Finite Group Databasebeta

← #14725393

Subgroups — #14725393

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077746C211yesmaximal, characteristic, complemented
2#13077653C211yesmaximal, characteristic, complemented
3C4×#66961C211yesmaximal, characteristic
4#13067529C211yesmaximal, characteristic, complemented
5#13067500C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067479C211yesmaximal, characteristic, complemented
8#13067458C211yesmaximal, characteristic, complemented
9#13067444C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic, complemented
13#13067040C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#1569C211yesmaximal, characteristic, complemented
16C2×#66961C411yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622746C411yescharacteristic
23#10622744C411yescharacteristic
24#10622741—21no—
25#10622741—21no—
26#10622734C411yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622451C2211yescharacteristic
30#10622451C2211yescharacteristic
31#10622451C2211yescharacteristic, complemented
32#10622451C2211yescharacteristic, complemented
33#10622450—21no—
34#10622447C2211yescharacteristic
35#10622447C2211yescharacteristic
36#10622446—21no—
37#10622443C2211yescharacteristic, complemented
38#10622443C2211yescharacteristic, complemented
39#10622339—21no—
40D11×C22⋊C8—21no—
41#10622324C411yescharacteristic
42#10622324C411yescharacteristic
43#10622323C411yescharacteristic
44#10622323C411yescharacteristic
45#10622319—21no—
46#10622319—21no—
47C4×D88C2211yescharacteristic
48C4×D88C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic, complemented
52C11×#335C2211yescharacteristic, complemented
53C11×#334C2211yescharacteristic, complemented
54C11×#334C2211yescharacteristic, complemented
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×#4339C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×M16—21no—
71C2×C11×M16C2×C411yescharacteristic
72C2×C11×M16C2×C411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C4×C22⋊D11—21no—
75C4×C22⋊D11—21no—
76C2×(C2×D11)⋊C4—21no—
77#66979C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79#66961—24no—
80C2×D88C2×C411yescharacteristic
81C2×D88C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×#4313—21no—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90C4×D44—21no—
91C4×D44—21no—
92C4×D44C2×C411yescharacteristic
93C4×D44C2×C411yescharacteristic
94C4×D44C2×C411yescharacteristic
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98#66925—21no—
99C42×D11—21no—
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C11×#97C2×C411yescharacteristic
110C11×#97C2×C411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)D411yescharacteristic
115C22⋊(C11⋊C8)D411yescharacteristic
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66882C2×C411yescharacteristic
129#66882C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)D411yescharacteristic
140C4⋊(C11⋊C8)D411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18052—111nomaximal, Sylow
146C23×D11—21no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152#4339—22no—
153#4339—41no—
154C2×D44—22no—
155C2×D44—21no—
156C2×D44—41no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—81no—
168C2×C4×D11—81no—
169C2×Dic22C22×C411yescharacteristic
170C11×M16—22no—
171C11×M16—41no—
172C11×M16—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C22×C411yescharacteristic
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208D88—22no—
209D88—22no—
210#4314—22no—
211#4314M1614yescomplemented
212#4313—81no—
213#4313—81no—
214#4313—81no—
215#4313—81no—
216C8×D11—81no—
217C8×D11—81no—
218#2991—111no—
219#2974—111no—
220C4×AGL(1,ℤ/8)—111no—
221#1594—111no—
222#1589—111no—
223#1588—111no—
224#1586—111no—
225#1583—111no—
226#1581—111no—
227SD16⋊C8—111no—
228C8×SD16—111no—
229#1569D1111yescharacteristic, complemented
230#1488—111no—
231#1486—111no—
232#1453—111no—
233C23×C11C4×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—81no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—42no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—81no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—42no—
264D44C2×M1612yes—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—81no—
274C4×D11—81no—
275Dic22—21no—
276Dic22C2×M1612yes—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11C2×M1612yes—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C2×AGL(1,ℤ/8)—111no—
292C4×#41—111no—
293C2×C4×D4—111no—
294C8×Q8—111no—
295C8×Q8—111no—
296#442—111no—
297#442—111no—
298#440—111no—
299#440—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—111no—
308#436—221no—
309#436—221no—
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432C2×D1111yescharacteristic
315#431—111no—
316#431—111no—
317#431—221no—
318#428—111no—
319#423—221no—
320#423C2×D1111yescharacteristic
321#418—111no—
322#417—111no—
323#407—221no—
324C2×C22⋊C8—221no—
325C4×M16C2×D1111yescharacteristic
326#335C2×D1111yescharacteristic, complemented
327#335C2×D1111yescharacteristic, complemented
328#334C2×D1111yescharacteristic, complemented
329#334C2×D1111yescharacteristic, complemented
330Q8⋊C8—111no—
331Q8⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338#322—111no—
339#322—111no—
340#322—111no—
341C82—111no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11C2×C4×D411yescharacteristic
346C2×D11—22no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—84no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11C22×M1611yescharacteristic
361C4×C11#56811yescharacteristic
362C4×C11#57611yescharacteristic
363C4×C11#57711yescharacteristic
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—41no—
368Dic11—41no—
369C2×#41—111no—
370C22×D4—111no—
371C23×C4—221no—
372AGL(1,ℤ/8)—224no—
373C2×SD16—111no—
374C2×SD16—111no—
375C2×D8—111no—
376C2×D8—111no—
377C2×M16—21no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16C4×D1111yescharacteristic
383C2×M16C4×D1111yescharacteristic
384C22×C8—221no—
385C22×C8—221no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—111no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4—221no—
398#117—111no—
399#117—221no—
400C2×C4⋊C4—111no—
401C2×C22⋊C4—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#107—111no—
405#107—111no—
406#106—111no—
407#106—111no—
408C4⋊C8—21no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8—221no—
414C4⋊C8C22×D1111yescharacteristic
415C4⋊C8C22×D1111yescharacteristic
416C4⋊C8C22×D1111yescharacteristic
417C4⋊C8C22×D1111yescharacteristic
418#103—111no—
419#103—111no—
420#102—111no—
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102—111no—
426C22⋊C8—21no—
427C22⋊C8—111no—
428C22⋊C8—111no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436#97—21no—
437#97C4×D1111yescharacteristic
438#97C4×D1111yescharacteristic
439C4×C8—111no—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8—221no—
444C4×C8—221no—
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C2×C11—41no—
448C2×C11D4×M1611yescharacteristic
449C2×C11#294611yescharacteristic
450C2×C11#295511yescharacteristic
451D11—42no—
452D11—81no—
453D11—81no—
454C24—221no—
455#41—222no—
456#41—441no—
457C2×Q8—111no—
458C2×D4—111no—
459C2×D4—111no—
460C2×D4—111no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—441no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—881no—
474C22×C4—881no—
475C22×C4C2×C4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4#434311yescharacteristic
478SD16—114no—
479SD16—222no—
480D8—222no—
481D8—222no—
482M16—22no—
483M16—41no—
484M16—81no—
485M16—881no—
486M16—881no—
487M16—881no—
488M16—881no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—881no—
500C2×C8—881no—
501C2×C8C2×C4×D1111yescharacteristic
502C2×C8C2×C4×D1111yescharacteristic
503C2×C8C2×C4×D1111yescharacteristic
504C2×C8C2×C4×D1111yescharacteristic
505C4⋊C4—111no—
506C4⋊C4—111no—
507C4⋊C4—111no—
508C4⋊C4—111no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42C2×C4×D1111yescharacteristic
523C42D4×D1111yescharacteristic
524C42#434311yescharacteristic
525C42C23×D1111yescharacteristic
526C11#1805211yescharacteristic, complemented, Sylow
527C23—221no—
528C23—221no—
529C23—221no—
530C23—442no—
531C23—442no—
532C23—881no—
533C23#6694611yescharacteristic
534Q8—112no—
535Q8—221no—
536D4—112no—
537D4—221no—
538D4—221no—
539D4—221no—
540D4—221no—
541D4—221no—
542D4—442no—
543D4—442no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—881no—
563C2×C4—881no—
564C2×C4—881no—
565C2×C4#6694611yescharacteristic
566C2×C4#6694611yescharacteristic
567C2×C4#6694611yescharacteristic
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4C2×#434311yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—221no—
579C8—221no—
580C8—221no—
581C8—221no—
582C8—441no—
583C8—441no—
584C8M16×D1112yes—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—222no—
589C22—441no—
590C22—441no—
591C22—441no—
592C22—441no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22—884no—
598C22C2×#6694611yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—222no—
604C4—441no—
605C4—441no—
606C4—441no—
607C4—441no—
608C4C2×M16×D1111yescharacteristic
609C4#1062327611yescharacteristic
610C4#1062330511yescharacteristic
611C4#1062330911yescharacteristic
612C2—41no—
613C2—442no—
614C2—881no—
615C2—881no—
616C2#1307735111yescharacteristic
617C2#1307744611yescharacteristic
618C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1569C2
socleC22×C11C2×C4×D4
prime radicalC2×#66961C4
cosocleC42×C11C24
hypercenter#1569D11
hypocenterC11#18052
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
1. #13077746C2semidirect
2. #13077653C2semidirect
4. #13067529C2semidirect
5. #13067500C2semidirect
6. #13067493C2semidirect
7. #13067479C2semidirect
8. #13067458C2semidirect
9. #13067444C2semidirect
10. #13067427C2semidirect
11. #13067415C2semidirect
12. #13067048C2semidirect
13. #13067040C2semidirect
14. #13066913C2semidirect
15. C11×#1569C2semidirect
31. #10622451C22semidirect
32. #10622451C22semidirect
37. #10622443C22semidirect
38. #10622443C22semidirect
51. C11×#335C22semidirect
52. C11×#335C22semidirect
53. C11×#334C22semidirect
54. C11×#334C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
61. #10622121C22semidirect
62. #10622121C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
211. #4314M16semidirect
229. #1569D11semidirect
326. #335C2×D11semidirect
327. #335C2×D11semidirect
328. #334C2×D11semidirect
329. #334C2×D11semidirect
526. C11#18052semidirect

Maximal subgroups

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

subgroupindex
#130777462
#130776532
C4×#669612
#130675292
#130675002
#130674932
#130674792
#130674582
#130674442
#130674272
#130674152
#130670482
#130670402
#130669132
C11×#15692
#1805211