Finite Group Databasebeta

← D13×#2237 #16017693

Subgroups — D13×#2237 #16017693

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#467C211yesmaximal, characteristic
2D13×#427C211yesmaximal, characteristic
3#13117047C211yesmaximal, characteristic, complemented
4#13117046C211yesmaximal, characteristic, complemented
5#13117045C211yesmaximal, characteristic, complemented
6#13117044C211yesmaximal, characteristic, complemented
7#13117043C211yesmaximal, characteristic, complemented
8#13117042C211yesmaximal, characteristic, complemented
9#13117041C211yesmaximal, characteristic, complemented
10D13×#367C211yesmaximal, characteristic, complemented
11D13×#366C211yesmaximal, characteristic, complemented
12D13×#358C211yesmaximal, characteristic, complemented
13D13×#358C211yesmaximal, characteristic, complemented
14D13×C22⋊C16C211yesmaximal, characteristic
15C13×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D13C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18D13×C22⋊Q8—21no—
19D13×#117—21no—
20C13×#467C2211yescharacteristic
21C13×#427C2211yescharacteristic
22#11718849C2211yescharacteristic
23#11718777C2211yescharacteristic
24#11718767C2211yescharacteristic
25#11718712—21no—
26#11718659—21no—
27C2×C16×D13C2211yescharacteristic
28C2×C16×D13C2211yescharacteristic
29#11718548C2211yescharacteristic
30#11718541C2211yescharacteristic
31#11718541C2211yescharacteristic
32D13×#107C2211yescharacteristic
33D13×#107C2211yescharacteristic
34D13×#107C2211yescharacteristic
35#11718521—21no—
36D13×#106—21no—
37#11718474—21no—
38D13×#103—21no—
39C13×#367C2211yescharacteristic, complemented
40C13×#366C2211yescharacteristic, complemented
41C13×#358C2211yescharacteristic, complemented
42C13×#358C2211yescharacteristic, complemented
43C13×C22⋊C16C2211yescharacteristic
44#11718156C2211yescharacteristic, complemented
45#11718156C2211yescharacteristic, complemented
46C22⋊#6090C2211yescharacteristic
47#11718099C2211yescharacteristic
48#11718099C2211yescharacteristic
49#11718097C2211yescharacteristic, complemented
50#11718096C2211yescharacteristic, complemented
51#11718095C2211yescharacteristic, complemented
52#11718095C2211yescharacteristic, complemented
53#11718084C2211yescharacteristic, complemented
54#11718084C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718082C2211yescharacteristic, complemented
57#11718081C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C2×Q8×D13—21no—
60C22×C4×D13D411yescharacteristic
61C2×C13×Q16C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C13×C22⋊Q8—21no—
64C13×#117—21no—
65#88200—21no—
66C2×#6107—21no—
67#88180—21no—
68#88178—21no—
69C22×#1055D411yescharacteristic
70Q16×D13—22no—
71Q16×D13—22no—
72C2×Dic52C2311yescharacteristic
73C2×C8×D13—22no—
74C2×C8×D13—22no—
75C2×C8×D13D411yescharacteristic
76C2×C8×D13D411yescharacteristic
77C2×C8×D13C2311yescharacteristic
78C2×C8×D13C2311yescharacteristic
79#88151—21no—
80#88150—41no—
81#88146—21no—
82#88146—21no—
83C4⋊C4×D13—21no—
84C4⋊C4×D13—21no—
85C4⋊C4×D13—21no—
86C4⋊C4×D13—41no—
87C22⋊C4×D13—41no—
88C22⋊C4×D13—41no—
89#88132—41no—
90#88131—41no—
91#88126—41no—
92C42×D13—41no—
93C2×C13×C16C2311yescharacteristic
94C2×C13×C16C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#106—21no—
99C13×#103—21no—
100#88075—21no—
101#88058C2311yescharacteristic
102#88058C2311yescharacteristic
103#88058C2311yescharacteristic
104#88057—21no—
105#88056—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108#88050—21no—
109#88048—21no—
110#88048—21no—
111#88047—21no—
112#88047—21no—
113#88047—21no—
114C16×D13—22no—
115C16×D13—22no—
116C2×#2237—131nomaximal, Sylow
117C23×D13D811yescharacteristic
118C2×Q8×C13—21no—
119C22×C4×C13C2×D411yescharacteristic
120C22×Dic13D811yescharacteristic
121Q8×D13—42no—
122Q8×D13—42no—
123C2×C4×D13—22no—
124C2×C4×D13—22no—
125C2×C4×D13—41no—
126C2×C4×D13—41no—
127C2×C4×D13—41no—
128C2×C4×D13—41no—
129C2×C4×D13D811yescharacteristic
130C2×C4×D13D811yescharacteristic
131C2×C4×D13C2×D411yescharacteristic
132C2×C4×D13C2×D411yescharacteristic
133C2×Dic26—21no—
134C2×Dic26—41no—
135C13×Q16—21no—
136C13×Q16—21no—
137C2×C8×C13—21no—
138C2×C8×C13—21no—
139C2×C8×C13C2×D411yescharacteristic
140C2×C8×C13C2411yescharacteristic
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C42×C13—41no—
148C22⋊Dic13—41no—
149C22⋊Dic13—41no—
150#6107—42no—
151#6103—41no—
152#6103—41no—
153#6103—41no—
154#6103—41no—
155C4⋊Dic13—21no—
156C4⋊Dic13—21no—
157C4⋊Dic13—21no—
158C4⋊Dic13—41no—
159#6101—41no—
160#6101—41no—
161#6101—41no—
162#6101—41no—
163#6101—41no—
164C4×Dic13—41no—
165C4×Dic13—41no—
166C4×Dic13—41no—
167C2×#1055—22no—
168C2×#1055C2×D411yescharacteristic
169C2×#1055C2×D411yescharacteristic
170Dic52—21no—
171Dic52—21no—
172C8×D13—22no—
173C8×D13—21no—
174C8×D13—21no—
175C8×D13—22no—
176C8×D13#4112yes—
177C8×D13#4112yes—
178C13×C16—21no—
179C13×C16—21no—
180#6090—21no—
181#6090—21no—
182C2×#467—131no—
183C2×#427—131no—
184#2237—131no—
185#2237—131no—
186#2237—131no—
187#2237—131no—
188#2237—131no—
189#2237—131no—
190#2237—131no—
191#2237D1311yescharacteristic, direct product factor
192C2×#367—131no—
193C2×#366—131no—
194C2×#358—131no—
195C2×#358—131no—
196C2×C22⋊C16—131no—
197C23×C13C2×D811yescharacteristic
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—22no—
201C22×D13C2×D811yescharacteristic
202C22×D13C2×D811yescharacteristic
203Q8×C13—41no—
204Q8×C13—41no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C22×D411yescharacteristic
213C2×Dic13—22no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13C2×D811yescharacteristic
219C2×Dic13C2×D811yescharacteristic
220C4×D13—22no—
221C4×D13—21no—
222C4×D13—21no—
223C4×D13—22no—
224C4×D13—82no—
225C4×D13—82no—
226C4×D13—82no—
227C4×D13—82no—
228C4×D13#12312yes—
229C4×D13#13712yes—
230Dic26—41no—
231Dic26—41no—
232Dic26—82no—
233C8×C13—21no—
234C8×C13C2×#4111yescharacteristic
235C8×C13C2×#4111yescharacteristic
236#1055—21no—
237#1055#12312yes—
238C22×Q16—131no—
239C23×C8—131no—
240C2×C22⋊Q8—261no—
241C2×#117—261no—
242C22×C16—131no—
243C22×C16—131no—
244#467—131no—
245#467—131no—
246#467—131no—
247#467—261no—
248#467—261no—
249#467C2×D1311yescharacteristic
250#427—131no—
251#427—131no—
252#427—131no—
253#427—261no—
254#427—261no—
255#427C2×D1311yescharacteristic
256C2×#107—131no—
257C2×#107—131no—
258C2×#107—131no—
259C2×#106—261no—
260C2×#103—261no—
261#367—131no—
262#367—131no—
263#367—131no—
264#367C2×D1311yescharacteristic, complemented
265#366—131no—
266#366—131no—
267#366—131no—
268#366C2×D1311yescharacteristic, complemented
269#358—131no—
270#358—131no—
271#358—131no—
272#358—131no—
273#358—131no—
274#358—131no—
275#358C2×D1311yescharacteristic, complemented
276#358C2×D1311yescharacteristic, complemented
277C22⋊C16—131no—
278C22⋊C16—131no—
279C22⋊C16—131no—
280C22⋊C16C2×D1311yescharacteristic
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13C22×D811yescharacteristic
285C2×D13—21no—
286C2×D13—21no—
287C2×D13—21no—
288C2×D13—44no—
289C2×D13#48012yes—
290C2×D13#50812yes—
291C2×D13#51012yes—
292C4×C13—21no—
293C4×C13—81no—
294C4×C13—81no—
295C4×C13—81no—
296C4×C13—81no—
297C4×C13C2×#12311yescharacteristic
298C4×C13C2×#13711yescharacteristic
299Dic13—21no—
300Dic13—81no—
301Dic13—81no—
302Dic13—81no—
303Dic13—81no—
304Dic13#48012yes—
305C22×Q8—261no—
306C23×C4—131no—
307C2×Q16—131no—
308C2×Q16—262no—
309C2×Q16—262no—
310C2×Q16—261no—
311C2×Q16C22×D1311yescharacteristic
312C22×C8—131no—
313C22×C8—131no—
314C22×C8—131no—
315C22×C8—131no—
316C22×C8—131no—
317C22×C8—262no—
318C22×C8—262no—
319C22×C8C22×D1311yescharacteristic
320C22⋊Q8—21no—
321C22⋊Q8—261no—
322C22⋊Q8—261no—
323C22⋊Q8—261no—
324C22⋊Q8—521no—
325C22⋊Q8—521no—
326#117—21no—
327#117—261no—
328#117—261no—
329#117—261no—
330#117—521no—
331#117—521no—
332C2×C4⋊C4—261no—
333C2×C4⋊C4—261no—
334C2×C4⋊C4—261no—
335C2×C4⋊C4—521no—
336C2×C22⋊C4—521no—
337C2×C22⋊C4—521no—
338C2×C42—521no—
339C2×C16—131no—
340C2×C16—131no—
341C2×C16—262no—
342C2×C16—262no—
343C2×C16C22×D1311yescharacteristic
344C2×C16C22×D1311yescharacteristic
345#107—131no—
346#107—131no—
347#107—131no—
348#107—261no—
349#107—261no—
350#107—261no—
351#107C22×D1311yescharacteristic
352#107C22×D1311yescharacteristic
353#107C22×D1311yescharacteristic
354#106—21no—
355#106—261no—
356#106—261no—
357#106—261no—
358#103—21no—
359#103—261no—
360#103—261no—
361#103—261no—
362C2×C13—41no—
363C2×C13C2×#48011yescharacteristic
364C2×C13C2×#50811yescharacteristic
365C2×C13C2×#51011yescharacteristic
366D13—41no—
367D13#223714yesdirect product factor
368C24—131no—
369C2×Q8—21no—
370C2×Q8—261no—
371C2×Q8—521no—
372C2×Q8—522no—
373C2×Q8—522no—
374C22×C4—131no—
375C22×C4—131no—
376C22×C4—131no—
377C22×C4—131no—
378C22×C4—131no—
379C22×C4—262no—
380C22×C4—262no—
381C22×C4—521no—
382C22×C4—521no—
383C22×C4—521no—
384C22×C4—521no—
385C22×C4D4×D1311yescharacteristic
386Q16—21no—
387Q16—21no—
388Q16—261no—
389Q16—261no—
390Q16—522no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—131no—
394C2×C8—132no—
395C2×C8—132no—
396C2×C8—131no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—261no—
401C2×C8—261no—
402C2×C8D4×D1311yescharacteristic
403C2×C8C23×D1311yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—261no—
409C4⋊C4—261no—
410C4⋊C4—261no—
411C4⋊C4—521no—
412C4⋊C4—521no—
413C4⋊C4—521no—
414C4⋊C4—521no—
415C4⋊C4—521no—
416C4⋊C4—521no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—521no—
420C22⋊C4—521no—
421C22⋊C4—521no—
422C22⋊C4—521no—
423C22⋊C4—521no—
424C22⋊C4—521no—
425C42—41no—
426C42—521no—
427C42—521no—
428C42—521no—
429C16—21no—
430C16—21no—
431C16—261no—
432C16—261no—
433C13C2×#223711yescharacteristic, complemented, Sylow
434C23—131no—
435C23—131no—
436C23—262no—
437C23—262no—
438C23—262no—
439C23D8×D1311yescharacteristic
440Q8—41no—
441Q8—41no—
442Q8—521no—
443Q8—521no—
444Q8—1042no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—131no—
452C2×C4—132no—
453C2×C4—132no—
454C2×C4—131no—
455C2×C4—262no—
456C2×C4—262no—
457C2×C4—262no—
458C2×C4—261no—
459C2×C4—261no—
460C2×C4—521no—
461C2×C4—521no—
462C2×C4—521no—
463C2×C4—521no—
464C2×C4—1042no—
465C2×C4—1042no—
466C2×C4—1042no—
467C2×C4—1042no—
468C2×C4D8×D1311yescharacteristic
469C2×C4C2×D4×D1311yescharacteristic
470C8—21no—
471C8—132no—
472C8—261no—
473C8#41×D1311yescharacteristic
474C8#41×D1311yescharacteristic
475C22—21no—
476C22—21no—
477C22—21no—
478C22—132no—
479C22—132no—
480C22—132no—
481C22—261no—
482C22—261no—
483C22—261no—
484C22—524no—
485C22C2×D8×D1311yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—132no—
492C4—261no—
493C4—1041no—
494C4—1041no—
495C4—1041no—
496C4—1041no—
497C4D13×#12311yescharacteristic
498C4D13×#13711yescharacteristic
499C2—41no—
500C2—134no—
501C2—521no—
502C2D13×#48011yescharacteristic
503C2D13×#50811yescharacteristic
504C2D13×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2237C2
socleC22×C13C22×D8
prime radicalC23×D13D8
hypercenter#2237D13
hypocenterC13C2×#2237
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
3. #13117047C2semidirect
4. #13117046C2semidirect
5. #13117045C2semidirect
6. #13117044C2semidirect
7. #13117043C2semidirect
8. #13117042C2semidirect
9. #13117041C2semidirect
10. D13×#367C2semidirect
11. D13×#366C2semidirect
12. D13×#358C2semidirect
13. D13×#358C2semidirect
15. C13×#2237C2semidirect
39. C13×#367C22semidirect
40. C13×#366C22semidirect
41. C13×#358C22semidirect
42. C13×#358C22semidirect
44. #11718156C22semidirect
45. #11718156C22semidirect
49. #11718097C22semidirect
50. #11718096C22semidirect
51. #11718095C22semidirect
52. #11718095C22semidirect
53. #11718084C22semidirect
54. #11718084C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
191. #2237D13direct (N × H)
264. #367C2×D13semidirect
268. #366C2×D13semidirect
275. #358C2×D13semidirect
276. #358C2×D13semidirect
367. D13#2237direct (N × H)
433. C13C2×#2237semidirect

Maximal subgroups

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

subgroupindex
D13×#4672
D13×#4272
#131170472
#131170462
#131170452
#131170442
#131170432
#131170422
#131170412
D13×#3672
D13×#3662
D13×#3582
D13×C22⋊C162
C13×#22372
C2×#223713