Finite Group Databasebeta

← C4×C11×#451 #14598642

Subgroups — C4×C11×#451 #14598642

Order 2816.

1448 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#451C211yesmaximal, characteristic
3C2×C4×C11×Q16C212yesmaximal, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic
5C11×#1878C212yesmaximal, complemented
6C11×#1872C211yesmaximal, characteristic
7C11×#1863C212yesmaximal, complemented
8C11×#1852C211yesmaximal, characteristic
9C11×#1787C211yesmaximal, characteristic
10C4×C11×#103C212yesmaximal, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11—28no—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2212yes—
21C22×C11×C4⋊C4—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C42×C11—21no—
24C22×C42×C11C2211yescharacteristic
25C11×#451C418yesdirect product factor
26C4×C11×Q16—28no—
27C2×C11×#107C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C4×C8×C11C2212yes—
35C11×#391C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#387—21no—
38C11×#385—21no—
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C22⋊C4—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C11×#336C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11C2×C414yes—
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2312yes—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×Q16—24no—
59C2×C11×Q16—24no—
60C2×C11×Q16C2×C418yescomplemented
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8C2×C414yes—
65C4×Q8×C11—28no—
66C4×Q8×C11—28no—
67C4×Q8×C11—24no—
68C4×Q8×C11—24no—
69C4×Q8×C11—24no—
70C4×Q8×C11—24no—
71C4×Q8×C11D418yes—
72C2×C11×C4⋊C4—28no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—28no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11—24no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11D411yescharacteristic
93C2×C42×C11D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C11×#107—24no—
97C11×#103—24no—
98C11×#103—24no—
99C11×#103—24no—
100C11×#103C2×C418yescomplemented
101C11×C22⋊C8—22no—
102C11×C22⋊C8C2×C414yes—
103C4×C8×C11—24no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C4×#451C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—24no—
112C2×Q8×C11—216no—
113C2×Q8×C11—24no—
114C2×Q8×C11—216no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—21no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11C22×C412yes—
123C2×Q8×C11C22×C414yes—
124C2×Q8×C11C2×D414yes—
125C2×Q8×C11#4114yes—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—41no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11Q1614yescomplemented
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C11×Q16—216no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11C22×C414yes—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4C2×D414yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—42no—
175C42×C11—28no—
176C42×C11—28no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—42no—
181C42×C11—42no—
182C42×C11C2×D414yes—
183C22×C4×Q8C2×C1111yescharacteristic
184C2×#451C2×C1111yescharacteristic
185C2×C4×Q16C2×C1112yescomplemented
186C4×C22⋊Q8C2×C1111yescharacteristic
187#1878C2×C1112yescomplemented
188#1872C2×C1111yescharacteristic
189#1863C2×C1112yescomplemented
190#1852C2×C1111yescharacteristic
191#1787C2×C1111yescharacteristic
192C4×#103C2×C1112yescomplemented
193C4×C22⋊C8C2×C1111yescharacteristic
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11C4×D412yes—
199C23×C11C2×Q1612yes—
200C23×C11#13512yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—216no—
203Q8×C11—24no—
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11—42no—
208Q8×C11C4×D418yes—
209C2×C4×C11—216no—
210C2×C4×C11—24no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—28no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—44no—
229C2×C4×C11—48no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
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—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C4×D412yes—
243C2×C4×C11#12012yes—
244C2×C4×C11#12012yes—
245C2×C4×C11C2×Q1612yes—
246C2×C4×C11C2×Q1612yes—
247C2×C4×C11#13712yes—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4111yescharacteristic
252C8×C11—24no—
253C8×C11—42no—
254C23×Q8C22×C1111yescharacteristic
255C22×Q16C22×C1112yes—
256C2×C22⋊Q8C22×C1111yescharacteristic
257C2×C4×Q8—28no—
258C2×C4×Q8—21no—
259C2×C4×Q8—21no—
260C2×C4×Q8C22×C1112yes—
261C2×C4×Q8C22×C1111yescharacteristic
262C2×C4×Q8C22×C1112yes—
263C22×C4⋊C4—21no—
264C22×C4⋊C4C22×C1111yescharacteristic
265C22×C42—21no—
266C22×C42C22×C1111yescharacteristic
267#451C4×C1118yesdirect product factor
268C4×Q16—28no—
269C2×#107C22×C1112yes—
270C2×#103C22×C1112yes—
271C2×#103C22×C1112yes—
272C2×#103C22×C1112yes—
273C2×#103C22×C1112yes—
274C2×C22⋊C8C22×C1111yescharacteristic
275C2×C22⋊C8C22×C1111yescharacteristic
276C2×C4×C8C22×C1112yes—
277#391C22×C1111yescharacteristic
278#389C22×C1111yescharacteristic
279#387—21no—
280#385—21no—
281#380C22×C1111yescharacteristic
282C4×C4⋊C4—21no—
283C4×C4⋊C4C22×C1111yescharacteristic
284C4×C22⋊C4—21no—
285#340C22×C1112yes—
286#340C22×C1112yes—
287#336C22×C1112yes—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11C4×Q1614yescomplemented
295C22×C11C2×C4×D411yescharacteristic
296C22×C11C2×#12011yescharacteristic
297C22×C11#52511yescharacteristic
298C22×C11C22×Q1611yescharacteristic
299C22×C11C2×#13511yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57511yescharacteristic
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—28no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—41no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#45114yesdirect product factor
313C4×C11C2×C4×D412yes—
314C4×C11#52512yes—
315C22×Q8—24no—
316C22×Q8—24no—
317C22×Q8—21no—
318C22×Q8—22no—
319C22×Q8C2×C4×C1114yes—
320C22×Q8C23×C1111yescharacteristic
321C22×Q8C23×C1112yes—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4D4×C1111yescharacteristic
325C23×C4D4×C1111yescharacteristic
326C23×C4C23×C1111yescharacteristic
327C2×Q16—24no—
328C2×Q16—24no—
329C2×Q16C2×C4×C1118yescomplemented
330C22×C8C23×C1112yes—
331C22×C8C23×C1112yes—
332C22⋊Q8—22no—
333C22⋊Q8C2×C4×C1114yes—
334C4×Q8—28no—
335C4×Q8—28no—
336C4×Q8—24no—
337C4×Q8—24no—
338C4×Q8—24no—
339C4×Q8—24no—
340C4×Q8D4×C1118yes—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—28no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42D4×C1111yescharacteristic
362C2×C42D4×C1111yescharacteristic
363C2×C42C23×C1111yescharacteristic
364C2×C42C23×C1111yescharacteristic
365#107—24no—
366#103—24no—
367#103—24no—
368#103—24no—
369#103C2×C4×C1118yescomplemented
370C22⋊C8—22no—
371C22⋊C8C2×C4×C1114yes—
372C4×C8—24no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C2×C11—24no—
379C2×C11C4×#12011yescharacteristic
380C2×C11C2×C4×Q1611yescharacteristic
381C2×C11C4×#13711yescharacteristic
382C2×C11C2×#45111yescharacteristic
383C2×C11#300211yescharacteristic
384C2×C11#310411yescharacteristic
385C2×C11#310811yescharacteristic
386C24C2×D4×C1111yescharacteristic
387C2×Q8—24no—
388C2×Q8—216no—
389C2×Q8—24no—
390C2×Q8—216no—
391C2×Q8—24no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8C22×C4×C1112yes—
399C2×Q8C22×C4×C1114yes—
400C2×Q8C2×D4×C1114yes—
401C2×Q8C11×#4114yes—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4C11×Q1614yescomplemented
422C22×C4C22×C4×C1112yes—
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C11×#4112yes—
429C22×C4C24×C1111yescharacteristic
430Q16—216no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8C22×C4×C1114yes—
437C4⋊C4—28no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—28no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4C22×C4×C1112yes—
448C4⋊C4C2×D4×C1114yes—
449C22⋊C4—24no—
450C22⋊C4—42no—
451C42—28no—
452C42—28no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—42no—
457C42—42no—
458C42C2×D4×C1114yes—
459C11C4×#45111yescharacteristic, direct product factor, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23C4×D4×C1112yes—
465C23C2×C11×Q1612yes—
466C23C11×#13512yes—
467C23C22×D4×C1111yescharacteristic
468Q8—216no—
469Q8—24no—
470Q8—24no—
471Q8—24no—
472Q8—24no—
473Q8—42no—
474Q8C4×D4×C1118yes—
475C2×C4—216no—
476C2×C4—24no—
477C2×C4—21no—
478C2×C4—24no—
479C2×C4—21no—
480C2×C4—24no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—28no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—24no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—44no—
495C2×C4—48no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4C4×D4×C1112yes—
509C2×C4C11×#12012yes—
510C2×C4C11×#12012yes—
511C2×C4C2×C11×Q1612yes—
512C2×C4C2×C11×Q1612yes—
513C2×C4C11×#13712yes—
514C2×C4C23×C4×C1111yescharacteristic
515C2×C4C22×D4×C1112yes—
516C2×C4C2×C11×#4112yes—
517C2×C4C2×C11×#4111yescharacteristic
518C8—24no—
519C8—42no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22C4×C11×Q1614yescomplemented
527C22C2×C4×D4×C1111yescharacteristic
528C22C2×C11×#12011yescharacteristic
529C22C11×#52511yescharacteristic
530C22C22×C11×Q1611yescharacteristic
531C22C2×C11×#13511yescharacteristic
532C22C2×C11×#13711yescharacteristic
533C22C11×#57511yescharacteristic
534C4—22no—
535C4—22no—
536C4—28no—
537C4—22no—
538C4—42no—
539C4—41no—
540C4—44no—
541C4—42no—
542C4—81no—
543C4—81no—
544C4C11×#45114yesdirect product factor
545C4C2×C4×D4×C1112yes—
546C4C11×#52512yes—
547C2—24no—
548C2C4×C11×#12011yescharacteristic
549C2C2×C4×C11×Q1611yescharacteristic
550C2C4×C11×#13711yescharacteristic
551C2C2×C11×#45111yescharacteristic
552C2C11×#300211yescharacteristic
553C2C11×#310411yescharacteristic
554C2C11×#310811yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×Q16C2semidirect
5. C11×#1878C2semidirect
7. C11×#1863C2semidirect
10. C4×C11×#103C2semidirect
25. C11×#451C4direct (N × H)
60. C2×C11×Q16C2×C4semidirect
100. C11×#103C2×C4semidirect
109. C4×#451C11direct (N × H)
145. C22×C4×C11Q16semidirect
185. C2×C4×Q16C2×C11semidirect
187. #1878C2×C11semidirect
189. #1863C2×C11semidirect
192. C4×#103C2×C11semidirect
267. #451C4×C11direct (N × H)
294. C22×C11C4×Q16semidirect
312. C4×C11#451direct (N × H)
329. C2×Q16C2×C4×C11semidirect
369. #103C2×C4×C11semidirect
421. C22×C4C11×Q16semidirect
459. C11C4×#451direct (N × H)
526. C22C4×C11×Q16semidirect
544. C4C11×#451direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C112
C2×C11×#4512
C2×C4×C11×Q162
C4×C11×C22⋊Q82
C11×#18782
C11×#18722
C11×#18632
C11×#18522
C11×#17872
C4×C11×#1032
C4×C11×C22⋊C82
C4×#45111