Finite Group Databasebeta

← C11×#21505 #14598698

Subgroups — C11×#21505 #14598698

Order 2816.

1140 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic
2C2×C11×#440C212yesmaximal, complemented
3C4×C11×#127C211yesmaximal, characteristic
4C42×Q8×C11C211yesmaximal, characteristic, complemented
5C11×#1982C211yesmaximal, characteristic
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1925C212yesmaximal, complemented
8C11×#1880C212yesmaximal, complemented
9C11×#1803C211yesmaximal, characteristic, complemented
10C11×#1767C211yesmaximal, characteristic, complemented
11C11×#1762C212yesmaximal, complemented
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2212yes—
20C11×#460C418yescomplemented
21C11×#440—28no—
22C2×C11×#107C2212yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#97C2212yes—
30C11×#390—21no—
31C11×#390—21no—
32C11×#390C2212yes—
33C11×#384C2211yescharacteristic
34C4×C11×C4⋊C4—21no—
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C43×C11—21no—
41C43×C11C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C23×C4×C11—22no—
50C2×C11×SD16—24no—
51C2×C11×SD16—24no—
52C2×C11×SD16C2×C418yescomplemented
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×#127—22no—
56C11×#127C2×C414yes—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11C2×C414yescomplemented
62C4×Q8×C11D414yescomplemented
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11—44no—
66C4×D4×C11—44no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11D411yescharacteristic
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D411yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C11×#107—24no—
93C11×C4⋊C8—22no—
94C11×C4⋊C8C2×C414yescomplemented
95C11×#103—24no—
96C11×#102—24no—
97C11×#102—24no—
98C11×#102C2×C418yescomplemented
99C11×#97—24no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103#21505C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C22×C412yes—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4112yes—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11C22×C414yes—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—44no—
129C22×C4×C11—44no—
130C22×C4×C11—44no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C11×SD16—216no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C22×C414yes—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C22×C412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4#4112yes—
158C11×C22⋊C4—44no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C42×C11—24no—
162C42×C11—24no—
163C42×C11—24no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—41no—
170C42×C11—42no—
171C42×C11—42no—
172C42×C11—42no—
173C42×C11C22×C412yes—
174C42×C11C2×D412yes—
175C42×C11#4112yes—
176C42×C11#4112yes—
177C2×#460C2×C1111yescharacteristic
178C2×#440C2×C1112yescomplemented
179C4×#127C2×C1111yescharacteristic
180C42×Q8C2×C1111yescharacteristic, complemented
181#1982C2×C1111yescharacteristic
182#1947C2×C1111yescharacteristic, complemented
183#1925C2×C1112yescomplemented
184#1880C2×C1112yescomplemented
185#1803C2×C1111yescharacteristic, complemented
186#1767C2×C1111yescharacteristic, complemented
187#1762C2×C1112yescomplemented
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11C22×D411yescharacteristic
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—22no—
199Q8×C11C4×D414yescomplemented
200D4×C11—24no—
201D4×C11—24no—
202D4×C11—48no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—48no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—88no—
233C2×C4×C11C4×D412yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#12112yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11#13712yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C8×C11—24no—
247C8×C11—42no—
248C22×SD16C22×C1112yes—
249C2×#127C22×C1111yescharacteristic
250C2×C4×Q8C22×C1111yescharacteristic
251C2×C4×Q8C22×C1111yescharacteristic
252C2×C4×Q8C22×C1111yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C22×C1112yes—
256#460C4×C1118yescomplemented
257#440—28no—
258C2×#107C22×C1112yes—
259C2×C4⋊C8C22×C1111yescharacteristic
260C2×C4⋊C8C22×C1111yescharacteristic
261C2×#103C22×C1112yes—
262C2×#102C22×C1112yes—
263C2×#102C22×C1112yes—
264C2×#102C22×C1112yes—
265C2×#97C22×C1112yes—
266#390—21no—
267#390—21no—
268#390C22×C1112yes—
269#384C22×C1111yescharacteristic
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4C22×C1111yescharacteristic
274C4×C4⋊C4C22×C1111yescharacteristic
275C4×C4⋊C4C22×C1111yescharacteristic
276C43—21no—
277C43C22×C1111yescharacteristic
278#340C22×C1112yes—
279#340C22×C1112yes—
280#336C22×C1112yes—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11C2×C4×D411yescharacteristic
289C22×C11C2×#12111yescharacteristic
290C22×C11#52511yescharacteristic
291C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11C2×#13711yescharacteristic
294C22×C11#57511yescharacteristic
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—24no—
300C4×C11—41no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—82no—
305C4×C11#44014yescomplemented
306C4×C11C2×C4×D411yescharacteristic
307C4×C11C4×#4111yescharacteristic
308C4×C11#52911yescharacteristic
309C4×C11#53211yescharacteristic
310C22×Q8C23×C1111yescharacteristic
311C22×D4—21no—
312C22×D4—21no—
313C22×D4C23×C1112yes—
314C23×C4—22no—
315C2×SD16—24no—
316C2×SD16—24no—
317C2×SD16C2×C4×C1118yescomplemented
318C22×C8C23×C1112yes—
319C22×C8C23×C1112yes—
320#127—22no—
321#127C2×C4×C1114yes—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8C2×C4×C1114yescomplemented
327C4×Q8D4×C1114yescomplemented
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—44no—
331C4×D4—44no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4C23×C1112yes—
338C2×C4⋊C4C23×C1111yescharacteristic
339C2×C4⋊C4C23×C1111yescharacteristic
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42D4×C1111yescharacteristic
351C2×C42D4×C1111yescharacteristic
352C2×C42D4×C1111yescharacteristic
353C2×C42D4×C1111yescharacteristic
354C2×C42C23×C1111yescharacteristic
355C2×C42C23×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357#107—24no—
358C4⋊C8—22no—
359C4⋊C8C2×C4×C1114yescomplemented
360#103—24no—
361#102—24no—
362#102—24no—
363#102C2×C4×C1118yescomplemented
364#97—24no—
365#95—21no—
366#95—21no—
367#95—21no—
368C2×C11—84no—
369C2×C11C4×#12111yescharacteristic
370C2×C11C2×#44011yescharacteristic
371C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
372C2×C11#303711yescharacteristic
373C2×C11#303811yescharacteristic
374C2×C11#311211yescharacteristic
375C2×C11#311511yescharacteristic
376C24—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8C22×C4×C1112yes—
381C2×Q8C2×D4×C1112yes—
382C2×Q8C11×#4112yes—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4C22×C4×C1114yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C24×C1111yescharacteristic
410SD16—216no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8C22×C4×C1114yes—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4C22×C4×C1112yes—
428C4⋊C4C2×D4×C1112yes—
429C4⋊C4C11×#4112yes—
430C22⋊C4—44no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C42—24no—
434C42—24no—
435C42—24no—
436C42—22no—
437C42—22no—
438C42—22no—
439C42—21no—
440C42—21no—
441C42—41no—
442C42—42no—
443C42—42no—
444C42—42no—
445C42C22×C4×C1112yes—
446C42C2×D4×C1112yes—
447C42C11×#4112yes—
448C42C11×#4112yes—
449C11#2150511yescharacteristic, direct product factor, Sylow
450C23—24no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23C22×D4×C1111yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—22no—
461Q8C4×D4×C1114yescomplemented
462D4—24no—
463D4—24no—
464D4—48no—
465D4—42no—
466D4—42no—
467D4—48no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—88no—
495C2×C4C4×D4×C1112yes—
496C2×C4C4×D4×C1112yes—
497C2×C4C11×#12112yes—
498C2×C4C11×#12112yes—
499C2×C4C11×AGL(1,ℤ/8)12yes—
500C2×C4C11×AGL(1,ℤ/8)12yes—
501C2×C4C11×#13712yes—
502C2×C4C23×C4×C1111yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C2×C4C2×C11×#4111yescharacteristic
505C2×C4C2×C11×#4111yescharacteristic
506C2×C4C2×C11×#4111yescharacteristic
507C2×C4C2×C11×#4111yescharacteristic
508C8—24no—
509C8—42no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22C2×C4×D4×C1111yescharacteristic
518C22C2×C11×#12111yescharacteristic
519C22C11×#52511yescharacteristic
520C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
521C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
522C22C2×C11×#13711yescharacteristic
523C22C11×#57511yescharacteristic
524C4—22no—
525C4—22no—
526C4—22no—
527C4—24no—
528C4—22no—
529C4—42no—
530C4—42no—
531C4—41no—
532C4—42no—
533C4—82no—
534C4C11×#44014yescomplemented
535C4C2×C4×D4×C1111yescharacteristic
536C4C4×C11×#4111yescharacteristic
537C4C11×#52911yescharacteristic
538C4C11×#53211yescharacteristic
539C2—84no—
540C2C4×C11×#12111yescharacteristic
541C2C2×C11×#44011yescharacteristic
542C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
543C2C11×#303711yescharacteristic
544C2C11×#303811yescharacteristic
545C2C11×#311211yescharacteristic
546C2C11×#311511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#440C2semidirect
4. C42×Q8×C11C2semidirect
6. C11×#1947C2semidirect
7. C11×#1925C2semidirect
8. C11×#1880C2semidirect
9. C11×#1803C2semidirect
10. C11×#1767C2semidirect
11. C11×#1762C2semidirect
20. C11×#460C4semidirect
52. C2×C11×SD16C2×C4semidirect
61. C4×Q8×C11C2×C4semidirect
62. C4×Q8×C11D4semidirect
94. C11×C4⋊C8C2×C4semidirect
98. C11×#102C2×C4semidirect
103. #21505C11direct (N × H)
178. C2×#440C2×C11semidirect
180. C42×Q8C2×C11semidirect
182. #1947C2×C11semidirect
183. #1925C2×C11semidirect
184. #1880C2×C11semidirect
185. #1803C2×C11semidirect
186. #1767C2×C11semidirect
187. #1762C2×C11semidirect
199. Q8×C11C4×D4semidirect
256. #460C4×C11semidirect
305. C4×C11#440semidirect
317. C2×SD16C2×C4×C11semidirect
326. C4×Q8C2×C4×C11semidirect
327. C4×Q8D4×C11semidirect
359. C4⋊C8C2×C4×C11semidirect
363. #102C2×C4×C11semidirect
449. C11#21505direct (N × H)
461. Q8C4×D4×C11semidirect
534. C4C11×#440semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C11×#4402
C4×C11×#1272
C42×Q8×C112
C11×#19822
C11×#19472
C11×#19252
C11×#18802
C11×#18032
C11×#17672
C11×#17622
#2150511