Finite Group Databasebeta

← #14803610

Subgroups — #14803610

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×#10622683C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic, complemented
4#13070019C212yesmaximal, complemented
5#13069926C212yesmaximal, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068616C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2366C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2212yes—
15C22×#4323C2212yes—
16C2×#66950—21no—
17C2×#66950—21no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#390—21no—
21C11×#390C2212yes—
22C11×#386—22no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28#10622685—24no—
29#10622683—24no—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32#10622552C2212yes—
33#10622548C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622290—22no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22—21no—
50C11×#127—22no—
51C11×#127D414yes—
52C4×D4×C11—24no—
53C4×D4×C11—42no—
54C4×D4×C11—44no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4323—24no—
66C2×#4323—24no—
67C2×#4323—42no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79#66950—44no—
80#66950—44no—
81C4×D44—22no—
82C4×D44—22no—
83#66922—22no—
84#66922—22no—
85C11×#95—21no—
86C11×#95D412yes—
87#66896—24no—
88#66896—24no—
89#66896—24no—
90#66873—22no—
91#66873—22no—
92C4⋊(C11⋊C8)—22no—
93C4⋊(C11⋊C8)—42no—
94C4×C11⋊C8—22no—
95#25318—111nomaximal, Sylow
96C24×C11—22no—
97C23×D11—21no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—81no—
108C2×D4×C11—81no—
109C2×D4×C11C2×D414yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11—82no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—22no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44#4112yes—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22—42no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4D814yescomplemented
139C11×C4⋊C4#4112yes—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—82no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—42no—
146C42×C11C2×D412yes—
147C42×C11#4112yes—
148#4323—48no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—42no—
151(C2×D11)⋊C4—44no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—44no—
157C4⋊Dic11—42no—
158C4⋊Dic11—44no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×#486—111no—
169C2×#459—111no—
170#2542—111no—
171#2366D1111yescharacteristic, complemented
172#2071—112no—
173#2054—112no—
174#1988—111no—
175#1939—111no—
176#1879—112no—
177#1802—112no—
178C4×#102—111no—
179C23×C11—24no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—41no—
194D4×C11—24no—
195D4×C11—24no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—48no—
199D4×C11—84no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—88no—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11C2×D814yes—
217C2×C4×C11C2×D812yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C2×Dic11—42no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—42no—
231D44—22no—
232D44—22no—
233D44—41no—
234D44—41no—
235C4×D11—84no—
236Dic22—84no—
237C11⋊C8—41no—
238C11⋊C8—42no—
239C11⋊C8—41no—
240C22×D8—112no—
241C2×C4⋊Q8—111no—
242C2×#127C2×D1111yescharacteristic
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C4×D4—21no—
246C2×C4×D4—111no—
247C2×C4×D4C2×D1112yes—
248#486—224no—
249#459—224no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8—112no—
252C2×#102—112no—
253C2×#102—112no—
254C2×#102—112no—
255C2×#102—111no—
256C2×#102—111no—
257C2×C4×C8—111no—
258#399—222no—
259#390—21no—
260#390—112no—
261#390C2×D1112yes—
262#386—22no—
263#384—112no—
264C4×C4⋊C4C2×D1111yescharacteristic
265C4×C4⋊C4C2×D1111yescharacteristic
266#340—112no—
267#340—111no—
268#340—112no—
269#340—111no—
270#336—112no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
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—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C4×C11—24no—
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11#45914yes—
298C4×C11#52911yescharacteristic
299C4×C11#54211yescharacteristic
300C4×C11#54611yescharacteristic
301C4×C11#54711yescharacteristic
302Dic11—82no—
303Dic11—81no—
304C22×Q8—221no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—111no—
308C22×D4C22×D1112yes—
309C23×C4—22no—
310C23×C4—221no—
311C2×D8—224no—
312C2×D8—224no—
313C2×D8—442no—
314C22×C8—112no—
315C22×C8—111no—
316C22×C8—111no—
317C4⋊Q8—222no—
318C4⋊Q8—222no—
319#127—22no—
320#127D4414yes—
321C22⋊Q8—444no—
322C22⋊Q8—444no—
323C4×D4—24no—
324C4×D4—42no—
325C4×D4—44no—
326C4×D4—222no—
327C4×D4—222no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—21no—
344C2×C42C22×D1112yes—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—222no—
347C4⋊C8—442no—
348#102—222no—
349#102—224no—
350#102—224no—
351#102—224no—
352#102—222no—
353C4×C8—222no—
354#95—21no—
355#95C22⋊D1112yes—
356C2×C11—84no—
357C2×C11#242711yescharacteristic
358C2×C11C2×#45911yescharacteristic
359C2×C11#304211yescharacteristic
360C2×C11#329411yescharacteristic
361C2×C11#333211yescharacteristic
362C2×C11#335811yescharacteristic
363C2×C11#337311yescharacteristic
364D11—82no—
365C24—22no—
366C24—221no—
367C2×Q8—442no—
368C2×Q8—442no—
369C2×Q8—442no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—81no—
380C2×D4—81no—
381C2×D4—112no—
382C2×D4—221no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4C2×D4414yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—44no—
391C22×C4—44no—
392C22×C4—82no—
393C22×C4—222no—
394C22×C4—221no—
395C22×C4—442no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4C2×C22⋊D1112yes—
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1112yes—
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403D8—448no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—222no—
407C2×C8—221no—
408C2×C8—221no—
409C2×C8—222no—
410C2×C8—221no—
411C2×C8—222no—
412C2×C8—221no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—221no—
418C4⋊C4—222no—
419C4⋊C4—221no—
420C4⋊C4—222no—
421C4⋊C4—444no—
422C4⋊C4—442no—
423C4⋊C4—444no—
424C4⋊C4#432314yescomplemented
425C4⋊C4#434112yes—
426C22⋊C4—44no—
427C22⋊C4—44no—
428C22⋊C4—82no—
429C22⋊C4—444no—
430C22⋊C4—442no—
431C22⋊C4—444no—
432C42—22no—
433C42—22no—
434C42—42no—
435C42C2×D4412yes—
436C42#433912yes—
437C11#2531811yescharacteristic, complemented, Sylow
438C23—24no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—222no—
446C23—441no—
447C23—441no—
448C23—441no—
449C23—441no—
450C23—441no—
451C23—441no—
452C23C22×C22⋊D1111yescharacteristic
453Q8—884no—
454D4—24no—
455D4—24no—
456D4—42no—
457D4—42no—
458D4—48no—
459D4—84no—
460D4—222no—
461D4—222no—
462D4—441no—
463D4—441no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—88no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—441no—
482C2×C4—442no—
483C2×C4—441no—
484C2×C4—884no—
485C2×C4#6698312yes—
486C2×C4#6698312yes—
487C2×C4C2×#432314yes—
488C2×C4C2×#432312yes—
489C2×C4#6700212yes—
490C2×C4C22×D4411yescharacteristic
491C2×C4C2×#433911yescharacteristic
492C2×C4C2×#434111yescharacteristic
493C2×C4#6703711yescharacteristic
494C2×C4#41×D1111yescharacteristic
495C2×C4#6704311yescharacteristic
496C8—442no—
497C8—441no—
498C8—441no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22—881no—
513C22C2×#6698311yescharacteristic
514C22C22×#432311yescharacteristic
515C22#1062333711yescharacteristic
516C22C2×#6700211yescharacteristic
517C22#1062336211yescharacteristic
518C22#1062336711yescharacteristic
519C22#1062336711yescharacteristic
520C4—24no—
521C4—22no—
522C4—42no—
523C4—42no—
524C4—81no—
525C4—881no—
526C4—882no—
527C4#1062262814yes—
528C4#1062308511yescharacteristic
529C4#1062308611yescharacteristic
530C4#1062308811yescharacteristic
531C4#1062309211yescharacteristic
532C2—84no—
533C2—882no—
534C2#1307218711yescharacteristic
535C2C2×#1062262811yescharacteristic
536C2#1307812811yescharacteristic
537C2#1308042911yescharacteristic
538C2#1308094311yescharacteristic
539C2#1308124711yescharacteristic
540C2#1308140411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenter#2366D11
hypocenterC11#25318
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
3. #13073565C2semidirect
4. #13070019C2semidirect
5. #13069926C2semidirect
6. #13069568C2semidirect
7. #13069335C2semidirect
8. #13068964C2semidirect
9. #13068616C2semidirect
10. C4×#66873C2semidirect
11. C11×#2366C2semidirect
138. C11×C4⋊C4D8semidirect
171. #2366D11semidirect
424. C4⋊C4#4323semidirect
437. C11#25318semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
C2×#106226852
#130735652
#130700192
#130699262
#130695682
#130693352
#130689642
#130686162
C4×#668732
C11×#23662
#2531811