Finite Group Databasebeta

← C4×C11×#448 #14598641

Subgroups — C4×C11×#448 #14598641

Order 2816.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#448C211yesmaximal, characteristic
3C2×C4×C11×SD16C212yesmaximal, complemented
4C4×C11×#121C211yesmaximal, characteristic
5C11×#1880C212yesmaximal, complemented
6C11×#1874C211yesmaximal, characteristic
7C11×#1865C212yesmaximal, complemented
8C11×#1853C211yesmaximal, characteristic, complemented
9C11×#1787C211yesmaximal, characteristic, complemented
10C4×C11×#103C212yesmaximal, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#121C2211yescharacteristic
15C2×C4×Q8×C11—28no—
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4—21no—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C42×C11—21no—
25C22×C42×C11C2211yescharacteristic
26C11×#448C418yesdirect product factor
27C4×C11×SD16—28no—
28C2×C11×#106C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C4×C8×C11C2212yes—
36C11×#390C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#386—21no—
40C11×#380C2211yescharacteristic
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×C414yescomplemented
51C22×Q8×C11C2312yes—
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16C2×C418yescomplemented
63C22×C8×C11C2312yes—
64C22×C8×C11C2312yes—
65C11×#121—22no—
66C11×#121C2×C414yes—
67C4×Q8×C11—28no—
68C4×Q8×C11—28no—
69C4×Q8×C11—24no—
70C4×Q8×C11—24no—
71C4×Q8×C11—24no—
72C4×Q8×C11D418yescomplemented
73C4×D4×C11—24no—
74C4×D4×C11—44no—
75C2×C11×C4⋊C4—28no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—28no—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11—24no—
94C2×C42×C11—21no—
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D411yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C11×#106—24no—
100C11×#103—24no—
101C11×#103—24no—
102C11×#103C2×C418yescomplemented
103C11×#102—24no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8C2×C414yescomplemented
106C4×C8×C11—24no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C4×#448C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—24no—
114C2×Q8×C11—216no—
115C2×Q8×C11—24no—
116C2×Q8×C11—216no—
117C2×Q8×C11—24no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11C22×C414yes—
122C2×Q8×C11C2×D414yes—
123C2×Q8×C11#4114yes—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11C22×C412yes—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—41no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11SD1614yescomplemented
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C11×SD16—216no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11C22×C414yes—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4C2×D414yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C42×C11—28no—
184C42×C11—28no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—42no—
189C42×C11C2×D414yes—
190C22×C4×Q8C2×C1111yescharacteristic, complemented
191C2×#448C2×C1111yescharacteristic
192C2×C4×SD16C2×C1112yescomplemented
193C4×#121C2×C1111yescharacteristic
194#1880C2×C1112yescomplemented
195#1874C2×C1111yescharacteristic
196#1865C2×C1112yescomplemented
197#1853C2×C1111yescharacteristic, complemented
198#1787C2×C1111yescharacteristic, complemented
199C4×#103C2×C1112yescomplemented
200C4×C22⋊C8C2×C1111yescharacteristic, complemented
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11C4×D412yes—
213C23×C11C2×SD1612yes—
214C23×C11#13512yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—216no—
217Q8×C11—24no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11C4×D418yescomplemented
221D4×C11—24no—
222D4×C11—48no—
223D4×C11—42no—
224C2×C4×C11—216no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—24no—
228C2×C4×C11—21no—
229C2×C4×C11—24no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—28no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—24no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—84no—
255C2×C4×C11C4×D412yes—
256C2×C4×C11#12012yes—
257C2×C4×C11#12012yes—
258C2×C4×C11C2×SD1612yes—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11#13712yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11C2×#4111yescharacteristic
265C8×C11—24no—
266C8×C11—42no—
267C23×Q8C22×C1111yescharacteristic
268C22×SD16C22×C1112yes—
269C2×#121C22×C1111yescharacteristic
270C2×C4×Q8—28no—
271C2×C4×Q8—21no—
272C2×C4×Q8—21no—
273C2×C4×Q8C22×C1112yes—
274C2×C4×Q8C22×C1112yes—
275C2×C4×D4—21no—
276C2×C4×D4C22×C1111yescharacteristic
277C22×C4⋊C4—21no—
278C22×C4⋊C4C22×C1111yescharacteristic
279C22×C42—21no—
280C22×C42C22×C1111yescharacteristic
281#448C4×C1118yesdirect product factor
282C4×SD16—28no—
283C2×#106C22×C1112yes—
284C2×#103C22×C1112yes—
285C2×#103C22×C1112yes—
286C2×#103C22×C1112yes—
287C2×#102C22×C1112yes—
288C2×C22⋊C8C22×C1111yescharacteristic
289C2×C22⋊C8C22×C1111yescharacteristic
290C2×C4×C8C22×C1112yes—
291#390C22×C1111yescharacteristic
292#389C22×C1111yescharacteristic
293#388—21no—
294#386—21no—
295#380C22×C1111yescharacteristic
296C4×C4⋊C4C22×C1111yescharacteristic
297C4×C22⋊C4—21no—
298#340C22×C1112yes—
299#340C22×C1112yes—
300#336C22×C1112yes—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C4×SD1614yescomplemented
315C22×C11C2×C4×D411yescharacteristic
316C22×C11C2×#12011yescharacteristic
317C22×C11#52511yescharacteristic
318C22×C11C22×SD1611yescharacteristic
319C22×C11C2×#13511yescharacteristic
320C22×C11C2×#13711yescharacteristic
321C22×C11#57511yescharacteristic
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—28no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—44no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#44814yesdirect product factor
332C4×C11C2×C4×D412yes—
333C4×C11#52512yes—
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8C2×C4×C1114yescomplemented
339C22×Q8C23×C1112yes—
340C22×D4—21no—
341C22×D4C23×C1111yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4D4×C1111yescharacteristic
346C23×C4D4×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16C2×C4×C1118yescomplemented
351C22×C8C23×C1112yes—
352C22×C8C23×C1112yes—
353#121—22no—
354#121C2×C4×C1114yes—
355C4×Q8—28no—
356C4×Q8—28no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8—24no—
360C4×Q8D4×C1118yescomplemented
361C4×D4—24no—
362C4×D4—44no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1111yescharacteristic
372C2×C4⋊C4C23×C1112yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C42—28no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—21no—
383C2×C42D4×C1111yescharacteristic
384C2×C42D4×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386C2×C42C23×C1111yescharacteristic
387#106—24no—
388#103—24no—
389#103—24no—
390#103C2×C4×C1118yescomplemented
391#102—24no—
392C22⋊C8—22no—
393C22⋊C8C2×C4×C1114yescomplemented
394C4×C8—24no—
395#95—21no—
396#95—21no—
397#95—21no—
398C2×C11—24no—
399C2×C11—82no—
400C2×C11C4×#12011yescharacteristic
401C2×C11C2×C4×SD1611yescharacteristic
402C2×C11C4×#13711yescharacteristic
403C2×C11C2×#44811yescharacteristic
404C2×C11#300211yescharacteristic
405C2×C11#310311yescharacteristic
406C2×C11#310811yescharacteristic
407C24—21no—
408C24C2×D4×C1111yescharacteristic
409C2×Q8—24no—
410C2×Q8—216no—
411C2×Q8—24no—
412C2×Q8—216no—
413C2×Q8—24no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8C22×C4×C1114yes—
418C2×Q8C2×D4×C1114yes—
419C2×Q8C11×#4114yes—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4C22×C4×C1112yes—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4C11×SD1614yescomplemented
449C22×C4C22×C4×C1112yes—
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C11×#4112yes—
456C22×C4C24×C1111yescharacteristic
457SD16—216no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8C22×C4×C1114yes—
464C4⋊C4—28no—
465C4⋊C4—24no—
466C4⋊C4—28no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—42no—
472C4⋊C4C22×C4×C1112yes—
473C4⋊C4C2×D4×C1114yes—
474C22⋊C4—24no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C42—28no—
480C42—28no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42—42no—
485C42C2×D4×C1114yes—
486C11C4×#44811yescharacteristic, direct product factor, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C4×D4×C1112yes—
499C23C2×C11×SD1612yes—
500C23C11×#13512yes—
501C23C22×D4×C1111yescharacteristic
502Q8—216no—
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8C4×D4×C1118yescomplemented
507D4—24no—
508D4—48no—
509D4—42no—
510C2×C4—216no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—24no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—28no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—44no—
529C2×C4—48no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—84no—
541C2×C4C4×D4×C1112yes—
542C2×C4C11×#12012yes—
543C2×C4C11×#12012yes—
544C2×C4C2×C11×SD1612yes—
545C2×C4C2×C11×SD1612yes—
546C2×C4C11×#13712yes—
547C2×C4C23×C4×C1111yescharacteristic
548C2×C4C22×D4×C1112yes—
549C2×C4C2×C11×#4112yes—
550C2×C4C2×C11×#4111yescharacteristic
551C8—24no—
552C8—42no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C4×C11×SD1614yescomplemented
567C22C2×C4×D4×C1111yescharacteristic
568C22C2×C11×#12011yescharacteristic
569C22C11×#52511yescharacteristic
570C22C22×C11×SD1611yescharacteristic
571C22C2×C11×#13511yescharacteristic
572C22C2×C11×#13711yescharacteristic
573C22C11×#57511yescharacteristic
574C4—22no—
575C4—22no—
576C4—28no—
577C4—22no—
578C4—42no—
579C4—41no—
580C4—44no—
581C4—81no—
582C4—81no—
583C4C11×#44814yesdirect product factor
584C4C2×C4×D4×C1112yes—
585C4C11×#52512yes—
586C2—24no—
587C2—82no—
588C2C4×C11×#12011yescharacteristic
589C2C2×C4×C11×SD1611yescharacteristic
590C2C4×C11×#13711yescharacteristic
591C2C2×C11×#44811yescharacteristic
592C2C11×#300211yescharacteristic
593C2C11×#310311yescharacteristic
594C2C11×#310811yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
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
1. C22×C4×Q8×C11C2semidirect
3. C2×C4×C11×SD16C2semidirect
5. C11×#1880C2semidirect
7. C11×#1865C2semidirect
8. C11×#1853C2semidirect
9. C11×#1787C2semidirect
10. C4×C11×#103C2semidirect
11. C4×C11×C22⋊C8C2semidirect
26. C11×#448C4direct (N × H)
50. C22×Q8×C11C2×C4semidirect
62. C2×C11×SD16C2×C4semidirect
72. C4×Q8×C11D4semidirect
102. C11×#103C2×C4semidirect
105. C11×C22⋊C8C2×C4semidirect
110. C4×#448C11direct (N × H)
152. C22×C4×C11SD16semidirect
190. C22×C4×Q8C2×C11semidirect
192. C2×C4×SD16C2×C11semidirect
194. #1880C2×C11semidirect
196. #1865C2×C11semidirect
197. #1853C2×C11semidirect
198. #1787C2×C11semidirect
199. C4×#103C2×C11semidirect
200. C4×C22⋊C8C2×C11semidirect
220. Q8×C11C4×D4semidirect
281. #448C4×C11direct (N × H)
314. C22×C11C4×SD16semidirect
331. C4×C11#448direct (N × H)
338. C22×Q8C2×C4×C11semidirect
350. C2×SD16C2×C4×C11semidirect
360. C4×Q8D4×C11semidirect
390. #103C2×C4×C11semidirect
393. C22⋊C8C2×C4×C11semidirect
448. C22×C4C11×SD16semidirect
486. C11C4×#448direct (N × H)
506. Q8C4×D4×C11semidirect
566. C22C4×C11×SD16semidirect
583. C4C11×#448direct (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×#4482
C2×C4×C11×SD162
C4×C11×#1212
C11×#18802
C11×#18742
C11×#18652
C11×#18532
C11×#17872
C4×C11×#1032
C4×C11×C22⋊C82
C4×#44811