Finite Group Databasebeta

← #14764915

Subgroups — #14764915

Order 2816.

1092 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622840C211yesmaximal, characteristic
2C4×#66983C211yesmaximal, characteristic
3#13069473C212yesmaximal, complemented
4#13069295C212yesmaximal, complemented
5#13069247C212yesmaximal, complemented
6#13068953C212yesmaximal, complemented
7#13068933C211yesmaximal, characteristic
8#13068809C211yesmaximal, characteristic, complemented
9#13068551C211yesmaximal, characteristic, complemented
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C2×C11×#391C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×#4325C2212yes—
16C2×#66983C2211yescharacteristic
17C2×C4×C22⋊D11—21no—
18C2×C4×D44C2211yescharacteristic
19C11×#391—21no—
20C11×#391—21no—
21C11×#391C2212yes—
22C11×#391C2212yes—
23C2×C11×#95—21no—
24C2×C11×#95—21no—
25#10622840C418yescomplemented
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29#10622826—21no—
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66873C2212yes—
34C2×#66872C2212yes—
35#10622553—21no—
36#10622552C2211yescharacteristic
37C4×(C2×D11)⋊C4—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39#10622541C2211yescharacteristic
40C2×C4×C11⋊C8C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yescomplemented
49C22×Q8×C11C2312yes—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—21no—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—42no—
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11—42no—
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—21no—
67C2×#4325—42no—
68C2×#4325—42no—
69C2×#4325C2×C418yescomplemented
70#66983—22no—
71#66983C2×C414yes—
72C4×C22⋊D11—44no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2312yes—
84C4×D44—42no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89#66899—42no—
90#66899—42no—
91#66899C2×C418yescomplemented
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)C2×C414yescomplemented
97#66873—42no—
98#66872—42no—
99C4×C11⋊C8—42no—
100#22041—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—21no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—48no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11—48no—
113C2×Q8×C11C22×C414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11SD1614yescomplemented
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—24no—
139C2×C22⋊D11—42no—
140C2×C22⋊D11—42no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C2×D44—21no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44C22×C412yes—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—41no—
157C42×C11—41no—
158C22⋊Dic11—42no—
159#4325—48no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—42no—
163(C2×D11)⋊C4—42no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—42no—
169C4×Dic11—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C22×C414yes—
176C2×#448—111no—
177C4×#121—111no—
178C2×#391D1111yescharacteristic, complemented
179#1968—112no—
180#1933—112no—
181#1927—112no—
182#1877—112no—
183#1874—111no—
184#1853—111no—
185#1787—111no—
186C4×C22⋊C8—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11C4×D412yes—
192C23×C11C2×SD1612yes—
193C23×C11#13512yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—24no—
203Q8×C11—24no—
204Q8×C11—48no—
205Q8×C11—42no—
206Q8×C11—42no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—48no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—84no—
230C2×C4×C11C4×D412yes—
231C2×C4×C11C2×SD1612yes—
232C2×C4×C11C2×SD1612yes—
233C2×C4×C11#13712yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)12yes—
237C2×C4×C11H(5,𝔽2)12yes—
238C22⋊D11—48no—
239C2×Dic11—22no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248D44—24no—
249D44—42no—
250C4×D11—84no—
251C11⋊C8—24no—
252C11⋊C8—42no—
253C23×Q8C2×D1111yescharacteristic
254C22×SD16—112no—
255C2×#121—111no—
256C2×C4×D4—111no—
257C2×C4×D4—221no—
258C22×C4⋊C4C2×D1111yescharacteristic
259C22×C42C2×D1111yescharacteristic
260#448—118no—
261C2×#106—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#102—112no—
266C2×C22⋊C8—111no—
267C2×C22⋊C8—111no—
268C2×C4×C8—112no—
269#391—21no—
270#391—21no—
271#391C2×D1112yes—
272#391C2×D1112yes—
273#390—111no—
274#389—111no—
275#388—221no—
276#386—221no—
277#380—111no—
278C4×C4⋊C4—111no—
279C4×C22⋊C4—221no—
280C2×#95—21no—
281C2×#95—21no—
282#340—112no—
283#340—112no—
284#336—112no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11C4×SD1614yes—
292C22×C11C2×C4×D411yescharacteristic
293C22×C11#53411yescharacteristic
294C22×C11#53511yescharacteristic
295C22×C11C22×SD1611yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C22×C11#57511yescharacteristic
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—41no—
312C4×C11—82no—
313C4×C11#51812yes—
314C4×C11#53812yes—
315Dic11—42no—
316Dic11—81no—
317Dic11—81no—
318C22×Q8—22no—
319C22×Q8—21no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8C4×D1114yescomplemented
323C22×Q8C22×D1112yes—
324C22×D4—111no—
325C22×D4—221no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—221no—
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22⋊D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C2×SD16—118no—
333C2×SD16—442no—
334C2×SD16—442no—
335C22×C8—112no—
336C22×C8—112no—
337#121—114no—
338#121—222no—
339C4×D4—442no—
340C4×D4—444no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4C22×D1112yes—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C42—42no—
354C2×C42—221no—
355C2×C42C22⋊D1111yescharacteristic
356C2×C42C22⋊D1111yescharacteristic
357C2×C42C22×D1111yescharacteristic
358C2×C42C22×D1111yescharacteristic
359#106—442no—
360#103—118no—
361#103—442no—
362#103—442no—
363#102—442no—
364C22⋊C8—114no—
365C22⋊C8—222no—
366C4×C8—442no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—221no—
372#95—221no—
373#95—221no—
374C2×C11—24no—
375C2×C11#232111yescharacteristic
376C2×C11C2×C4×SD1611yescharacteristic
377C2×C11C4×#13711yescharacteristic
378C2×C11#318711yescharacteristic
379C2×C11#319011yescharacteristic
380C2×C11#320611yescharacteristic
381C2×C11#321111yescharacteristic
382D11—82no—
383C24—221no—
384C24C2×C22⋊D1111yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—48no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—48no—
395C2×Q8C2×C4×D1114yes—
396C2×D4—112no—
397C2×D4—224no—
398C2×D4—221no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—442no—
402C2×D4—442no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4#432514yescomplemented
425C22×C4C2×C4×D1112yes—
426C22×C4#433912yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434C2×C8—114no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4—112no—
444C4⋊C4—221no—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—442no—
448C22⋊C4—224no—
449C22⋊C4—442no—
450C22⋊C4—442no—
451C22⋊C4—442no—
452C22⋊C4—442no—
453C42—22no—
454C42—22no—
455C42—41no—
456C42—41no—
457C42—442no—
458C11#2204111yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23C4×C22⋊D1112yes—
471C23C2×#432512yes—
472C23#6700312yes—
473C23C22×C22⋊D1111yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479D4—224no—
480D4—448no—
481D4—442no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—48no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—84no—
505C2×C4—222no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—884no—
515C2×C4C4×C22⋊D1112yes—
516C2×C4C2×#432512yes—
517C2×C4C2×#432512yes—
518C2×C4#6699512yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4#6703712yes—
522C2×C4#6703712yes—
523C8—224no—
524C8—442no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22C4×#432514yes—
539C22C2×C4×C22⋊D1111yescharacteristic
540C22#1062333511yescharacteristic
541C22#1062333611yescharacteristic
542C22C22×#432511yescharacteristic
543C22C2×#6699511yescharacteristic
544C22C2×#6700311yescharacteristic
545C22#1062335311yescharacteristic
546C4—22no—
547C4—22no—
548C4—22no—
549C4—22no—
550C4—41no—
551C4—44no—
552C4—82no—
553C4—442no—
554C4—881no—
555C4—881no—
556C4#1062301712yes—
557C4#1062302512yes—
558C2—24no—
559C2—882no—
560C2#1307127411yescharacteristic
561C2C2×C4×#432511yescharacteristic
562C2C4×#6699511yescharacteristic
563C2#1307936911yescharacteristic
564C2#1307939711yescharacteristic
565C2#1307954111yescharacteristic
566C2#1307958111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC2×#391D11
hypocenterC11#22041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #13069473C2semidirect
4. #13069295C2semidirect
5. #13069247C2semidirect
6. #13068953C2semidirect
8. #13068809C2semidirect
9. #13068551C2semidirect
10. C4×C22⋊(C11⋊C8)C2semidirect
11. C2×C11×#391C2semidirect
25. #10622840C4semidirect
48. C22×Q8×C11C2×C4semidirect
69. C2×#4325C2×C4semidirect
91. #66899C2×C4semidirect
96. C22⋊(C11⋊C8)C2×C4semidirect
129. C22×C4×C11SD16semidirect
178. C2×#391D11semidirect
322. C22×Q8C4×D11semidirect
424. C22×C4#4325semidirect
458. C11#22041semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
C4×#669832
#130694732
#130692952
#130692472
#130689532
#130689332
#130688092
#130685512
C4×C22⋊(C11⋊C8)2
C2×C11×#3912
#2204111