Finite Group Databasebeta

← #14755166

Subgroups — #14755166

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×#66985C211yesmaximal, characteristic
2C2×#10623329C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic, complemented
4#13071209C211yesmaximal, characteristic, complemented
5#13068962C214yesmaximal, complemented
6#13068948C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C22×C11×#102C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C22⋊Dic11—22no—
15#10623329—24no—
16#10623329—24no—
17C2×D4×Dic11—22no—
18C2×D4×Dic11C2214yes—
19C22×#4324C2212yes—
20C2×#66985—24no—
21C2×#66985—24no—
22C2×#66985C418yescomplemented
23C22×#4323C2212yes—
24C2×#66979C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C2×C11×#102—24no—
28C2×C11×#102C2214yes—
29#10622826—22no—
30#10622726—24no—
31C2×#66885C2212yescomplemented
32C2×#66880C2212yescomplemented
33#10622601C2212yescomplemented
34#10622600—22no—
35#10622587C2212yescomplemented
36#10622188C2214yescomplemented
37#10622167C2214yescomplemented
38C25×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11C2×C414yes—
44C22×D4×C11D414yes—
45C22×D4×C11D414yes—
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C23×Dic11—24no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339C2×C414yescomplemented
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
59C22×Dic22C2311yescharacteristic
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11C2312yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2312yes—
68C2×C22⋊Dic11—216no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11D412yes—
72D4×Dic11—216no—
73D4×Dic11—28no—
74D4×Dic11—28no—
75C2×#4324—24no—
76C2×#4324—24no—
77C2×#4324C2×C418yescomplemented
78#66985—232no—
79C2×#4323—24no—
80C2×#4323—24no—
81C2×#4323C2×C418yescomplemented
82C2×(C2×D11)⋊C4—24no—
83#66979—22no—
84#66979—22no—
85#66979—22no—
86#66979D414yes—
87C2×C4⋊Dic11D412yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2312yes—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2×C414yescomplemented
94C22×C11⋊C8C2312yes—
95C11×#102—28no—
96C11⋊#95—24no—
97#66885—24no—
98#66880—24no—
99#20929—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—82no—
105C24×C11—82no—
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C2×D4×C11—28no—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—28no—
112C2×D4×C11—24no—
113C2×D4×C11—28no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C22⋊C4116yescomplemented
118C2×D4×C11C22×C414yes—
119C2×D4×C11C2×D414yes—
120C2×D4×C11C2×D414yes—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—82no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—24no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C22×Dic11—216no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—84no—
139C22×Dic11—84no—
140C22×Dic11C2×D414yes—
141#4339—28no—
142#4339—28no—
143#4339—44no—
144#4339—44no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44C22×C412yes—
151C2×C4×D11—24no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22C22×C412yes—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—44no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C22⋊Dic11—216no—
168C22⋊Dic11—24no—
169C22⋊Dic11—24no—
170#4324—216no—
171#4323—216no—
172(C2×D11)⋊C4—84no—
173C4⋊Dic11—24no—
174C4⋊Dic11—22no—
175C4⋊Dic11C2×D414yes—
176C4×Dic11—24no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179#4318—28no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C22×C414yes—
183C22×AGL(1,ℤ/8)—111no—
184C2×#518—111no—
185C2×#416—111no—
186C22×#102D1111yescharacteristic, complemented
187#2311—111no—
188#1879—114no—
189#1877—114no—
190#1736—111no—
191#1729—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—216no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—88no—
201C23×C11—88no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11C4×D412yes—
205C23×C11#12012yes—
206C23×C11#12112yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—42no—
213D4×C11—24no—
214D4×C11—24no—
215D4×C11—24no—
216D4×C11—216no—
217D4×C11C2×C22⋊C418yes—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—84no—
221C2×C4×C11C2×C22⋊C414yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11C4×D412yes—
224C2×C4×C11#12012yes—
225C2×C4×C11#12114yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12314yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C22⋊D11—48no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—816no—
245D44—22no—
246D44—22no—
247D44—41no—
248D44—41no—
249C4×D11—48no—
250Dic22—22no—
251Dic22—22no—
252Dic22—41no—
253Dic22—41no—
254C8×C11—42no—
255C11⋊C8—24no—
256C22×#41—111no—
257C23×D4C2×D1111yescharacteristic
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×M16—111no—
264C23×C8C2×D1111yescharacteristic
265#518—224no—
266#518—224no—
267C2×C4×D4—114no—
268C2×C4×D4—222no—
269C2×#117—111no—
270C2×#117—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—222no—
273#416—224no—
274C2×#103—112no—
275C2×#102—24no—
276C2×#102—112no—
277C2×#102C2×D1114yes—
278#391—112no—
279#390—112no—
280#386—222no—
281#380—222no—
282#340—114no—
283#336—114no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—28no—
289C22×C11—48no—
290C22×C11—48no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—816no—
294C22×C11#38614yes—
295C22×C11C2×C4×D411yescharacteristic
296C22×C11C2×#12011yescharacteristic
297C22×C11C2×#12111yescharacteristic
298C22×C11#57612yes—
299C22×C11#57712yes—
300C2×D11—44no—
301C2×D11—42no—
302C2×D11—82no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—82no—
306C4×C11#38614yes—
307C4×C11C22×C22⋊C411yescharacteristic
308C4×C11C2×C4×D411yescharacteristic
309C4×C11C2×#12111yescharacteristic
310C4×C11C2×#12311yescharacteristic
311Dic11—44no—
312Dic11—44no—
313Dic11—42no—
314C25—21no—
315C2×#41—114no—
316C2×#41—222no—
317C2×#41—222no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—222no—
321C22×Q8—111no—
322C22×D4—21no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—111no—
327C22×D4—221no—
328C22×D4C4×D1114yes—
329C22×D4D4414yes—
330C22×D4C22⋊D1114yes—
331C22×D4C22×D1112yes—
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—114no—
344C2×M16—222no—
345C2×M16—222no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—112no—
350C22×C8C22×D1112yes—
351C4×D4—228no—
352C4×D4—2216no—
353C4×D4—228no—
354#117—114no—
355#117—222no—
356#117—222no—
357#117—222no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—2216no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—224no—
369C2×C42—112no—
370C2×C42—221no—
371#103—224no—
372#102—28no—
373#102—224no—
374#95—224no—
375C2×C11—24no—
376C2×C11—48no—
377C2×C11C2×#38611yescharacteristic
378C2×C11#294612yes—
379C2×C11#301212yes—
380C2×C11#304111yescharacteristic
381C2×C11#304211yescharacteristic
382D11—82no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—82no—
388C24—82no—
389C24—221no—
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—28no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—112no—
411C2×D4—224no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4(C2×D11)⋊C4116yescomplemented
420C2×D4C2×C4×D1114yes—
421C2×D4C2×D4414yes—
422C2×D4C2×C22⋊D1114yes—
423C22×C4—22no—
424C22×C4—42no—
425C22×C4—82no—
426C22×C4—114no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—2216no—
430C22×C4—224no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4—884no—
434C22×C4—884no—
435C22×C4C2×C4×D1112yes—
436C22×C4C2×D4412yes—
437C22×C4D4×D1111yescharacteristic
438C22×C4D4×D1112yes—
439C22×C4#434112yes—
440C22×C4#434112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C23×D1111yescharacteristic
443SD16—2216no—
444D8—2216no—
445M16—228no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—44no—
450C2×C8—114no—
451C2×C8—222no—
452C2×C8—222no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4—114no—
457C4⋊C4—224no—
458C4⋊C4—222no—
459C22⋊C4—2216no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4—884no—
463C42—224no—
464C42—222no—
465C42—222no—
466C11#2092911yescharacteristic, complemented, Sylow
467C23—22no—
468C23—22no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—216no—
473C23—44no—
474C23—44no—
475C23—84no—
476C23—84no—
477C23—88no—
478C23—88no—
479C23—222no—
480C23—441no—
481C23—442no—
482C23—442no—
483C23—441no—
484C23(C22⋊D11)⋊C412yes—
485C23#6693512yes—
486C23#6699212yes—
487C23C2×D4×D1111yescharacteristic
488Q8—222no—
489Q8—222no—
490Q8—441no—
491Q8—441no—
492D4—24no—
493D4—24no—
494D4—24no—
495D4—216no—
496D4—222no—
497D4—222no—
498D4—448no—
499D4—441no—
500D4—441no—
501D4C2×(C2×D11)⋊C418yes—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—84no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—441no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—448no—
515C2×C4—8816no—
516C2×C4(C22⋊D11)⋊C414yes—
517C2×C4(C22⋊D11)⋊C412yes—
518C2×C4#6693512yes—
519C2×C4#6693914yes—
520C2×C4C2×(C2×D11)⋊C414yes—
521C2×C4#6699214yes—
522C2×C4#6699212yes—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C22×D4411yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C2×#434111yescharacteristic
527C2×C4C2×#434111yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C8—42no—
530C8—224no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—24no—
535C22—28no—
536C22—44no—
537C22—44no—
538C22—48no—
539C22—48no—
540C22—816no—
541C22—442no—
542C22—444no—
543C22—881no—
544C22—881no—
545C22—882no—
546C22#1062257114yes—
547C22C2×(C22⋊D11)⋊C411yescharacteristic
548C22C2×#6693511yescharacteristic
549C22#1062328812yes—
550C22#1062329312yes—
551C22C2×#6699211yescharacteristic
552C4—82no—
553C4—444no—
554C4—444no—
555C4—442no—
556C4#1062257114yes—
557C4C2×(C22⋊D11)⋊C411yescharacteristic
558C4C2×#6693911yescharacteristic
559C4C22×(C2×D11)⋊C411yescharacteristic
560C4C2×#6699211yescharacteristic
561C2—24no—
562C2—48no—
563C2—882no—
564C2C2×#1062257111yescharacteristic
565C2#1307744212yes—
566C2#1307792512yes—
567C2#1307811611yescharacteristic
568C2#1307812511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11#20929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10623329C2semidirect
3. C2×#10622726C2semidirect
4. #13071209C2semidirect
5. #13068962C2semidirect
6. #13068948C2semidirect
7. #13068335C2semidirect
8. #13068312C2semidirect
9. C22×C11×#102C2semidirect
22. C2×#66985C4semidirect
31. C2×#66885C22semidirect
32. C2×#66880C22semidirect
33. #10622601C22semidirect
35. #10622587C22semidirect
36. #10622188C22semidirect
37. #10622167C22semidirect
56. C2×#4339C2×C4semidirect
77. C2×#4324C2×C4semidirect
81. C2×#4323C2×C4semidirect
93. C2×#4318C2×C4semidirect
117. C2×D4×C11C22⋊C4semidirect
186. C22×#102D11semidirect
419. C2×D4(C2×D11)⋊C4semidirect
466. C11#20929semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106233292
C2×#106227262
#130712092
#130689622
#130689482
#130683352
#130683122
C22×C11×#1022
#2092911