Finite Group Databasebeta

← #16795591

Subgroups — #16795591

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131778C211yesmaximal, characteristic, complemented
2#13131683C211yesmaximal, characteristic, complemented
3#13130457C211yesmaximal, characteristic, complemented
4#13130451C211yesmaximal, characteristic, complemented
5#13130439C211yesmaximal, characteristic, complemented
6#13130437C211yesmaximal, characteristic, complemented
7#13130432C211yesmaximal, characteristic, complemented
8#13130427C211yesmaximal, characteristic, complemented
9#13130419C211yesmaximal, characteristic, complemented
10D8×#1057C211yesmaximal, characteristic, complemented
11#13130412C211yesmaximal, characteristic, complemented
12#13130161C211yesmaximal, characteristic, complemented
13#13130147C211yesmaximal, characteristic, complemented
14#13130057C211yesmaximal, characteristic, complemented
15#13124878C211yesmaximal, characteristic
16C2×D4×Dic13C2211yescharacteristic
17#11719305C2211yescharacteristic
18C2×C22⋊#1057—21no—
19C2×C22⋊#1057—21no—
20#11719145—21no—
21#11719145C2211yescharacteristic, complemented
22#11719144—21no—
23D4×#1057—21no—
24D4×#1057—21no—
25D4×#1057C2211yescharacteristic
26D4×#1057C2211yescharacteristic
27D4×#1057C2211yescharacteristic
28D4×#1057C2211yescharacteristic
29D4×#1057C2211yescharacteristic, complemented
30#11719129C2211yescharacteristic
31#11719125C2211yescharacteristic
32#11719119C2211yescharacteristic
33#11719119C2211yescharacteristic
34#11719080C2211yescharacteristic, complemented
35#11719074C2211yescharacteristic, complemented
36#11719068—21no—
37#11719067—21no—
38C13×#447C411yescharacteristic
39#11718879C411yescharacteristic
40#11718814C411yescharacteristic
41#11718814C411yescharacteristic
42D8×Dic13C2211yescharacteristic
43D8×Dic13C2211yescharacteristic
44#11718695C411yescharacteristic
45#11718427C411yescharacteristic
46#11718427C411yescharacteristic
47#11718419C2211yescharacteristic
48#11718419C2211yescharacteristic
49#11718383C411yescharacteristic
50#11718379C2211yescharacteristic
51D4⋊#1057C2211yescharacteristic
52D4⋊#1057C2211yescharacteristic
53D4⋊#1057C2211yescharacteristic
54D4⋊#1057C2211yescharacteristic
55D4⋊#1057C2211yescharacteristic, complemented
56D4⋊#1057C2211yescharacteristic, complemented
57#11718256C2211yescharacteristic, complemented
58#11718255C2211yescharacteristic, complemented
59#11718254C2211yescharacteristic, complemented
60#11718253C2211yescharacteristic, complemented
61#1057⋊C8C2211yescharacteristic, complemented
62#1057⋊C8C2211yescharacteristic, complemented
63#11718251C2211yescharacteristic, complemented
64C8×#1057C2211yescharacteristic, complemented
65#11718244C2211yescharacteristic, complemented
66#11718244C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×Dic13—21no—
69C2×#6122—21no—
70C2×#6122—21no—
71C22×#1057—21no—
72C22×#1057—21no—
73C22×#1057—21no—
74C22×#1057—21no—
75C22×#1057—21no—
76C2×C13×D8C2×C411yescharacteristic
77C2×C13×D8C2×C411yescharacteristic
78C13×#121C2×C411yescharacteristic
79C2×C22⋊Dic13—21no—
80#88190C2×C411yescharacteristic
81#88189—21no—
82D4×Dic13—21no—
83D4×Dic13—21no—
84D4×Dic13—21no—
85D4×Dic13C2×C411yescharacteristic
86D4×Dic13C2×C411yescharacteristic
87D4×Dic13C2311yescharacteristic
88D4×Dic13C2311yescharacteristic
89D4×Dic13C2311yescharacteristic
90C2×#6105C2×C411yescharacteristic
91C2×#6105C2×C411yescharacteristic
92C2×C4⋊Dic13C2×C411yescharacteristic
93#88178C2×C411yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95#88144C2×C411yescharacteristic
96#88141C2311yescharacteristic
97#88133—21no—
98#88131—21no—
99C22⋊#1057—21no—
100C22⋊#1057—21no—
101C22⋊#1057—21no—
102C22⋊#1057—21no—
103C22⋊#1057—21no—
104C22⋊#1057—21no—
105C22⋊#1057—21no—
106C22⋊#1057—21no—
107C22⋊#1057D411yescharacteristic
108C22⋊#1057D411yescharacteristic
109#88112—21no—
110#88112—21no—
111#88112—21no—
112#88110—21no—
113C4⋊#1057—21no—
114C4⋊#1057D411yescharacteristic
115C4⋊#1057D411yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4⋊#1057C2311yescharacteristic
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057C2311yescharacteristic
123C4×#1057C2311yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C13×#102C2×C411yescharacteristic
127C13×#102C2×C411yescharacteristic
128C13×C22⋊C8C2×C411yescharacteristic
129#88072C2×C411yescharacteristic
130#88072C2×C411yescharacteristic
131#88072C2×C411yescharacteristic
132#88072C2×C411yescharacteristic
133C22⋊#1055C2×C411yescharacteristic
134#88058C2×C411yescharacteristic
135#88058C2×C411yescharacteristic
136#88056C2×C411yescharacteristic
137#88056C2×C411yescharacteristic
138#88054C2×C411yescharacteristic
139#88054C2×C411yescharacteristic
140C8×Dic13C2311yescharacteristic
141C8×Dic13C2311yescharacteristic
142#88048C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#17918—131nomaximal, Sylow
145C24×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13C22×C411yescharacteristic
151C2×D4×C13C22×C411yescharacteristic
152C2×D4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—81no—
161C22×Dic13—81no—
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13#4111yescharacteristic
164C2×Dic26C22×C411yescharacteristic
165#6122—81no—
166#6122—81no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—81no—
174C2×#1057—81no—
175C2×#1057—81no—
176C2×#1057—81no—
177C2×#1057—81no—
178C2×#1057C2×D411yescharacteristic
179C2×#1057C2×D411yescharacteristic
180C2×#1057C2×D411yescharacteristic
181C2×#1057C2×D411yescharacteristic
182C13×D8—22no—
183C13×D8—22no—
184C2×C8×C13C22×C411yescharacteristic
185C2×C8×C13C22×C411yescharacteristic
186C13×C4⋊C4C22×C411yescharacteristic
187C13×C22⋊C4—21no—
188C22⋊Dic13—21no—
189C22⋊Dic13—21no—
190C22⋊Dic13—21no—
191C22⋊Dic13—21no—
192C22⋊Dic13—21no—
193C22⋊Dic13—21no—
194C22⋊Dic13—21no—
195C22⋊Dic13—21no—
196#6105—22no—
197#6105—22no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13C22×C411yescharacteristic
201C4⋊Dic13C22×C411yescharacteristic
202C4⋊Dic13C22×C411yescharacteristic
203#6101—21no—
204#6101—21no—
205#6101—21no—
206C4×Dic13—21no—
207C4×Dic13C22×C411yescharacteristic
208C4×Dic13C2×D411yescharacteristic
209C4×Dic13#4111yescharacteristic
210C4×Dic13C2411yescharacteristic
211C2×#1055C22×C411yescharacteristic
212C2×#1055C22×C411yescharacteristic
213#3105—131no—
214#2993—131no—
215#2972—131no—
216#1586—131no—
217#1585—131no—
218#1582—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1574—131no—
225#1486—131no—
226#1482—131no—
227#1454—131no—
228C23×C13—24no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—81no—
233C23×C13—81no—
234C23×C13C4×D411yescharacteristic
235D4×C13—24no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—81no—
241D4×C13#13112yes—
242D4×C13#13112yes—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—81no—
262C2×Dic13—81no—
263C2×Dic13—81no—
264C2×Dic13C4×D411yescharacteristic
265C2×Dic13C4×D411yescharacteristic
266C2×Dic13C22×D411yescharacteristic
267C2×Dic13C2×#4111yescharacteristic
268Dic26—21no—
269Dic26—21no—
270#1057—21no—
271#1057—21no—
272#1057—21no—
273#1057—21no—
274#1057—41no—
275#1057—41no—
276#1057—41no—
277#1057—41no—
278#1057—41no—
279#1057—41no—
280C8×C13—21no—
281C8×C13—21no—
282#1055—21no—
283#1055—21no—
284#529—131no—
285C2×C4×D4—131no—
286#484—131no—
287#481—131no—
288#478—131no—
289#478—131no—
290#463—131no—
291#463—131no—
292#450—131no—
293#447#26111yescharacteristic
294#446—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436—131no—
301#436—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—261no—
309C8×D4—261no—
310#433—261no—
311#431—131no—
312#431—131no—
313#431—131no—
314#431—131no—
315#424—261no—
316#423—131no—
317C2×C22⋊C8—261no—
318C2×C22⋊C8—261no—
319#335—131no—
320#335—131no—
321#334—131no—
322#334—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331#322—131no—
332#322—131no—
333#322—131no—
334C82—131no—
335C22×C13—21no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—84no—
348C22×C13C2×C4×D411yescharacteristic
349C4×C13—21no—
350C4×C13—41no—
351C4×C13C2×#13111yescharacteristic
352C4×C13C2×#13111yescharacteristic
353Dic13—21no—
354Dic13—21no—
355Dic13—21no—
356Dic13—41no—
357Dic13—41no—
358Dic13—41no—
359Dic13—41no—
360Dic13#57611yescharacteristic
361Dic13#57711yescharacteristic
362C22×D4C2×#26111yescharacteristic
363C23×C4—261no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×D8C2×#26111yescharacteristic
367C2×D8C2×#26111yescharacteristic
368C2×M16—261no—
369C2×M16—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375#126—261no—
376#125—131no—
377#124—131no—
378#123—261no—
379C22⋊Q8—131no—
380#121C2×#26111yescharacteristic
381C4×Q8—131no—
382C4×D4—131no—
383C4×D4—131no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—261no—
388C4×D4—261no—
389C4×D4—261no—
390#117—261no—
391C2×C4⋊C4—131no—
392C2×C22⋊C4—261no—
393C2×C42—131no—
394#107—131no—
395#107—131no—
396#106—131no—
397#106—131no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8—261no—
410#103—131no—
411#103—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102C2×#26111yescharacteristic
417#102C2×#26111yescharacteristic
418C22⋊C8—131no—
419C22⋊C8—131no—
420C22⋊C8—131no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8C2×#26111yescharacteristic
430#97—261no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—131no—
437C4×C8—261no—
438C4×C8—261no—
439C2×C13—41no—
440C2×C13—42no—
441C2×C13—42no—
442C2×C13—81no—
443C2×C13#292911yescharacteristic
444C2×C13#294611yescharacteristic
445C2×C13#295711yescharacteristic
446C24—21no—
447C2×Q8—131no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4C22×#26111yescharacteristic
453C2×D4C22×#26111yescharacteristic
454C2×D4C22×#26111yescharacteristic
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—1041no—
464C22×C4—1041no—
465C22×C4C22×#26111yescharacteristic
466SD16—262no—
467SD16—262no—
468D8—22no—
469D8—22no—
470M16—1041no—
471M16—1041no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—1041no—
485C2×C8—1041no—
486C2×C8—1041no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8C22×#26111yescharacteristic
490C2×C8C22×#26111yescharacteristic
491C4⋊C4—131no—
492C4⋊C4—131no—
493C4⋊C4—131no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4C22×#26111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—131no—
510C42—131no—
511C42—131no—
512C42—131no—
513C42—261no—
514C13#1791811yescharacteristic, complemented, Sylow
515C23—24no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—81no—
520C23—81no—
521C23D4×#26111yescharacteristic
522Q8—261no—
523Q8—261no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—81no—
530D4#8823812yes—
531D4#8823812yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—131no—
536C2×C4—131no—
537C2×C4—131no—
538C2×C4—131no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—1041no—
553C2×C4—1041no—
554C2×C4—1041no—
555C2×C4D4×#26111yescharacteristic
556C2×C4C23×#26111yescharacteristic
557C8—21no—
558C8—21no—
559C8—261no—
560C8—261no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—261no—
565C8—521no—
566C8—521no—
567C8—521no—
568C8—521no—
569C8—521no—
570C8—521no—
571C22—21no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—84no—
584C22C2×D4×#26111yescharacteristic
585C4—21no—
586C4—41no—
587C4—131no—
588C4—131no—
589C4—261no—
590C4—261no—
591C4—261no—
592C4—521no—
593C4—521no—
594C4—521no—
595C4—521no—
596C4C2×#8823811yescharacteristic
597C4C2×#8823811yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2#1313155111yescharacteristic
603C2#1313159311yescharacteristic
604C2#1313161211yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
Fitting, prime radicalC13×#447C4
socleC22×C13C2×C4×D4
cosocleC4×Dic13C24
hypercenter#447#261
hypocenterC13#17918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #13131778C2semidirect
2. #13131683C2semidirect
3. #13130457C2semidirect
4. #13130451C2semidirect
5. #13130439C2semidirect
6. #13130437C2semidirect
7. #13130432C2semidirect
8. #13130427C2semidirect
9. #13130419C2semidirect
10. D8×#1057C2semidirect
11. #13130412C2semidirect
12. #13130161C2semidirect
13. #13130147C2semidirect
14. #13130057C2semidirect
21. #11719145C22semidirect
29. D4×#1057C22semidirect
34. #11719080C22semidirect
35. #11719074C22semidirect
55. D4⋊#1057C22semidirect
56. D4⋊#1057C22semidirect
57. #11718256C22semidirect
58. #11718255C22semidirect
59. #11718254C22semidirect
60. #11718253C22semidirect
61. #1057⋊C8C22semidirect
62. #1057⋊C8C22semidirect
63. #11718251C22semidirect
64. C8×#1057C22semidirect
65. #11718244C22semidirect
66. #11718244C22semidirect
514. C13#17918semidirect

Maximal subgroups

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

subgroupindex
#131317782
#131316832
#131304572
#131304512
#131304392
#131304372
#131304322
#131304272
#131304192
D8×#10572
#131304122
#131301612
#131301472
#131300572
#131248782
#1791813