Finite Group Databasebeta

← #15867340

Subgroups — #15867340

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123634C211yesmaximal, characteristic
2#13123481C211yesmaximal, characteristic, complemented
3#13123480C211yesmaximal, characteristic, complemented
4#13115726C211yesmaximal, characteristic
5#13115721C211yesmaximal, characteristic
6#13115588C211yesmaximal, characteristic, complemented
7#13115583C211yesmaximal, characteristic, complemented
8#13115548C211yesmaximal, characteristic, complemented
9#13115544C211yesmaximal, characteristic, complemented
10#13115541C211yesmaximal, characteristic, complemented
11#13115537C211yesmaximal, characteristic, complemented
12#13114743C211yesmaximal, characteristic, complemented
13#13114647C211yesmaximal, characteristic, complemented
14#13114523C211yesmaximal, characteristic, complemented
15C13×#1759C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17C2×#88204C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19C2×C13×#104C2211yescharacteristic
20C2×C13×#104C2211yescharacteristic
21C4×C13×M16C2211yescharacteristic
22C13×#376C2211yescharacteristic
23#11718895C2211yescharacteristic
24#11718895C2211yescharacteristic
25#11718894C2211yescharacteristic
26#11718790C2211yescharacteristic
27#11718790C2211yescharacteristic
28C2×#88062C2211yescharacteristic
29C2×#88062C2211yescharacteristic
30#11718780C2211yescharacteristic
31#11718780C2211yescharacteristic
32#11718691C412yescomplemented
33#11718687C412yescomplemented
34#11718679C412yescomplemented
35#11718675C412yescomplemented
36#11718663C2211yescharacteristic
37#11718661—22no—
38#11718660C2211yescharacteristic
39#11718660C2211yescharacteristic
40#11718659C2211yescharacteristic
41C2×#88045C2211yescharacteristic
42C2×#88045C2211yescharacteristic
43#11718586—22no—
44C4×#6099C2211yescharacteristic
45C2×#88043C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47C2×#88043C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718370—22no—
52#11718346—22no—
53C13×#339C2211yescharacteristic
54C13×#339C2211yescharacteristic
55#11718150C2211yescharacteristic
56#11718150C2211yescharacteristic
57#11718115C2211yescharacteristic
58#11718115C2211yescharacteristic
59C2×C13×#41C2311yescharacteristic
60C2×#6127C2311yescharacteristic
61C2×C13×M16C2311yescharacteristic
62C2×C13×M16C2311yescharacteristic
63C4×Q8×C13C2×C412yes—
64C4×D4×C13—22no—
65C4×D4×C13C2×C412yes—
66C13×#117—21no—
67C13×#117C2311yescharacteristic
68C2×C42×C13—21no—
69C2×C42×C13C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72#88204—22no—
73#88204—22no—
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C2×#6104C2×C411yescharacteristic
78C4×C22⋊D13—22no—
79#88180C2311yescharacteristic
80C2×#6099C2311yescharacteristic
81C2×#6099C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C4×D52C2×C412yes—
87#88126—21no—
88C42×D13—21no—
89C4×Dic26C2×C412yes—
90C13×#104—22no—
91C13×#104—22no—
92C13×#97—21no—
93C4×C8×C13—21no—
94C13×#95—22no—
95#88075C2×C412yes—
96#88072C2×C412yes—
97C22⋊#1055—22no—
98C22⋊#1055—22no—
99#88062—22no—
100#88062—22no—
101#88060—22no—
102#88060—22no—
103#88054—22no—
104#88054—22no—
105#88050C2×C412yes—
106#88049C2×C412yes—
107#88048C2×C412yes—
108#88047C2×C412yes—
109#88045—22no—
110#88045—22no—
111C4⋊#1055—22no—
112C4⋊#1055—22no—
113#88043—21no—
114#88043—22no—
115#88043—22no—
116#88043C2×C412yes—
117#88043C2×C412yes—
118C4×#1055—21no—
119C4×#1055—22no—
120C4×#1055—22no—
121C4×#1055D412yes—
122C4×#1055D412yes—
123#21296—131nomaximal, Sylow
124C13×#41—21no—
125C13×#41—21no—
126C13×#41—21no—
127C13×#41—21no—
128C2×Q8×C13C22×C411yescharacteristic
129C2×D4×C13—21no—
130C2×D4×C13C22×C411yescharacteristic
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C2×C22⋊D13—21no—
138#6127—21no—
139#6127—21no—
140#6127—21no—
141#6127—21no—
142C2×D52C22×C411yescharacteristic
143C2×C4×D13—22no—
144C2×C4×D13—21no—
145C2×Dic26C22×C411yescharacteristic
146C13×M16—21no—
147C13×M16—21no—
148C13×M16—21no—
149C13×M16—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4C22×C412yes—
154C13×C22⋊C4—21no—
155C13×C22⋊C4—22no—
156C42×C13—22no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13C22×C412yes—
161C42×C13C2×D411yescharacteristic
162C42×C13C2×D411yescharacteristic
163C42×C13#4112yes—
164C42×C13#4112yes—
165C22⋊Dic13—21no—
166#6107—22no—
167#6106—22no—
168#6105—22no—
169#6104—22no—
170#6103—22no—
171C4⋊Dic13C22×C412yes—
172#6101—22no—
173C4×Dic13—22no—
174C4×Dic13—21no—
175#6099—21no—
176#6099—21no—
177#6099—21no—
178#6099—21no—
179C2×#1055—21no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055C22×C412yes—
188C2×#1055C22×C411yescharacteristic
189C2×#1055C22×C411yescharacteristic
190C2×#1055C2×D412yes—
191C2×#1055C2×D412yes—
192C2×#1055#4112yes—
193C2×#1055#4112yes—
194#2943—131no—
195#2922—131no—
196#2922—131no—
197#1975—131no—
198#1974—131no—
199#1946—131no—
200#1945—131no—
201#1938—131no—
202#1938—131no—
203#1937—131no—
204#1937—131no—
205#1778—131no—
206#1759—131no—
207#1759D1311yescharacteristic, complemented
208#1726—131no—
209C23×C13—21no—
210C23×C13C2×#4111yescharacteristic
211C22×D13—21no—
212Q8×C13—21no—
213Q8×C13—21no—
214D4×C13—21no—
215D4×C13—21no—
216D4×C13—41no—
217D4×C13—41no—
218C2×C4×C13—22no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—42no—
223C2×C4×C13—44no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13C4×D412yes—
229C2×C4×C13C4×D412yes—
230C2×C4×C13C23×C411yescharacteristic
231C2×C4×C13C22×D411yescharacteristic
232C2×C4×C13C2×#4111yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C22⋊D13—41no—
237C22⋊D13—41no—
238C2×Dic13—21no—
239C2×Dic13—22no—
240D52—21no—
241D52—21no—
242C4×D13—44no—
243C4×D13—41no—
244C4×D13—41no—
245Dic26—21no—
246Dic26—21no—
247C8×C13—41no—
248C8×C13—41no—
249#1055—22no—
250#1055—22no—
251#1055—22no—
252#1055—41no—
253#1055—41no—
254#1055#11712yes—
255#1055#11712yes—
256C2×#135—131no—
257C4×#41—131no—
258C4×#41C2×D1311yescharacteristic
259#442—132no—
260#441—132no—
261#440—132no—
262#440—132no—
263#433—262no—
264#433—262no—
265#431—262no—
266#431—262no—
267C2×#108—131no—
268C2×#108—131no—
269#427—131no—
270#424—131no—
271#424—131no—
272#424—131no—
273#424—131no—
274C2×#104—131no—
275C2×#104—131no—
276C2×#104C2×D1311yescharacteristic
277C2×#104C2×D1311yescharacteristic
278#416—131no—
279#416—131no—
280#408—131no—
281#408—131no—
282#408—131no—
283#408—131no—
284C4×M16—131no—
285C4×M16C2×D1311yescharacteristic
286C2×#97—131no—
287C2×#97—131no—
288C2×#97—131no—
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291C2×C4×C8—131no—
292#376C2×D1311yescharacteristic
293#341—131no—
294#341—131no—
295#339—131no—
296#339—131no—
297#339C2×D1311yescharacteristic
298#339C2×D1311yescharacteristic
299C22×C13—22no—
300C22×C13—42no—
301C22×C13—41no—
302C22×C13C2×C4×D411yescharacteristic
303C22×C13#52911yescharacteristic
304C22×C13#52911yescharacteristic
305C2×D13—42no—
306C2×D13—41no—
307C4×C13—22no—
308C4×C13—22no—
309C4×C13—42no—
310C4×C13—42no—
311C4×C13—42no—
312C4×C13—41no—
313C4×C13C2×#11711yescharacteristic
314C4×C13C4×#4111yescharacteristic
315C4×C13#53211yescharacteristic
316C4×C13#53211yescharacteristic
317Dic13—42no—
318Dic13—41no—
319C2×#41—131no—
320C2×#41C22×D1311yescharacteristic
321#135—262no—
322#135—262no—
323C2×Q16—131no—
324C2×SD16—131no—
325C2×SD16—131no—
326C2×D8—131no—
327C2×M16—131no—
328C2×M16—131no—
329C2×M16C22×D1311yescharacteristic
330C2×M16C22×D1311yescharacteristic
331C22×C8—131no—
332C22×C8—131no—
333C22×C8—131no—
334C22×C8—131no—
335C4×Q8—132no—
336C4×Q8C4×D1312yes—
337C4×D4—22no—
338C4×D4—132no—
339C4×D4—262no—
340C4×D4C4×D1312yes—
341#117—21no—
342#117—131no—
343#117—261no—
344#117C22×D1311yescharacteristic
345C2×C42—21no—
346C2×C42—261no—
347C2×C42C22×D1311yescharacteristic
348C2×C42C22×D1311yescharacteristic
349C2×C42C22×D1311yescharacteristic
350#108—262no—
351#108—262no—
352#107—132no—
353#106—132no—
354C4⋊C8—262no—
355C4⋊C8—262no—
356C4⋊C8—262no—
357C4⋊C8—262no—
358#104—22no—
359#104—22no—
360#104—262no—
361#104—262no—
362#103—132no—
363#103—132no—
364#102—132no—
365#102—132no—
366C22⋊C8—262no—
367C22⋊C8—262no—
368C22⋊C8—262no—
369C22⋊C8—262no—
370#97—21no—
371#97—132no—
372#97—132no—
373#97—262no—
374#97—262no—
375#97—261no—
376C4×C8—21no—
377C4×C8—132no—
378C4×C8—132no—
379C4×C8—262no—
380C4×C8—262no—
381C4×C8—261no—
382#95—22no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—81no—
386C2×C13#229311yescharacteristic
387C2×C13#295512yes—
388D13—81no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—261no—
394#41—261no—
395#41—261no—
396#41—261no—
397C2×Q8—131no—
398C2×Q8C2×C4×D1311yescharacteristic
399C2×D4—21no—
400C2×D4—131no—
401C2×D4—261no—
402C2×D4C2×C4×D1311yescharacteristic
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—262no—
408C22×C4—261no—
409C22×C4#612912yes—
410C22×C4C23×D1311yescharacteristic
411Q16—262no—
412SD16—262no—
413SD16—262no—
414D8—262no—
415M16—21no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—261no—
420M16—261no—
421M16—261no—
422M16—261no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—131no—
426C2×C8—131no—
427C2×C8—132no—
428C2×C8—132no—
429C2×C8—132no—
430C2×C8—132no—
431C2×C8—132no—
432C2×C8—261no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C4⋊C4—22no—
441C4⋊C4—132no—
442C4⋊C4—262no—
443C4⋊C4C2×C4×D1312yes—
444C22⋊C4—21no—
445C22⋊C4—22no—
446C22⋊C4—261no—
447C22⋊C4—262no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—21no—
452C42—262no—
453C42—261no—
454C42C2×C4×D1312yes—
455C42#612712yes—
456C42#612712yes—
457C42D4×D1311yescharacteristic
458C42D4×D1311yescharacteristic
459C13#2129611yescharacteristic, complemented, Sylow
460C23—21no—
461C23—261no—
462C23C2×#612911yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—261no—
466Q8—261no—
467D4—21no—
468D4—21no—
469D4—41no—
470D4—41no—
471D4—261no—
472D4—261no—
473D4—521no—
474D4—521no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—262no—
486C2×C4—261no—
487C2×C4—524no—
488C2×C4—521no—
489C2×C4—521no—
490C2×C4#8813512yes—
491C2×C4#8813512yes—
492C2×C4C22×C4×D1311yescharacteristic
493C2×C4C2×#612711yescharacteristic
494C2×C4C2×#612711yescharacteristic
495C2×C4C2×D4×D1311yescharacteristic
496C2×C4#41×D1311yescharacteristic
497C2×C4#41×D1311yescharacteristic
498C8—41no—
499C8—41no—
500C8—132no—
501C8—132no—
502C8—262no—
503C8—262no—
504C8—262no—
505C8—521no—
506C8—521no—
507C22—22no—
508C22—41no—
509C22—42no—
510C22—521no—
511C22—522no—
512C22C2×#8813511yescharacteristic
513C22#1171924311yescharacteristic
514C22#1171924311yescharacteristic
515C4—22no—
516C4—22no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—521no—
522C4—522no—
523C4C4×#612711yescharacteristic
524C4D13×#11711yescharacteristic
525C4#1171925311yescharacteristic
526C4#1171925311yescharacteristic
527C2—21no—
528C2—21no—
529C2—81no—
530C2—1041no—
531C2#1311729911yescharacteristic
532C2#1312373512yes—
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1759C2
socleC22×C13C2×C4×D4
prime radicalC2×#88204C22
cosocleC22×C4×C13C24
hypercenter#1759D13
hypocenterC13#21296
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #13123481C2semidirect
3. #13123480C2semidirect
6. #13115588C2semidirect
7. #13115583C2semidirect
8. #13115548C2semidirect
9. #13115544C2semidirect
10. #13115541C2semidirect
11. #13115537C2semidirect
12. #13114743C2semidirect
13. #13114647C2semidirect
14. #13114523C2semidirect
15. C13×#1759C2semidirect
32. #11718691C4semidirect
33. #11718687C4semidirect
34. #11718679C4semidirect
35. #11718675C4semidirect
207. #1759D13semidirect
459. C13#21296semidirect

Maximal subgroups

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

subgroupindex
#131236342
#131234812
#131234802
#131157262
#131157212
#131155882
#131155832
#131155482
#131155442
#131155412
#131155372
#131147432
#131146472
#131145232
C13×#17592
#2129613