Finite Group Databasebeta

← #14764918

Subgroups — #14764918

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
1#121×Dic11C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic, complemented
3#13069472C212yesmaximal, complemented
4#13069294C212yesmaximal, complemented
5#13069252C212yesmaximal, complemented
6#13068952C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic
8#13068811C211yesmaximal, characteristic, complemented
9#13068551C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#448C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#121C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C11×#448C418yescomplemented
20C2×C11×#103C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22#10622843—21no—
23#10622843—21no—
24#10622843C2212yes—
25#10622843C2212yes—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28#10622834C2211yescharacteristic
29#10622833—21no—
30C2×#66896C2212yes—
31#10622825C2211yescharacteristic
32C2×C11⋊#95—21no—
33C2×C11⋊#95—21no—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66881C2212yes—
36C2×C8×Dic11C2212yes—
37#10622598C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622564—21no—
40C22⋊C4×Dic11—21no—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yescomplemented
49C22×Q8×C11C2312yes—
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C23×Dic11D411yescharacteristic
58C2×C11×SD16—42no—
59C2×C11×SD16—42no—
60C2×C11×SD16C2×C418yescomplemented
61C22×C8×C11C2312yes—
62C11×#121—22no—
63C11×#121C2×C414yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70D4×Dic11—42no—
71D4×Dic11—44no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4×Dic11—21no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C11×#103C2×C418yescomplemented
86C11×C22⋊C8C2×C414yescomplemented
87#66899—42no—
88#66899—42no—
89#66896—42no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C22⋊(C11⋊C8)—22no—
98#66881—42no—
99C8×Dic11—42no—
100#22041—111nomaximal, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
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—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11C22×C412yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11SD1614yescomplemented
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C11×SD16—48no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11C22×C414yes—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C22⋊C4—24no—
158C22⋊Dic11—42no—
159C22⋊Dic11—42no—
160C22⋊Dic11—42no—
161C22⋊Dic11—42no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×#448D1111yescharacteristic
177C4×#121—111no—
178C2×#391—111no—
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×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C4×D412yes—
199C23×C11C2×SD1612yes—
200C23×C11#13512yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—24no—
203Q8×C11—24no—
204Q8×C11—48no—
205Q8×C11—42no—
206Q8×C11—42no—
207D4×C11—24no—
208D4×C11—48no—
209D4×C11—42no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—48no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)12yes—
225C2×C4×C11H(5,𝔽2)12yes—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—84no—
247C2×Dic11—84no—
248C2×Dic11C2×SD1612yes—
249C2×Dic11C2×SD1612yes—
250C2×Dic11#13712yes—
251C8×C11—24no—
252C11⋊C8—42no—
253C23×Q8C2×D1111yescharacteristic
254C22×SD16C2×D1112yes—
255C2×#121C2×D1111yescharacteristic
256C2×C4×D4—111no—
257C2×C4×D4—221no—
258C22×C4⋊C4—111no—
259C22×C42—111no—
260#448Dic1118yescomplemented
261C2×#106—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103C2×D1112yes—
265C2×#102—112no—
266C2×C22⋊C8—111no—
267C2×C22⋊C8C2×D1111yescharacteristic
268C2×C4×C8—112no—
269#391—112no—
270#391—112no—
271#391—221no—
272#391—221no—
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—221no—
281C2×#95—221no—
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×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C4×SD1614yes—
299C22×C11C2×C4×D411yescharacteristic
300C22×C11#53411yescharacteristic
301C22×C11#53511yescharacteristic
302C22×C11C22×SD1611yescharacteristic
303C22×C11C2×#13511yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57511yescharacteristic
306C4×C11—22no—
307C4×C11—44no—
308C4×C11—42no—
309C4×C11#51812yes—
310C4×C11#53812yes—
311Dic11—22no—
312Dic11—22no—
313Dic11—22no—
314Dic11—41no—
315Dic11—81no—
316Dic11—81no—
317Dic11—82no—
318C22×Q8—21no—
319C22×Q8—22no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8C2×Dic1114yescomplemented
323C22×Q8C22×D1112yes—
324C22×D4—21no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—221no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C2×SD16—42no—
333C2×SD16—42no—
334C2×SD16C2×Dic1118yescomplemented
335C22×C8—112no—
336C22×C8C22×D1112yes—
337#121—22no—
338#121C2×Dic1114yes—
339C4×D4—442no—
340C4×D4—444no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—442no—
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—221no—
358C2×C42—442no—
359#106—442no—
360#103—442no—
361#103—442no—
362#103C2×Dic1118yescomplemented
363#102—442no—
364C22⋊C8—222no—
365C22⋊C8C2×Dic1114yescomplemented
366C4×C8—442no—
367#95—222no—
368#95—222no—
369#95—222no—
370#95—222no—
371#95—221no—
372#95—221no—
373#95—221no—
374C2×C11—24no—
375C2×C11—82no—
376C2×C11#232111yescharacteristic
377C2×C11C2×C4×SD1611yescharacteristic
378C2×C11C4×#13711yescharacteristic
379C2×C11#318711yescharacteristic
380C2×C11#319011yescharacteristic
381C2×C11#320611yescharacteristic
382C2×C11#321111yescharacteristic
383C24—21no—
384C24D4×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×Q8C22×Dic1114yes—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4C22×Dic1112yes—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—114no—
414C22×C4—111no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—442no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4D4×D1111yescharacteristic
430C22×C4#434112yes—
431C22×C4C22×Dic1112yes—
432C22×C4C23×D1111yescharacteristic
433SD16—48no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8C22×Dic1114yes—
440C4⋊C4—21no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—442no—
446C4⋊C4—442no—
447C4⋊C4C22×Dic1112yes—
448C22⋊C4—24no—
449C22⋊C4—442no—
450C22⋊C4—442no—
451C22⋊C4—442no—
452C22⋊C4—442no—
453C42—222no—
454C42—222no—
455C42—441no—
456C42—441no—
457C42—442no—
458C11#2204111yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23SD16×D1112yes—
471C23#6696912yes—
472C23D4×Dic1112yes—
473C23C2×D4×D1111yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479D4—24no—
480D4—48no—
481D4—42no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—48no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—112no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—441no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—441no—
516C2×C4—884no—
517C2×C4—884no—
518C2×C4D4×Dic1112yes—
519C2×C4C2×#434111yescharacteristic
520C2×C4#6703712yes—
521C2×C4#6703712yes—
522C2×C4C23×Dic1111yescharacteristic
523C8—24no—
524C8—442no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22SD16×Dic1114yes—
539C22#1062312011yescharacteristic
540C22#1062312311yescharacteristic
541C22C2×SD16×D1111yescharacteristic
542C22C2×#6696911yescharacteristic
543C22D11×#13711yescharacteristic
544C22#1062330811yescharacteristic
545C22C2×D4×Dic1111yescharacteristic
546C4—22no—
547C4—42no—
548C4—44no—
549C4—222no—
550C4—222no—
551C4—222no—
552C4—441no—
553C4—882no—
554C4—881no—
555C4—881no—
556C4#1062312412yes—
557C4#1062332912yes—
558C2—24no—
559C2—82no—
560C2#1307127711yescharacteristic
561C2C2×SD16×Dic1111yescharacteristic
562C2#137×Dic1111yescharacteristic
563C2#1307937111yescharacteristic
564C2#1307939411yescharacteristic
565C2#1307953911yescharacteristic
566C2#1307958011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#448D11
hypocenterC11#22041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×#10622843C2semidirect
3. #13069472C2semidirect
4. #13069294C2semidirect
5. #13069252C2semidirect
6. #13068952C2semidirect
8. #13068811C2semidirect
9. #13068551C2semidirect
10. C22⋊C8×Dic11C2semidirect
19. C11×#448C4semidirect
48. C22×Q8×C11C2×C4semidirect
60. C2×C11×SD16C2×C4semidirect
85. C11×#103C2×C4semidirect
86. C11×C22⋊C8C2×C4semidirect
146. C22×Dic11SD16semidirect
260. #448Dic11semidirect
322. C22×Q8C2×Dic11semidirect
334. C2×SD16C2×Dic11semidirect
362. #103C2×Dic11semidirect
365. C22⋊C8C2×Dic11semidirect
458. C11#22041semidirect

Maximal subgroups

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

subgroupindex
#121×Dic112
C2×#106228432
#130694722
#130692942
#130692522
#130689522
#130689342
#130688112
#130685512
C22⋊C8×Dic112
C2×C11×#4482
#2204111