Finite Group Databasebeta

← #14723359

Subgroups — #14723359

Order 2816.

748 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077579C211yesmaximal, characteristic, complemented
2C4×#66964C211yesmaximal, characteristic
3C8×D4×D11C211yesmaximal, characteristic, complemented
4#13067478C211yesmaximal, characteristic, complemented
5#13067475C211yesmaximal, characteristic, complemented
6#13067473C211yesmaximal, characteristic, complemented
7#13067451C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067446C211yesmaximal, characteristic, complemented
11#13067365C211yesmaximal, characteristic, complemented
12#13067005C211yesmaximal, characteristic, complemented
13#13067000C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, characteristic, complemented
16C2×#66964C411yescharacteristic
17C22×C8×D11—21no—
18C4×D4×D11C2211yescharacteristic
19C4×#4341C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#436C2211yescharacteristic, complemented
22C8×D4×C11C2211yescharacteristic
23#10622765C411yescharacteristic
24#10622740—21no—
25M16×Dic11—21no—
26C8×C22⋊D11—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic, complemented
30D4×C11⋊C8C2211yescharacteristic
31#10622502C411yescharacteristic
32#10622494C411yescharacteristic
33#10622447C2211yescharacteristic
34#10622446C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622444C2211yescharacteristic, complemented
37#10622398C411yescharacteristic
38#10622384C411yescharacteristic
39#10622383C411yescharacteristic
40#10622370C411yescharacteristic
41#10622341—21no—
42(C22⋊D11)⋊C8—21no—
43D11×C22⋊C8—21no—
44#10622331—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic, complemented
51C11×#334C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×#4341C2×C411yescharacteristic
68C2×D4×D11C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×D8C2×C411yescharacteristic
71C2×C11×M16—21no—
72C22×C8×C11—21no—
73C4×D4×C11C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84#66964—24no—
85C2×#4314C2×C411yescharacteristic
86C2×#4313C2×C411yescharacteristic
87C2×#4313C2×C411yescharacteristic
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11—44no—
92C2×C8×D11D411yescharacteristic
93C2×C8×D11D411yescharacteristic
94#66946C2×C411yescharacteristic
95#66945C2×C411yescharacteristic
96C4⋊C4×D11C2×C411yescharacteristic
97#66940C2×C411yescharacteristic
98(C22⋊D11)⋊C4—21no—
99(C22⋊D11)⋊C4—21no—
100C22⋊C4×D11—21no—
101#66930—21no—
102C4×D44C2311yescharacteristic
103C42×D11C2311yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×#107C2×C411yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119#66885C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66881C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128#66879C2×C411yescharacteristic
129#66879C2×C411yescharacteristic
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134C8×Dic11—21no—
135C8×Dic11D411yescharacteristic
136C8×Dic11D411yescharacteristic
137#66874C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66872C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#17869—111nomaximal, Sylow
147C23×D11—21no—
148C2×D4×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157#4341—22no—
158#4341—22no—
159D4×D11—22no—
160D4×D11M1614yescomplemented
161C2×D44C22×C411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11C22×C411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11#4111yescharacteristic
170C2×Dic22C22×C411yescharacteristic
171C11×D8—22no—
172C11×M16—42no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—42no—
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187C22⋊Dic11—21no—
188#4324—22no—
189#4323—22no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11C22×C411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11#4111yescharacteristic
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#4314—22no—
214#4313—22no—
215#4313—22no—
216C8×D11—22no—
217C8×D11—41no—
218C8×D11—42no—
219C8×D11—42no—
220C8×D11—42no—
221#2965—111no—
222C4×AGL(1,ℤ/8)—111no—
223C2×C8×D4—111no—
224#1586—111no—
225#1586D1111yescharacteristic, complemented
226#1585—111no—
227#1585—111no—
228#1582—111no—
229#1582—111no—
230#1581—111no—
231#1581—111no—
232#1565—111no—
233#1478—111no—
234#1477—111no—
235#1451—111no—
236C23×C11—21no—
237C23×C11—21no—
238C22×D11—21no—
239C22×D11—24no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11C4×D411yescharacteristic
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11C2×M1612yes—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—24no—
257C22⋊D11—42no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11C4×D411yescharacteristic
265C2×Dic11C4×D411yescharacteristic
266C2×Dic11C4×D411yescharacteristic
267D44—21no—
268D44C2×M1612yes—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—41no—
272C4×D11—42no—
273C4×D11—42no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11C2×M1612yes—
277C4×D11#13112yes—
278Dic22—21no—
279Dic22—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8AGL(1,ℤ/8)12yescomplemented
294C2×AGL(1,ℤ/8)—111no—
295C23×C8—221no—
296C4×#41—111no—
297C2×C4×D4—111no—
298#446—111no—
299#446—111no—
300#442—111no—
301#442—111no—
302#440—111no—
303#440—111no—
304C4×SD16—111no—
305C4×SD16—111no—
306C4×D8—111no—
307C4×D8C2×D1111yescharacteristic
308#436—111no—
309#436C2×D1111yescharacteristic, complemented
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314C8×D4—111no—
315C8×D4—221no—
316C8×D4—221no—
317C8×D4C2×D1111yescharacteristic
318#431—111no—
319#431—111no—
320#431—221no—
321#428—111no—
322C2×C4⋊C8—111no—
323#418—111no—
324#417—111no—
325C2×C22⋊C8—221no—
326C4×M16—111no—
327C4×M16—221no—
328C2×C4×C8—111no—
329#335—111no—
330#335—111no—
331#334—111no—
332#334C2×D1111yescharacteristic, complemented
333Q8⋊C8—111no—
334Q8⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8C2×D1111yescharacteristic
340D4⋊C8C2×D1111yescharacteristic, complemented
341#322—111no—
342#322—111no—
343#322—111no—
344#322C2×D1111yescharacteristic, complemented
345C22×C11—22no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×C4×D411yescharacteristic
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—22no—
355C2×D11—48no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11#43512yes—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11C22×M1611yescharacteristic
363C4×C11C2×#13111yescharacteristic
364C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C4×C11#57511yescharacteristic
366Dic11—21no—
367Dic11—21no—
368Dic11—41no—
369Dic11—41no—
370Dic11—41no—
371Dic11#43512yes—
372C2×#41—111no—
373C22×D4—111no—
374C23×C4—221no—
375AGL(1,ℤ/8)—224no—
376C2×SD16—111no—
377C2×SD16—111no—
378C2×D8—111no—
379C2×D8C4×D1111yescharacteristic
380C2×M16—21no—
381C2×M16—111no—
382C2×M16—111no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—221no—
388C22×C8—221no—
389C22×C8—221no—
390C22×C8—221no—
391C22×C8—444no—
392C4×Q8—111no—
393C4×Q8—111no—
394C4×D4—111no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4—221no—
401C4×D4—221no—
402C4×D4C22×D1111yescharacteristic
403C4×D4C22×D1111yescharacteristic
404#117—111no—
405#117—221no—
406C2×C4⋊C4—111no—
407C2×C22⋊C4—221no—
408C2×C42—111no—
409C2×C42—221no—
410#107—111no—
411#107C4×D1111yescharacteristic
412#106—111no—
413#106—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—221no—
417C4⋊C8—221no—
418C4⋊C8—221no—
419C4⋊C8—221no—
420C4⋊C8C22×D1111yescharacteristic
421C4⋊C8C22×D1111yescharacteristic
422#103—111no—
423#103—111no—
424#102—111no—
425#102—111no—
426#102—111no—
427#102—111no—
428#102C4×D1111yescharacteristic
429#102C4×D1111yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438#97—111no—
439#97—111no—
440#97—221no—
441#97—221no—
442C4×C8—111no—
443C4×C8—111no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—221no—
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1111yescharacteristic
450C4×C8C22×D1111yescharacteristic
451C2×C11—42no—
452C2×C11—81no—
453C2×C11C2×#43511yescharacteristic
454C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
455C2×C11#295511yescharacteristic
456D11—22no—
457D11—42no—
458C24—221no—
459#41—222no—
460#41—222no—
461C2×Q8—111no—
462C2×D4—114no—
463C2×D4—111no—
464C2×D4—222no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4C2×C4×D1111yescharacteristic
468C2×D4C2×C4×D1111yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—442no—
481C22×C4—442no—
482SD16—222no—
483SD16—222no—
484D8—22no—
485D8—222no—
486M16—42no—
487M16—222no—
488M16—222no—
489M16—442no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—111no—
498C2×C8—222no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—441no—
503C2×C8—442no—
504C2×C8—442no—
505C2×C8—442no—
506C2×C8—442no—
507C2×C8C2×C4×D1111yescharacteristic
508C2×C8C2×C4×D1111yescharacteristic
509C2×C8D4×D1111yescharacteristic
510C2×C8D4×D1111yescharacteristic
511C4⋊C4—111no—
512C4⋊C4—111no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4C2×C4×D1111yescharacteristic
517C4⋊C4C2×C4×D1111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—221no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42C23×D1111yescharacteristic
532C11#1786911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—21no—
535C23—111no—
536C23—224no—
537C23—221no—
538C23—442no—
539C23—442no—
540Q8—221no—
541Q8—221no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—112no—
546D4—224no—
547D4—221no—
548D4—442no—
549D4M16×D1112yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—111no—
557C2×C4—112no—
558C2×C4—112no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—441no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8—21no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8—112no—
585C8—221no—
586C8—221no—
587C8—221no—
588C8—441no—
589C8—441no—
590C8—441no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—112no—
598C22—221no—
599C22—221no—
600C22—222no—
601C22—448no—
602C22—441no—
603C22—441no—
604C22C4×D4×D1111yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—112no—
609C4—221no—
610C4—221no—
611C4—441no—
612C4—441no—
613C4—441no—
614C4C2×M16×D1111yescharacteristic
615C4D11×#13111yescharacteristic
616C4D11×AGL(1,ℤ/8)11yescharacteristic
617C4#1062330411yescharacteristic
618C2—42no—
619C2—81no—
620C2—222no—
621C2—442no—
622C2D11×#43511yescharacteristic
623C2#1307742711yescharacteristic
624C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radicalC2×#66964C4
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#17869
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. #13077579C2semidirect
3. C8×D4×D11C2semidirect
4. #13067478C2semidirect
5. #13067475C2semidirect
6. #13067473C2semidirect
7. #13067451C2semidirect
8. #13067449C2semidirect
9. #13067448C2semidirect
10. #13067446C2semidirect
11. #13067365C2semidirect
12. #13067005C2semidirect
13. #13067000C2semidirect
14. #13066904C2semidirect
15. C11×#1586C2semidirect
21. C11×#436C22semidirect
29. #10622625C22semidirect
36. #10622444C22semidirect
50. #10622292C22semidirect
51. C11×#334C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622096C22semidirect
63. #10622094C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
160. D4×D11M16semidirect
225. #1586D11semidirect
293. C11⋊C8AGL(1,ℤ/8)semidirect
309. #436C2×D11semidirect
332. #334C2×D11semidirect
340. D4⋊C8C2×D11semidirect
344. #322C2×D11semidirect
532. C11#17869semidirect

Maximal subgroups

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

subgroupindex
#130775792
C4×#669642
C8×D4×D112
#130674782
#130674752
#130674732
#130674512
#130674492
#130674482
#130674462
#130673652
#130670052
#130670002
#130669042
C11×#15862
#1786911