Finite Group Databasebeta

← D13×#2234 #16017685

Subgroups — D13×#2234 #16017685

Order 3328.

638 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
1D13×#466C211yesmaximal, characteristic
2D13×#427C211yesmaximal, characteristic, complemented
3#13117030C211yesmaximal, characteristic, complemented
4#13117029C211yesmaximal, characteristic, complemented
5#13117028C211yesmaximal, characteristic, complemented
6#13117027C211yesmaximal, characteristic, complemented
7#13117026C211yesmaximal, characteristic, complemented
8#13117025C211yesmaximal, characteristic, complemented
9#13117024C211yesmaximal, characteristic, complemented
10D13×#367C211yesmaximal, characteristic, complemented
11D13×#366C211yesmaximal, characteristic, complemented
12D13×#357C211yesmaximal, characteristic, complemented
13D13×#357C211yesmaximal, characteristic, complemented
14D13×C22⋊C16C211yesmaximal, characteristic, complemented
15C13×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D13C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18D13×#121—21no—
19D13×#117—21no—
20C13×#466C2211yescharacteristic
21C13×#427C2211yescharacteristic, complemented
22#11718818C2211yescharacteristic
23#11718776C2211yescharacteristic
24#11718767C2211yescharacteristic, complemented
25#11718699—21no—
26#11718659—21no—
27C2×C16×D13C2211yescharacteristic
28C2×C16×D13C2211yescharacteristic
29#11718544C2211yescharacteristic
30#11718541C2211yescharacteristic, complemented
31#11718541C2211yescharacteristic, complemented
32D13×#107C2211yescharacteristic
33D13×#107C2211yescharacteristic
34D13×#107C2211yescharacteristic
35#11718521—21no—
36D13×#106—21no—
37#11718436—21no—
38D13×#102—21no—
39C13×#367C2211yescharacteristic, complemented
40C13×#366C2211yescharacteristic, complemented
41C13×#357C2211yescharacteristic, complemented
42C13×#357C2211yescharacteristic, complemented
43C13×C22⋊C16C2211yescharacteristic, complemented
44#11718154C2211yescharacteristic, complemented
45#11718154C2211yescharacteristic, complemented
46C22⋊#6090C2211yescharacteristic, complemented
47#11718101C2211yescharacteristic, complemented
48#11718101C2211yescharacteristic, complemented
49#11718099C2211yescharacteristic, complemented
50#11718099C2211yescharacteristic, complemented
51#11718097C2211yescharacteristic, complemented
52#11718096C2211yescharacteristic, complemented
53#11718083C2211yescharacteristic, complemented
54#11718083C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718082C2211yescharacteristic, complemented
57#11718081C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C2×D4×D13—21no—
60C2×D4×D13—41no—
61C22×C4×D13D411yescharacteristic
62C2×C13×D8C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×#121—21no—
65C13×#117—21no—
66#88193—41no—
67#88192—21no—
68C2×#6104—21no—
69#88184—21no—
70#88180—21no—
71C22×#1055D411yescharacteristic
72D8×D13—22no—
73D8×D13—22no—
74C2×D104C2311yescharacteristic
75C2×C8×D13—22no—
76C2×C8×D13—22no—
77C2×C8×D13D411yescharacteristic
78C2×C8×D13D411yescharacteristic
79C2×C8×D13C2311yescharacteristic
80C2×C8×D13C2311yescharacteristic
81#88149—21no—
82#88146—21no—
83#88146—21no—
84C4⋊C4×D13—21no—
85C4⋊C4×D13—21no—
86C4⋊C4×D13—21no—
87#88138—41no—
88C22⋊C4×D13—41no—
89C22⋊C4×D13—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×#102—21no—
100#88072—21no—
101#88061—21no—
102#88058C2311yescharacteristic
103#88058C2311yescharacteristic
104#88058C2311yescharacteristic
105#88057—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108#88049—21no—
109#88048—21no—
110#88048—21no—
111#88047—21no—
112#88047—21no—
113#88047—21no—
114C16×D13—22no—
115C16×D13—22no—
116C2×#2234—131nomaximal, Sylow
117C23×D13—41no—
118C23×D13D811yescharacteristic
119C2×D4×C13—21no—
120C2×D4×C13—41no—
121C22×C4×C13C2×D411yescharacteristic
122C2×C22⋊D13—41no—
123C2×C22⋊D13—41no—
124C2×C22⋊D13—41no—
125C22×Dic13D811yescharacteristic
126D4×D13—42no—
127D4×D13—42no—
128D4×D13—84no—
129C2×D52—21no—
130C2×D52—41no—
131C2×C4×D13—22no—
132C2×C4×D13—22no—
133C2×C4×D13—41no—
134C2×C4×D13—41no—
135C2×C4×D13—41no—
136C2×C4×D13D811yescharacteristic
137C2×C4×D13D811yescharacteristic
138C2×C4×D13C2×D411yescharacteristic
139C2×C4×D13C2×D411yescharacteristic
140C13×D8—21no—
141C13×D8—21no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2411yescharacteristic
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C42×C13—41no—
152C22⋊Dic13—41no—
153C22⋊Dic13—41no—
154#6104—42no—
155#6103—41no—
156#6103—41no—
157#6103—41no—
158#6103—41no—
159C4⋊Dic13—21no—
160C4⋊Dic13—21no—
161C4⋊Dic13—21no—
162#6101—41no—
163#6101—41no—
164#6101—41no—
165C4×Dic13—41no—
166C4×Dic13—41no—
167C4×Dic13—41no—
168C2×#1055—22no—
169C2×#1055C2×D411yescharacteristic
170C2×#1055C2×D411yescharacteristic
171D104—21no—
172D104—21no—
173C8×D13—22no—
174C8×D13—21no—
175C8×D13—21no—
176C8×D13—22no—
177C8×D13#4112yes—
178C8×D13#4112yes—
179C13×C16—21no—
180C13×C16—21no—
181#6090—21no—
182#6090—21no—
183C2×#466—131no—
184C2×#427—131no—
185#2234—131no—
186#2234—131no—
187#2234—131no—
188#2234—131no—
189#2234—131no—
190#2234—131no—
191#2234—131no—
192#2234D1311yescharacteristic, direct product factor
193C2×#367—131no—
194C2×#366—131no—
195C2×#357—131no—
196C2×#357—131no—
197C2×C22⋊C16—131no—
198C23×C13—41no—
199C23×C13C2×D811yescharacteristic
200C22×D13—22no—
201C22×D13—22no—
202C22×D13—22no—
203C22×D13—41no—
204C22×D13—82no—
205C22×D13—82no—
206C22×D13—82no—
207C22×D13C2×D811yescharacteristic
208C22×D13C2×D811yescharacteristic
209D4×C13—41no—
210D4×C13—41no—
211D4×C13—82no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C22⋊D13—82no—
220C22⋊D13—82no—
221C22⋊D13—82no—
222C2×Dic13—22no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225C2×Dic13—41no—
226C2×Dic13C2×D811yescharacteristic
227C2×Dic13C2×D811yescharacteristic
228D52—41no—
229D52—41no—
230D52—82no—
231C4×D13—22no—
232C4×D13—21no—
233C4×D13—21no—
234C4×D13—22no—
235C4×D13—82no—
236C4×D13—82no—
237C4×D13—82no—
238C4×D13#12312yes—
239C4×D13#13712yes—
240C8×C13—21no—
241C8×C13C2×#4111yescharacteristic
242C8×C13C2×#4111yescharacteristic
243#1055—21no—
244#1055#12312yes—
245C22×D8—131no—
246C23×C8—131no—
247C2×#121—261no—
248C2×#117—261no—
249C22×C16—131no—
250C22×C16—131no—
251#466—131no—
252#466—131no—
253#466—131no—
254#466—261no—
255#466—261no—
256#466C2×D1311yescharacteristic
257#427—131no—
258#427—131no—
259#427—131no—
260#427—261no—
261#427—261no—
262#427C2×D1311yescharacteristic, complemented
263C2×#107—131no—
264C2×#107—131no—
265C2×#107—131no—
266C2×#106—261no—
267C2×#102—261no—
268#367—131no—
269#367—131no—
270#367—131no—
271#367C2×D1311yescharacteristic, complemented
272#366—131no—
273#366—131no—
274#366—131no—
275#366C2×D1311yescharacteristic, complemented
276#357—131no—
277#357—131no—
278#357—131no—
279#357—131no—
280#357—131no—
281#357—131no—
282#357C2×D1311yescharacteristic, complemented
283#357C2×D1311yescharacteristic, complemented
284C22⋊C16—131no—
285C22⋊C16—131no—
286C22⋊C16—131no—
287C22⋊C16C2×D1311yescharacteristic, complemented
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—81no—
292C22×C13—81no—
293C22×C13—81no—
294C22×C13C22×D811yescharacteristic
295C2×D13—21no—
296C2×D13—21no—
297C2×D13—21no—
298C2×D13—44no—
299C2×D13—81no—
300C2×D13—81no—
301C2×D13—81no—
302C2×D13—164no—
303C2×D13#48012yes—
304C2×D13#50812yes—
305C2×D13#50912yes—
306C4×C13—21no—
307C4×C13—81no—
308C4×C13—81no—
309C4×C13—81no—
310C4×C13C2×#12311yescharacteristic
311C4×C13C2×#13711yescharacteristic
312Dic13—21no—
313Dic13—81no—
314Dic13—81no—
315Dic13—81no—
316Dic13#48012yes—
317C22×D4—261no—
318C22×D4—521no—
319C23×C4—131no—
320C2×D8—131no—
321C2×D8—262no—
322C2×D8—262no—
323C2×D8—261no—
324C2×D8C22×D1311yescharacteristic
325C22×C8—131no—
326C22×C8—131no—
327C22×C8—131no—
328C22×C8—131no—
329C22×C8—131no—
330C22×C8—262no—
331C22×C8—262no—
332C22×C8C22×D1311yescharacteristic
333#121—21no—
334#121—261no—
335#121—261no—
336#121—261no—
337#121—521no—
338#121—521no—
339#117—21no—
340#117—261no—
341#117—261no—
342#117—261no—
343#117—521no—
344#117—521no—
345C2×C4⋊C4—261no—
346C2×C4⋊C4—261no—
347C2×C4⋊C4—261no—
348C2×C22⋊C4—521no—
349C2×C22⋊C4—521no—
350C2×C42—521no—
351C2×C16—131no—
352C2×C16—131no—
353C2×C16—262no—
354C2×C16—262no—
355C2×C16C22×D1311yescharacteristic
356C2×C16C22×D1311yescharacteristic
357#107—131no—
358#107—131no—
359#107—131no—
360#107—261no—
361#107—261no—
362#107—261no—
363#107C22×D1311yescharacteristic
364#107C22×D1311yescharacteristic
365#107C22×D1311yescharacteristic
366#106—21no—
367#106—261no—
368#106—261no—
369#106—261no—
370#102—21no—
371#102—261no—
372#102—261no—
373#102—261no—
374C2×C13—41no—
375C2×C13—161no—
376C2×C13C2×#48011yescharacteristic
377C2×C13C2×#50811yescharacteristic
378C2×C13C2×#50911yescharacteristic
379D13—41no—
380D13—161no—
381D13#223414yesdirect product factor
382C24—131no—
383C24—521no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—261no—
387C2×D4—521no—
388C2×D4—522no—
389C2×D4—522no—
390C2×D4—521no—
391C2×D4—521no—
392C2×D4—521no—
393C2×D4—1044no—
394C22×C4—131no—
395C22×C4—131no—
396C22×C4—131no—
397C22×C4—131no—
398C22×C4—131no—
399C22×C4—262no—
400C22×C4—262no—
401C22×C4—521no—
402C22×C4—521no—
403C22×C4—521no—
404C22×C4D4×D1311yescharacteristic
405D8—21no—
406D8—21no—
407D8—261no—
408D8—261no—
409D8—522no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—131no—
413C2×C8—132no—
414C2×C8—132no—
415C2×C8—131no—
416C2×C8—262no—
417C2×C8—262no—
418C2×C8—262no—
419C2×C8—261no—
420C2×C8—261no—
421C2×C8D4×D1311yescharacteristic
422C2×C8C23×D1311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—261no—
427C4⋊C4—261no—
428C4⋊C4—261no—
429C4⋊C4—521no—
430C4⋊C4—521no—
431C4⋊C4—521no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—521no—
435C22⋊C4—521no—
436C22⋊C4—521no—
437C22⋊C4—521no—
438C22⋊C4—521no—
439C22⋊C4—521no—
440C42—41no—
441C42—521no—
442C42—521no—
443C42—521no—
444C16—21no—
445C16—21no—
446C16—261no—
447C16—261no—
448C13C2×#223411yescharacteristic, complemented, Sylow
449C23—41no—
450C23—131no—
451C23—131no—
452C23—262no—
453C23—262no—
454C23—262no—
455C23—521no—
456C23—1042no—
457C23—1042no—
458C23—1042no—
459C23D8×D1311yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—521no—
464D4—521no—
465D4—1042no—
466D4—1042no—
467D4—1042no—
468D4—1042no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—131no—
475C2×C4—132no—
476C2×C4—132no—
477C2×C4—131no—
478C2×C4—262no—
479C2×C4—262no—
480C2×C4—262no—
481C2×C4—261no—
482C2×C4—261no—
483C2×C4—521no—
484C2×C4—521no—
485C2×C4—521no—
486C2×C4—1042no—
487C2×C4—1042no—
488C2×C4—1042no—
489C2×C4D8×D1311yescharacteristic
490C2×C4C2×D4×D1311yescharacteristic
491C8—21no—
492C8—132no—
493C8—261no—
494C8#41×D1311yescharacteristic
495C8#41×D1311yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—132no—
503C22—132no—
504C22—132no—
505C22—261no—
506C22—261no—
507C22—261no—
508C22—524no—
509C22—1041no—
510C22—1041no—
511C22—1041no—
512C22—2084no—
513C22C2×D8×D1311yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—132no—
519C4—261no—
520C4—1041no—
521C4—1041no—
522C4—1041no—
523C4D13×#12311yescharacteristic
524C4D13×#13711yescharacteristic
525C2—41no—
526C2—134no—
527C2—161no—
528C2—521no—
529C2—2081no—
530C2D13×#48011yescharacteristic
531C2D13×#50811yescharacteristic
532C2D13×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2234C2
socleC22×C13C22×D8
prime radicalD13×#466C2
hypercenter#2234D13
hypocenterC13C2×#2234
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. D13×#427C2semidirect
3. #13117030C2semidirect
4. #13117029C2semidirect
5. #13117028C2semidirect
6. #13117027C2semidirect
7. #13117026C2semidirect
8. #13117025C2semidirect
9. #13117024C2semidirect
10. D13×#367C2semidirect
11. D13×#366C2semidirect
12. D13×#357C2semidirect
13. D13×#357C2semidirect
14. D13×C22⋊C16C2semidirect
15. C13×#2234C2semidirect
21. C13×#427C22semidirect
24. #11718767C22semidirect
30. #11718541C22semidirect
31. #11718541C22semidirect
39. C13×#367C22semidirect
40. C13×#366C22semidirect
41. C13×#357C22semidirect
42. C13×#357C22semidirect
43. C13×C22⋊C16C22semidirect
44. #11718154C22semidirect
45. #11718154C22semidirect
46. C22⋊#6090C22semidirect
47. #11718101C22semidirect
48. #11718101C22semidirect
49. #11718099C22semidirect
50. #11718099C22semidirect
51. #11718097C22semidirect
52. #11718096C22semidirect
53. #11718083C22semidirect
54. #11718083C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
192. #2234D13direct (N × H)
262. #427C2×D13semidirect
271. #367C2×D13semidirect
275. #366C2×D13semidirect
282. #357C2×D13semidirect
283. #357C2×D13semidirect
287. C22⋊C16C2×D13semidirect
381. D13#2234direct (N × H)
448. C13C2×#2234semidirect

Maximal subgroups

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

subgroupindex
D13×#4662
D13×#4272
#131170302
#131170292
#131170282
#131170272
#131170262
#131170252
#131170242
D13×#3672
D13×#3662
D13×#3572
D13×C22⋊C162
C13×#22342
C2×#223413