Finite Group Databasebeta

← #13126377

Subgroups — #13126377

Order 1664.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#550C211yesmaximal, characteristic, complemented
2C2×#88204C211yesmaximal, characteristic, complemented
3C2×#88203C211yesmaximal, characteristic, complemented
4#11719255C211yesmaximal, characteristic, complemented
5#11718900C211yesmaximal, characteristic, complemented
6#11718899C211yesmaximal, characteristic, complemented
7#11718735C211yesmaximal, characteristic, complemented
8#11718733C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718699C211yesmaximal, characteristic, complemented
11#11718698C211yesmaximal, characteristic, complemented
12#11718697C211yesmaximal, characteristic, complemented
13#11718689C211yesmaximal, characteristic, complemented
14#11718687C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic, complemented
18C2×#6127C2211yescharacteristic
19C22×D52C2211yescharacteristic
20C13×#127—21no—
21C13×#127C2211yescharacteristic, complemented
22C13×#121—21no—
23C13×#121—21no—
24C13×#121C2211yescharacteristic
25C13×#121C2211yescharacteristic, complemented
26C4×Q8×C13C2211yescharacteristic, complemented
27C4×D4×C13—21no—
28C4×D4×C13C2211yescharacteristic
29#88204—24no—
30#88203—24no—
31C2×#6107C2211yescharacteristic, complemented
32C2×#6106C2211yescharacteristic
33C2×#6106C2211yescharacteristic
34#88191—21no—
35C2×#6105C2211yescharacteristic, complemented
36C2×#6105C2211yescharacteristic, complemented
37C2×#6104C2211yescharacteristic
38C2×#6104C2211yescharacteristic
39C2×#6104C2211yescharacteristic
40C2×#6104C2211yescharacteristic
41#88184C2211yescharacteristic
42#88178C2211yescharacteristic
43C2×#6099C2211yescharacteristic
44C22×#1055C2211yescharacteristic, complemented
45#88148—21no—
46#88138—21no—
47C22⋊C4×D13—21no—
48#88129C2211yescharacteristic
49C4×D52C2211yescharacteristic
50#88075C2211yescharacteristic, complemented
51#88072C2211yescharacteristic, complemented
52#88072C2211yescharacteristic, complemented
53C22⋊#1055C2211yescharacteristic
54C22⋊#1055C2211yescharacteristic, complemented
55#88050C2211yescharacteristic, complemented
56#88049C2211yescharacteristic
57#88049C2211yescharacteristic
58#88047C2211yescharacteristic, complemented
59C4⋊#1055C2211yescharacteristic, complemented
60#88043C2211yescharacteristic, complemented
61C23×D13—21no—
62C13×#41—22no—
63C13×#41—22no—
64C13×#41—41no—
65C13×#41—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13D411yescharacteristic
74C2×D4×C13C2311yescharacteristic
75C2×D4×C13C2311yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C2311yescharacteristic
79C22×C4×C13C2311yescharacteristic
80C2×C22⋊D13—21no—
81C2×C22⋊D13—21no—
82#6127—22no—
83#6127—41no—
84C2×D52—22no—
85C2×D52—21no—
86C2×D52—41no—
87C2×D52C2311yescharacteristic
88C2×D52C2311yescharacteristic
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×Dic26C2311yescharacteristic
92C13×C4⋊C4—21no—
93C13×C4⋊C4D411yescharacteristic
94C13×C4⋊C4C2311yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4D411yescharacteristic
98C13×C22⋊C4D411yescharacteristic
99C42×C13—21no—
100C42×C13C2311yescharacteristic
101C22⋊Dic13—21no—
102#6107—22no—
103#6106—22no—
104#6106D414yescomplemented
105#6105—22no—
106#6105—41no—
107#6104—22no—
108#6104—22no—
109#6104—22no—
110#6104—41no—
111#6103—21no—
112#6103—21no—
113#6103—21no—
114#6103—21no—
115C4⋊Dic13C2311yescharacteristic
116#6101—21no—
117#6099—22no—
118C2×#1055—22no—
119C2×#1055C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121C2×#1055C2311yescharacteristic
122C2×#1055C2311yescharacteristic
123#3268—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13—21no—
126C23×C13C2×D411yescharacteristic
127C23×C13C2×D411yescharacteristic
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—42no—
131C22×D13—42no—
132C22×D13—81no—
133Q8×C13—21no—
134Q8×C13C2×D412yes—
135D4×C13—21no—
136D4×C13—21no—
137D4×C13—21no—
138D4×C13—21no—
139D4×C13—41no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—42no—
143D4×C13—81no—
144D4×C13—81no—
145D4×C13—81no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13C2×D411yescharacteristic
155C2×C4×C13C2×D411yescharacteristic
156C2×C4×C13C2×D411yescharacteristic
157C2×C4×C13C2×D411yescharacteristic
158C2×C4×C13C2411yescharacteristic
159C22⋊D13—42no—
160C22⋊D13—81no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163D52—21no—
164D52—21no—
165D52—21no—
166D52—42no—
167D52C2×D412yes—
168C4×D13—42no—
169C4×D13—81no—
170Dic26—21no—
171Dic26—21no—
172#1055—21no—
173#1055—21no—
174#1055—21no—
175#1055C2×D412yes—
176C2×AGL(1,ℤ/8)—131no—
177C2×#135—131no—
178#550D1311yescharacteristic, complemented
179#546—131no—
180#496—131no—
181#468—131no—
182#466—131no—
183#464—131no—
184#459—131no—
185#452—131no—
186#449—131no—
187#449—131no—
188#447—131no—
189#440—131no—
190#435—131no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13C22×D411yescharacteristic
204C2×D13—22no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—84no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—22no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—41no—
217C4×C13C22×D411yescharacteristic
218C4×C13H(5,𝔽2)11yescharacteristic
219Dic13—41no—
220Dic13—41no—
221C2×#41—131no—
222C2×#41C2×D1311yescharacteristic
223C2×#41C2×D1311yescharacteristic, complemented
224C22×D4—131no—
225AGL(1,ℤ/8)—264no—
226#135—264no—
227C2×Q16—131no—
228C2×SD16—131no—
229C2×SD16—131no—
230C2×SD16—131no—
231C2×SD16—131no—
232C2×D8—131no—
233C2×D8—131no—
234C2×D8—131no—
235C2×D8—131no—
236C2×M16—131no—
237C22×C8—131no—
238#127—21no—
239#127C2×D1311yescharacteristic, complemented
240#124—131no—
241#123—261no—
242C22⋊Q8—131no—
243#121—21no—
244#121—21no—
245#121—131no—
246#121—261no—
247#121C2×D1311yescharacteristic
248#121C2×D1311yescharacteristic, complemented
249#120—261no—
250C4×Q8C2×D1311yescharacteristic, complemented
251C4×D4—21no—
252C4×D4—131no—
253C4×D4C2×D1311yescharacteristic
254C2×C22⋊C4—261no—
255#107—131no—
256C4⋊C8—131no—
257#103—131no—
258#103—131no—
259#102—131no—
260#102—131no—
261#102—131no—
262#102—131no—
263C22⋊C8—131no—
264C22⋊C8—131no—
265#97—131no—
266C2×C13—41no—
267C2×C13—41no—
268C2×C13—81no—
269C2×C13—81no—
270C2×C13D4211yescharacteristic
271C2×C13#57511yescharacteristic
272C2×C13#57611yescharacteristic
273D13—42no—
274D13—81no—
275C24—261no—
276#41—22no—
277#41—22no—
278#41—41no—
279#41—41no—
280#41—262no—
281#41—521no—
282C2×Q8—131no—
283C2×Q8C22×D1311yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—131no—
291C2×D4—131no—
292C2×D4—262no—
293C2×D4—261no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—521no—
297C2×D4C22⋊D1311yescharacteristic
298C2×D4C22×D1311yescharacteristic
299C2×D4C22×D1311yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—261no—
303C22×C4—261no—
304C22×C4C22×D1311yescharacteristic
305C22×C4C22×D1311yescharacteristic
306Q16—262no—
307SD16—134no—
308SD16—262no—
309SD16—262no—
310SD16—521no—
311D8—262no—
312D8—262no—
313D8—262no—
314D8—521no—
315M16—262no—
316C2×C8—131no—
317C2×C8—131no—
318C2×C8—131no—
319C2×C8—131no—
320C2×C8—262no—
321C4⋊C4—21no—
322C4⋊C4—131no—
323C4⋊C4—261no—
324C4⋊C4C22⋊D1311yescharacteristic
325C4⋊C4C22×D1311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—261no—
329C22⋊C4—261no—
330C22⋊C4—261no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4C22⋊D1311yescharacteristic
334C22⋊C4C22⋊D1311yescharacteristic
335C42—21no—
336C42C22×D1311yescharacteristic
337C13#326811yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—261no—
341C23—261no—
342C23—522no—
343C23—522no—
344C23—1041no—
345C23C2×C22⋊D1311yescharacteristic
346C23C2×C22⋊D1311yescharacteristic
347Q8—21no—
348Q8—261no—
349Q8—261no—
350Q8D4×D1312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—132no—
363D4—261no—
364D4—261no—
365D4—261no—
366D4—522no—
367D4—522no—
368D4—1041no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—522no—
380C2×C4—1041no—
381C2×C4C2×C22⋊D1311yescharacteristic
382C2×C4C2×C22⋊D1311yescharacteristic
383C2×C4C2×C22⋊D1311yescharacteristic
384C2×C4C2×C22⋊D1311yescharacteristic
385C2×C4C23×D1311yescharacteristic
386C8—132no—
387C8—261no—
388C8—261no—
389C8—261no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—262no—
403C22—521no—
404C22—521no—
405C22—521no—
406C22—521no—
407C22—521no—
408C22—1044no—
409C22C22×C22⋊D1311yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—521no—
417C4—521no—
418C4C2×D4×D1311yescharacteristic
419C4#8825111yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—522no—
425C2—1041no—
426C2D4×C22⋊D1311yescharacteristic
427C2#1171952711yescharacteristic
428C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#550C2
socleC22×C13C22×D4
hypercenter#550D13
hypocenterC13#3268
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C13×#550C2semidirect
2. C2×#88204C2semidirect
3. C2×#88203C2semidirect
4. #11719255C2semidirect
5. #11718900C2semidirect
6. #11718899C2semidirect
7. #11718735C2semidirect
8. #11718733C2semidirect
9. #11718703C2semidirect
10. #11718699C2semidirect
11. #11718698C2semidirect
12. #11718697C2semidirect
13. #11718689C2semidirect
14. #11718687C2semidirect
15. #11718672C2semidirect
17. C2×C13×#41C22semidirect
21. C13×#127C22semidirect
25. C13×#121C22semidirect
26. C4×Q8×C13C22semidirect
31. C2×#6107C22semidirect
35. C2×#6105C22semidirect
36. C2×#6105C22semidirect
44. C22×#1055C22semidirect
50. #88075C22semidirect
51. #88072C22semidirect
52. #88072C22semidirect
54. C22⋊#1055C22semidirect
55. #88050C22semidirect
58. #88047C22semidirect
59. C4⋊#1055C22semidirect
60. #88043C22semidirect
104. #6106D4semidirect
178. #550D13semidirect
223. C2×#41C2×D13semidirect
239. #127C2×D13semidirect
248. #121C2×D13semidirect
250. C4×Q8C2×D13semidirect
337. C13#3268semidirect

Maximal subgroups

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

subgroupindex
C13×#5502
C2×#882042
C2×#882032
#117192552
#117189002
#117188992
#117187352
#117187332
#117187032
#117186992
#117186982
#117186972
#117186892
#117186872
#117186722
#326813