Finite Group Databasebeta

← #14786402

Subgroups — #14786402

Order 2816.

1844 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C212yesmaximal, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3#13069795C214yesmaximal, complemented
4#13068934C212yesmaximal, complemented
5#13068804C212yesmaximal, complemented
6#13068547C212yesmaximal, complemented
7#13068526C211yesmaximal, characteristic, complemented
8C22×C11×#121C211yesmaximal, characteristic
9C23×D4×C11—21no—
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#121—21no—
13C2×C11×#121—21no—
14C2×C11×#121—28no—
15C2×C11×#121C2212yes—
16C2×C11×#121C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4—21no—
19C22×C22⋊Dic11—21no—
20C22×C4⋊Dic11C2211yescharacteristic, complemented
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22C2×#66896C2214yescomplemented
23C2×#66896C2214yescomplemented
24#10622825—21no—
25#10622825—21no—
26#10622825C2212yes—
27#10622825C2212yescomplemented
28C2×C11⋊#95—21no—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yescomplemented
31C2×C22⋊(C11⋊C8)C2212yescomplemented
32#10622646—28no—
33C2×#66871C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11—21no—
36C25×C11D411yescharacteristic
37C22×D4×C11—28no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—24no—
41C22×D4×C11—21no—
42C22×D4×C11—24no—
43C22×D4×C11—42no—
44C22×D4×C11—44no—
45C22×D4×C11—44no—
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—42no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—21no—
58C23×Dic11—21no—
59C11×#121—28no—
60C11×#121—28no—
61C11×#121—24no—
62C11×#121—24no—
63C11×#121—24no—
64C11×#121D418yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—28no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—44no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2312yes—
80C22×C11⋊C8C2314yes—
81#66896—28no—
82#66896—44no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C22⋊(C11⋊C8)—24no—
86C22⋊(C11⋊C8)—24no—
87C22⋊(C11⋊C8)—42no—
88#66871—28no—
89#24002—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11D814yes—
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D411yescharacteristic
108C2×D4×C11—24no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—22no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—416no—
115C2×D4×C11—42no—
116C2×D4×C11—432no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—42no—
122C2×D4×C11C2×D414yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—416no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4114yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D414yes—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—28no—
163C22⋊Dic11—44no—
164C22⋊Dic11—44no—
165C4⋊Dic11—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—42no—
168C4⋊Dic11—42no—
169C2×C11⋊C8—24no—
170C2×C11⋊C8—24no—
171C2×C11⋊C8—24no—
172C22×#121D1111yescharacteristic
173C2×#480—112no—
174C2×#380—111no—
175#2033—114no—
176#1874—112no—
177#1852—112no—
178#1786—112no—
179#1779—111no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—24no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—48no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—84no—
212C23×C11—84no—
213C23×C11—84no—
214C23×C11—84no—
215C23×C11#12012yes—
216C23×C11#12312yes—
217C23×C11C2×D812yes—
218C23×C11C2×D812yes—
219C23×C11C2×D812yes—
220C23×C11AGL(1,ℤ/8)12yes—
221C23×C11#13712yes—
222C23×C11C22×D411yescharacteristic
223D4×C11—28no—
224D4×C11—48no—
225D4×C11—416no—
226D4×C11—416no—
227D4×C11—44no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—28no—
233C2×C4×C11—28no—
234C2×C4×C11—21no—
235C2×C4×C11—24no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11—48no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—44no—
245C2×C4×C11#12012yes—
246C2×C4×C11#12312yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4112yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—84no—
257C2×Dic11—84no—
258C11⋊C8—44no—
259C23×D4—21no—
260C23×D4C2×D1111yescharacteristic
261C24×C4C2×D1111yescharacteristic
262C2×#121—21no—
263C2×#121—21no—
264C2×#121—28no—
265C2×#121C2×D1112yes—
266C2×#121C2×D1112yes—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C22⋊C4—21no—
271C22×C22⋊C4—221no—
272#480—228no—
273C2×#107—114no—
274C2×#102—114no—
275C2×#102—114no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279#380—112no—
280#380—112no—
281#380—221no—
282#380—221no—
283C2×#95—221no—
284#340—114no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—416no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—816no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11#44714yes—
314C22×C11#48014yescomplemented
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12311yescharacteristic
317C22×C11#53411yescharacteristic
318C22×C11C22×D811yescharacteristic
319C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C11C2×#13711yescharacteristic
321C22×C11#57511yescharacteristic
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—41no—
325C4×C11—44no—
326C4×C11#54614yes—
327Dic11—82no—
328Dic11—82no—
329C25—21no—
330C25C22⋊D1111yescharacteristic
331C22×D4—28no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—21no—
337C22×D4—42no—
338C22×D4—44no—
339C22×D4—44no—
340C22×D4C22×D1112yes—
341C23×C4—21no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—42no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4C22⋊D1111yescharacteristic
348C23×C4C22⋊D1111yescharacteristic
349C23×C4C22⋊D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C22×C8—114no—
354#121—28no—
355#121—28no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121C22⋊D1118yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—442no—
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—444no—
375#107—228no—
376#102—228no—
377#102—444no—
378C22⋊C8—224no—
379C22⋊C8—224no—
380C22⋊C8—442no—
381#95—222no—
382#95—222no—
383C2×C11—24no—
384C2×C11—24no—
385C2×C11—42no—
386C2×C11—84no—
387C2×C11#240511yescharacteristic
388C2×C11C2×#44711yescharacteristic
389C2×C11#300711yescharacteristic
390C2×C11C2×#48011yescharacteristic
391C2×C11#309411yescharacteristic
392C2×C11#318611yescharacteristic
393C2×C11#319311yescharacteristic
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—22no—
400C24—41no—
401C24—41no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24#432314yes—
409C24C2×C22⋊D1111yescharacteristic
410C24C2×C22⋊D1111yescharacteristic
411C24C2×C22⋊D1111yescharacteristic
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—416no—
419C2×D4—42no—
420C2×D4—432no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4C2×C22⋊D1114yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—416no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4#434114yes—
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1114yes—
461C22×C4C23×D1111yescharacteristic
462C2×C8—224no—
463C2×C8—224no—
464C2×C8—224no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4C2×C22⋊D1114yes—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—444no—
475C22⋊C4—444no—
476C11#2400211yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—28no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—28no—
493C23—24no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—48no—
500C23—48no—
501C23—48no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—84no—
509C23—84no—
510C23—84no—
511C23—84no—
512C23C2×#432312yes—
513C23C2×#432312yes—
514C23C2×#432312yes—
515C23#6698512yes—
516C23#6698812yes—
517C23#6700412yes—
518C23#6700612yes—
519C23C22×C22⋊D1111yescharacteristic
520D4—28no—
521D4—48no—
522D4—416no—
523D4—416no—
524D4—44no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—884no—
549C2×C4—884no—
550C2×C4#6698812yes—
551C2×C4#6700612yes—
552C2×C4C2×#434112yes—
553C2×C4#6703712yes—
554C2×C4C22×C22⋊D1112yes—
555C8—444no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—416no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—816no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22#1062264614yescomplemented
585C22#1062283014yes—
586C22C22×#432311yescharacteristic
587C22C2×#6698511yescharacteristic
588C22C2×#6698811yescharacteristic
589C22#1062333511yescharacteristic
590C22#1062335311yescharacteristic
591C22C2×#6700411yescharacteristic
592C22C2×#6700611yescharacteristic
593C4—22no—
594C4—22no—
595C4—44no—
596C4—41no—
597C4—882no—
598C4—882no—
599C4#1062333714yes—
600C2—24no—
601C2—24no—
602C2—42no—
603C2—84no—
604C2#1307193911yescharacteristic
605C2C2×#1062283011yescharacteristic
606C2#1307787611yescharacteristic
607C2C2×#1062264611yescharacteristic
608C2#1307855211yescharacteristic
609C2#1307936411yescharacteristic
610C2#1307942211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C22×D4
hypercenterC22×#121D11
hypocenterC11#24002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622646C2semidirect
2. C2×#10622825C2semidirect
3. #13069795C2semidirect
4. #13068934C2semidirect
5. #13068804C2semidirect
6. #13068547C2semidirect
7. #13068526C2semidirect
20. C22×C4⋊Dic11C22semidirect
21. C22×C4⋊Dic11C22semidirect
22. C2×#66896C22semidirect
23. C2×#66896C22semidirect
27. #10622825C22semidirect
30. C2×C22⋊(C11⋊C8)C22semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
33. C2×#66871C22semidirect
34. #10622167C22semidirect
314. C22×C11#480semidirect
476. C11#24002semidirect
584. C22#10622646semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
C2×#106228252
#130697952
#130689342
#130688042
#130685472
#130685262
C22×C11×#1212
#2400211