Finite Group Databasebeta

← #15867351

Subgroups — #15867351

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123634C211yesmaximal, characteristic
2#13123488C211yesmaximal, characteristic, complemented
3#13123487C211yesmaximal, 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
13C4×#88045C211yesmaximal, characteristic, complemented
14C4×#88043C211yesmaximal, characteristic, complemented
15C4×C13×#104C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17C2×#88204C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19C2×C13×#104C2211yescharacteristic
20C2×C13×#104C2211yescharacteristic
21C4×C13×M16C2211yescharacteristic
22C43×C13C2211yescharacteristic
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#11718587—22no—
44C4×#6099C2211yescharacteristic
45C2×#88043C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47C2×#88043C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718366—22no—
52#11718351—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×C13—22no—
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73#88204—22no—
74#88204—22no—
75C2×#6107C2×C411yescharacteristic
76C2×#6106C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C4×C22⋊D13—22no—
80#88180C2311yescharacteristic
81C2×#6099C2311yescharacteristic
82C2×#6099C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C4×D52C2×C412yes—
88#88126—21no—
89C42×D13—21no—
90C4×Dic26C2×C412yes—
91C13×#104—22no—
92C13×#104—22no—
93C13×#97—21no—
94C4×C8×C13—21no—
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—
118#88043D412yes—
119#88043D412yes—
120C4×#1055—21no—
121C4×#1055—22no—
122C4×#1055—22no—
123#21297—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—21no—
134C22×C4×C13—22no—
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—21no—
144C2×C4×D13—22no—
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×C13—44no—
161C42×C13C22×C412yes—
162C42×C13C2×D411yescharacteristic
163C42×C13C2×D411yescharacteristic
164C42×C13#4112yes—
165C42×C13#4112yes—
166C22⋊Dic13—21no—
167#6107—22no—
168#6106—22no—
169#6105—22no—
170#6104—22no—
171#6103—22no—
172C4⋊Dic13C22×C412yes—
173#6101—22no—
174C4×Dic13—22no—
175C4×Dic13—21no—
176#6099—21no—
177#6099—21no—
178#6099—21no—
179#6099—21no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055C22×C412yes—
189C2×#1055C22×C411yescharacteristic
190C2×#1055C22×C411yescharacteristic
191C2×#1055C2×D412yes—
192C2×#1055C2×D412yes—
193C2×#1055#4112yes—
194C2×#1055#4112yes—
195#2943—131no—
196#2923—131no—
197#2923—131no—
198#1975—131no—
199#1974—131no—
200#1946—131no—
201#1945—131no—
202#1938—131no—
203#1938—131no—
204#1937—131no—
205#1937—131no—
206#1778—131no—
207C4×#104—131no—
208C4×#104D1311yescharacteristic, complemented
209C4×#97—131no—
210C23×C13—21no—
211C23×C13C2×#4111yescharacteristic
212C22×D13—21no—
213Q8×C13—21no—
214Q8×C13—21no—
215D4×C13—21no—
216D4×C13—21no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—82no—
229C2×C4×C13C4×D412yes—
230C2×C4×C13C4×D412yes—
231C2×C4×C13C23×C411yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C22⋊D13—41no—
238C22⋊D13—41no—
239C2×Dic13—21no—
240C2×Dic13—22no—
241D52—21no—
242D52—21no—
243C4×D13—41no—
244C4×D13—41no—
245C4×D13—82no—
246Dic26—21no—
247Dic26—21no—
248C8×C13—41no—
249C8×C13—41no—
250#1055—22no—
251#1055—22no—
252#1055—22no—
253#1055—41no—
254#1055—41no—
255#1055#11712yes—
256#1055#11712yes—
257C2×#135—131no—
258C4×#41—131no—
259C4×#41C2×D1311yescharacteristic
260#442—132no—
261#441—132no—
262#440—132no—
263#440—132no—
264#433—262no—
265#433—262no—
266#432—262no—
267#432—262no—
268C2×#108—131no—
269C2×#108—131no—
270#427—131no—
271#424—131no—
272#424—131no—
273#424—131no—
274#424—131no—
275C2×#104—131no—
276C2×#104—131no—
277C2×#104C2×D1311yescharacteristic
278C2×#104C2×D1311yescharacteristic
279#416—131no—
280#416—131no—
281#408—131no—
282#408—131no—
283#408—131no—
284#408—131no—
285C4×M16—131no—
286C4×M16C2×D1311yescharacteristic
287C2×#97—131no—
288C2×#97—131no—
289C2×#97—131no—
290C2×#97—131no—
291C2×C4×C8—131no—
292C2×C4×C8—131no—
293C43C2×D1311yescharacteristic
294#341—131no—
295#341—131no—
296#339—131no—
297#339—131no—
298#339C2×D1311yescharacteristic
299#339C2×D1311yescharacteristic
300C22×C13—22no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13C2×C4×D411yescharacteristic
304C22×C13#52911yescharacteristic
305C22×C13#52911yescharacteristic
306C2×D13—42no—
307C2×D13—41no—
308C4×C13—24no—
309C4×C13—22no—
310C4×C13—22no—
311C4×C13—42no—
312C4×C13—42no—
313C4×C13—41no—
314C4×C13C2×#11711yescharacteristic
315C4×C13C4×#4111yescharacteristic
316C4×C13#53211yescharacteristic
317C4×C13#53211yescharacteristic
318Dic13—42no—
319Dic13—41no—
320C2×#41—131no—
321C2×#41C22×D1311yescharacteristic
322#135—262no—
323#135—262no—
324C2×Q16—131no—
325C2×SD16—131no—
326C2×SD16—131no—
327C2×D8—131no—
328C2×M16—131no—
329C2×M16—131no—
330C2×M16C22×D1311yescharacteristic
331C2×M16C22×D1311yescharacteristic
332C22×C8—131no—
333C22×C8—131no—
334C22×C8—131no—
335C22×C8—131no—
336C4×Q8—132no—
337C4×Q8C4×D1312yes—
338C4×D4—22no—
339C4×D4—132no—
340C4×D4—262no—
341C4×D4C4×D1312yes—
342#117—21no—
343#117—131no—
344#117—261no—
345#117C22×D1311yescharacteristic
346C2×C42—21no—
347C2×C42—22no—
348C2×C42—261no—
349C2×C42C22×D1311yescharacteristic
350C2×C42C22×D1311yescharacteristic
351C2×C42C22×D1311yescharacteristic
352#108—262no—
353#108—262no—
354#107—132no—
355#106—132no—
356C4⋊C8—262no—
357C4⋊C8—262no—
358C4⋊C8—262no—
359C4⋊C8—262no—
360#104—22no—
361#104—22no—
362#104—262no—
363#104—262no—
364#103—132no—
365#103—132no—
366#102—132no—
367#102—132no—
368C22⋊C8—262no—
369C22⋊C8—262no—
370C22⋊C8—262no—
371C22⋊C8—262no—
372#97—21no—
373#97—132no—
374#97—132no—
375#97—132no—
376#97—132no—
377#97—262no—
378#97—262no—
379#97—261no—
380C4×C8—21no—
381C4×C8—262no—
382C4×C8—262no—
383C4×C8—261no—
384C2×C13—21no—
385C2×C13—21no—
386C2×C13—81no—
387C2×C13#229311yescharacteristic
388C2×C13#295612yes—
389D13—81no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—261no—
395#41—261no—
396#41—261no—
397#41—261no—
398C2×Q8—131no—
399C2×Q8C2×C4×D1311yescharacteristic
400C2×D4—21no—
401C2×D4—131no—
402C2×D4—261no—
403C2×D4C2×C4×D1311yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—261no—
409C22×C4—262no—
410C22×C4#612912yes—
411C22×C4C23×D1311yescharacteristic
412Q16—262no—
413SD16—262no—
414SD16—262no—
415D8—262no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—261no—
421M16—261no—
422M16—261no—
423M16—261no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—131no—
427C2×C8—131no—
428C2×C8—132no—
429C2×C8—132no—
430C2×C8—132no—
431C2×C8—132no—
432C2×C8—132no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C4⋊C4—22no—
442C4⋊C4—132no—
443C4⋊C4—262no—
444C4⋊C4C2×C4×D1312yes—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—261no—
448C22⋊C4—262no—
449C42—22no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—44no—
454C42—262no—
455C42—261no—
456C42C2×C4×D1312yes—
457C42#612712yes—
458C42#612712yes—
459C42D4×D1311yescharacteristic
460C42D4×D1311yescharacteristic
461C13#2129711yescharacteristic, complemented, Sylow
462C23—21no—
463C23—261no—
464C23C2×#612911yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—261no—
468Q8—261no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—261no—
474D4—261no—
475D4—521no—
476D4—521no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—262no—
488C2×C4—261no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4—1042no—
492C2×C4#8813512yes—
493C2×C4#8813512yes—
494C2×C4C22×C4×D1311yescharacteristic
495C2×C4C2×#612711yescharacteristic
496C2×C4C2×#612711yescharacteristic
497C2×C4C2×D4×D1311yescharacteristic
498C2×C4#41×D1311yescharacteristic
499C2×C4#41×D1311yescharacteristic
500C8—41no—
501C8—41no—
502C8—132no—
503C8—132no—
504C8—262no—
505C8—262no—
506C8—262no—
507C8—521no—
508C8—521no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—521no—
513C22—522no—
514C22C2×#8813511yescharacteristic
515C22#1171924311yescharacteristic
516C22#1171924311yescharacteristic
517C4—24no—
518C4—22no—
519C4—22no—
520C4—42no—
521C4—41no—
522C4—42no—
523C4—521no—
524C4—522no—
525C4C4×#612711yescharacteristic
526C4D13×#11711yescharacteristic
527C4#1171925311yescharacteristic
528C4#1171925311yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—1041no—
533C2#1311729911yescharacteristic
534C2#1312374212yes—
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#104C2
socleC22×C13C2×C4×D4
prime radicalC2×#88204C22
cosocleC22×C4×C13C24
hypercenterC4×#104D13
hypocenterC13#21297
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. #13123488C2semidirect
3. #13123487C2semidirect
6. #13115588C2semidirect
7. #13115583C2semidirect
8. #13115548C2semidirect
9. #13115544C2semidirect
10. #13115541C2semidirect
11. #13115537C2semidirect
12. #13114743C2semidirect
13. C4×#88045C2semidirect
14. C4×#88043C2semidirect
15. C4×C13×#104C2semidirect
32. #11718691C4semidirect
33. #11718687C4semidirect
34. #11718679C4semidirect
35. #11718675C4semidirect
208. C4×#104D13semidirect
461. C13#21297semidirect

Maximal subgroups

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

subgroupindex
#131236342
#131234882
#131234872
#131157262
#131157212
#131155882
#131155832
#131155482
#131155442
#131155412
#131155372
#131147432
C4×#880452
C4×#880432
C4×C13×#1042
#2129713