Finite Group Databasebeta

← #14810427

Subgroups — #14810427

Order 2816.

1320 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
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622408C212yesmaximal, complemented
3#13076919C211yesmaximal, characteristic
4#13069755C212yesmaximal, complemented
5#13069751C212yesmaximal, complemented
6#13069587C212yesmaximal, complemented
7#13068933C211yesmaximal, characteristic
8#13068931C211yesmaximal, characteristic
9#13068924C211yesmaximal, characteristic, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C23×Dic22—21no—
13C2×C11×C22⋊Q8C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#67000C2211yescharacteristic
16C2×#66983C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66941—21no—
21C2×#66941—21no—
22C2×#66941—28no—
23C2×#66941C2212yes—
24C2×#66941C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2212yes—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66879C2212yes—
32#10622603—21no—
33#10622603—21no—
34#10622601C2211yescharacteristic
35#10622590C2211yescharacteristic
36C2×#66873C2212yes—
37#10622571—21no—
38#10622571—21no—
39#10622408—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×D44C2311yescharacteristic
53C22×Dic22—28no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—44no—
57C22×Dic22—44no—
58C22×C8×C11C2312yes—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67#67000—24no—
68#66983—22no—
69#66983—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—28no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66941—28no—
89#66941—28no—
90#66941—24no—
91#66941—24no—
92#66941—24no—
93#66941D418yescomplemented
94C11×#103—24no—
95C11×C22⋊C8—22no—
96#66899—24no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C22⋊(C11⋊C8)—22no—
102#66885—24no—
103#66879—24no—
104#66873—24no—
105#25908—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—42no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—22no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—22no—
146C2×Dic22—28no—
147C2×Dic22—28no—
148C2×Dic22—432no—
149C2×Dic22—44no—
150C2×Dic22—44no—
151C2×Dic22—44no—
152C2×Dic22—44no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4C2×D414yes—
162C11×C22⋊C4—42no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—24no—
169C4⋊Dic11—22no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11C2×D414yes—
173Dic11⋊C4—28no—
174Dic11⋊C4—28no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11C2×D414yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C22×C4⋊Q8—111no—
183C2×#489—112no—
184#2850—111no—
185#2024—112no—
186#2023—112no—
187#1993—112no—
188#1874—111no—
189#1874—111no—
190#1872—111no—
191#1872D1111yescharacteristic, complemented
192#1749—111no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11#12412yes—
198C23×C11AGL(1,ℤ/8)12yes—
199C23×C11#13712yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208Q8×C11—42no—
209Q8×C11—42no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—48no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11#12412yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C112−1+412yes—
229C22⋊D11—84no—
230C2×Dic11—28no—
231C2×Dic11—28no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—24no—
241C2×Dic11—48no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11#12012yes—
248C2×Dic11#12012yes—
249C2×Dic11AGL(1,ℤ/8)12yes—
250C2×Dic11#13712yes—
251D44—42no—
252D44—42no—
253Dic22—416no—
254Dic22—416no—
255C8×C11—42no—
256C11⋊C8—42no—
257C23×Q8—221no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8—112no—
260C2×C4⋊Q8—221no—
261C2×C4⋊Q8—221no—
262C2×C4⋊Q8—228no—
263C2×#124—111no—
264C2×C22⋊Q8C2×D1111yescharacteristic
265C2×#121—111no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—221no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C42—111no—
270#489—228no—
271C2×#103—112no—
272C2×#103C2×D1112yes—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8—111no—
276C2×C22⋊C8C2×D1111yescharacteristic
277C2×#97—112no—
278#391—111no—
279#390—111no—
280#388—221no—
281#388—221no—
282#386—221no—
283#386—221no—
284#382—111no—
285#340—112no—
286#340—112no—
287#340—112no—
288#340C2×D1112yes—
289#336—112no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11#48914yescomplemented
297C22×C11C2×#12011yescharacteristic
298C22×C11C2×#12411yescharacteristic
299C22×C11#53611yescharacteristic
300C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—22no—
312C4×C11—44no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11#54812yes—
316C4×C11#54812yes—
317Dic11—22no—
318Dic11—22no—
319Dic11—22no—
320Dic11—22no—
321Dic11—44no—
322Dic11—81no—
323C22×Q8—222no—
324C22×Q8—222no—
325C22×Q8—228no—
326C22×Q8—444no—
327C22×Q8—444no—
328C22×Q8C22×D1111yescharacteristic
329C22×D4—111no—
330C22×D4—221no—
331C23×C4—21no—
332C23×C4—111no—
333C23×C4—111no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336C22×C8—112no—
337C22×C8C22×D1112yes—
338C4⋊Q8—118no—
339C4⋊Q8—224no—
340C4⋊Q8—224no—
341C4⋊Q8—228no—
342C4⋊Q8—228no—
343C4⋊Q8—224no—
344#124—224no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347#121—222no—
348#121—222no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—228no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C42—111no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—224no—
372#103—24no—
373#103—224no—
374#102—224no—
375#102—224no—
376C22⋊C8—22no—
377C22⋊C8—222no—
378#97—224no—
379#95—221no—
380#95—221no—
381#95—221no—
382#95—221no—
383C2×C11—24no—
384C2×C11#243611yescharacteristic
385C2×C11#300311yescharacteristic
386C2×C11#300411yescharacteristic
387C2×C11C2×#48911yescharacteristic
388C2×C11#314111yescharacteristic
389C2×C11#323811yescharacteristic
390C2×C11#323911yescharacteristic
391D11—161no—
392C24—221no—
393C24D4×D1111yescharacteristic
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—228no—
399C2×Q8—228no—
400C2×Q8—444no—
401C2×Q8—4432no—
402C2×Q8—444no—
403C2×Q8—444no—
404C2×Q8—444no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4—221no—
408C2×D4—222no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4—442no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4#433912yes—
436C22×C4D4×D1111yescharacteristic
437C22×C4#434112yes—
438C22×C4C23×D1111yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—42no—
450C4⋊C4—114no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—224no—
454C4⋊C4—222no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4D4×D1114yes—
458C22⋊C4—42no—
459C22⋊C4—442no—
460C22⋊C4—442no—
461C22⋊C4—442no—
462C22⋊C4—442no—
463C22⋊C4—442no—
464C42—114no—
465C42—222no—
466C42—222no—
467C42—222no—
468C11#2590811yescharacteristic, complemented, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—441no—
474C23—441no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23#6693812yes—
481C23#6696712yes—
482C23#6697112yes—
483C23C2×D4×D1111yescharacteristic
484Q8—42no—
485Q8—42no—
486Q8—4416no—
487Q8—4416no—
488D4—442no—
489D4—442no—
490D4—884no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—48no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—228no—
510C2×C4—228no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—224no—
520C2×C4—448no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4#6693812yes—
527C2×C4C2×#433911yescharacteristic
528C2×C4C2×D4×D1112yes—
529C2×C4C2×#434111yescharacteristic
530C2×C4#6704312yes—
531C8—42no—
532C8—442no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—881no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22#1062240814yescomplemented
547C22C2×#6693811yescharacteristic
548C22D11×#12011yescharacteristic
549C22#1062317911yescharacteristic
550C22C2×#6696711yescharacteristic
551C22C2×#6697111yescharacteristic
552C22D11×AGL(1,ℤ/8)11yescharacteristic
553C22D11×#13711yescharacteristic
554C4—22no—
555C4—44no—
556C4—81no—
557C4—81no—
558C4—222no—
559C4—222no—
560C4—222no—
561C4—222no—
562C4—444no—
563C4—881no—
564C4#1062308312yes—
565C4#1062312912yes—
566C2—24no—
567C2—1761no—
568C2#1307227211yescharacteristic
569C2#1307784411yescharacteristic
570C2#1307785111yescharacteristic
571C2C2×#1062240811yescharacteristic
572C2#1307900711yescharacteristic
573C2#1307984011yescharacteristic
574C2#1307984911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1872D11
hypocenterC11#25908
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622408C2semidirect
4. #13069755C2semidirect
5. #13069751C2semidirect
6. #13069587C2semidirect
9. #13068924C2semidirect
10. #13068380C2semidirect
11. C11×#1872C2semidirect
93. #66941D4semidirect
191. #1872D11semidirect
296. C22×C11#489semidirect
468. C11#25908semidirect
546. C22#10622408semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106224082
#130769192
#130697552
#130697512
#130695872
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