Finite Group Databasebeta

← #14763605

Subgroups — #14763605

Order 2816.

1324 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13077247C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13069605C211yesmaximal, characteristic, complemented
5#13069604C211yesmaximal, characteristic, complemented
6#13069457C211yesmaximal, characteristic, complemented
7#13069076C214yesmaximal, complemented
8#13068606C214yesmaximal, complemented
9C11×#1965C211yesmaximal, characteristic, complemented
10C22×#4341C412yes—
11C2×C11×#127C2211yescharacteristic
12C2×#66991C412yes—
13C2×#66991C2212yes—
14C2×#66989C412yes—
15C2×D4×Dic11C412yes—
16C2×D4×Dic11C2212yes—
17C2×M16×D11C2212yes—
18#10623247—21no—
19#10623247—21no—
20#10623247—21no—
21#10623247—21no—
22#10623247—21no—
23#10623247—21no—
24#10623247—21no—
25#10623247—21no—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#423C2211yescharacteristic
29C2×C11×#100C2214yes—
30C4×C11×M16C2211yescharacteristic
31C2×#66897C2214yes—
32#10622739C2212yes—
33#10622731C2212yes—
34#10622731C2212yes—
35#10622537C2211yescharacteristic
36C4×#4318C2211yescharacteristic
37#10622450—21no—
38#10622450—21no—
39D11×C4⋊C8—21no—
40D11×C4⋊C8—21no—
41#10622318—21no—
42#10622318—21no—
43#10622298—21no—
44#10622298—21no—
45#10622192C2214yes—
46#10622192C2214yes—
47C22×D4×C11C2×C412yes—
48C22×D4×C11C2×C412yes—
49C22×D4×C11C2312yes—
50C22×C22⋊D11C2×C414yes—
51C23×Dic11C2×C414yes—
52C2×#4341—22no—
53C2×#4341—22no—
54C2×#4341—22no—
55C2×#4341—22no—
56C2×#4341—48no—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22C2×C412yes—
61C2×C11×M16C2312yes—
62C2×C11×M16C2312yes—
63C11×#127—21no—
64C11×#127—21no—
65C11×#127—21no—
66C11×#127—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11C2×C414yes—
69C2×C22⋊Dic11C2×C414yes—
70#66991—22no—
71#66991—22no—
72#66991—22no—
73#66991—22no—
74#66991—22no—
75#66991—22no—
76#66991—22no—
77#66991—22no—
78#66989—22no—
79#66989—22no—
80#66989—22no—
81#66989—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11—22no—
89D4×Dic11—22no—
90C2×C4⋊Dic11C2×C412yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11C2×C411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×#4318C2312yes—
96C2×#4318C2312yes—
97M16×D11—44no—
98C2×#4313—22no—
99C2×C8×D11—22no—
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11D411yescharacteristic
106C42×D11D411yescharacteristic
107C42×D11D411yescharacteristic
108#66922—21no—
109#66922—21no—
110#66922—21no—
111#66922—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×#100—44no—
115C11×#97—21no—
116C4×C8×C11—21no—
117#66897—44no—
118(C2×D11)⋊C8—22no—
119(C2×D11)⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8—22no—
123Dic11⋊C8—22no—
124C4⋊(C11⋊C8)—21no—
125C4⋊(C11⋊C8)—21no—
126#66867—21no—
127C4×C11⋊C8—21no—
128#21878—111nomaximal, Sylow
129C24×C11C22×C414yes—
130C23×D11C22×C411yescharacteristic
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—24no—
146C2×C22⋊D11—48no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—48no—
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C414yes—
153C22×Dic11C22×C411yescharacteristic
154#4341—48no—
155#4341—48no—
156#4341—48no—
157#4341—48no—
158C2×C4×D11—24no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—42no—
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22⋊C411yescharacteristic
165C2×C4×D11C22⋊C411yescharacteristic
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—44no—
177C11×M16—22no—
178C11×M16—24no—
179C11×M16—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C22⋊Dic11—24no—
187C22⋊Dic11—24no—
188C22⋊Dic11—24no—
189C22⋊Dic11—24no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C22⋊C411yescharacteristic
197C4×Dic11C22⋊C411yescharacteristic
198C4×Dic11C22⋊C411yescharacteristic
199C4×Dic11C22⋊C411yescharacteristic
200C4×Dic11C22⋊C411yescharacteristic
201C4×Dic11C22⋊C411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11C2×D411yescharacteristic
204C4×Dic11C2×D411yescharacteristic
205C4×Dic11C2×D411yescharacteristic
206#4318—22no—
207#4318—24no—
208#4318—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211#4313—44no—
212C8×D11—44no—
213C2×#532—111no—
214#2920—111no—
215C2×#423—111no—
216#1997—111no—
217#1997—111no—
218#1965—111no—
219#1965D1111yescharacteristic, complemented
220#1900—114no—
221#1800—114no—
222C23×C11—24no—
223C23×C11—28no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11C23×C411yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—41no—
230C22×D11C2×C22⋊C411yescharacteristic
231C22×D11C2×C22⋊C411yescharacteristic
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—44no—
237D4×C11—44no—
238D4×C11—44no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11C2×C22⋊C411yescharacteristic
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11C2×C22⋊C411yescharacteristic
244C2×C4×C11C2×C22⋊C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11H(5,𝔽2)12yes—
248C2×C4×C112−1+412yes—
249C22⋊D11—48no—
250C22⋊D11—48no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—41no—
255C2×Dic11—48no—
256C2×Dic11—48no—
257C2×Dic11—44no—
258C2×Dic11C2×C22⋊C411yescharacteristic
259C2×Dic11C2×C22⋊C411yescharacteristic
260C2×Dic11C2×C22⋊C411yescharacteristic
261C2×Dic11C2×C22⋊C411yescharacteristic
262C2×Dic11C2×C22⋊C411yescharacteristic
263C2×Dic11C2×C22⋊C411yescharacteristic
264C4×D11—22no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11#10014yescomplemented
278Dic22—44no—
279Dic22—44no—
280C8×C11—42no—
281C8×C11—42no—
282C11⋊C8—42no—
283C11⋊C8—42no—
284C22×#41—112no—
285C22×M16—112no—
286#532—221no—
287#532—221no—
288#532—221no—
289#532—221no—
290#532—221no—
291#532—221no—
292#532—221no—
293#532—221no—
294C2×C4⋊Q8—111no—
295C2×#127C2×D1111yescharacteristic
296C2×#124—112no—
297C2×#121—112no—
298C2×#121—112no—
299C2×C4×D4—112no—
300C2×C4×D4—112no—
301C22×C42—111no—
302#432—221no—
303#432—221no—
304#431—221no—
305#431—221no—
306#423—112no—
307#423—112no—
308#423—111no—
309#423—221no—
310#423—221no—
311#423C2×D1111yescharacteristic
312C2×C4⋊C8—221no—
313C2×C4⋊C8—221no—
314C2×#100—114no—
315C2×#100C2×D1114yes—
316#407—112no—
317C4×M16—111no—
318C4×M16C2×D1111yescharacteristic
319#343—114no—
320#343—114no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—88no—
327C22×C11C22×C22⋊C411yescharacteristic
328C22×C11#52012yes—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—44no—
335C2×D11C2×#10012yes—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11C2×#10012yes—
339C4×C11#41312yes—
340C4×C11#53511yescharacteristic
341C4×C11#53611yescharacteristic
342C4×C11#53712yes—
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—21no—
348Dic11—44no—
349Dic11C2×#10012yes—
350C2×#41—222no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—448no—
355C22×Q8—112no—
356C22×D4—114no—
357C22×D4C4×D1112yes—
358C22×D4C4×D1112yes—
359C22×D4C22×D1112yes—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—114no—
364C2×M16—112no—
365C2×M16—112no—
366C2×M16—222no—
367C2×M16—444no—
368C2×M16C22×D1112yes—
369C2×M16C22×D1112yes—
370C22×C8—222no—
371C4⋊Q8—221no—
372C4⋊Q8—221no—
373C4⋊Q8—221no—
374C4⋊Q8—221no—
375#127—21no—
376#127—21no—
377#127—21no—
378#127—21no—
379#124—222no—
380#124—222no—
381#124—222no—
382#124—222no—
383#121—222no—
384#121—222no—
385#121—222no—
386#121—222no—
387#121—222no—
388#121—222no—
389#121—222no—
390#121—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—112no—
401C2×C22⋊C4—114no—
402C2×C22⋊C4—114no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42C22×D1111yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—222no—
418C4⋊C8—222no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421C4⋊C8—221no—
422C4⋊C8—221no—
423#100—44no—
424#100—444no—
425C22⋊C8—222no—
426C22⋊C8—222no—
427#97—21no—
428#97—221no—
429C4×C8—21no—
430C4×C8—221no—
431C2×C11—22no—
432C2×C11—84no—
433C2×C11#231111yescharacteristic
434C2×C11C22×#10011yescharacteristic
435C2×C11C2×#41311yescharacteristic
436D11—22no—
437D11—41no—
438C24—111no—
439C24C2×C4×D1114yes—
440#41—448no—
441#41—448no—
442#41—448no—
443#41—448no—
444C2×Q8—222no—
445C2×Q8—222no—
446C2×Q8—444no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—448no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—114no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—442no—
482C22×C4—448no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486M16—22no—
487M16—24no—
488M16—22no—
489M16—222no—
490M16—224no—
491M16—222no—
492M16—444no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—444no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C22⋊C4—224no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4—224no—
506C42—111no—
507C42—111no—
508C42—111no—
509C42—111no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—111no—
516C42—111no—
517C42—111no—
518C42D4×D1111yescharacteristic
519C42D4×D1111yescharacteristic
520C42D4×D1111yescharacteristic
521C42D4×D1111yescharacteristic
522C11#2187811yescharacteristic, complemented, Sylow
523C23—24no—
524C23—28no—
525C23—44no—
526C23—44no—
527C23—111no—
528C23—111no—
529C23—222no—
530C23—222no—
531C23—441no—
532C23C22×C4×D1111yescharacteristic
533Q8—444no—
534Q8—444no—
535D4—44no—
536D4—44no—
537D4—42no—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—42no—
542D4—448no—
543D4—448no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—111no—
547C2×C4—114no—
548C2×C4—111no—
549C2×C4—111no—
550C2×C4—111no—
551C2×C4—111no—
552C2×C4—111no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—224no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—448no—
570C2×C4—441no—
571C2×C4—448no—
572C2×C4—444no—
573C2×C4C22⋊C4×D1111yescharacteristic
574C2×C4C22⋊C4×D1111yescharacteristic
575C2×C4C22⋊C4×D1111yescharacteristic
576C2×C4C22⋊C4×D1111yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6703712yes—
580C2×C4#6704312yes—
581C8—42no—
582C8—42no—
583C8—442no—
584C8—442no—
585C22—21no—
586C22—21no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—88no—
591C22—112no—
592C22—221no—
593C22—221no—
594C22—221no—
595C22—221no—
596C22—221no—
597C22—444no—
598C22C2×C22⋊C4×D1111yescharacteristic
599C22#1062307712yes—
600C4—21no—
601C4—21no—
602C4—112no—
603C4—221no—
604C4—221no—
605C4—221no—
606C4—221no—
607C4—221no—
608C4—444no—
609C4D11×#10012yes—
610C4#1062235812yes—
611C4#1062313912yes—
612C4#1062320611yescharacteristic
613C4#1062324611yescharacteristic
614C2—22no—
615C2—84no—
616C2—222no—
617C2—441no—
618C2#1307120611yescharacteristic
619C2C2×D11×#10011yescharacteristic
620C2C2×#1062235811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1965C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623247C2
cosocleC22×C4×C11C24
hypercenter#1965D11
hypocenterC11#21878
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #13077247C2semidirect
3. D11×#423C2semidirect
4. #13069605C2semidirect
5. #13069604C2semidirect
6. #13069457C2semidirect
7. #13069076C2semidirect
8. #13068606C2semidirect
9. C11×#1965C2semidirect
219. #1965D11semidirect
277. C4×D11#100semidirect
522. C11#21878semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130772472
D11×#4232
#130696052
#130696042
#130694572
#130690762
#130686062
C11×#19652
#2187811