Finite Group Databasebeta

← #14804507

Subgroups — #14804507

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×#10622654C212yesmaximal, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13073569C211yesmaximal, characteristic, complemented
5#13069812C212yesmaximal, complemented
6#13069619C212yesmaximal, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069037C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4324C2212yes—
17C2×#66977C2212yes—
18C2×#66977C2212yes—
19C23×C11⋊C8C2212yes—
20C2×#66922C2211yescharacteristic
21C11×#394—22no—
22C11×#384C2211yescharacteristic
23C11×#380—21no—
24C11×#380C2212yes—
25#10622834—21no—
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622654—28no—
30#10622632—24no—
31D4×C11⋊C8—24no—
32#10622589—21no—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66872C2212yes—
37#10622562—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2312yes—
49C22×Dic22C2312yes—
50C11×#121—24no—
51C11×#121—42no—
52C11×#121—44no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4D412yes—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×#4324—24no—
70C2×#4324—24no—
71C2×#4324—42no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76#66977—24no—
77#66977—24no—
78#66977—42no—
79#66977—42no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—21no—
83C22×C11⋊C8—24no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—42no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89#66922—22no—
90#66922—22no—
91C11×#95—22no—
92#66896—22no—
93#66896D414yescomplemented
94C11⋊#95—21no—
95C22⋊(C11⋊C8)—24no—
96#66874—24no—
97#66874—24no—
98#66874—42no—
99#66872—24no—
100C4⋊(C11⋊C8)D414yescomplemented
101C4×C11⋊C8—22no—
102#25385—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11C2×D412yes—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—82no—
115C2×D4×C11SD1614yescomplemented
116C2×D4×C11C2×D412yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—81no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—42no—
152C42×C11C2×D412yes—
153C42×C11#4112yes—
154C22⋊Dic11—44no—
155C22⋊Dic11—44no—
156#4324—48no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—42no—
160C4⋊Dic11—42no—
161C4⋊Dic11C2×D412yes—
162C4⋊Dic11#4112yes—
163Dic11⋊C4—44no—
164Dic11⋊C4—44no—
165C4×Dic11—42no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—48no—
174C2×C11⋊C8C2×D414yes—
175C2×C11⋊C8C2×D412yes—
176C2×#465—112no—
177C2×#461—111no—
178C2×C8×D4—111no—
179#2542—111no—
180#2537D1111yescharacteristic
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×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11C2×SD1614yes—
201C23×C11C22×D411yescharacteristic
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—28no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—88no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—84no—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11#13512yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243Dic22—42no—
244Dic22—42no—
245Dic22—42no—
246Dic22—42no—
247C11⋊C8—22no—
248C11⋊C8—24no—
249C11⋊C8—41no—
250C22×SD16—112no—
251C23×C8—112no—
252C2×C4⋊Q8—111no—
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—112no—
255C2×#121—21no—
256C2×#121C2×D1112yes—
257C2×C4×D4C2×D1111yescharacteristic
258C2×C4×D4C2×D1111yescharacteristic
259#465—228no—
260#461—224no—
261C8×D4—224no—
262C2×#106—112no—
263C2×C4⋊C8—111no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#103—112no—
267C2×#102—111no—
268C2×#102—111no—
269C2×C22⋊C8—112no—
270C2×C4×C8—111no—
271#399—222no—
272#394—22no—
273#390—221no—
274#384—221no—
275#384C2×D1111yescharacteristic
276#380—21no—
277#380C2×D1112yes—
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×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11C2×#12111yescharacteristic
297C22×C11D4211yescharacteristic
298C22×C11#54611yescharacteristic
299C22×C11C22×SD1611yescharacteristic
300C22×C11C2×#13511yescharacteristic
301C22×C11#57711yescharacteristic
302C22×C11#57811yescharacteristic
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—82no—
306C4×C11—81no—
307C4×C11#46514yescomplemented
308C4×C11#53211yescharacteristic
309C4×C11#54011yescharacteristic
310C4×C11D4211yescharacteristic
311C4×C11#55011yescharacteristic
312Dic11—42no—
313Dic11—42no—
314Dic11—82no—
315C22×Q8—112no—
316C22×D4—22no—
317C22×D4C22⋊D1111yescharacteristic
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4C22×D1112yes—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—111no—
325C22×C8—112no—
326C22×C8—111no—
327C22×C8—224no—
328C22×C8—224no—
329C22×C8—442no—
330C4⋊Q8—222no—
331C4⋊Q8—222no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—442no—
335C22⋊Q8—442no—
336#121—24no—
337#121—42no—
338#121—44no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1112yes—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4C22⋊D1112yes—
360C2×C42—221no—
361C2×C42C22×D1111yescharacteristic
362#106—224no—
363C4⋊C8—114no—
364#103—224no—
365#103—224no—
366#103—442no—
367#102—114no—
368#102—222no—
369C22⋊C8—224no—
370C4×C8—222no—
371#95—22no—
372#95—221no—
373C2×C11—44no—
374C2×C11—82no—
375C2×C11#242811yescharacteristic
376C2×C11C2×#46511yescharacteristic
377C2×C11#306311yescharacteristic
378C2×C11D4×SD1611yescharacteristic
379C2×C11#328311yescharacteristic
380C2×C11#329811yescharacteristic
381C2×C11#330311yescharacteristic
382C24—21no—
383C24C2×C22⋊D1112yes—
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—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—82no—
400C2×D4#432414yescomplemented
401C2×D4D4×D1112yes—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420SD16—448no—
421C2×C8—114no—
422C2×C8—112no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—221no—
426C2×C8—222no—
427C2×C8—221no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—448no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—42no—
437C4⋊C4—81no—
438C4⋊C4—112no—
439C4⋊C4—112no—
440C4⋊C4—221no—
441C4⋊C4—221no—
442C4⋊C4—444no—
443C4⋊C4—444no—
444C4⋊C4—442no—
445C4⋊C4—442no—
446C22⋊C4—24no—
447C22⋊C4—44no—
448C22⋊C4—44no—
449C22⋊C4—42no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C42—442no—
453C42D4×D1112yes—
454C42#434112yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23C2×#432414yes—
470C23C22×C22⋊D1111yescharacteristic
471Q8—442no—
472Q8—442no—
473Q8—442no—
474Q8—442no—
475D4—22no—
476D4—22no—
477D4—28no—
478D4—41no—
479D4—41no—
480D4—88no—
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—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—84no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4C2×#432412yes—
507C2×C4#6699212yes—
508C2×C4#6699212yes—
509C2×C4#6700312yes—
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C2×#434111yescharacteristic
513C2×C4#6703711yescharacteristic
514C2×C4#41×D1111yescharacteristic
515C2×C4#6704211yescharacteristic
516C8—222no—
517C8—224no—
518C8—441no—
519C22—24no—
520C22—24no—
521C22—24no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22C22×#432411yescharacteristic
534C22D4×C22⋊D1111yescharacteristic
535C22C2×#6699211yescharacteristic
536C22C2×#6700311yescharacteristic
537C22#1062336011yescharacteristic
538C22#1062336711yescharacteristic
539C22#1062336911yescharacteristic
540C4—22no—
541C4—42no—
542C4—81no—
543C4—82no—
544C4—442no—
545C4—442no—
546C4—882no—
547C4#1062265414yescomplemented
548C4#1062312711yescharacteristic
549C4#1062313011yescharacteristic
550C4#1062314011yescharacteristic
551C4#1062315011yescharacteristic
552C2—44no—
553C2—82no—
554C2#1307220611yescharacteristic
555C2C2×#1062265411yescharacteristic
556C2#1307830911yescharacteristic
557C2D4×#432411yescharacteristic
558C2#1308033411yescharacteristic
559C2#1308047511yescharacteristic
560C2#1308053811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#10622654C2semidirect
2. C2×#10622632C2semidirect
3. C2×D4×C11⋊C8C2semidirect
4. #13073569C2semidirect
5. #13069812C2semidirect
6. #13069619C2semidirect
7. #13069417C2semidirect
8. #13069377C2semidirect
9. #13069037C2semidirect
10. C4×#66896C2semidirect
93. #66896D4semidirect
100. C4⋊(C11⋊C8)D4semidirect
115. C2×D4×C11SD16semidirect
307. C4×C11#465semidirect
400. C2×D4#4324semidirect
455. C11#25385semidirect
547. C4#10622654semidirect

Maximal subgroups

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

subgroupindex
C2×#106226542
C2×#106226322
C2×D4×C11⋊C82
#130735692
#130698122
#130696192
#130694172
#130693772
#130690372
C4×#668962
C11×#25372
#2538511