Finite Group Databasebeta

← #13126981

Subgroups — #13126981

Order 1664.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C22⋊D13C211yesmaximal, characteristic, complemented
2#11719323C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4C2×#88072C211yesmaximal, characteristic, complemented
5#11718820C211yesmaximal, characteristic, complemented
6#11718817C211yesmaximal, characteristic, complemented
7#11718813C211yesmaximal, characteristic, complemented
8#11718811C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718440C211yesmaximal, characteristic, complemented
11#11718431C211yesmaximal, characteristic, complemented
12#11718425C211yesmaximal, characteristic, complemented
13#11718424C211yesmaximal, characteristic, complemented
14#11718396C211yesmaximal, characteristic, complemented
15#11718391C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×C22⋊D13—21no—
18C2×D4×D13C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic, complemented
21C13×#121C2211yescharacteristic, complemented
22#88207—21no—
23#88194C2211yescharacteristic
24#88193—21no—
25#88193—21no—
26#88192C2211yescharacteristic
27#88192C2211yescharacteristic, complemented
28#88191—21no—
29D4×Dic13—21no—
30D4×Dic13C2211yescharacteristic
31D4×Dic13C2211yescharacteristic, complemented
32C2×#6104C2211yescharacteristic, complemented
33#88184C2211yescharacteristic
34C4×C22⋊D13C2211yescharacteristic
35C2×C4⋊Dic13C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic, complemented
37C2×#6094C2211yescharacteristic, complemented
38#88146C2211yescharacteristic, complemented
39#88144C2211yescharacteristic, complemented
40#88140—21no—
41#88133—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic, complemented
44C13×C22⋊C8C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic, complemented
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50#88061C2211yescharacteristic, complemented
51#88061C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88057C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88049C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C24×C13—21no—
60C23×D13—21no—
61C2×D4×C13—22no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C2×D4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C2×C22⋊D13—44no—
76C2×C22⋊D13D411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80D4×D13—22no—
81D4×D13—41no—
82C2×D52C2311yescharacteristic
83C2×C4×D13C2311yescharacteristic
84C13×D8—22no—
85C13×D8—41no—
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13D411yescharacteristic
95#6104—41no—
96#6103—21no—
97#6103—21no—
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055—41no—
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#6094—41no—
112#3318—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—81no—
119C23×C13C2×D411yescharacteristic
120C22×D13—21no—
121C22×D13—42no—
122C22×D13—42no—
123C22×D13—81no—
124C22×D13C2×D411yescharacteristic
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—21no—
130D4×C13—42no—
131D4×C13—42no—
132D4×C13#4112yes—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C22⋊D13—22no—
139C22⋊D13—42no—
140C22⋊D13—42no—
141C22⋊D13—42no—
142C22⋊D13—42no—
143C22⋊D13—81no—
144C22⋊D13—81no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—42no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13C2×D411yescharacteristic
152C2×Dic13C2×D411yescharacteristic
153C2×Dic13C2×D411yescharacteristic
154D52—21no—
155D52—21no—
156C4×D13—21no—
157C4×D13—21no—
158C8×C13—21no—
159C8×C13—21no—
160#1055—21no—
161#1055—21no—
162#553—131no—
163D42—131no—
164#490—131no—
165#482—131no—
166#481—131no—
167#478—131no—
168#469—131no—
169#466—131no—
170#459—131no—
171#447—131no—
172#447D1311yescharacteristic, complemented
173#442—131no—
174#435—131no—
175#418—131no—
176C2×#102—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—84no—
189C22×C13AGL(1,ℤ/8)12yes—
190C22×C13C22×D411yescharacteristic
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—21no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—84no—
198C4×C13—21no—
199C4×C13—41no—
200C4×C13C2×#4111yescharacteristic
201C4×C13H(5,𝔽2)11yescharacteristic
202Dic13—21no—
203Dic13—21no—
204Dic13—21no—
205Dic13—41no—
206Dic13—41no—
207Dic13—41no—
208C22×D4—131no—
209C22×D4—261no—
210C22×D4C2×D1311yescharacteristic
211C2×D8—131no—
212C2×D8C2×D1311yescharacteristic
213C2×D8C2×D1311yescharacteristic, complemented
214C2×M16—131no—
215C22×C8—131no—
216#127—131no—
217#126—261no—
218#125—131no—
219#123—261no—
220#121—131no—
221#121—131no—
222#121—131no—
223#121—261no—
224#121—261no—
225#121C2×D1311yescharacteristic, complemented
226#120—261no—
227#120—261no—
228C4×D4—131no—
229C4×D4—131no—
230C4×D4—131no—
231C4×D4—261no—
232#117—131no—
233C2×C4⋊C4—131no—
234#107—131no—
235#106—131no—
236#106—131no—
237C4⋊C8—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102C2×D1311yescharacteristic
247#102C2×D1311yescharacteristic, complemented
248C22⋊C8—131no—
249C22⋊C8C2×D1311yescharacteristic, complemented
250#97—131no—
251C2×C13—22no—
252C2×C13—42no—
253C2×C13—81no—
254C2×C13—81no—
255C2×C13#54611yescharacteristic
256C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
257C2×C13#57611yescharacteristic
258D13—41no—
259D13—81no—
260C24—21no—
261C24—261no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—131no—
267C2×D4—131no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—262no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—521no—
276C2×D4—524no—
277C2×D4C22×D1311yescharacteristic
278C2×D4C22×D1311yescharacteristic
279C2×D4C22×D1311yescharacteristic
280C22×C4—131no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4C22×D1311yescharacteristic
285D8—22no—
286D8—41no—
287D8—521no—
288M16—521no—
289C2×C8—131no—
290C2×C8—131no—
291C2×C8—521no—
292C2×C8C22×D1311yescharacteristic
293C2×C8C22×D1311yescharacteristic
294C4⋊C4—131no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4—131no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4C22×D1311yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—131no—
304C22⋊C4—131no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C42—131no—
312C42—261no—
313C13#331811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—131no—
321C23—261no—
322C23—522no—
323C23—522no—
324C23—1041no—
325C23D4×D1311yescharacteristic
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—42no—
333D4—262no—
334D4—261no—
335D4—261no—
336D4—522no—
337D4—522no—
338D4—522no—
339D4—522no—
340D4—1041no—
341D4—1041no—
342D4#612912yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—522no—
355C2×C4—1041no—
356C2×C4—1041no—
357C2×C4D4×D1311yescharacteristic
358C2×C4C23×D1311yescharacteristic
359C8—21no—
360C8—21no—
361C8—261no—
362C8—261no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—84no—
375C22—261no—
376C22—261no—
377C22—261no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—1044no—
382C22#8816512yes—
383C22C2×D4×D1311yescharacteristic
384C4—21no—
385C4—41no—
386C4—261no—
387C4—261no—
388C4—261no—
389C4—521no—
390C4—521no—
391C4—521no—
392C4C2×#612911yescharacteristic
393C4#8825111yescharacteristic
394C2—22no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—521no—
399C2—1041no—
400C2#1171929611yescharacteristic
401C2C2×#8816511yescharacteristic
402C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3318
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. D4×C22⋊D13C2semidirect
2. #11719323C2semidirect
3. C13×#447C2semidirect
4. C2×#88072C2semidirect
5. #11718820C2semidirect
6. #11718817C2semidirect
7. #11718813C2semidirect
8. #11718811C2semidirect
9. #11718699C2semidirect
10. #11718440C2semidirect
11. #11718431C2semidirect
12. #11718425C2semidirect
13. #11718424C2semidirect
14. #11718396C2semidirect
15. #11718391C2semidirect
20. C2×C13×D8C22semidirect
21. C13×#121C22semidirect
27. #88192C22semidirect
31. D4×Dic13C22semidirect
32. C2×#6104C22semidirect
35. C2×C4⋊Dic13C22semidirect
36. C22×#1055C22semidirect
37. C2×#6094C22semidirect
38. #88146C22semidirect
39. #88144C22semidirect
43. C13×#102C22semidirect
44. C13×C22⋊C8C22semidirect
47. #88072C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
50. #88061C22semidirect
51. #88061C22semidirect
52. #88060C22semidirect
53. #88057C22semidirect
54. #88057C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
57. #88049C22semidirect
58. #88047C22semidirect
172. #447D13semidirect
213. C2×D8C2×D13semidirect
225. #121C2×D13semidirect
247. #102C2×D13semidirect
249. C22⋊C8C2×D13semidirect
313. C13#3318semidirect

Maximal subgroups

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

subgroupindex
D4×C22⋊D132
#117193232
C13×#4472
C2×#880722
#117188202
#117188172
#117188132
#117188112
#117186992
#117184402
#117184312
#117184252
#117184242
#117183962
#117183912
#331813