Finite Group Databasebeta

← D13×#2175 #16016204

Subgroups — D13×#2175 #16016204

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×SD32C211yesmaximal, characteristic
2C4×Q16×D13C211yesmaximal, characteristic, complemented
3C4×D8×D13C211yesmaximal, characteristic
4#13116703C211yesmaximal, characteristic, complemented
5#13116702C211yesmaximal, characteristic, complemented
6#13116701C211yesmaximal, characteristic, complemented
7#13116700C211yesmaximal, characteristic, complemented
8#13116699C211yesmaximal, characteristic, complemented
9#13116698C211yesmaximal, characteristic, complemented
10#13116697C211yesmaximal, characteristic, complemented
11D13×#366C211yesmaximal, characteristic, complemented
12D13×#358C211yesmaximal, characteristic, complemented
13D13×#357C211yesmaximal, characteristic
14D13×#346C211yesmaximal, characteristic, complemented
15C13×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D13C2211yescharacteristic
17C2×D8×D13C2211yescharacteristic
18C4×Q8×D13—21no—
19C4×D4×D13—21no—
20C2×C13×SD32C2211yescharacteristic
21C4×C13×Q16C2211yescharacteristic, complemented
22C4×C13×D8C2211yescharacteristic
23Q16×Dic13C2211yescharacteristic, complemented
24C2×#88068C2211yescharacteristic
25D8×Dic13C2211yescharacteristic
26C2×#88067C2211yescharacteristic
27C4×#6107—21no—
28C4×#6104—21no—
29D13×SD32C418yescomplemented
30C2×#88040C2211yescharacteristic
31C2×C16×D13C2211yescharacteristic
32C2×C16×D13C2211yescharacteristic
33D13×#107C2211yescharacteristic
34D13×#107C2211yescharacteristic
35#11718534C2211yescharacteristic, complemented
36#11718533C2211yescharacteristic
37D13×#103—21no—
38#11718451—21no—
39D13×#102—21no—
40#11718417—21no—
41C4×Dic52C2211yescharacteristic, complemented
42C4×D104C2211yescharacteristic
43C4×C8×D13C2211yescharacteristic
44C13×#366C2211yescharacteristic, complemented
45C13×#358C2211yescharacteristic, complemented
46C13×#357C2211yescharacteristic
47C13×#346C2211yescharacteristic, complemented
48#11718156C2211yescharacteristic, complemented
49#11718154C2211yescharacteristic
50#11718101C2211yescharacteristic
51#11718096C2211yescharacteristic, complemented
52#11718095C2211yescharacteristic, complemented
53#11718094C2211yescharacteristic, complemented
54#11718094C2211yescharacteristic, complemented
55#11718084C2211yescharacteristic, complemented
56#11718083C2211yescharacteristic
57#11718081C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59#11718053C2211yescharacteristic, complemented
60C2×Q8×D13—21no—
61C2×D4×D13—21no—
62C22×C4×D13—41no—
63C2×C13×Q16C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C4×Q8×C13—21no—
66C4×D4×C13—21no—
67Q8×Dic13—21no—
68C2×#6107—21no—
69D4×Dic13—21no—
70C2×#6104—21no—
71C4×C22⋊D13—41no—
72Q16×D13—22no—
73Q16×D13C2×C414yescomplemented
74D8×D13—22no—
75D8×D13C2×C414yes—
76C2×Dic52C2311yescharacteristic
77C2×D104C2311yescharacteristic
78C2×C8×D13D411yescharacteristic
79C2×C8×D13C2311yescharacteristic
80#88147—21no—
81C4⋊C4×D13—21no—
82C4⋊C4×D13—21no—
83C4⋊C4×D13—41no—
84#88141—21no—
85#88141—41no—
86#88135—41no—
87C22⋊C4×D13—41no—
88C4×D52—21no—
89C42×D13—41no—
90C42×D13D411yescharacteristic
91C4×Dic26—21no—
92C4×Dic26—41no—
93C13×SD32C2×C414yescomplemented
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#103—21no—
99C13×#102—21no—
100C4×C8×C13C2311yescharacteristic
101#88075—21no—
102#88072—21no—
103#88068C2×C414yescomplemented
104#88067C2×C414yescomplemented
105#88061—21no—
106#88058C2311yescharacteristic
107#88058C2311yescharacteristic
108#88056—21no—
109C8×Dic13D411yescharacteristic
110C8×Dic13C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112C2×#6090C2311yescharacteristic
113#88050—21no—
114#88049—21no—
115#88047—21no—
116#88047—21no—
117C4×#1055D411yescharacteristic
118#88040C2×C414yescomplemented
119C16×D13—22no—
120C16×D13C2×C414yescomplemented
121C2×#2175—131nomaximal, Sylow
122C23×D13—41no—
123C2×Q8×C13—21no—
124C2×D4×C13—21no—
125C22×C4×C13—41no—
126C2×C22⋊D13—41no—
127C22×Dic13—41no—
128Q8×D13—24no—
129Q8×D13—42no—
130D4×D13—24no—
131D4×D13—42no—
132C2×D52—21no—
133C2×C4×D13—41no—
134C2×C4×D13—41no—
135C2×C4×D13—41no—
136C2×C4×D13—41no—
137C2×C4×D13—41no—
138C2×C4×D13—84no—
139C2×C4×D13D811yescharacteristic
140C2×C4×D13D811yescharacteristic
141C2×C4×D13C2×D411yescharacteristic
142C2×Dic26—21no—
143C2×Dic26—41no—
144C13×Q16—21no—
145C13×Q16C22×C412yescomplemented
146C13×D8—21no—
147C13×D8C22×C412yes—
148C2×C8×C13C2×D411yescharacteristic
149C2×C8×C13C2411yescharacteristic
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—41no—
153C13×C22⋊C4—41no—
154C42×C13—41no—
155C42×C13C2×D411yescharacteristic
156C22⋊Dic13—41no—
157#6107—24no—
158#6104—24no—
159#6103—41no—
160#6103—41no—
161C4⋊Dic13—21no—
162C4⋊Dic13—21no—
163C4⋊Dic13—41no—
164#6101—41no—
165#6101—41no—
166#6101—41no—
167#6101—41no—
168C4×Dic13—41no—
169C4×Dic13—41no—
170C4×Dic13—41no—
171C4×Dic13D811yescharacteristic
172C4×Dic13D811yescharacteristic
173C4×Dic13C2×D411yescharacteristic
174C2×#1055C2×D411yescharacteristic
175C2×#1055C2×D411yescharacteristic
176Dic52—21no—
177Dic52C22×C412yescomplemented
178D104—21no—
179D104C22×C412yes—
180C8×D13—22no—
181C8×D13C22×C412yes—
182C8×D13#4112yes—
183C13×C16—21no—
184C13×C16C22×C412yescomplemented
185#6090—21no—
186#6090C22×C412yescomplemented
187C22×SD32—131no—
188C2×C4×Q16—131no—
189C2×C4×D8—131no—
190#2175—131no—
191#2175—131no—
192#2175—131no—
193#2175—131no—
194#2175—131no—
195#2175—131no—
196#2175—131no—
197#2175D1311yescharacteristic, direct product factor
198C2×#366—131no—
199C2×#358—131no—
200C2×#357—131no—
201C2×#346—131no—
202C23×C13—41no—
203C22×D13—41no—
204C22×D13—44no—
205C22×D13—82no—
206C22×D13—82no—
207C22×D13C2×D811yescharacteristic
208Q8×C13—22no—
209Q8×C13—41no—
210D4×C13—22no—
211D4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—82no—
216C2×C4×C13C2×D811yescharacteristic
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C22⋊D13—44no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—82no—
224C2×Dic13C2×D811yescharacteristic
225C2×Dic13C2×D811yescharacteristic
226C2×Dic13C2×D811yescharacteristic
227D52—22no—
228D52—41no—
229C4×D13—22no—
230C4×D13—22no—
231C4×D13—44no—
232C4×D13—82no—
233C4×D13—82no—
234C4×D13—82no—
235C4×D13—82no—
236C4×D13C4×D412yes—
237C4×D13#13512yes—
238Dic26—22no—
239Dic26—41no—
240Dic26—44no—
241C8×C13—21no—
242C8×C13C23×C411yescharacteristic
243C8×C13C2×#4111yescharacteristic
244#1055—21no—
245#1055C4×D412yes—
246C22×Q16—131no—
247C22×D8—131no—
248C2×C4×Q8—261no—
249C2×C4×D4—261no—
250C2×SD32—131no—
251C2×SD32—131no—
252C2×SD32—138no—
253C2×SD32—131no—
254C2×SD32C2×D1311yescharacteristic
255C22×C16—131no—
256C22×C16—131no—
257C4×Q16—131no—
258C4×Q16—131no—
259C4×Q16—131no—
260C4×Q16—261no—
261C4×Q16—261no—
262C4×Q16C2×D1311yescharacteristic, complemented
263C4×D8—131no—
264C4×D8—131no—
265C4×D8—131no—
266C4×D8—261no—
267C4×D8—261no—
268C4×D8C2×D1311yescharacteristic
269C2×#107—131no—
270C2×#107—131no—
271C2×#103—261no—
272C2×#102—261no—
273C2×C4×C8—131no—
274#366—131no—
275#366—131no—
276#366—131no—
277#366C2×D1311yescharacteristic, complemented
278#358—131no—
279#358—131no—
280#358—131no—
281#358C2×D1311yescharacteristic, complemented
282#357—131no—
283#357—131no—
284#357—131no—
285#357C2×D1311yescharacteristic
286#346—131no—
287#346—131no—
288#346—131no—
289#346C2×D1311yescharacteristic, complemented
290C22×C13—42no—
291C22×C13—81no—
292C22×C13—81no—
293C22×C13C22×D811yescharacteristic
294C2×D13—42no—
295C2×D13—81no—
296C2×D13—81no—
297C2×D13—88no—
298C2×D13C4×D812yes—
299C2×D13#50912yes—
300C2×D13#51012yes—
301C4×C13—21no—
302C4×C13—21no—
303C4×C13—42no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13C2×C4×D411yescharacteristic
307C4×C13C2×#13511yescharacteristic
308Dic13—21no—
309Dic13—21no—
310Dic13—42no—
311Dic13—81no—
312Dic13—81no—
313Dic13C4×D812yes—
314C22×Q8—261no—
315C22×D4—261no—
316C23×C4—521no—
317C2×Q16—134no—
318C2×Q16—131no—
319C2×Q16—262no—
320C2×Q16—261no—
321C2×Q16C22×D1311yescharacteristic
322C2×D8—134no—
323C2×D8—131no—
324C2×D8—262no—
325C2×D8—261no—
326C2×D8C22×D1311yescharacteristic
327C22×C8—131no—
328C22×C8—131no—
329C4×Q8—21no—
330C4×Q8—261no—
331C4×Q8—261no—
332C4×Q8—261no—
333C4×Q8—521no—
334C4×Q8—521no—
335C4×D4—21no—
336C4×D4—261no—
337C4×D4—261no—
338C4×D4—261no—
339C4×D4—521no—
340C4×D4—521no—
341C2×C4⋊C4—261no—
342C2×C4⋊C4—261no—
343C2×C4⋊C4—521no—
344C2×C22⋊C4—521no—
345C2×C42—131no—
346C2×C42—521no—
347SD32—134no—
348SD32—134no—
349SD32—134no—
350SD32C4×D1314yescomplemented
351C2×C16—131no—
352C2×C16—134no—
353C2×C16—131no—
354C2×C16—262no—
355C2×C16C22×D1311yescharacteristic
356C2×C16C22×D1311yescharacteristic
357#107—131no—
358#107—131no—
359#107—261no—
360#107—261no—
361#107C22×D1311yescharacteristic
362#107C22×D1311yescharacteristic
363#103—21no—
364#103—261no—
365#103—261no—
366#103—261no—
367#102—21no—
368#102—261no—
369#102—261no—
370#102—261no—
371C4×C8—131no—
372C4×C8—131no—
373C4×C8—131no—
374C4×C8C22×D1311yescharacteristic
375C2×C13—82no—
376C2×C13C2×C4×D811yescharacteristic
377C2×C13C2×#50911yescharacteristic
378C2×C13C2×#51011yescharacteristic
379D13—82no—
380D13#217514yesdirect product factor
381C24—521no—
382C2×Q8—21no—
383C2×Q8—264no—
384C2×Q8—261no—
385C2×Q8—521no—
386C2×Q8—522no—
387C2×D4—21no—
388C2×D4—264no—
389C2×D4—261no—
390C2×D4—522no—
391C2×D4—521no—
392C22×C4—41no—
393C22×C4—131no—
394C22×C4—131no—
395C22×C4—131no—
396C22×C4—521no—
397C22×C4—521no—
398C22×C4—521no—
399C22×C4—521no—
400C22×C4—521no—
401C22×C4—521no—
402C22×C4—1044no—
403Q16—21no—
404Q16—132no—
405Q16—264no—
406Q16—261no—
407Q16C2×C4×D1312yescomplemented
408D8—21no—
409D8—132no—
410D8—264no—
411D8—261no—
412D8C2×C4×D1312yes—
413C2×C8—131no—
414C2×C8—132no—
415C2×C8—132no—
416C2×C8—131no—
417C2×C8—262no—
418C2×C8D4×D1311yescharacteristic
419C2×C8C23×D1311yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—261no—
424C4⋊C4—261no—
425C4⋊C4—521no—
426C4⋊C4—521no—
427C4⋊C4—521no—
428C4⋊C4—521no—
429C4⋊C4—521no—
430C22⋊C4—41no—
431C22⋊C4—521no—
432C22⋊C4—521no—
433C22⋊C4—521no—
434C42—41no—
435C42—131no—
436C42—131no—
437C42—131no—
438C42—521no—
439C42—521no—
440C42—521no—
441C42D4×D1311yescharacteristic
442C16—21no—
443C16—132no—
444C16—261no—
445C16C2×C4×D1312yescomplemented
446C13C2×#217511yescharacteristic, complemented, Sylow
447C23—41no—
448C23—131no—
449C23—524no—
450C23—521no—
451C23—1042no—
452C23—1042no—
453Q8—22no—
454Q8—41no—
455Q8—262no—
456Q8—524no—
457Q8—521no—
458D4—22no—
459D4—41no—
460D4—262no—
461D4—524no—
462D4—521no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—131no—
468C2×C4—132no—
469C2×C4—132no—
470C2×C4—131no—
471C2×C4—131no—
472C2×C4—262no—
473C2×C4—262no—
474C2×C4—524no—
475C2×C4—521no—
476C2×C4—521no—
477C2×C4—521no—
478C2×C4—1042no—
479C2×C4—1042no—
480C2×C4—1042no—
481C2×C4—1042no—
482C2×C4—1042no—
483C2×C4D8×D1311yescharacteristic
484C2×C4D8×D1311yescharacteristic
485C2×C4C2×D4×D1311yescharacteristic
486C8—21no—
487C8—132no—
488C8—261no—
489C8C22×C4×D1311yescharacteristic
490C8#41×D1311yescharacteristic
491C22—42no—
492C22—81no—
493C22—81no—
494C22—132no—
495C22—132no—
496C22—132no—
497C22—522no—
498C22—1048no—
499C22—1041no—
500C22—1041no—
501C22C2×D8×D1311yescharacteristic
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—132no—
508C4—261no—
509C4—261no—
510C4—522no—
511C4—1041no—
512C4—1041no—
513C4C4×D4×D1311yescharacteristic
514C4D13×#13511yescharacteristic
515C2—82no—
516C2—134no—
517C2—1042no—
518C2C4×D8×D1311yescharacteristic
519C2D13×#50911yescharacteristic
520C2D13×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2175C2
socleC22×C13C22×D8
prime radicalC2×D8×D13C22
cosocleC2×C8×C13C24
hypercenter#2175D13
hypocenterC13C2×#2175
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D13C2semidirect
4. #13116703C2semidirect
5. #13116702C2semidirect
6. #13116701C2semidirect
7. #13116700C2semidirect
8. #13116699C2semidirect
9. #13116698C2semidirect
10. #13116697C2semidirect
11. D13×#366C2semidirect
12. D13×#358C2semidirect
14. D13×#346C2semidirect
15. C13×#2175C2semidirect
21. C4×C13×Q16C22semidirect
23. Q16×Dic13C22semidirect
29. D13×SD32C4semidirect
35. #11718534C22semidirect
41. C4×Dic52C22semidirect
44. C13×#366C22semidirect
45. C13×#358C22semidirect
47. C13×#346C22semidirect
48. #11718156C22semidirect
51. #11718096C22semidirect
52. #11718095C22semidirect
53. #11718094C22semidirect
54. #11718094C22semidirect
55. #11718084C22semidirect
57. #11718081C22semidirect
58. #11718081C22semidirect
59. #11718053C22semidirect
73. Q16×D13C2×C4semidirect
93. C13×SD32C2×C4semidirect
103. #88068C2×C4semidirect
104. #88067C2×C4semidirect
118. #88040C2×C4semidirect
120. C16×D13C2×C4semidirect
145. C13×Q16C22×C4semidirect
177. Dic52C22×C4semidirect
184. C13×C16C22×C4semidirect
186. #6090C22×C4semidirect
197. #2175D13direct (N × H)
262. C4×Q16C2×D13semidirect
277. #366C2×D13semidirect
281. #358C2×D13semidirect
289. #346C2×D13semidirect
350. SD32C4×D13semidirect
380. D13#2175direct (N × H)
407. Q16C2×C4×D13semidirect
445. C16C2×C4×D13semidirect
446. C13C2×#2175semidirect

Maximal subgroups

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

subgroupindex
C2×D13×SD322
C4×Q16×D132
C4×D8×D132
#131167032
#131167022
#131167012
#131167002
#131166992
#131166982
#131166972
D13×#3662
D13×#3582
D13×#3572
D13×#3462
C13×#21752
C2×#217513