Finite Group Databasebeta

← #14755170

Subgroups — #14755170

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C2×#10622615C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13071209C211yesmaximal, characteristic, complemented
6#13068965C214yesmaximal, complemented
7#13068951C214yesmaximal, complemented
8#13068314C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C2×#66961—24no—
18C2×#66961—24no—
19C2×#66961C418yescomplemented
20C22×D88C2212yes—
21C22×#4314C2212yes—
22#10623052—24no—
23#10623052—24no—
24C2×#66946C2214yes—
25C2×C22⋊C4×D11—22no—
26C2×C4×D44—22no—
27#10622826—22no—
28#10622615—24no—
29#10622601C2212yescomplemented
30#10622600—22no—
31#10622587C2212yescomplemented
32C2×#66874C2212yescomplemented
33C2×#66873—24no—
34C2×#66873C2214yes—
35C2×#66873C2212yescomplemented
36C11×#340C2214yescomplemented
37#10622188C2214yescomplemented
38C24×D11—21no—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—21no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339C2×C414yescomplemented
48C22×D44—21no—
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—22no—
52C22×D44C2×C414yes—
53C22×D44D414yes—
54C22×D44D414yes—
55C22×D44C2311yescharacteristic
56C22×D44C2312yes—
57C22×C4×D11—21no—
58C22×C4×D11—24no—
59C22×Dic22C2311yescharacteristic
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16C2×C414yescomplemented
63C22×C8×C11C2312yes—
64C11×#117—22no—
65C11×#117D414yes—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C22⋊Dic11D412yes—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76#66979—22no—
77#66979—22no—
78C2×C4⋊Dic11D412yes—
79C2×C4×Dic11C2312yes—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8C2312yes—
84#66961—232no—
85C2×D88—24no—
86C2×D88—24no—
87C2×D88C2×C418yescomplemented
88C2×#4314—24no—
89C2×#4314—24no—
90C2×#4314C2×C418yescomplemented
91#66946—28no—
92#66946—28no—
93C22⋊C4×D11—216no—
94C4×D44—216no—
95C11⋊#95—24no—
96#66874—24no—
97#66873—28no—
98#66873—24no—
99#20929—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11—22no—
102C23×D11—24no—
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—21no—
106C23×D11—82no—
107C23×D11—82no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—82no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—24no—
121C2×C22⋊D11—42no—
122C2×C22⋊D11—42no—
123C22×Dic11—21no—
124C22×Dic11C2×D414yes—
125#4339—28no—
126#4339—28no—
127#4339—44no—
128#4339—44no—
129C2×D44—28no—
130C2×D44—24no—
131C2×D44—24no—
132C2×D44—24no—
133C2×D44—28no—
134C2×D44—28no—
135C2×D44—22no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C22⋊C4116yescomplemented
144C2×D44C22×C412yes—
145C2×D44C22×C414yes—
146C2×D44C2×D414yes—
147C2×D44C2×D414yes—
148C2×C4×D11—216no—
149C2×C4×D11—24no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—84no—
153C2×C4×D11—84no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22C22×C412yes—
160C11×M16—28no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11C22×C414yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4C2×D414yes—
169C11×C22⋊C4—24no—
170C42×C11—24no—
171C22⋊Dic11—24no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—84no—
174C4⋊Dic11—24no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—44no—
181D88—216no—
182#4314—216no—
183C22×AGL(1,ℤ/8)—111no—
184C2×#518—111no—
185C2×#416—111no—
186C22×#102—111no—
187#2311—111no—
188#1879—114no—
189#1877—114no—
190#1736D1111yescharacteristic, complemented
191#1729—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11C4×D412yes—
195C23×C11#12012yes—
196C23×C11#12112yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—216no—
202C22×D11—22no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—88no—
210C22×D11—88no—
211C22×D11—84no—
212C22×D11—84no—
213C2×C4×C11—24no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—44no—
218C2×C4×C11—84no—
219C2×C4×C11C2×C22⋊C414yes—
220C2×C4×C11C4×D414yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#12112yes—
224C2×C4×C11#12114yes—
225C2×C4×C11#12314yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C22⋊D11—48no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239D44—22no—
240D44—24no—
241D44—22no—
242D44—24no—
243D44—24no—
244D44—216no—
245D44—41no—
246D44—41no—
247D44C2×C22⋊C418yes—
248C4×D11—48no—
249C4×D11—816no—
250Dic22—22no—
251Dic22—22no—
252Dic22—41no—
253Dic22—41no—
254C8×C11—24no—
255C11⋊C8—42no—
256C22×#41—111no—
257C23×D4—111no—
258C2×AGL(1,ℤ/8)—118no—
259C2×AGL(1,ℤ/8)—224no—
260C2×AGL(1,ℤ/8)—224no—
261C22×SD16—112no—
262C22×D8—112no—
263C22×M16C2×D1111yescharacteristic
264C23×C8—111no—
265#518—224no—
266#518—224no—
267C2×C4×D4—114no—
268C2×C4×D4—222no—
269C2×#117—111no—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—222no—
273#416—224no—
274C2×#103—112no—
275C2×#102—114no—
276C2×#102—112no—
277C2×#102—224no—
278#391—112no—
279#390—112no—
280#386—222no—
281#380—222no—
282#340C2×D1114yescomplemented
283#336—114no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11#38614yes—
289C22×C11C2×C4×D411yescharacteristic
290C22×C11C2×#12011yescharacteristic
291C22×C11C2×#12111yescharacteristic
292C22×C11#57612yes—
293C22×C11#57712yes—
294C2×D11—28no—
295C2×D11—48no—
296C2×D11—48no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—42no—
301C2×D11—816no—
302C2×D11—82no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—44no—
306C4×C11—82no—
307C4×C11#38614yes—
308C4×C11C22×C22⋊C411yescharacteristic
309C4×C11C2×C4×D411yescharacteristic
310C4×C11C2×#12111yescharacteristic
311C4×C11C2×#12311yescharacteristic
312Dic11—44no—
313Dic11—42no—
314C25—221no—
315C2×#41—114no—
316C2×#41—222no—
317C2×#41—222no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—222no—
321C22×Q8—111no—
322C22×D4—114no—
323C22×D4—114no—
324C22×D4—114no—
325C22×D4—112no—
326C22×D4—111no—
327C22×D4—221no—
328C22×D4—222no—
329C22×D4—222no—
330C22×D4—221no—
331C22×D4—222no—
332C23×C4—21no—
333C23×C4—224no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336AGL(1,ℤ/8)—2232no—
337C2×SD16—118no—
338C2×SD16—224no—
339C2×SD16—224no—
340C2×D8—118no—
341C2×D8—224no—
342C2×D8—224no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16C4×D1114yescomplemented
346C22×C8—112no—
347C22×C8—222no—
348C22×C8—222no—
349C22×C8—222no—
350C22×C8C22×D1112yes—
351C4×D4—2216no—
352C4×D4—228no—
353C4×D4—228no—
354#117—22no—
355#117—222no—
356#117—222no—
357#117D4414yes—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—2216no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—224no—
369C2×C42—21no—
370C2×C42—112no—
371#103—224no—
372#102—228no—
373#102—224no—
374#95—224no—
375C2×C11—24no—
376C2×C11C2×#38611yescharacteristic
377C2×C11#294612yes—
378C2×C11#301212yes—
379C2×C11#304111yescharacteristic
380C2×C11#304211yescharacteristic
381D11—48no—
382D11—82no—
383C24—222no—
384C24—224no—
385C24—224no—
386C24—224no—
387C24—221no—
388C24—882no—
389C24—882no—
390C24D4×D1111yescharacteristic
391#41—228no—
392#41—228no—
393#41—444no—
394#41—444no—
395C2×Q8—112no—
396C2×Q8—221no—
397C2×Q8—221no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—221no—
401C2×D4—1116no—
402C2×D4—114no—
403C2×D4—112no—
404C2×D4—114no—
405C2×D4—114no—
406C2×D4—224no—
407C2×D4—228no—
408C2×D4—224no—
409C2×D4—224no—
410C2×D4—224no—
411C2×D4—228no—
412C2×D4—228no—
413C2×D4—222no—
414C2×D4—221no—
415C2×D4—222no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—222no—
420C2×D4—221no—
421C2×D4—442no—
422C2×D4—442no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—82no—
427C22×C4—114no—
428C22×C4—2216no—
429C22×C4—221no—
430C22×C4—224no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4—884no—
434C22×C4—884no—
435C22×C4C2×C4×D1112yes—
436C22×C4C2×D4412yes—
437C22×C4#433912yes—
438C22×C4D4×D1112yes—
439C22×C4D4×D1112yes—
440C22×C4D4×D1111yescharacteristic
441C22×C4#434312yes—
442C22×C4C23×D1111yescharacteristic
443SD16—2216no—
444D8—2216no—
445M16—28no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—444no—
452C2×C8C2×C4×D1114yes—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—224no—
458C4⋊C4C2×D4414yes—
459C22⋊C4—24no—
460C22⋊C4—2216no—
461C22⋊C4—224no—
462C22⋊C4—884no—
463C42—24no—
464C42—222no—
465C42—222no—
466C11#2092911yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—224no—
470C23—224no—
471C23—224no—
472C23—2216no—
473C23—222no—
474C23—444no—
475C23—444no—
476C23—441no—
477C23—441no—
478C23—442no—
479C23—442no—
480C23—884no—
481C23—884no—
482C23—888no—
483C23—888no—
484C23#6693512yes—
485C23#6693712yes—
486C23#6694612yes—
487C23C2×D4×D1111yescharacteristic
488Q8—222no—
489Q8—222no—
490Q8—441no—
491Q8—441no—
492D4—118no—
493D4—224no—
494D4—222no—
495D4—222no—
496D4—224no—
497D4—224no—
498D4—2216no—
499D4—448no—
500D4—441no—
501D4—441no—
502C2×C4—24no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—84no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—448no—
515C2×C4—8816no—
516C2×C4C4×D4414yes—
517C2×C4C22⋊C4×D1114yes—
518C2×C4#6693512yes—
519C2×C4#6693712yes—
520C2×C4#6694612yes—
521C2×C4#6694714yes—
522C2×C4#6694814yes—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C22×D4411yescharacteristic
525C2×C4C2×#433911yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434311yescharacteristic
529C8—24no—
530C8—442no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—24no—
535C22—228no—
536C22—444no—
537C22—444no—
538C22—448no—
539C22—448no—
540C22—442no—
541C22—444no—
542C22—8816no—
543C22—881no—
544C22—881no—
545C22—882no—
546C22#1062227814yes—
547C22C2×#6693511yescharacteristic
548C22C2×#6693711yescharacteristic
549C22C2×#6694611yescharacteristic
550C22#1062330512yes—
551C22#1062330912yes—
552C4—44no—
553C4—82no—
554C4—444no—
555C4—442no—
556C4#1062227814yes—
557C4C2×C4×D4411yescharacteristic
558C4C2×C22⋊C4×D1111yescharacteristic
559C4C2×#6694711yescharacteristic
560C4C2×#6694811yescharacteristic
561C2—24no—
562C2—448no—
563C2—882no—
564C2C2×#1062227811yescharacteristic
565C2#1307744612yes—
566C2#1307792212yes—
567C2#1307811811yescharacteristic
568C2#1307812711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#10622615C2semidirect
4. C22×#66873C2semidirect
5. #13071209C2semidirect
6. #13068965C2semidirect
7. #13068951C2semidirect
8. #13068314C2semidirect
9. C11×#1736C2semidirect
19. C2×#66961C4semidirect
29. #10622601C22semidirect
31. #10622587C22semidirect
32. C2×#66874C22semidirect
35. C2×#66873C22semidirect
36. C11×#340C22semidirect
37. #10622188C22semidirect
47. C2×#4339C2×C4semidirect
62. C2×C11×M16C2×C4semidirect
87. C2×D88C2×C4semidirect
90. C2×#4314C2×C4semidirect
143. C2×D44C22⋊C4semidirect
190. #1736D11semidirect
282. #340C2×D11semidirect
345. C2×M16C4×D11semidirect
466. C11#20929semidirect

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106230522
C2×#106226152
C22×#668732
#130712092
#130689652
#130689512
#130683142
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