Finite Group Databasebeta

← #14804525

Subgroups — #14804525

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622477C212yesmaximal, complemented
2C2×#10622461C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic, complemented
4#13073558C211yesmaximal, characteristic
5#13073539C211yesmaximal, characteristic, complemented
6#13069807C212yesmaximal, complemented
7#13069622C212yesmaximal, complemented
8#13069421C211yesmaximal, characteristic, complemented
9#13069043C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C22×C8×D11C2212yes—
14C2×#66950C2212yes—
15C2×#66948C2212yes—
16C2×#66948C2212yes—
17C2×#66927—21no—
18C2×#66927C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27#10622607—22no—
28#10622601—21no—
29#10622600C2212yes—
30#10622598—21no—
31C2×#66874C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35#10622552—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622477—28no—
38#10622461—24no—
39#10622447—24no—
40#10622284—22no—
41C11×#340C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D44—21no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—21no—
48C22×D44D411yescharacteristic
49C22×D44C2312yes—
50C22×C4×D11C2312yes—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C2×#4314—24no—
73C2×#4314—24no—
74C2×#4314—42no—
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C2×C8×D11—42no—
78#66950—24no—
79#66950—42no—
80#66948—24no—
81#66948—24no—
82#66948—42no—
83#66948—42no—
84#66927—22no—
85#66927—22no—
86#66927—44no—
87C4×D44—22no—
88C4×D44—22no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×#106—24no—
92C11×C4⋊C8D414yescomplemented
93C11×#95—21no—
94C11⋊#95—22no—
95#66885—24no—
96(C2×D11)⋊C8—24no—
97#66874—22no—
98#66874D414yescomplemented
99#66873—24no—
100#66873—42no—
101C4×C11⋊C8—22no—
102#25387—111nomaximal, Sylow
103C23×D11—22no—
104C23×D11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11C2×D412yes—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—44no—
123C2×D44—44no—
124C2×D44—44no—
125C2×D44—44no—
126C2×D44—42no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—42no—
130C2×D44—81no—
131C2×D44—81no—
132C2×D44—82no—
133C2×D44—82no—
134C2×D44SD1614yescomplemented
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22C2×D412yes—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11C2×D414yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4#4112yes—
158C42×C11—42no—
159C42×C11C2×D412yes—
160C42×C11#4112yes—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—82no—
166C4⋊Dic11—22no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—44no—
170Dic11⋊C4—42no—
171C4×Dic11—42no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8C2×D412yes—
178#4314—48no—
179C8×D11—48no—
180C2×#465—112no—
181C2×#460—111no—
182C2×C8×D4—111no—
183#2541—111no—
184#2538—111no—
185#2034—112no—
186#2000—112no—
187#1957—111no—
188#1948D1111yescharacteristic, complemented
189#1893—112no—
190C4×#103—111no—
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11C2×SD1614yes—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11#12112yes—
218C2×C4×C11#12112yes—
219C2×C4×C11C2×SD1612yes—
220C2×C4×C11#13512yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236D44—28no—
237D44—42no—
238D44—42no—
239D44—42no—
240D44—42no—
241D44—84no—
242D44—88no—
243D44—88no—
244D44—84no—
245C4×D11—42no—
246C4×D11—42no—
247C4×D11—42no—
248C4×D11—42no—
249Dic22—22no—
250Dic22—22no—
251Dic22—41no—
252Dic22—41no—
253C8×C11—24no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C22×SD16—112no—
257C23×C8—112no—
258C2×#127—111no—
259C2×#127—221no—
260C2×C22⋊Q8—112no—
261C2×#121—112no—
262C2×#121—112no—
263C2×C4×Q8—111no—
264C2×C4×D4—111no—
265#465—228no—
266#460—224no—
267C8×D4—224no—
268C2×#106C2×D1112yes—
269C2×C4⋊C8C2×D1111yescharacteristic
270C2×#103—111no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8—112no—
276C2×C4×C8—111no—
277#396—222no—
278#392—222no—
279#390—221no—
280#390—221no—
281#389—221no—
282#384C2×D1111yescharacteristic
283#380—112no—
284C4×C4⋊C4C2×D1111yescharacteristic
285#340—111no—
286#340—111no—
287#340C2×D1112yes—
288C22×C11C2×#12111yescharacteristic
289C22×C11D4211yescharacteristic
290C22×C11#54611yescharacteristic
291C22×C11C22×SD1611yescharacteristic
292C22×C11C2×#13511yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—82no—
313C4×C11#46514yescomplemented
314C4×C11#53211yescharacteristic
315C4×C11#54011yescharacteristic
316C4×C11D4211yescharacteristic
317C4×C11#55011yescharacteristic
318Dic11—42no—
319Dic11—42no—
320Dic11—81no—
321C22×Q8—111no—
322C22×D4—111no—
323C22×D4—112no—
324C22×D4—222no—
325C22×D4—222no—
326C22×D4—221no—
327C22×D4—221no—
328C23×C4—112no—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—442no—
332C22×C8—111no—
333C22×C8—111no—
334C22×C8—224no—
335C22×C8—224no—
336C22×C8—442no—
337C22×C8C22×D1112yes—
338#127—222no—
339#127—222no—
340#127—444no—
341C22⋊Q8—224no—
342C22⋊Q8—442no—
343#121—224no—
344#121—224no—
345#121—442no—
346#121—442no—
347C4×Q8—222no—
348C4×Q8—222no—
349C4×D4—222no—
350C4×D4—222no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1112yes—
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C22⋊C4—112no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C42—21no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368#106—24no—
369C4⋊C8D4414yescomplemented
370#103—114no—
371#103—222no—
372#102—224no—
373#102—224no—
374#102—442no—
375C22⋊C8—224no—
376C4×C8—222no—
377#95—21no—
378#95—222no—
379C2×C11#242811yescharacteristic
380C2×C11C2×#46511yescharacteristic
381C2×C11#306211yescharacteristic
382C2×C11D4×SD1611yescharacteristic
383C2×C11#328711yescharacteristic
384C2×C11#329511yescharacteristic
385C2×C11#330411yescharacteristic
386D11—44no—
387D11—162no—
388C24—112no—
389C24—222no—
390C2×Q8—112no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—221no—
396C2×D4—114no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—444no—
406C2×D4—444no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—442no—
413C2×D4—881no—
414C2×D4—881no—
415C2×D4—882no—
416C2×D4—882no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—112no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432SD16—448no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—448no—
442C2×C8C2×D4414yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—81no—
449C4⋊C4—222no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—444no—
453C4⋊C4—442no—
454C4⋊C4D4×D1112yes—
455C4⋊C4#434312yes—
456C22⋊C4—224no—
457C22⋊C4—444no—
458C22⋊C4—444no—
459C22⋊C4—444no—
460C22⋊C4—882no—
461C42—42no—
462C42—442no—
463C42C2×D4412yes—
464C42#434312yes—
465C11#2538711yescharacteristic, complemented, Sylow
466C23—114no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23—222no—
471C23—222no—
472C23—222no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23—442no—
480C23C2×D4×D1111yescharacteristic
481Q8—222no—
482Q8—222no—
483Q8—441no—
484Q8—441no—
485D4—228no—
486D4—442no—
487D4—442no—
488D4—442no—
489D4—442no—
490D4—884no—
491D4—888no—
492D4—888no—
493D4—884no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4#6694812yes—
519C2×C4#6694812yes—
520C2×C4SD16×D1112yes—
521C2×C4#6696912yes—
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434311yescharacteristic
525C2×C4C2×#434311yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4#6704211yescharacteristic
528C8—24no—
529C8—222no—
530C8—441no—
531C22—224no—
532C22—224no—
533C22—224no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—882no—
539C22—882no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22C2×#6694811yescharacteristic
546C22#1062314011yescharacteristic
547C22#1062316111yescharacteristic
548C22C2×SD16×D1111yescharacteristic
549C22C2×#6696911yescharacteristic
550C22#1062330511yescharacteristic
551C22#1062330911yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—442no—
557C4—442no—
558C4—881no—
559C4#1062247714yescomplemented
560C4D4×D4411yescharacteristic
561C4#1062310811yescharacteristic
562C4#1062322911yescharacteristic
563C4#1062325611yescharacteristic
564C2—444no—
565C2—1762no—
566C2#1307220211yescharacteristic
567C2C2×#1062247711yescharacteristic
568C2#1307829711yescharacteristic
569C2#1308031511yescharacteristic
570C2#1308037111yescharacteristic
571C2#1308043711yescharacteristic
572C2#1308055211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radical#13073558C2
hypercenter#1948D11
hypocenterC11#25387
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#10622477C2semidirect
2. C2×#10622461C2semidirect
3. C2×#10622447C2semidirect
5. #13073539C2semidirect
6. #13069807C2semidirect
7. #13069622C2semidirect
8. #13069421C2semidirect
9. #13069043C2semidirect
10. C4×#66874C2semidirect
11. C11×#1948C2semidirect
92. C11×C4⋊C8D4semidirect
98. #66874D4semidirect
134. C2×D44SD16semidirect
188. #1948D11semidirect
313. C4×C11#465semidirect
369. C4⋊C8D44semidirect
465. C11#25387semidirect
559. C4#10622477semidirect

Maximal subgroups

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

subgroupindex
C2×#106224772
C2×#106224612
C2×#106224472
#130735582
#130735392
#130698072
#130696222
#130694212
#130690432
C4×#668742
C11×#19482
#2538711