Finite Group Databasebeta

← #14725416

Subgroups — #14725416

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077748C211yesmaximal, characteristic
2#13077706C211yesmaximal, characteristic, complemented
3C4×#67004C211yesmaximal, characteristic
4#13067515C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067463C211yesmaximal, characteristic, complemented
9#13067462C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067046C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1488C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C2×#67004C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622845C411yescharacteristic
22#10622643C411yescharacteristic
23#10622643C411yescharacteristic
24C4×#4326C2211yescharacteristic
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27Q8×C11⋊C8C2211yescharacteristic
28#10622631C411yescharacteristic
29#10622631C411yescharacteristic
30C4×#4324C2211yescharacteristic
31C4×#4324C2211yescharacteristic
32#10622625—21no—
33#10622625—21no—
34#10622625C2211yescharacteristic
35#10622625C2211yescharacteristic
36#10622617C411yescharacteristic
37#10622608C411yescharacteristic
38#10622538—21no—
39#10622538C2211yescharacteristic
40#10622537—21no—
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622444C2211yescharacteristic
44#10622444C2211yescharacteristic
45#10622443C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622332—21no—
48#10622331—21no—
49#10622314—21no—
50#10622314—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622094C2211yescharacteristic
60#10622094C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C4×Q8×C11C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C11×#117—21no—
76C11×#117C2×C411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79#67004—24no—
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4324C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318C2×C411yescharacteristic
91C2×#4318C2×C411yescharacteristic
92C4×Dic22—21no—
93C4×Dic22—21no—
94C4×Dic22C2×C411yescharacteristic
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8—21no—
103C11×#97—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113C22⋊(C11⋊C8)D411yescharacteristic
114#66879—21no—
115#66879—21no—
116Dic11⋊C8—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120C8×Dic11—21no—
121C8×Dic11—21no—
122#66874C2×C411yescharacteristic
123#66874C2×C411yescharacteristic
124#66874C2×C411yescharacteristic
125#66874C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66872C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)D411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867C2×C411yescharacteristic
138#66867C2×C411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18053—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C2×Dic22—22no—
160C2×Dic22—21no—
161C2×Dic22—41no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182#4326—22no—
183#4326M1614yescomplemented
184#4324—22no—
185#4324—22no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197#4318—22no—
198#4318—41no—
199#4318—81no—
200#4318—81no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#2991—111no—
213#2984—111no—
214C4×#137—111no—
215#1592—111no—
216#1590—111no—
217#1588—111no—
218#1587—111no—
219#1584—111no—
220#1583—111no—
221#1579—111no—
222C8×Q16—111no—
223#1569—111no—
224#1488D1111yescharacteristic
225#1487—111no—
226#1453—111no—
227C23×C11—21no—
228C23×C11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11C2×M1612yes—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258Dic22—21no—
259Dic22—21no—
260Dic22—21no—
261Dic22—42no—
262Dic22C2×M1612yes—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8C2×M1612yes—
277C2×#137—111no—
278C4×#41C2×D1111yescharacteristic
279C2×C4×Q8—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8—111no—
288#441—111no—
289#441—111no—
290#440—111no—
291#440—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296#436—111no—
297#436—111no—
298#436—221no—
299#436—221no—
300#432—221no—
301#432C2×D1111yescharacteristic
302#431—111no—
303#431—221no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#428—111no—
307#423—111no—
308#423—221no—
309#419—111no—
310#417—111no—
311C4×M16—111no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8C2×D1111yescharacteristic
321Q8⋊C8C2×D1111yescharacteristic
322D4⋊C8C2×D1111yescharacteristic
323D4⋊C8C2×D1111yescharacteristic
324#322—111no—
325#322—111no—
326#322—111no—
327C82—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×C4×D411yescharacteristic
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11C22×M1611yescharacteristic
343C4×C11#56811yescharacteristic
344C4×C11#57711yescharacteristic
345C4×C11#57811yescharacteristic
346Dic11—22no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41C4×D1111yescharacteristic
351C22×Q8—111no—
352#137—224no—
353C2×Q16—111no—
354C2×Q16—111no—
355C2×SD16—111no—
356C2×SD16—111no—
357C2×M16—111no—
358C2×M16—111no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—221no—
367C4×Q8—221no—
368C4×Q8C4×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4C4×D1111yescharacteristic
373C4×D4C22×D1111yescharacteristic
374#117—21no—
375#117C4×D1111yescharacteristic
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C42—21no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—111no—
410C22⋊C8—111no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—111no—
415#97—111no—
416#97—221no—
417#97—221no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—81no—
430C2×C11D4×M1611yescharacteristic
431C2×C11#294711yescharacteristic
432C2×C11#295511yescharacteristic
433#41—22no—
434#41—41no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×Q8—222no—
438C2×Q8—221no—
439C2×Q8—441no—
440C2×Q8C2×C4×D1111yescharacteristic
441C2×D4—21no—
442C2×D4C2×C4×D1111yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4#434111yescharacteristic
451Q16—114no—
452Q16—222no—
453SD16—222no—
454SD16—222no—
455M16—222no—
456M16—441no—
457M16—881no—
458M16—881no—
459M16—881no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—221no—
473C2×C8—221no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4C2×C4×D1111yescharacteristic
484C4⋊C4C2×C4×D1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42C2×C4×D1111yescharacteristic
496C42D4×D1111yescharacteristic
497C42#434111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1805311yescharacteristic, complemented, Sylow
500C23—21no—
501C23(C22⋊D11)⋊C411yescharacteristic
502Q8—21no—
503Q8—112no—
504Q8—221no—
505Q8—221no—
506Q8—221no—
507Q8—442no—
508Q8M16×D1112yes—
509D4—21no—
510D4—21no—
511D4—42no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4(C22⋊D11)⋊C411yescharacteristic
531C2×C4(C22⋊D11)⋊C411yescharacteristic
532C2×C4(C22⋊D11)⋊C411yescharacteristic
533C2×C4C22×C4×D1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—112no—
541C8—221no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—221no—
548C8—441no—
549C8—441no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22C2×(C22⋊D11)⋊C411yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—222no—
565C4—441no—
566C4—441no—
567C4—441no—
568C4C2×M16×D1111yescharacteristic
569C4#1062327611yescharacteristic
570C4#1062330111yescharacteristic
571C4#1062330211yescharacteristic
572C2—41no—
573C2—81no—
574C2#1307734811yescharacteristic
575C2#1307746211yescharacteristic
576C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1488C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#1488D11
hypocenterC11#18053
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #13077706C2semidirect
4. #13067515C2semidirect
5. #13067509C2semidirect
6. #13067497C2semidirect
7. #13067484C2semidirect
8. #13067463C2semidirect
9. #13067462C2semidirect
10. #13067432C2semidirect
11. #13067420C2semidirect
12. #13067384C2semidirect
13. #13067046C2semidirect
14. #13066911C2semidirect
183. #4326M16semidirect
499. C11#18053semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130777062
C4×#670042
#130675152
#130675092
#130674972
#130674842
#130674632
#130674622
#130674322
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C11×#14882
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