Finite Group Databasebeta

← C11×#24708 #14601901

Subgroups — C11×#24708 #14601901

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic, complemented
2C2×C11×#432C211yesmaximal, characteristic, complemented
3C11×#2857C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic
5C11×#2077C212yesmaximal, complemented
6C11×#2033C212yesmaximal
7C11×#1987C211yesmaximal, characteristic, complemented
8C11×#1947C211yesmaximal, characteristic, complemented
9C11×#1943C212yesmaximal, complemented
10C11×#1936C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C2×C11×#121C2211yescharacteristic
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#476—24no—
19C11×#432—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×C22⋊C8C2212yes—
27C2×C11×#97C2212yes—
28C11×#391—21no—
29C11×#390C2211yescharacteristic
30C11×#389—21no—
31C11×#389C2212yes—
32C11×#389C2211yescharacteristic
33C11×#388—21no—
34C11×#386—21no—
35C11×#384C2211yescharacteristic
36C11×#380—21no—
37C11×#380C2212yes—
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C22⋊Q8—44no—
57C11×#121—22no—
58C11×#121—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—44no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11—21no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×#107—24no—
86C11×#106—24no—
87C11×C4⋊C8—22no—
88C11×C4⋊C8D414yescomplemented
89C11×#102—24no—
90C11×#102—24no—
91C11×C22⋊C8—24no—
92C11×#97—24no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—22no—
97C11×#95—22no—
98#24708C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C2×D4×C11—24no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11#4112yes—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—41no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D414yes—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4#4112yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4—42no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—42no—
171C42×C11C2×D412yes—
172C42×C11#4112yes—
173C2×#476C2×C1111yescharacteristic, complemented
174C2×#432C2×C1111yescharacteristic, complemented
175#2857C2×C1111yescharacteristic, complemented
176C4×#121C2×C1111yescharacteristic
177#2077C2×C1112yescomplemented
178#2033C2×C1112yes—
179#1987C2×C1111yescharacteristic, complemented
180#1947C2×C1111yescharacteristic, complemented
181#1943C2×C1112yescomplemented
182#1936C2×C1112yescomplemented
183#1802C2×C1111yescharacteristic, complemented
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11AGL(1,ℤ/8)12yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—84no—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—48no—
203D4×C11—41no—
204D4×C11—41no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—44no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—44no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11#12112yes—
239C2×C4×C11#12112yes—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11#13712yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C8×C11—24no—
249C8×C11—42no—
250C2×C4⋊Q8C22×C1111yescharacteristic
251C2×C22⋊Q8—21no—
252C2×#121C22×C1111yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C22×C1111yescharacteristic
255C22×C42C22×C1111yescharacteristic
256#476—24no—
257#432—24no—
258C2×#107C22×C1112yes—
259C2×#106C22×C1112yes—
260C2×C4⋊C8C22×C1111yescharacteristic
261C2×C4⋊C8C22×C1111yescharacteristic
262C2×#102C22×C1112yes—
263C2×#102C22×C1112yes—
264C2×C22⋊C8C22×C1112yes—
265C2×#97C22×C1112yes—
266#391—21no—
267#390C22×C1111yescharacteristic
268#389—21no—
269#389C22×C1112yes—
270#389C22×C1111yescharacteristic
271#388—21no—
272#386—21no—
273#384C22×C1111yescharacteristic
274#380—21no—
275#380C22×C1111yescharacteristic
276#380C22×C1112yes—
277C4×C4⋊C4C22×C1111yescharacteristic
278C4×C22⋊C4—21no—
279#340C22×C1112yes—
280#340C22×C1112yes—
281#340C22×C1112yes—
282#340C22×C1112yes—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11C2×#12111yescharacteristic
298C22×C11#52511yescharacteristic
299C22×C11#53611yescharacteristic
300C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11#57511yescharacteristic
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11—82no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11—82no—
313C4×C11#46814yes—
314C4×C11#54711yescharacteristic
315C4×C11#54811yescharacteristic
316C4×C11#55211yescharacteristic
317C4×C11#55611yescharacteristic
318C22×Q8—21no—
319C22×D4—21no—
320C22×D4C23×C1111yescharacteristic
321C23×C4—21no—
322C23×C4D4×C1111yescharacteristic
323C23×C4D4×C1111yescharacteristic
324C23×C4C23×C1111yescharacteristic
325C22×C8C23×C1112yes—
326C22×C8C23×C1112yes—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C22⋊Q8—44no—
330#121—22no—
331#121—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—44no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C4⋊C4C23×C1112yes—
342C2×C4⋊C4C23×C1111yescharacteristic
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—21no—
354C2×C42D4×C1111yescharacteristic
355C2×C42D4×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358#107—24no—
359#106—24no—
360C4⋊C8—22no—
361C4⋊C8D4×C1114yescomplemented
362#102—24no—
363#102—24no—
364C22⋊C8—24no—
365#97—24no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—22no—
370#95—22no—
371C2×C11—42no—
372C2×C11—82no—
373C2×C11#241511yescharacteristic
374C2×C11C2×#46811yescharacteristic
375C2×C11#305511yescharacteristic
376C2×C11#310911yescharacteristic
377C2×C11#311611yescharacteristic
378C2×C11#323511yescharacteristic
379C2×C11#323811yescharacteristic
380C24—21no—
381C24C2×D4×C1111yescharacteristic
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4C11×#4112yes—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—41no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C24×C1111yescharacteristic
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8C2×D4×C1114yes—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4—44no—
438C4⋊C4—42no—
439C4⋊C4—42no—
440C4⋊C4C11×#4112yes—
441C22⋊C4—24no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—44no—
446C22⋊C4—42no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—42no—
452C42C2×D4×C1112yes—
453C42C11×#4112yes—
454C11#2470811yescharacteristic, direct product factor, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23C11×AGL(1,ℤ/8)12yes—
469C23C22×D4×C1111yescharacteristic
470Q8—84no—
471D4—22no—
472D4—22no—
473D4—48no—
474D4—41no—
475D4—41no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4C11×#12112yes—
510C2×C4C11×#12112yes—
511C2×C4C11×AGL(1,ℤ/8)12yes—
512C2×C4C11×#13712yes—
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C2×C11×#4111yescharacteristic
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C2×C11×#4111yescharacteristic
517C2×C4C11×2−1+411yescharacteristic
518C2×C4C11×2−1+411yescharacteristic
519C8—24no—
520C8—42no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22C2×C11×#12111yescharacteristic
536C22C11×#52511yescharacteristic
537C22C11×#53611yescharacteristic
538C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
539C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
540C22C2×C11×#13711yescharacteristic
541C22C11×#57511yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—81no—
548C4—81no—
549C4—82no—
550C4—82no—
551C4C11×#46814yes—
552C4C11×#54711yescharacteristic
553C4C11×#54811yescharacteristic
554C4C11×#55211yescharacteristic
555C4C11×#55611yescharacteristic
556C2—42no—
557C2—82no—
558C2C11×#241511yescharacteristic
559C2C2×C11×#46811yescharacteristic
560C2C11×#305511yescharacteristic
561C2C11×#310911yescharacteristic
562C2C11×#311611yescharacteristic
563C2C11×#323511yescharacteristic
564C2C11×#323811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#476C2semidirect
2. C2×C11×#432C2semidirect
3. C11×#2857C2semidirect
5. C11×#2077C2semidirect
7. C11×#1987C2semidirect
8. C11×#1947C2semidirect
9. C11×#1943C2semidirect
10. C11×#1936C2semidirect
11. C11×#1802C2semidirect
88. C11×C4⋊C8D4semidirect
98. #24708C11direct (N × H)
173. C2×#476C2×C11semidirect
174. C2×#432C2×C11semidirect
175. #2857C2×C11semidirect
177. #2077C2×C11semidirect
179. #1987C2×C11semidirect
180. #1947C2×C11semidirect
181. #1943C2×C11semidirect
182. #1936C2×C11semidirect
183. #1802C2×C11semidirect
361. C4⋊C8D4×C11semidirect
454. C11#24708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C2×C11×#4322
C11×#28572
C4×C11×#1212
C11×#20772
C11×#20332
C11×#19872
C11×#19472
C11×#19432
C11×#19362
C11×#18022
#2470811