Finite Group Databasebeta

← #14787701

Subgroups — #14787701

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×#10623263C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13069821C212yesmaximal, complemented
5#13069620C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069409C211yesmaximal, characteristic, complemented
8#13068935C212yesmaximal, complemented
9#13068812C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C2×C11×#474C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#67000—21no—
15C2×Q8×Dic11—21no—
16C2×#66991C2212yes—
17C22×#4324C2211yescharacteristic
18C2×#66983—21no—
19#10623263—24no—
20#10623263—24no—
21C2×#66951—22no—
22C2×#66950C2212yes—
23C2×#66945C2212yes—
24C2×C4×D44C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#474—24no—
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×#66896C2211yescharacteristic
31#10622825—21no—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66880C2212yes—
35C4×#4324—24no—
36#10622600C2212yes—
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622574—22no—
40#10622548C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C22×D44D411yescharacteristic
50C22×C4×D11C2312yes—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yescomplemented
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63#67000—28no—
64Q8×Dic11—28no—
65#66991—24no—
66#66991—42no—
67C2×#4324—22no—
68C2×#4324—22no—
69C2×#4324—22no—
70#66983—44no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—22no—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86#66951—216no—
87#66950—24no—
88#66950—24no—
89#66945—24no—
90#66945—24no—
91C4×D44—22no—
92C4×D44—22no—
93C4×Dic22—22no—
94C4×Dic22D414yescomplemented
95C11×#107—24no—
96C11×C4⋊C8—22no—
97C11×#102—24no—
98#66896—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—42no—
102#66880—42no—
103#66874—22no—
104#66872—22no—
105C4×C11⋊C8—22no—
106#24119—111nomaximal, Sylow
107C24×C11—21no—
108C23×D11C2×D412yes—
109C2×Q8×C11—24no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11#4112yes—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C2×C22⋊D11—82no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11C2×D412yes—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
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×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22C2×D412yes—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—42no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C22⋊Dic11—44no—
160#4324—28no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—44no—
165C4⋊Dic11—28no—
166C4⋊Dic11—22no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11—81no—
172C4⋊Dic11C2×D412yes—
173Dic11⋊C4—24no—
174C4×Dic11—28no—
175C4×Dic11—24no—
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×#474D1111yescharacteristic, complemented
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#1803—111no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208Q8×C11—48no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—41no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—84no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#13512yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C22⋊D11—88no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245D44—44no—
246C4×D11—42no—
247C4×D11—42no—
248C4×D11—42no—
249C4×D11—42no—
250Dic22—22no—
251Dic22—22no—
252Dic22—41no—
253Dic22—41no—
254C8×C11—42no—
255C11⋊C8—22no—
256C11⋊C8—41no—
257C22×SD16—111no—
258#556—224no—
259#556—224no—
260C2×C4⋊Q8C2×D1111yescharacteristic
261C2×#126—222no—
262C2×#124—221no—
263C2×C22⋊Q8—112no—
264C2×#121—112no—
265C2×#121—221no—
266C2×C4×Q8—111no—
267C2×C4×Q8—221no—
268C2×C4×D4—111no—
269C2×C4×D4C2×D1111yescharacteristic
270C2×#117—112no—
271#474—24no—
272C4×SD16—224no—
273C2×#107C2×D1112yes—
274C2×#106—111no—
275C2×C4⋊C8C2×D1111yescharacteristic
276C2×#103—111no—
277C2×#103—112no—
278C2×#102—111no—
279C2×#102C2×D1112yes—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283#394—222no—
284#384—111no—
285#380—112no—
286#380—221no—
287#340—112no—
288#340—112no—
289#340—112no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11C2×#12011yescharacteristic
298C22×C11#54611yescharacteristic
299C22×C11#54711yescharacteristic
300C22×C11C2×#13511yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11#57711yescharacteristic
303C22×C11#57811yescharacteristic
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C4×C11—22no—
312C4×C11—44no—
313C4×C11—81no—
314C4×C11#44914yes—
315C4×C11#52511yescharacteristic
316C4×C11#53711yescharacteristic
317C4×C11#54811yescharacteristic
318C4×C11#55011yescharacteristic
319Dic11—42no—
320Dic11—42no—
321Dic11—42no—
322Dic11—82no—
323C22×Q8—21no—
324C22×Q8—111no—
325C22×D4—111no—
326C22×D4—222no—
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C23×C4—112no—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×SD16—222no—
333C22×C8—111no—
334C22×C8—111no—
335C22×C8C22×D1112yes—
336C4⋊Q8—22no—
337C4⋊Q8C22⋊D1114yescomplemented
338#126—2216no—
339#124—228no—
340C22⋊Q8—224no—
341C22⋊Q8—224no—
342#121—224no—
343#121—442no—
344#121—444no—
345C4×Q8—114no—
346C4×Q8—228no—
347C4×Q8—222no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—222no—
351C4×D4—222no—
352#117—224no—
353#117—224no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C42—222no—
371C2×C42—221no—
372C2×C42C22×D1111yescharacteristic
373#107—24no—
374#106—222no—
375C4⋊C8—22no—
376#103—222no—
377#103—442no—
378#102—24no—
379#102—222no—
380C22⋊C8—224no—
381C22⋊C8—442no—
382C4×C8—222no—
383#95—222no—
384C2×C11—82no—
385C2×C11#240711yescharacteristic
386C2×C11C2×#44911yescharacteristic
387C2×C11#301311yescharacteristic
388C2×C11#330211yescharacteristic
389C2×C11#332411yescharacteristic
390C2×C11#334011yescharacteristic
391C2×C11#335311yescharacteristic
392D11—82no—
393C24—21no—
394C24—112no—
395C2×Q8—24no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8—112no—
399C2×Q8—221no—
400C2×Q8—221no—
401C2×Q8—221no—
402C2×Q8—221no—
403C2×Q8—221no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4—882no—
415C2×D4#434312yes—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—112no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
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—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—112no—
449C4⋊C4—228no—
450C4⋊C4—222no—
451C4⋊C4—224no—
452C4⋊C4—221no—
453C4⋊C4—222no—
454C4⋊C4—222no—
455C4⋊C4—442no—
456C4⋊C4—881no—
457C4⋊C4C2×C22⋊D1114yes—
458C22⋊C4—42no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—224no—
462C22⋊C4—444no—
463C22⋊C4—444no—
464C42—228no—
465C42—224no—
466C42D4×D1112yes—
467C42C2×C22⋊D1112yes—
468C11#2411911yescharacteristic, complemented, Sylow
469C23—22no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—222no—
483C23C2×D4×D1111yescharacteristic
484Q8—48no—
485Q8—222no—
486Q8—222no—
487Q8—441no—
488Q8—441no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—444no—
494D4—888no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—84no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4#6696412yes—
521C2×C4#6696512yes—
522C2×C4#6699012yes—
523C2×C4#6699012yes—
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×#434311yescharacteristic
526C2×C4#6704011yescharacteristic
527C2×C4#41×D1111yescharacteristic
528C2×C4#6704211yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—42no—
531C8—222no—
532C8—441no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22—442no—
546C22—442no—
547C22#1062316111yescharacteristic
548C22#1062316211yescharacteristic
549C22C2×#6696411yescharacteristic
550C22C2×#6696511yescharacteristic
551C22#1062330911yescharacteristic
552C22#1062331011yescharacteristic
553C22C2×#6699011yescharacteristic
554C4—22no—
555C4—44no—
556C4—81no—
557C4—442no—
558C4—442no—
559C4—442no—
560C4—882no—
561C4#1062277114yes—
562C4#1062315811yescharacteristic
563C4#1062316011yescharacteristic
564C4#1062334811yescharacteristic
565C4#1062336511yescharacteristic
566C2—82no—
567C2—882no—
568C2#1307196311yescharacteristic
569C2C2×#1062277111yescharacteristic
570C2#1307793011yescharacteristic
571C2#1308053011yescharacteristic
572C2#1308084411yescharacteristic
573C2#1308102611yescharacteristic
574C2#1308119711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#474D11
hypocenterC11#24119
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
2. C2×C4×#4324C2semidirect
4. #13069821C2semidirect
5. #13069620C2semidirect
6. #13069578C2semidirect
7. #13069409C2semidirect
8. #13068935C2semidirect
9. #13068812C2semidirect
10. #13068622C2semidirect
11. C2×C11×#474C2semidirect
54. C11×C4⋊Q8D4semidirect
94. C4×Dic22D4semidirect
183. C2×#474D11semidirect
337. C4⋊Q8C22⋊D11semidirect
468. C11#24119semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×C4×#43242
#130735292
#130698212
#130696202
#130695782
#130694092
#130689352
#130688122
#130686222
C2×C11×#4742
#2411911