Finite Group Databasebeta

← #14803616

Subgroups — #14803616

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13073569C211yesmaximal, characteristic, complemented
4#13071680C211yesmaximal, characteristic, complemented
5#13070023C212yesmaximal, complemented
6#13069925C212yesmaximal, complemented
7#13069568C211yesmaximal, characteristic, complemented
8#13069334C211yesmaximal, characteristic, complemented
9#13068961C212yesmaximal, complemented
10#13068615C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2212yes—
14C2×#66977—21no—
15C2×#66977—21no—
16C2×#66946C2212yes—
17C2×#66927C2211yescharacteristic
18C2×C4×D44—21no—
19C2×#66922C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622834C2212yes—
25C2×#66885C2212yes—
26C2×#66885C2212yes—
27C2×Dic11⋊C8C2212yes—
28#10622628—24no—
29#10622601C2212yes—
30#10622589C2212yes—
31C2×#66873C2212yes—
32#10622562—22no—
33#10622552—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622307—24no—
37#10622278—22no—
38C11×#340C2211yescharacteristic
39C11×#340C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×Dic22—21no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×#4323—24no—
63C2×#4323—24no—
64C2×#4323—42no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2312yes—
72#66977—44no—
73#66977—44no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66946—24no—
79#66946—42no—
80#66927—22no—
81#66927D414yes—
82C4×D44—44no—
83#66922—22no—
84#66922—22no—
85C11×#102—22no—
86C11×#102—22no—
87C4×C8×C11—22no—
88C11×#95—21no—
89C11⋊#95D412yes—
90#66885—24no—
91#66885—24no—
92Dic11⋊C8—42no—
93#66873—24no—
94C4⋊(C11⋊C8)—22no—
95#25318—111nomaximal, Sylow
96C24×C11—21no—
97C23×D11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—22no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×D44—24no—
117C2×D44—24no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—81no—
126C2×D44—81no—
127C2×D44C2×D414yes—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—82no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22—42no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4#4112yes—
146C11×C22⋊C4—42no—
147C42×C11—42no—
148C42×C11C2×D412yes—
149C42×C11#4112yes—
150C22⋊Dic11—44no—
151C22⋊Dic11—44no—
152#4323—48no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—82no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—42no—
160C4⋊Dic11D814yescomplemented
161Dic11⋊C4—44no—
162Dic11⋊C4—44no—
163C4×Dic11—22no—
164C4×Dic11—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#486—111no—
169C2×#459—111no—
170#2542—111no—
171#2366—111no—
172#2071—112no—
173#2054—112no—
174#1988—111no—
175#1939—111no—
176#1879—112no—
177#1802—112no—
178C4×#102D1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—41no—
197D4×C11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11C2×D812yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11C2×D814yes—
229D44—24no—
230D44—24no—
231D44—42no—
232D44—42no—
233D44—48no—
234D44—84no—
235C4×D11—88no—
236Dic22—84no—
237C8×C11—41no—
238C8×C11—41no—
239C11⋊C8—42no—
240C22×D8—112no—
241C2×C4⋊Q8—111no—
242C2×#127—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C4×D4—112no—
246C2×C4×D4—221no—
247C2×C4×D4C2×D1111yescharacteristic
248#486—224no—
249#459—224no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8—112no—
252C2×#102—112no—
253C2×#102—112no—
254C2×#102—112no—
255C2×#102C2×D1111yescharacteristic
256C2×#102C2×D1111yescharacteristic
257C2×C4×C8C2×D1111yescharacteristic
258#399—222no—
259#390—112no—
260#390—112no—
261#390—221no—
262#386—222no—
263#384—112no—
264C4×C4⋊C4—111no—
265C4×C4⋊C4C2×D1111yescharacteristic
266#340—112no—
267#340—112no—
268#340C2×D1111yescharacteristic
269#340C2×D1111yescharacteristic
270#336—112no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C2×#12111yescharacteristic
279C22×C11#54611yescharacteristic
280C22×C11#54811yescharacteristic
281C22×C11C22×D811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57711yescharacteristic
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—44no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—82no—
291C2×D11—82no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11#45914yes—
297C4×C11#52911yescharacteristic
298C4×C11#54211yescharacteristic
299C4×C11#54611yescharacteristic
300C4×C11#54711yescharacteristic
301Dic11—24no—
302Dic11—42no—
303Dic11—82no—
304C22×Q8—221no—
305C22×D4—112no—
306C22×D4—221no—
307C22×D4—221no—
308C22×D4C22×D1111yescharacteristic
309C23×C4—21no—
310C23×C4—222no—
311C2×D8—224no—
312C2×D8—224no—
313C2×D8—442no—
314C22×C8—112no—
315C22×C8C22×D1111yescharacteristic
316C22×C8C22×D1111yescharacteristic
317C4⋊Q8—222no—
318C4⋊Q8—222no—
319#127—114no—
320#127—222no—
321C22⋊Q8—444no—
322C22⋊Q8—444no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—224no—
326C4×D4—444no—
327C4×D4—442no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—21no—
344C2×C42—112no—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—222no—
347C4⋊C8—442no—
348#102—22no—
349#102—22no—
350#102—224no—
351#102—224no—
352#102—224no—
353C4×C8—22no—
354#95—21no—
355#95—112no—
356C2×C11—82no—
357C2×C11#242711yescharacteristic
358C2×C11C2×#45911yescharacteristic
359C2×C11#304211yescharacteristic
360C2×C11#329411yescharacteristic
361C2×C11#333211yescharacteristic
362C2×C11#335811yescharacteristic
363C2×C11#337311yescharacteristic
364D11—84no—
365C24—21no—
366C24—222no—
367C2×Q8—442no—
368C2×Q8—442no—
369C2×Q8—442no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—114no—
376C2×D4—224no—
377C2×D4—224no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—881no—
386C2×D4—881no—
387C2×D4#433912yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—222no—
397C22×C4—444no—
398C22×C4—444no—
399C22×C4—882no—
400C22×C4D4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403D8—448no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—222no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—114no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4—444no—
423C4⋊C4—444no—
424C4⋊C4—442no—
425C4⋊C4#433912yes—
426C22⋊C4—42no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C22⋊C4—444no—
430C22⋊C4—444no—
431C22⋊C4—882no—
432C42—42no—
433C42—222no—
434C42—222no—
435C42#433912yes—
436C42D4×D1112yes—
437C11#2531811yescharacteristic, complemented, Sylow
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—224no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23—442no—
451C23—442no—
452C23C2×D4×D1111yescharacteristic
453Q8—884no—
454D4—22no—
455D4—22no—
456D4—41no—
457D4—41no—
458D4—224no—
459D4—224no—
460D4—442no—
461D4—442no—
462D4—448no—
463D4—884no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—84no—
476C2×C4—114no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—888no—
486C2×C4#6693712yes—
487C2×C4#6693712yes—
488C2×C4D8×D1112yes—
489C2×C4#6696712yes—
490C2×C4C2×#433911yescharacteristic
491C2×C4C2×#433911yescharacteristic
492C2×C4C2×#433911yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4#6704211yescharacteristic
495C2×C4#6704311yescharacteristic
496C8—41no—
497C8—41no—
498C8—442no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—444no—
507C22—444no—
508C22—444no—
509C22—882no—
510C22—882no—
511C22—882no—
512C22—882no—
513C22C2×#6693711yescharacteristic
514C22#1062308111yescharacteristic
515C22#1062308311yescharacteristic
516C22C2×D8×D1111yescharacteristic
517C22C2×#6696711yescharacteristic
518C22#1062330111yescharacteristic
519C22#1062330111yescharacteristic
520C4—22no—
521C4—42no—
522C4—81no—
523C4—81no—
524C4—224no—
525C4—442no—
526C4—882no—
527C4#1062239914yes—
528C4#1062301011yescharacteristic
529C4#1062306511yescharacteristic
530C4#1062308111yescharacteristic
531C4#1062308211yescharacteristic
532C2—82no—
533C2—884no—
534C2#1307219311yescharacteristic
535C2C2×#1062239911yescharacteristic
536C2#1307813111yescharacteristic
537C2#1308043111yescharacteristic
538C2#1308094511yescharacteristic
539C2#1308124911yescharacteristic
540C2#1308140611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC4×#102D11
hypocenterC11#25318
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622307C2semidirect
3. #13073569C2semidirect
4. #13071680C2semidirect
5. #13070023C2semidirect
6. #13069925C2semidirect
7. #13069568C2semidirect
8. #13069334C2semidirect
9. #13068961C2semidirect
10. #13068615C2semidirect
11. C4×C11×#102C2semidirect
160. C4⋊Dic11D8semidirect
178. C4×#102D11semidirect
437. C11#25318semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106226282
#130735692
#130716802
#130700232
#130699252
#130695682
#130693342
#130689612
#130686152
C4×C11×#1022
#2531811