no—
373#102—22no—
374#102—24no—
375#102—42no—
376C4×C8—22no—
377#95—22no—
378#95D4×C1112yes—
379C2×C11—82no—
380C2×C11—162no—
381C2×C11#241611yescharacteristic
382C2×C11C2×#46011yescharacteristic
383C2×C11#304511yescharacteristic
384C2×C11#327411yescharacteristic
385C2×C11D4×SD1611yescharacteristic
386C2×C11#336211yescharacteristic
387C2×C11#336811yescharacteristic
388C24—21no—
389C24—22no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8C2×D4×C1112yes—
394C2×Q8C2×D4×C1112yes—
395C2×Q8C11×#4112yes—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—81no—
416C2×D4—82no—
417C2×D4—81no—
418C2×D4—82no—
419C2×D4C2×D4×C1112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1112yes—
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C24×C1111yescharacteristic
432SD16—28no—
433SD16—48no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8C2×D4×C1112yes—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—44no—
451C4⋊C4—42no—
452C4⋊C4—81no—
453C4⋊C4—82no—
454C4⋊C4C11×SD1614yescomplemented
455C4⋊C4C2×D4×C1112yes—
456C22⋊C4—44no—
457C22⋊C4—42no—
458C22⋊C4—44no—
459C42—24no—
460C42—22no—
461C42—22no—
462C42—44no—
463C42C2×D4×C1112yes—
464C42C11×#4112yes—
465C11#2472811yescharacteristic, direct product factor, Sylow
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23C22×D4×C1111yescharacteristic
481Q8—22no—
482Q8—22no—
483Q8—22no—
484Q8C11×#12114yescomplemented
485D4—22no—
486D4—22no—
487D4—42no—
488D4—41no—
489D4—42no—
490D4—42no—
491D4—41no—
492D4—42no—
493D4—88no—
494D4—84no—
495D4—88no—
496D4—84no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—84no—
517C2×C4C11×#12112yes—
518C2×C4C11×#12112yes—
519C2×C4C2×C11×SD1614yes—
520C2×C4C2×C11×SD1612yes—
521C2×C4C11×AGL(1,ℤ/8)12yes—
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C2×C11×#4111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C2×C4C11×H(5,𝔽2)11yescharacteristic
527C2×C4C11×2−1+411yescharacteristic
528C8—22no—
529C8—42no—
530C8—41no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—82no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22C2×C11×#12111yescharacteristic
546C22D42×C1111yescharacteristic
547C22C11×#54811yescharacteristic
548C22C22×C11×SD1611yescharacteristic
549C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
550C22C11×#57611yescharacteristic
551C22C11×#57711yescharacteristic
552C4—24no—
553C4—24no—
554C4—22no—
555C4—42no—
556C4—42no—
557C4—82no—
558C4—81no—
559C4C11×#46014yescomplemented
560C4C2×C11×#12111yescharacteristic
561C4C11×#53711yescharacteristic
562C4C11×#54711yescharacteristic
563C4C11×#55311yescharacteristic
564C2—82no—
565C2—162no—
566C2C11×#241611yescharacteristic
567C2C2×C11×#46011yescharacteristic
568C2C11×#304511yescharacteristic
569C2C11×#327411yescharacteristic
570C2D4×C11×SD1611yescharacteristic
571C2C11×#336211yescharacteristic
572C2C11×#336811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#460C2semidirect
2. C2×C11×#460C2semidirect
3. C2×C4×C11×SD16C2semidirect
5. Q8×C11×C4⋊C4C2semidirect
6. C11×#2065C2semidirect
7. C11×#2041C2semidirect
8. C11×#1957C2semidirect
9. C11×#1939C2semidirect
10. C11×#1880C2semidirect
11. C11×#1802C2semidirect
57. C2×C11×SD16D4semidirect
70. C4×Q8×C11D4semidirect
102. #24728C11direct (N × H)
169. C11×C4⋊C4SD16semidirect
180. C2×#460C2×C11semidirect
181. C2×#460C2×C11semidirect
182. C2×C4×SD16C2×C11semidirect
184. Q8×C4⋊C4C2×C11semidirect
185. #2065C2×C11semidirect
186. #2041C2×C11semidirect
187. #1957C2×C11semidirect
188. #1939C2×C11semidirect
189. #1880C2×C11semidirect
190. #1802C2×C11semidirect
209. Q8×C11#121semidirect
316. C4×C11#460semidirect
334. C2×SD16D4×C11semidirect
347. C4×Q8D4×C11semidirect
454. C4⋊C4C11×SD16semidirect
465. C11#24728direct (N × H)
484. Q8C11×#121semidirect
559. C4C11×#460semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C4×C11×SD162
C11×#25412
Q8×C11×C4⋊C42
C11×#20652
C11×#20412
C11×#19572
C11×#19392
C11×#18802
C11×#18022
#2472811