Finite Group Databasebeta

← #14804499

Subgroups — #14804499

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622727C212yesmaximal, complemented
2C2×#10622454C211yesmaximal, characteristic, complemented
3#13073569C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic
5#13069813C212yesmaximal, complemented
6#13069621C212yesmaximal, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069039C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991—21no—
15C2×#66983C2212yes—
16C2×#66977C2212yes—
17C2×#66977C2212yes—
18C22×#4314C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C8×D4×C11—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25#10622834—21no—
26#10622825C2212yes—
27#10622727—28no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66881C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34#10622600—21no—
35#10622589—21no—
36#10622574—22no—
37#10622562—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622454—24no—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×C22⋊D11—22no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2312yes—
50C22×C8×C11—24no—
51C22×C8×C11—24no—
52C22×C8×C11—42no—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64#66991—44no—
65#66983—24no—
66#66983—42no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77#66977—24no—
78#66977—24no—
79#66977—42no—
80#66977—42no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C2×#4314—24no—
85C2×#4314—24no—
86C2×#4314—42no—
87C4×D44—22no—
88C4×D44—22no—
89#66922—22no—
90#66922—22no—
91C11×C4⋊C8D414yescomplemented
92C11×C22⋊C8—24no—
93C4×C8×C11—22no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96#66885—22no—
97#66885D414yescomplemented
98#66881—24no—
99#66880—24no—
100#66880—24no—
101#66880—42no—
102#25385—111nomaximal, Sylow
103C24×C11C2×D412yes—
104C23×D11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11SD1614yescomplemented
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C2×C22⋊D11—82no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44C2×D412yes—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—48no—
149C2×C8×C11C2×D412yes—
150C2×C8×C11C2×D414yes—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—24no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155C22⋊Dic11—44no—
156C22⋊Dic11—44no—
157C22⋊Dic11—44no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—42no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C4⋊Dic11—42no—
169C4⋊Dic11—81no—
170C4⋊Dic11C2×D412yes—
171C4⋊Dic11#4112yes—
172Dic11⋊C4—44no—
173Dic11⋊C4—44no—
174C4×Dic11—42no—
175#4314—48no—
176C2×#465—112no—
177C2×#461—111no—
178C2×C8×D4D1111yescharacteristic, complemented
179#2542—111no—
180#2537—111no—
181#2035—112no—
182#2000—112no—
183#1956—111no—
184#1948—111no—
185#1892—112no—
186C4×#102—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11C2×SD1614yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202D4×C11—28no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11#12112yes—
213C2×C4×C11#12112yes—
214C2×C4×C11C2×SD1612yes—
215C2×C4×C11#13512yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C22⋊D11—88no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238D44—22no—
239D44—22no—
240D44—41no—
241D44—41no—
242C4×D11—84no—
243Dic22—42no—
244Dic22—42no—
245Dic22—42no—
246Dic22—42no—
247C8×C11—24no—
248C8×C11—22no—
249C8×C11—41no—
250C22×SD16—112no—
251C23×C8C2×D1112yes—
252C2×C4⋊Q8—111no—
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—112no—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—111no—
258C2×C4×D4C2×D1111yescharacteristic
259#465—228no—
260#461—224no—
261C8×D4—24no—
262C2×#106—112no—
263C2×C4⋊C8C2×D1111yescharacteristic
264C2×#103—112no—
265C2×#103—112no—
266C2×#103—112no—
267C2×#102—111no—
268C2×#102—111no—
269C2×C22⋊C8C2×D1112yes—
270C2×C4×C8C2×D1111yescharacteristic
271#399—222no—
272#394—222no—
273#390—221no—
274#384—111no—
275#384—221no—
276#380—112no—
277#380—221no—
278C4×C4⋊C4—111no—
279#340—111no—
280#340—112no—
281#340—111no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11C2×#12111yescharacteristic
290C22×C11D4211yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11C22×SD1611yescharacteristic
293C22×C11C2×#13511yescharacteristic
294C22×C11#57711yescharacteristic
295C22×C11#57811yescharacteristic
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11#46514yescomplemented
306C4×C11#53211yescharacteristic
307C4×C11#54011yescharacteristic
308C4×C11D4211yescharacteristic
309C4×C11#55011yescharacteristic
310Dic11—42no—
311Dic11—42no—
312Dic11—82no—
313Dic11—82no—
314Dic11—81no—
315C22×Q8—112no—
316C22×D4—111no—
317C22×D4—222no—
318C22×D4D4411yescharacteristic
319C23×C4—221no—
320C23×C4C22×D1112yes—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—42no—
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329C22×C8C22×D1112yes—
330C4⋊Q8—222no—
331C4⋊Q8—222no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—442no—
335C22⋊Q8—442no—
336#121—224no—
337#121—442no—
338#121—444no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—222no—
342C4×D4—222no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4D4411yescharacteristic
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4D4412yes—
360C2×C42—221no—
361C2×C42C22×D1111yescharacteristic
362#106—224no—
363C4⋊C8C22⋊D1114yescomplemented
364#103—224no—
365#103—224no—
366#103—442no—
367#102—114no—
368#102—222no—
369C22⋊C8—24no—
370C4×C8—22no—
371#95—221no—
372#95—222no—
373C2×C11—44no—
374C2×C11#242811yescharacteristic
375C2×C11C2×#46511yescharacteristic
376C2×C11#306311yescharacteristic
377C2×C11D4×SD1611yescharacteristic
378C2×C11#328311yescharacteristic
379C2×C11#329811yescharacteristic
380C2×C11#330311yescharacteristic
381D11—82no—
382C24—221no—
383C24C2×D4412yes—
384C2×Q8—222no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—112no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—444no—
399C2×D4—444no—
400C2×D4—882no—
401C2×D4#431414yescomplemented
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—442no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4C2×D4412yes—
417C22×C4C2×D4411yescharacteristic
418C22×C4C2×D4411yescharacteristic
419C22×C4C23×D1111yescharacteristic
420SD16—448no—
421C2×C8—22no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—48no—
429C2×C8D4×D1112yes—
430C2×C8C2×C22⋊D1114yes—
431C4⋊C4—22no—
432C4⋊C4—112no—
433C4⋊C4—112no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4—222no—
439C4⋊C4—221no—
440C4⋊C4—444no—
441C4⋊C4—444no—
442C4⋊C4—442no—
443C4⋊C4—442no—
444C4⋊C4—442no—
445C4⋊C4—881no—
446C22⋊C4—24no—
447C22⋊C4—444no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—442no—
452C42—442no—
453C42#433912yes—
454C42C2×C22⋊D1112yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—222no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23C2×#431414yes—
470C23C22×D4411yescharacteristic
471Q8—442no—
472Q8—442no—
473Q8—442no—
474Q8—442no—
475D4—28no—
476D4—222no—
477D4—222no—
478D4—441no—
479D4—441no—
480D4—888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—441no—
499C2×C4—442no—
500C2×C4—441no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—884no—
506C2×C4C2×#431412yes—
507C2×C4#6695712yes—
508C2×C4#6698312yes—
509C2×C4#6698312yes—
510C2×C4C2×#433911yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4#6703711yescharacteristic
513C2×C4#41×D1111yescharacteristic
514C2×C4#6704211yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—22no—
517C8—24no—
518C8—41no—
519C22—24no—
520C22—24no—
521C22—24no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—881no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22D4×D4411yescharacteristic
534C22#1062308511yescharacteristic
535C22C22×#431411yescharacteristic
536C22C2×#6695711yescharacteristic
537C22#1062328211yescharacteristic
538C22#1062328411yescharacteristic
539C22C2×#6698311yescharacteristic
540C4—22no—
541C4—42no—
542C4—442no—
543C4—442no—
544C4—882no—
545C4—881no—
546C4—882no—
547C4#1062272714yescomplemented
548C4#1062307911yescharacteristic
549C4#1062309311yescharacteristic
550C4D4×C22⋊D1111yescharacteristic
551C4#1062336511yescharacteristic
552C2—44no—
553C2—882no—
554C2#1307219811yescharacteristic
555C2C2×#1062272711yescharacteristic
556C2#1307830711yescharacteristic
557C2D4×#431411yescharacteristic
558C2#1308033811yescharacteristic
559C2#1308048211yescharacteristic
560C2#1308054511yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×C8×D4D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622727C2semidirect
2. C2×#10622454C2semidirect
3. #13073569C2semidirect
5. #13069813C2semidirect
6. #13069621C2semidirect
7. #13069418C2semidirect
8. #13069380C2semidirect
9. #13069039C2semidirect
10. C4×#66885C2semidirect
11. C2×C8×D4×C11C2semidirect
91. C11×C4⋊C8D4semidirect
97. #66885D4semidirect
107. C2×D4×C11SD16semidirect
178. C2×C8×D4D11semidirect
305. C4×C11#465semidirect
363. C4⋊C8C22⋊D11semidirect
401. C2×D4#4314semidirect
455. C11#25385semidirect
547. C4#10622727semidirect

Maximal subgroups

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

subgroupindex
C2×#106227272
C2×#106224542
#130735692
#130735292
#130698132
#130696212
#130694182
#130693802
#130690392
C4×#668852
C2×C8×D4×C112
#2538511