Finite Group Databasebeta

← #14787700

Subgroups — #14787700

Order 2816.

1174 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
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13073532C211yesmaximal, characteristic
5#13069818C212yesmaximal, complemented
6#13069618C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069409C211yesmaximal, characteristic, complemented
9#13068937C212yesmaximal, complemented
10#13068818C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×#4325C2211yescharacteristic
15#10623115—24no—
16#10623115—24no—
17C2×#66951—22no—
18C2×#66948—21no—
19C2×#66948C2212yes—
20C2×#66945C2212yes—
21C2×#66928—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C11×#384C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×#66882C2212yes—
34C4×#4325—24no—
35#10622604—22no—
36#10622600—21no—
37#10622600C2212yes—
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622459—24no—
42C11×#340C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D44—22no—
47C22×D44D411yescharacteristic
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11C2312yes—
51C22×Dic22—21no—
52C22×C8×C11C2312yes—
53C4×Q8×C11—22no—
54C4×Q8×C11D414yescomplemented
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#66999—24no—
63#66999—24no—
64C2×#4325—22no—
65C2×#4325—22no—
66C2×#4325—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81#66951—216no—
82#66948—24no—
83#66948—42no—
84#66948—44no—
85#66945—24no—
86#66945—24no—
87#66928—28no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44—22no—
91C4×D44—22no—
92#66922—22no—
93#66922D414yescomplemented
94C4×Dic22—28no—
95C11×C4⋊C8—22no—
96C11×#103—42no—
97#66899—22no—
98C11⋊#95—22no—
99#66885—24no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—42no—
102#66882—24no—
103#66873—22no—
104#66872—22no—
105C4×C11⋊C8—22no—
106#24119—111nomaximal, Sylow
107C23×D11—21no—
108C23×D11C2×D412yes—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C2×D412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11C2×D412yes—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—44no—
133C2×D44—44no—
134C2×D44—82no—
135C2×D44#4112yes—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×Dic22—24no—
146C2×Dic22—42no—
147C2×Dic22—42no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4C2×D412yes—
158C42×C11—24no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161#4325—28no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—22no—
169C4⋊Dic11—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11C2×D414yes—
174Dic11⋊C4—28no—
175C4×Dic11—28no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8#4112yes—
182C2×#556—111no—
183C2×#474—111no—
184C2×C4×SD16—111no—
185#2537—111no—
186#2036—112no—
187#2000—112no—
188#1990—111no—
189#1954—111no—
190#1875—112no—
191#1854—112no—
192#1803D1111yescharacteristic, complemented
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—41no—
211Q8×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11#13512yes—
226C2×C4×C11AGL(1,ℤ/8)12yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242D44—22no—
243D44—22no—
244D44—41no—
245D44—41no—
246D44—44no—
247D44—88no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—84no—
253Dic22—48no—
254C8×C11—42no—
255C11⋊C8—22no—
256C11⋊C8—41no—
257C22×SD16—111no—
258#556—224no—
259#556—224no—
260C2×C4⋊Q8—111no—
261C2×#126—222no—
262C2×#124—221no—
263C2×C22⋊Q8—112no—
264C2×#121—112no—
265C2×#121—221no—
266C2×C4×Q8—221no—
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×D4—111no—
269C2×C4×D4—111no—
270C2×#117—112no—
271#474—224no—
272C4×SD16—224no—
273C2×#107—112no—
274C2×#106—111no—
275C2×C4⋊C8C2×D1111yescharacteristic
276C2×#103—111no—
277C2×#103C2×D1112yes—
278C2×#102—112no—
279C2×#102—111no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283#394—222no—
284#384C2×D1111yescharacteristic
285#380—112no—
286#380—221no—
287#340—112no—
288#340—112no—
289#340C2×D1112yes—
290C22×C11C2×#12011yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11#54711yescharacteristic
293C22×C11C2×#13511yescharacteristic
294C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C11#57711yescharacteristic
296C22×C11#57811yescharacteristic
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—82no—
315C4×C11#44914yes—
316C4×C11#52511yescharacteristic
317C4×C11#53711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—42no—
321Dic11—44no—
322Dic11—81no—
323C22×Q8—221no—
324C22×Q8C22×D1111yescharacteristic
325C22×D4—111no—
326C22×D4—111no—
327C22×D4—222no—
328C23×C4—112no—
329C23×C4—221no—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×SD16—222no—
333C22×C8—111no—
334C22×C8—111no—
335C22×C8C22×D1112yes—
336C4⋊Q8—114no—
337C4⋊Q8—222no—
338#126—2216no—
339#124—228no—
340C22⋊Q8—224no—
341C22⋊Q8—224no—
342#121—224no—
343#121—442no—
344#121—444no—
345C4×Q8—22no—
346C4×Q8—228no—
347C4×Q8D4414yescomplemented
348C4×D4—222no—
349C4×D4—222no—
350C4×D4—222no—
351C4×D4—222no—
352#117—224no—
353#117—224no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—112no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—221no—
370C2×C42—21no—
371C2×C42—222no—
372C2×C42C22×D1111yescharacteristic
373#107—224no—
374#106—222no—
375C4⋊C8—22no—
376#103—42no—
377#103—222no—
378#102—224no—
379#102—222no—
380C22⋊C8—224no—
381C22⋊C8—442no—
382C4×C8—222no—
383#95—222no—
384C2×C11#240711yescharacteristic
385C2×C11C2×#44911yescharacteristic
386C2×C11#301311yescharacteristic
387C2×C11#330211yescharacteristic
388C2×C11#332411yescharacteristic
389C2×C11#334011yescharacteristic
390C2×C11#335311yescharacteristic
391D11—82no—
392D11—82no—
393C24—112no—
394C24—221no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—224no—
401C2×Q8—442no—
402C2×Q8—442no—
403C2×Q8C2×D4412yes—
404C2×D4—112no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—882no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—112no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—221no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4—442no—
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434SD16—228no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—112no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—81no—
450C4⋊C4—114no—
451C4⋊C4—228no—
452C4⋊C4—222no—
453C4⋊C4—224no—
454C4⋊C4—222no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4C2×D4412yes—
458C22⋊C4—228no—
459C22⋊C4—228no—
460C22⋊C4—224no—
461C22⋊C4—444no—
462C22⋊C4—444no—
463C22⋊C4—442no—
464C42—24no—
465C42—228no—
466C42C2×D4412yes—
467C42D4×D1112yes—
468C11#2411911yescharacteristic, complemented, Sylow
469C23—222no—
470C23—222no—
471C23—222no—
472C23—222no—
473C23—222no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23—441no—
482C23—441no—
483C23C2×D4×D1111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—448no—
489D4—222no—
490D4—222no—
491D4—441no—
492D4—441no—
493D4—444no—
494D4—888no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—884no—
520C2×C4#6693512yes—
521C2×C4#6693512yes—
522C2×C4#6696712yes—
523C2×C4#6697212yes—
524C2×C4C22×D4411yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4#6703711yescharacteristic
527C2×C4#6704011yescharacteristic
528C2×C4#41×D1111yescharacteristic
529C2×C4#41×D1111yescharacteristic
530C8—42no—
531C8—222no—
532C8—441no—
533C22—442no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22C2×#6693511yescharacteristic
548C22#1062314311yescharacteristic
549C22#1062316211yescharacteristic
550C22C2×#6696711yescharacteristic
551C22C2×#6697211yescharacteristic
552C22#1062330611yescharacteristic
553C22#1062331011yescharacteristic
554C4—22no—
555C4—42no—
556C4—42no—
557C4—82no—
558C4—444no—
559C4—442no—
560C4—881no—
561C4#1062242414yes—
562C4#1062304111yescharacteristic
563C4#1062305511yescharacteristic
564C4#1062313011yescharacteristic
565C4#1062316411yescharacteristic
566C2—882no—
567C2—882no—
568C2#1307196211yescharacteristic
569C2C2×#1062242411yescharacteristic
570C2#1307793311yescharacteristic
571C2#1308053611yescharacteristic
572C2#1308085011yescharacteristic
573C2#1308103211yescharacteristic
574C2#1308120311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radical#13073532C2
hypercenter#1803D11
hypocenterC11#24119
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
2. C2×#10622459C2semidirect
3. C2×C4×#4325C2semidirect
5. #13069818C2semidirect
6. #13069618C2semidirect
7. #13069576C2semidirect
8. #13069409C2semidirect
9. #13068937C2semidirect
10. #13068818C2semidirect
11. C11×#1803C2semidirect
54. C4×Q8×C11D4semidirect
93. #66922D4semidirect
192. #1803D11semidirect
347. C4×Q8D44semidirect
468. C11#24119semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106224592
C2×C4×#43252
#130735322
#130698182
#130696182
#130695762
#130694092
#130689372
#130688182
C11×#18032
#2411911