Finite Group Databasebeta

← C11×C22⋊C4×SD16 #14599640

Subgroups — C11×C22⋊C4×SD16 #14599640

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic
2C2×C4×C11×SD16C212yesmaximal, complemented
3Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic
5C11×#1968C212yesmaximal, complemented
6C11×#1880C212yesmaximal, complemented
7C11×#1877C212yesmaximal, complemented
8C11×#1807C211yesmaximal, characteristic, complemented
9C11×#1787C211yesmaximal, characteristic, complemented
10C11×#1786C211yesmaximal, characteristic
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—28no—
15C22×C11×SD16C418yescomplemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yescomplemented
22C2×C4×D4×C11C2212yes—
23C22×C11×C22⋊C4—21no—
24C4×C11×SD16—28no—
25C2×C11×#106C2212yescomplemented
26C2×C11×#103C2212yescomplemented
27C2×C11×#103C2212yescomplemented
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C4×C8×C11C2212yescomplemented
32C11×#391—22no—
33C11×#391C2212yescomplemented
34C11×#390C2212yes—
35C11×#386—22no—
36C11×#380—21no—
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#379—21no—
40C4×C11×C22⋊C4—21no—
41C4×C11×C22⋊C4C2211yescharacteristic
42C11×#340C2212yescomplemented
43C11×#336C2212yescomplemented
44C25×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—24no—
48C22×Q8×C11—42no—
49C22×Q8×C11C2×C414yescomplemented
50C22×Q8×C11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11—42no—
56C22×D4×C11C2×C414yes—
57C22×D4×C11C2311yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—22no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—232no—
65C2×C11×SD16—24no—
66C2×C11×SD16C2×C414yes—
67C2×C11×SD16C2×C414yes—
68C2×C11×SD16C2×C414yescomplemented
69C2×C11×SD16C2×C414yescomplemented
70C2×C11×SD16D418yes—
71C22×C8×C11—24no—
72C22×C8×C11C2×C414yescomplemented
73C22×C8×C11C2312yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×Q8×C11—24no—
77C4×Q8×C11—42no—
78C4×D4×C11—24no—
79C4×D4×C11—42no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—44no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11—22no—
92C2×C42×C11C2312yes—
93C11×#106—24no—
94C11×#103—24no—
95C11×#103—42no—
96C11×#102—24no—
97C11×#102—42no—
98C11×C22⋊C8—22no—
99C4×C8×C11—24no—
100C11×#95—22no—
101C11×#95—22no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95D412yes—
105C22⋊C4×SD16C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—24no—
109C24×C11—44no—
110C24×C11—42no—
111C24×C11—42no—
112C24×C11—82no—
113C24×C11C2×D411yescharacteristic
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—44no—
122C2×Q8×C11—44no—
123C2×Q8×C11—48no—
124C2×Q8×C11C22×C412yes—
125C2×Q8×C11C22×C412yes—
126C2×Q8×C11C2×D414yes—
127C2×D4×C11—28no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—44no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11C22×C412yes—
138C2×D4×C11C22×C412yes—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—82no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C11×SD16—28no—
158C11×SD16—28no—
159C11×SD16—28no—
160C11×SD16C22⋊C4116yesdirect product factor
161C2×C8×C11—28no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11C22×C412yes—
167C2×C8×C11C22×C412yes—
168C2×C8×C11C2×D414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—44no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—82no—
180C11×C22⋊C4SD1614yesdirect product factor
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—44no—
184C23×SD16C2×C1111yescharacteristic
185C2×C4×SD16C2×C1112yescomplemented
186Q8×C22⋊C4C2×C1111yescharacteristic, complemented
187D4×C22⋊C4C2×C1111yescharacteristic
188#1968C2×C1112yescomplemented
189#1880C2×C1112yescomplemented
190#1877C2×C1112yescomplemented
191#1807C2×C1111yescharacteristic, complemented
192#1787C2×C1111yescharacteristic, complemented
193#1786C2×C1111yescharacteristic
194C8×C22⋊C4C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—48no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—48no—
209C23×C11—84no—
210C23×C11—88no—
211C23×C11—88no—
212C23×C11C4×D412yes—
213C23×C11C2×SD1612yes—
214C23×C11#13512yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—24no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—48no—
221Q8×C11—42no—
222Q8×C11C2×C22⋊C414yescomplemented
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—42no—
229D4×C11C2×C22⋊C414yes—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—88no—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C2×SD1614yescomplemented
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)12yes—
257C8×C11—22no—
258C8×C11—42no—
259C8×C11C2×C22⋊C414yescomplemented
260C23×Q8C22×C1111yescharacteristic
261C23×D4C22×C1111yescharacteristic
262C22×SD16—28no—
263C22×SD16C4×C1118yescomplemented
264C22×SD16C22×C1111yescharacteristic
265C22×SD16C22×C1111yescharacteristic
266C22×SD16C22×C1111yescharacteristic
267C22×SD16C22×C1111yescharacteristic
268C23×C8C22×C1111yescharacteristic
269C2×C4×Q8C22×C1112yescomplemented
270C2×C4×D4C22×C1112yes—
271C22×C22⋊C4—21no—
272C4×SD16—28no—
273C2×#106C22×C1112yescomplemented
274C2×#103C22×C1112yescomplemented
275C2×#103C22×C1112yescomplemented
276C2×#102C22×C1112yes—
277C2×#102C22×C1112yes—
278C2×C22⋊C8C22×C1111yescharacteristic
279C2×C4×C8C22×C1112yescomplemented
280#391—22no—
281#391C22×C1112yescomplemented
282#390C22×C1112yes—
283#386—22no—
284#380—21no—
285#380C22×C1111yescharacteristic
286#380C22×C1111yescharacteristic
287#379—21no—
288C4×C22⋊C4—21no—
289C4×C22⋊C4C22×C1111yescharacteristic
290#340C22×C1112yescomplemented
291#336C22×C1112yescomplemented
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—816no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11C4×SD1614yescomplemented
308C22×C11C2×C4×D411yescharacteristic
309C22×C11D4212yes—
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11#57712yes—
313C4×C11—22no—
314C4×C11—24no—
315C4×C11—24no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—82no—
319C4×C11—82no—
320C4×C11C22×C22⋊C411yescharacteristic
321C4×C11#51811yescharacteristic
322C4×C11#54612yes—
323C25—21no—
324C22×Q8—21no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—42no—
328C22×Q8C2×C4×C1114yescomplemented
329C22×Q8C23×C1111yescharacteristic
330C22×Q8C23×C1111yescharacteristic
331C22×D4—24no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—42no—
335C22×D4C2×C4×C1114yes—
336C22×D4C23×C1111yescharacteristic
337C22×D4C23×C1111yescharacteristic
338C23×C4—21no—
339C23×C4—22no—
340C23×C4C23×C1111yescharacteristic
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—232no—
344C2×SD16—24no—
345C2×SD16C2×C4×C1114yes—
346C2×SD16C2×C4×C1114yes—
347C2×SD16C2×C4×C1114yescomplemented
348C2×SD16C2×C4×C1114yescomplemented
349C2×SD16D4×C1118yes—
350C22×C8—24no—
351C22×C8C2×C4×C1114yescomplemented
352C22×C8C23×C1112yes—
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1111yescharacteristic
355C4×Q8—24no—
356C4×Q8—42no—
357C4×D4—24no—
358C4×D4—42no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4C23×C1112yes—
361C2×C4⋊C4C23×C1112yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4D4×C1111yescharacteristic
369C2×C22⋊C4D4×C1111yescharacteristic
370C2×C42—22no—
371C2×C42C23×C1112yes—
372#106—24no—
373#103—24no—
374#103—42no—
375#102—24no—
376#102—42no—
377C22⋊C8—22no—
378C4×C8—24no—
379#95—22no—
380#95—22no—
381#95—21no—
382#95—21no—
383#95D4×C1112yes—
384C2×C11—24no—
385C2×C11—44no—
386C2×C11—82no—
387C2×C11D4×C22⋊C411yescharacteristic
388C2×C11C2×C4×SD1611yescharacteristic
389C2×C11#294911yescharacteristic
390C2×C11D4×SD1612yes—
391C2×C11#328212yes—
392C24—21no—
393C24—21no—
394C24—24no—
395C24—44no—
396C24—42no—
397C24—42no—
398C24—82no—
399C24C2×D4×C1111yescharacteristic
400C2×Q8—24no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8C22×C4×C1112yes—
411C2×Q8C22×C4×C1112yes—
412C2×Q8C2×D4×C1114yes—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—44no—
421C2×D4—48no—
422C2×D4—44no—
423C2×D4C22×C4×C1112yes—
424C2×D4C22×C4×C1112yes—
425C2×D4C2×D4×C1114yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—82no—
437C22×C4C22×C4×C1112yes—
438C22×C4C2×D4×C1112yes—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1112yes—
441C22×C4C11×#4112yes—
442C22×C4C24×C1111yescharacteristic
443SD16—28no—
444SD16—28no—
445SD16—28no—
446SD16C11×C22⋊C4116yesdirect product factor
447C2×C8—22no—
448C2×C8—28no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8C22×C4×C1112yes—
453C2×C8C22×C4×C1112yes—
454C2×C8C2×D4×C1114yes—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—44no—
460C22⋊C4—22no—
461C22⋊C4—44no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—44no—
465C22⋊C4—82no—
466C22⋊C4C11×SD1614yesdirect product factor
467C42—22no—
468C42—22no—
469C42—44no—
470C11C22⋊C4×SD1611yescharacteristic, direct product factor, Sylow
471C23—22no—
472C23—22no—
473C23—22no—
474C23—24no—
475C23—22no—
476C23—48no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—41no—
482C23—41no—
483C23—48no—
484C23—42no—
485C23—84no—
486C23—88no—
487C23—88no—
488C23C4×D4×C1112yes—
489C23C2×C11×SD1612yes—
490C23C11×#13512yes—
491C23C22×D4×C1111yescharacteristic
492Q8—22no—
493Q8—24no—
494Q8—22no—
495Q8—22no—
496Q8—48no—
497Q8—42no—
498Q8C2×C11×C22⋊C414yescomplemented
499D4—22no—
500D4—22no—
501D4—22no—
502D4—24no—
503D4—48no—
504D4—42no—
505D4C2×C11×C22⋊C414yes—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—88no—
527C2×C4C4×D4×C1112yes—
528C2×C4C2×C11×SD1614yescomplemented
529C2×C4C23×C4×C1111yescharacteristic
530C2×C4C22×D4×C1112yes—
531C2×C4C2×C11×#4111yescharacteristic
532C2×C4C11×H(5,𝔽2)12yes—
533C8—22no—
534C8—42no—
535C8C2×C11×C22⋊C414yescomplemented
536C22—22no—
537C22—24no—
538C22—24no—
539C22—22no—
540C22—24no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—44no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—816no—
549C22—82no—
550C22—82no—
551C22C4×C11×SD1614yescomplemented
552C22C2×C4×D4×C1111yescharacteristic
553C22D42×C1112yes—
554C22C22×C11×SD1611yescharacteristic
555C22C2×C11×#13511yescharacteristic
556C22C11×#57712yes—
557C4—24no—
558C4—22no—
559C4—24no—
560C4—42no—
561C4—42no—
562C4—82no—
563C4—82no—
564C4C22×C11×C22⋊C411yescharacteristic
565C4C11×#51811yescharacteristic
566C4C11×#54612yes—
567C2—24no—
568C2—44no—
569C2—82no—
570C2D4×C11×C22⋊C411yescharacteristic
571C2C2×C4×C11×SD1611yescharacteristic
572C2C11×#294911yescharacteristic
573C2D4×C11×SD1612yes—
574C2C11×#328212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×SD16C2semidirect
3. Q8×C11×C22⋊C4C2semidirect
5. C11×#1968C2semidirect
6. C11×#1880C2semidirect
7. C11×#1877C2semidirect
8. C11×#1807C2semidirect
9. C11×#1787C2semidirect
11. C8×C11×C22⋊C4C2semidirect
15. C22×C11×SD16C4semidirect
21. C2×C4×Q8×C11C22semidirect
25. C2×C11×#106C22semidirect
26. C2×C11×#103C22semidirect
27. C2×C11×#103C22semidirect
31. C2×C4×C8×C11C22semidirect
33. C11×#391C22semidirect
42. C11×#340C22semidirect
43. C11×#336C22semidirect
49. C22×Q8×C11C2×C4semidirect
68. C2×C11×SD16C2×C4semidirect
69. C2×C11×SD16C2×C4semidirect
72. C22×C8×C11C2×C4semidirect
105. C22⋊C4×SD16C11direct (N × H)
160. C11×SD16C22⋊C4direct (N × H)
180. C11×C22⋊C4SD16direct (N × H)
185. C2×C4×SD16C2×C11semidirect
186. Q8×C22⋊C4C2×C11semidirect
188. #1968C2×C11semidirect
189. #1880C2×C11semidirect
190. #1877C2×C11semidirect
191. #1807C2×C11semidirect
192. #1787C2×C11semidirect
194. C8×C22⋊C4C2×C11semidirect
222. Q8×C11C2×C22⋊C4semidirect
252. C2×C4×C11C2×SD16semidirect
259. C8×C11C2×C22⋊C4semidirect
263. C22×SD16C4×C11semidirect
269. C2×C4×Q8C22×C11semidirect
273. C2×#106C22×C11semidirect
274. C2×#103C22×C11semidirect
275. C2×#103C22×C11semidirect
279. C2×C4×C8C22×C11semidirect
281. #391C22×C11semidirect
290. #340C22×C11semidirect
291. #336C22×C11semidirect
307. C22×C11C4×SD16semidirect
328. C22×Q8C2×C4×C11semidirect
347. C2×SD16C2×C4×C11semidirect
348. C2×SD16C2×C4×C11semidirect
351. C22×C8C2×C4×C11semidirect
446. SD16C11×C22⋊C4direct (N × H)
466. C22⋊C4C11×SD16direct (N × H)
470. C11C22⋊C4×SD16direct (N × H)
498. Q8C2×C11×C22⋊C4semidirect
528. C2×C4C2×C11×SD16semidirect
535. C8C2×C11×C22⋊C4semidirect
551. C22C4×C11×SD16semidirect

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C2×C4×C11×SD162
Q8×C11×C22⋊C42
D4×C11×C22⋊C42
C11×#19682
C11×#18802
C11×#18772
C11×#18072
C11×#17872
C11×#17862
C8×C11×C22⋊C42
C22⋊C4×SD1611