Finite Group Databasebeta

← #14787708

Subgroups — #14787708

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3C2×C4×#4314C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic, complemented
5#13069806C212yesmaximal, complemented
6#13069621C212yesmaximal, complemented
7#13069577C211yesmaximal, characteristic, complemented
8#13068921C212yesmaximal, complemented
9#13068811C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66983C2212yes—
15C22×C4⋊Dic11C2212yes—
16C2×#66977C2212yes—
17C22×#4314C2211yescharacteristic
18#10623086—24no—
19#10623086—24no—
20C2×#66950—21no—
21C2×#66939—22no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29#10622834—21no—
30#10622825C2212yes—
31C2×#66885C2211yescharacteristic
32C2×#66885C2212yes—
33C2×#66881C2211yescharacteristic
34C2×#66881C2212yes—
35C2×#66880C2212yes—
36C2×#66880C2211yescharacteristic
37#10622586—21no—
38#10622561—22no—
39#10622548C2211yescharacteristic
40#10622464—24no—
41C4×#4314—24no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C23×Dic11—22no—
49C2×#4341—28no—
50C2×#4341—44no—
51C2×#4341—44no—
52C22×D44C2311yescharacteristic
53C22×C4×D11—21no—
54C22×Dic22—21no—
55C22×Dic22C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66#66983—24no—
67#66983—24no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—24no—
81#66977—42no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—21no—
85C2×#4314—22no—
86C2×#4314—22no—
87C2×#4314—22no—
88#66950—28no—
89#66939—216no—
90C4×D44—22no—
91C4×D44D414yes—
92#66922—22no—
93#66922D414yes—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C11×C4⋊C8—22no—
97C11×C22⋊C8—24no—
98C11×C22⋊C8—42no—
99C4×C8×C11—22no—
100C11⋊#95—22no—
101#66885—22no—
102#66885—42no—
103#66881—24no—
104#66881—22no—
105#66880—24no—
106#66880—22no—
107#24120—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C23×D11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11SD1614yescomplemented
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—28no—
124C2×C22⋊D11—44no—
125C2×C22⋊D11—44no—
126C22×Dic11—28no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—44no—
133C22×Dic11—44no—
134#4341—432no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×D412yes—
141C2×C4×D11—24no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×Dic22—24no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—42no—
151C2×Dic22—42no—
152C2×Dic22#4112yescomplemented
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11#4112yescomplemented
162C11×C4⋊C4—22no—
163C11×C22⋊C4—24no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—44no—
167C22⋊Dic11—82no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—24no—
170C4⋊Dic11—28no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—42no—
179C4⋊Dic11—81no—
180C4⋊Dic11C2×D414yes—
181C4⋊Dic11C2×D412yes—
182Dic11⋊C4—44no—
183Dic11⋊C4—42no—
184C4×Dic11—42no—
185#4314—28no—
186C2×#547—111no—
187C2×#475—111no—
188C2×C4×SD16—111no—
189#2538—111no—
190#2034—112no—
191#2000—112no—
192#1990—111no—
193#1954D1111yescharacteristic, complemented
194#1872—112no—
195#1853—112no—
196#1802—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11C2×SD1614yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212D4×C11—28no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11C2×SD1612yes—
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—416no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—416no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249D44—22no—
250D44—22no—
251D44—41no—
252D44—41no—
253C4×D11—48no—
254Dic22—22no—
255Dic22—22no—
256Dic22—41no—
257Dic22—41no—
258Dic22—48no—
259C8×C11—22no—
260C8×C11—41no—
261C8×C11—42no—
262C22×#41—221no—
263C22×SD16—111no—
264#547—224no—
265#547—224no—
266C2×C4⋊Q8—111no—
267C2×#123—222no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—221no—
270C2×#121—112no—
271C2×C4×Q8—111no—
272C2×C4×D4—111no—
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275#475—224no—
276C4×SD16—224no—
277C2×#106—112no—
278C2×#106—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×#103—112no—
281C2×#103—111no—
282C2×#102—111no—
283C2×#102—112no—
284C2×C22⋊C8C2×D1112yes—
285C2×C22⋊C8C2×D1112yes—
286C2×C4×C8C2×D1111yescharacteristic
287#396—222no—
288#390—221no—
289#389—221no—
290#384—111no—
291#380—112no—
292#340—112no—
293#340—112no—
294#340—112no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11#54711yescharacteristic
305C22×C11C22×SD1611yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57811yescharacteristic
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11#45014yes—
319C4×C11#52511yescharacteristic
320C4×C11#53711yescharacteristic
321C4×C11#54811yescharacteristic
322C4×C11#55011yescharacteristic
323Dic11—42no—
324Dic11—44no—
325Dic11—42no—
326Dic11—82no—
327Dic11—81no—
328C2×#41—228no—
329C2×#41—444no—
330C2×#41—444no—
331C22×Q8—111no—
332C22×Q8—221no—
333C22×D4—111no—
334C22×D4—222no—
335C22×D4D4411yescharacteristic
336C23×C4—222no—
337C23×C4—221no—
338C23×C4C22×D1112yes—
339C2×SD16—222no—
340C2×SD16—222no—
341C2×SD16—222no—
342C22×C8C22×D1111yescharacteristic
343C22×C8C22×D1112yes—
344C22×C8C22×D1111yescharacteristic
345C4⋊Q8—114no—
346C4⋊Q8—222no—
347#123—2216no—
348C22⋊Q8—228no—
349C22⋊Q8—224no—
350C22⋊Q8—442no—
351#121—224no—
352#121—224no—
353C4×Q8—222no—
354C4×Q8—222no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—114no—
358C4×D4—222no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4D4411yescharacteristic
372C2×C22⋊C4—221no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4D4412yes—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#106—222no—
380#106—224no—
381C4⋊C8—22no—
382#103—222no—
383#103—224no—
384#102—222no—
385#102—442no—
386C22⋊C8—24no—
387C22⋊C8—42no—
388C4×C8—22no—
389#95—222no—
390C2×C11—44no—
391C2×C11#240711yescharacteristic
392C2×C11C2×#45011yescharacteristic
393C2×C11#301311yescharacteristic
394C2×C11#329811yescharacteristic
395C2×C11#333211yescharacteristic
396C2×C11#333511yescharacteristic
397C2×C11#335311yescharacteristic
398D11—82no—
399C24—221no—
400C24C2×D4412yes—
401#41—4432no—
402C2×Q8—112no—
403C2×Q8—224no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—442no—
410C2×Q8—442no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—112no—
414C2×D4—228no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—444no—
421C2×D4—444no—
422C2×D4#431414yescomplemented
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—228no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—221no—
435C22×C4—222no—
436C22×C4—444no—
437C22×C4—444no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4C2×D4412yes—
441C22×C4C2×D4411yescharacteristic
442C22×C4C2×D4411yescharacteristic
443C22×C4C23×D1111yescharacteristic
444SD16—228no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8#434112yescomplemented
454C4⋊C4—22no—
455C4⋊C4—112no—
456C4⋊C4—114no—
457C4⋊C4—228no—
458C4⋊C4—224no—
459C4⋊C4—221no—
460C4⋊C4—222no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—444no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—881no—
469C22⋊C4—24no—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C22⋊C4—444no—
473C22⋊C4—882no—
474C42—442no—
475C42D4×D1112yes—
476C42D4×D1112yes—
477C11#2412011yescharacteristic, complemented, Sylow
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—222no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C2×#431414yes—
492C23C22×D4411yescharacteristic
493Q8—222no—
494Q8—222no—
495Q8—441no—
496Q8—448no—
497Q8—441no—
498D4—28no—
499D4—222no—
500D4—222no—
501D4—4416no—
502D4—441no—
503D4—441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—4416no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—448no—
524C2×C4—441no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—442no—
530C2×C4#6693512yes—
531C2×C4#6693512yes—
532C2×C4C2×#431412yes—
533C2×C4#6696112yes—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×#434111yescharacteristic
537C2×C4#6703711yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#6704311yescharacteristic
540C8—22no—
541C8—42no—
542C8—41no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22C2×#6693511yescharacteristic
558C22#1062308511yescharacteristic
559C22#1062308611yescharacteristic
560C22C22×#431411yescharacteristic
561C22C2×#6696111yescharacteristic
562C22#1062328211yescharacteristic
563C22#1062328411yescharacteristic
564C4—22no—
565C4—42no—
566C4—442no—
567C4—444no—
568C4—442no—
569C4—882no—
570C4—881no—
571C4#1062234414yes—
572C4#1062313711yescharacteristic
573C4#1062313911yescharacteristic
574C4#1062320811yescharacteristic
575C4#1062324911yescharacteristic
576C2—44no—
577C2—882no—
578C2#1307195911yescharacteristic
579C2C2×#1062234411yescharacteristic
580C2#1307793411yescharacteristic
581C2#1308048211yescharacteristic
582C2#1308094411yescharacteristic
583C2#1308097411yescharacteristic
584C2#1308120111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenter#1954D11
hypocenterC11#24120
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×C4×#4314C2semidirect
4. #13073538C2semidirect
5. #13069806C2semidirect
6. #13069621C2semidirect
7. #13069577C2semidirect
8. #13068921C2semidirect
9. #13068811C2semidirect
10. #13068617C2semidirect
11. C11×#1954C2semidirect
112. C2×D4×C11SD16semidirect
152. C2×Dic22#41semidirect
161. C2×C8×C11#41semidirect
193. #1954D11semidirect
422. C2×D4#4314semidirect
453. C2×C8#4341semidirect
477. C11#24120semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106224642
C2×C4×#43142
#130735382
#130698062
#130696212
#130695772
#130689212
#130688112
#130686172
C11×#19542
#2412011