Finite Group Databasebeta

← #14725299

Subgroups — #14725299

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077628C211yesmaximal, characteristic, complemented
2C4×#66985C211yesmaximal, characteristic
3D4×#4318C211yesmaximal, characteristic, complemented
4#13067515C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067483C211yesmaximal, characteristic, complemented
7#13067470C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067056C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#1490C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66985C411yescharacteristic
18C22×#4318—21no—
19C4×#4339C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622828C411yescharacteristic
23#10622820—21no—
24#10622631C411yescharacteristic
25#10622631C411yescharacteristic
26C4×#4324C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622627C411yescharacteristic
29#10622627C411yescharacteristic
30C4×#4323C2211yescharacteristic
31C4×#4323C2211yescharacteristic
32#10622625C2211yescharacteristic
33#10622625C2211yescharacteristic
34#10622624—21no—
35#10622624—21no—
36D4×C11⋊C8C2211yescharacteristic
37D4×C11⋊C8C2211yescharacteristic
38#10622579C411yescharacteristic
39#10622577C411yescharacteristic
40#10622537C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622447C2211yescharacteristic, complemented
44#10622447C2211yescharacteristic, complemented
45#10622444C2211yescharacteristic, complemented
46#10622444C2211yescharacteristic, complemented
47#10622341—21no—
48#10622341—21no—
49#10622318—21no—
50D11×#97—21no—
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622094C2211yescharacteristic, complemented
62#10622094C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×#4339C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4324C2×C411yescharacteristic
81C2×#4324C2×C411yescharacteristic
82#66985—24no—
83C2×#4323C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C4×C22⋊D11—21no—
86C4×C22⋊D11—21no—
87#66979C2×C411yescharacteristic
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318—21no—
91C2×#4318—44no—
92C2×#4318C2×C411yescharacteristic
93C2×#4318C2×C411yescharacteristic
94C2×#4318D411yescharacteristic
95C2×#4318D411yescharacteristic
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C2×C8×D11—21no—
99C2×C8×D11—21no—
100C4×D44C2×C411yescharacteristic
101C4×D44C2311yescharacteristic
102#66925—21no—
103C42×D11—21no—
104C4×Dic22C2×C411yescharacteristic
105C4×Dic22C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C22⋊C8—21no—
109C11×#97—21no—
110C11×#97—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867C2×C411yescharacteristic
139#66867C2×C411yescharacteristic
140#66867D411yescharacteristic
141#66867D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#18046—111nomaximal, Sylow
147C24×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—41no—
151C2×D4×C11C22×C411yescharacteristic
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C2×C22⋊D11—21no—
164#4339—22no—
165#4339—41no—
166C2×D44C22×C411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×Dic22C22×C411yescharacteristic
171C11×M16—42no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11C22×C411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—21no—
188#4324—22no—
189#4324—22no—
190#4323—22no—
191#4323M1614yescomplemented
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201#4318—22no—
202#4318—22no—
203#4318—41no—
204#4318—41no—
205#4318—42no—
206#4318—42no—
207#4318—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—42no—
211C2×C11⋊C8—42no—
212C2×C11⋊C8C22×C411yescharacteristic
213C2×C11⋊C8C22×C411yescharacteristic
214C2×C11⋊C8C22×C411yescharacteristic
215C2×C11⋊C8C22×C411yescharacteristic
216C2×C11⋊C8C2×D411yescharacteristic
217C2×C11⋊C8C2×D411yescharacteristic
218C2×C11⋊C8C2×D411yescharacteristic
219C2×C11⋊C8C2×D411yescharacteristic
220C8×D11—42no—
221C8×D11—42no—
222#2970—111no—
223C4×AGL(1,ℤ/8)—111no—
224D4×M16—111no—
225#1592—111no—
226#1590—111no—
227#1586—111no—
228#1585—111no—
229#1582—111no—
230#1581—111no—
231#1580—111no—
232C8×D8—111no—
233#1569—111no—
234#1490D1111yescharacteristic, complemented
235#1489—111no—
236#1455—111no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—81no—
242C23×C11C4×D411yescharacteristic
243C22×D11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—42no—
248D4×C11C2×M1612yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C22⋊D11—42no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273D44—21no—
274D44C2×M1612yescomplemented
275C4×D11—42no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—81no—
279Dic22—21no—
280Dic22—21no—
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8C2×M1612yescomplemented
294C11⋊C8AGL(1,ℤ/8)12yescomplemented
295C2×AGL(1,ℤ/8)—111no—
296C22×M16—221no—
297C4×#41—111no—
298C2×C4×D4C2×D1111yescharacteristic
299#446—111no—
300#446—111no—
301#442—111no—
302#442—111no—
303#440—111no—
304#440—111no—
305C4×SD16—111no—
306C4×SD16—111no—
307C4×D8—111no—
308C4×D8—111no—
309#436—111no—
310#436—111no—
311#435—221no—
312#435—221no—
313#435—221no—
314#435—221no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4—111no—
318C8×D4—111no—
319#432—221no—
320#432C2×D1111yescharacteristic
321#428—111no—
322#423—111no—
323#418—111no—
324#417—111no—
325#407—221no—
326C4×M16—111no—
327C4×M16—111no—
328C4×M16C2×D1111yescharacteristic
329C2×#97—221no—
330#335—111no—
331#335—111no—
332#334—111no—
333#334—111no—
334Q8⋊C8—111no—
335Q8⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8C2×D1111yescharacteristic
339D4⋊C8C2×D1111yescharacteristic
340D4⋊C8C2×D1111yescharacteristic
341D4⋊C8C2×D1111yescharacteristic
342#322—111no—
343#322—111no—
344#322—111no—
345C82—111no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—84no—
356C22×C11C2×C4×D411yescharacteristic
357C2×D11—22no—
358C2×D11—41no—
359C2×D11—41no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11C22×M1611yescharacteristic
367C4×C11#56811yescharacteristic
368C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C11#57511yescharacteristic
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373C2×#41—111no—
374C22×D4C4×D1111yescharacteristic
375C23×C4—21no—
376AGL(1,ℤ/8)—224no—
377C2×SD16—111no—
378C2×SD16—111no—
379C2×D8—111no—
380C2×D8—111no—
381C2×M16—21no—
382C2×M16—111no—
383C2×M16—111no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—444no—
390C22×C8—221no—
391C22×C8—221no—
392C22×C8—221no—
393C22×C8—221no—
394C4×Q8—111no—
395C4×Q8—111no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—221no—
401C4×D4—221no—
402C4×D4C4×D1111yescharacteristic
403C4×D4C4×D1111yescharacteristic
404C4×D4C22×D1111yescharacteristic
405C4×D4C22×D1111yescharacteristic
406#117—111no—
407#117—221no—
408C2×C4⋊C4C4×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C42—221no—
411C2×C42C22×D1111yescharacteristic
412#107—111no—
413#107—111no—
414#106—111no—
415#106—111no—
416C4⋊C8—111no—
417C4⋊C8—111no—
418C4⋊C8—221no—
419C4⋊C8—221no—
420C4⋊C8—221no—
421C4⋊C8C22×D1111yescharacteristic
422C4⋊C8C22×D1111yescharacteristic
423#103—111no—
424#103—111no—
425#102—111no—
426#102—111no—
427#102—111no—
428#102—111no—
429#102—111no—
430#102—111no—
431C22⋊C8—21no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438#97—21no—
439#97—21no—
440#97—111no—
441#97—111no—
442#97—111no—
443#97—111no—
444#97—221no—
445#97—221no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8—111no—
449C4×C8—111no—
450C4×C8C22×D1111yescharacteristic
451C4×C8C22×D1111yescharacteristic
452C2×C11—41no—
453C2×C11—42no—
454C2×C11—81no—
455C2×C11D4×M1611yescharacteristic
456C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
457C2×C11#295611yescharacteristic
458D11—42no—
459C24—21no—
460#41—222no—
461#41—441no—
462C2×Q8—111no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—111no—
467C2×D4—221no—
468C2×D4C2×C4×D1111yescharacteristic
469C2×D4C2×C4×D1111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4#434111yescharacteristic
483SD16—222no—
484SD16—222no—
485D8—114no—
486D8—222no—
487M16—42no—
488M16—222no—
489M16—222no—
490M16—442no—
491M16—441no—
492M16—441no—
493M16—442no—
494M16—442no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—442no—
510C2×C8—442no—
511C2×C8—442no—
512C2×C8—442no—
513C4⋊C4—21no—
514C4⋊C4—111no—
515C4⋊C4—111no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4C2×C4×D1111yescharacteristic
519C4⋊C4C2×C4×D1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42C2×C4×D1111yescharacteristic
531C42D4×D1111yescharacteristic
532C42#434111yescharacteristic
533C42C23×D1111yescharacteristic
534C11#1804611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—42no—
538C23—42no—
539C23—81no—
540C23—221no—
541C23(C22⋊D11)⋊C411yescharacteristic
542Q8—221no—
543Q8—221no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—42no—
548D4—112no—
549D4—221no—
550D4—442no—
551D4M16×D1112yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—442no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—881no—
573C2×C4(C22⋊D11)⋊C411yescharacteristic
574C2×C4(C22⋊D11)⋊C411yescharacteristic
575C2×C4(C22⋊D11)⋊C411yescharacteristic
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C8—22no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—112no—
584C8—112no—
585C8—221no—
586C8—221no—
587C8—221no—
588C8—221no—
589C8—221no—
590C8—221no—
591C8—441no—
592C8—441no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—84no—
603C22—222no—
604C22—441no—
605C22—441no—
606C22C2×(C22⋊D11)⋊C411yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4C2×M16×D1111yescharacteristic
617C4#1062327611yescharacteristic
618C4D11×AGL(1,ℤ/8)11yescharacteristic
619C4#1062330411yescharacteristic
620C2—41no—
621C2—42no—
622C2—81no—
623C2—442no—
624C2#1307734811yescharacteristic
625C2#1307742011yescharacteristic
626C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1490C2
socleC22×C11C2×C4×D4
prime radicalC2×#66985C4
cosocleC42×C11C24
hypercenter#1490D11
hypocenterC11#18046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
1. #13077628C2semidirect
3. D4×#4318C2semidirect
4. #13067515C2semidirect
5. #13067509C2semidirect
6. #13067483C2semidirect
7. #13067470C2semidirect
8. #13067449C2semidirect
9. #13067448C2semidirect
10. #13067437C2semidirect
11. #13067408C2semidirect
12. #13067384C2semidirect
13. #13067056C2semidirect
14. #13066919C2semidirect
15. C11×#1490C2semidirect
43. #10622447C22semidirect
44. #10622447C22semidirect
45. #10622444C22semidirect
46. #10622444C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622094C22semidirect
62. #10622094C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
191. #4323M16semidirect
234. #1490D11semidirect
274. D44C2×M16semidirect
293. C11⋊C8C2×M16semidirect
294. C11⋊C8AGL(1,ℤ/8)semidirect
534. C11#18046semidirect

Maximal subgroups

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

subgroupindex
#130776282
C4×#669852
D4×#43182
#130675152
#130675092
#130674832
#130674702
#130674492
#130674482
#130674372
#130674082
#130673842
#130670562
#130669192
C11×#14902
#1804611