Finite Group Databasebeta

← #13126857

Subgroups — #13126857

Order 1664.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D42×C13C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3#11718879C211yesmaximal, characteristic, complemented
4#11718879C211yesmaximal, characteristic, complemented
5#11718876C211yesmaximal, characteristic, complemented
6C2×#88072C211yesmaximal, characteristic, complemented
7#11718736C211yesmaximal, characteristic, complemented
8#11718732C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718702C211yesmaximal, characteristic, complemented
11#11718696C211yesmaximal, characteristic, complemented
12#11718694C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14#11718672C211yesmaximal, characteristic, complemented
15#11718670C211yesmaximal, characteristic, complemented
16C22×D4×C13—21no—
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C13×#127C2211yescharacteristic
20C13×#121—21no—
21C13×#121C2211yescharacteristic
22C13×#121C2211yescharacteristic
23C13×#120—21no—
24C13×#120—21no—
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic
27#88189—21no—
28C2×#6105C2211yescharacteristic
29C2×#6105C2211yescharacteristic, complemented
30C2×#6105C2211yescharacteristic, complemented
31#88180C2211yescharacteristic, complemented
32C2×C4⋊Dic13C2211yescharacteristic, complemented
33#88178C2211yescharacteristic, complemented
34#88178C2211yescharacteristic, complemented
35C2×#6099C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic, complemented
37#88143—21no—
38#88133—21no—
39#88131—21no—
40#88124C2211yescharacteristic, complemented
41C4×Dic26C2211yescharacteristic, complemented
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic, complemented
46#88072C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50#88072C2211yescharacteristic, complemented
51C22⋊#1055C2211yescharacteristic, complemented
52C22⋊#1055C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88048C2211yescharacteristic, complemented
55#88047C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57C4⋊#1055C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C24×C13—21no—
60C24×C13—21no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—44no—
72C2×D4×C13D411yescharacteristic
73C2×D4×C13C2311yescharacteristic
74C2×D4×C13C2311yescharacteristic
75C2×D4×C13C2311yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13C2311yescharacteristic
78C22×C4×C13C2311yescharacteristic
79C22×Dic13—21no—
80C2×Dic26C2311yescharacteristic
81C13×C4⋊C4D411yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4D411yescharacteristic
87C13×C22⋊C4D411yescharacteristic
88C42×C13C2311yescharacteristic
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92#6105—22no—
93#6105—41no—
94#6105—41no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106#6099—41no—
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#3310—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—81no—
121C23×C13—81no—
122C23×C13C2×D411yescharacteristic
123C23×C13C2×D411yescharacteristic
124D4×C13—22no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—21no—
130D4×C13—42no—
131D4×C13—42no—
132D4×C13—42no—
133D4×C13—42no—
134D4×C13—42no—
135D4×C13—81no—
136D4×C13#4112yes—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—42no—
143C2×C4×C13C2×D411yescharacteristic
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2×D411yescharacteristic
146C2×C4×C13C2×D411yescharacteristic
147C2×C4×C13C2411yescharacteristic
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—42no—
153Dic26—21no—
154Dic26—21no—
155#1055—21no—
156#1055—21no—
157#1055—21no—
158#1055—21no—
159#552—131no—
160D42D1311yescharacteristic
161#490—131no—
162#482—131no—
163#480—131no—
164#478—131no—
165#468—131no—
166#465—131no—
167#460—131no—
168#450—131no—
169#450—131no—
170#440—131no—
171#435—131no—
172#418—131no—
173C2×#102—131no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—21no—
179C22×C13—21no—
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×C13—84no—
190C22×C13AGL(1,ℤ/8)12yes—
191C22×C13C22×D411yescharacteristic
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—41no—
197C4×C13C2×#4111yescharacteristic
198C4×C13H(5,𝔽2)11yescharacteristic
199Dic13—41no—
200Dic13—41no—
201Dic13—41no—
202Dic13—41no—
203C22×D4—21no—
204C22×D4C2×D1311yescharacteristic
205C22×D4C2×D1311yescharacteristic
206C2×SD16—131no—
207C2×SD16—131no—
208C2×SD16—131no—
209C2×M16—131no—
210C22×C8—131no—
211#127C2×D1311yescharacteristic
212#126—261no—
213#125—131no—
214#125—261no—
215#123—261no—
216C22⋊Q8—131no—
217C22⋊Q8—131no—
218#121—21no—
219#121C2×D1311yescharacteristic
220#121C2×D1311yescharacteristic
221#120—21no—
222#120—21no—
223C4×Q8—131no—
224C4×D4C2×D1311yescharacteristic
225C4×D4C2×D1311yescharacteristic
226#117—131no—
227#117—261no—
228C2×C4⋊C4—131no—
229#107—131no—
230#107—131no—
231#106—131no—
232C4⋊C8—131no—
233#103—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242#102—131no—
243C22⋊C8—131no—
244C22⋊C8—131no—
245#97—131no—
246C2×C13—22no—
247C2×C13—41no—
248C2×C13—42no—
249C2×C13—81no—
250C2×C13—81no—
251C2×C13#54611yescharacteristic
252C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
253C2×C13#57711yescharacteristic
254C24—21no—
255C24—21no—
256C2×Q8—131no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—44no—
268C2×D4C22⋊D1311yescharacteristic
269C2×D4C22×D1311yescharacteristic
270C2×D4C22×D1311yescharacteristic
271C2×D4C22×D1311yescharacteristic
272C22×C4—21no—
273C22×C4—261no—
274C22×C4C22×D1311yescharacteristic
275C22×C4C22×D1311yescharacteristic
276SD16—262no—
277SD16—521no—
278SD16—521no—
279M16—521no—
280C2×C8—131no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8—521no—
285C4⋊C4—131no—
286C4⋊C4—131no—
287C4⋊C4—131no—
288C4⋊C4—261no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4C22⋊D1311yescharacteristic
295C4⋊C4C22×D1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4C22⋊D1311yescharacteristic
303C22⋊C4C22⋊D1311yescharacteristic
304C42—261no—
305C42—261no—
306C42C22×D1311yescharacteristic
307C13#331011yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D1311yescharacteristic
318C23C2×C22⋊D1311yescharacteristic
319Q8—261no—
320Q8—261no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#612912yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—522no—
345C2×C4C2×C22⋊D1311yescharacteristic
346C2×C4C2×C22⋊D1311yescharacteristic
347C2×C4C2×C22⋊D1311yescharacteristic
348C2×C4C2×C22⋊D1311yescharacteristic
349C2×C4C23×D1311yescharacteristic
350C8—261no—
351C8—261no—
352C8—261no—
353C8—261no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#8818612yes—
371C22C22×C22⋊D1311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—521no—
378C4—521no—
379C4—521no—
380C4—521no—
381C4C2×#612911yescharacteristic
382C4#8825111yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2C2×#8818611yescharacteristic
389C2#1171951111yescharacteristic
390C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalD42×C13C2
socleC22×C13C22×D4
hypercenterD42D13
hypocenterC13#3310
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. #11718879C2semidirect
4. #11718879C2semidirect
5. #11718876C2semidirect
6. C2×#88072C2semidirect
7. #11718736C2semidirect
8. #11718732C2semidirect
9. #11718703C2semidirect
10. #11718702C2semidirect
11. #11718696C2semidirect
12. #11718694C2semidirect
13. #11718679C2semidirect
14. #11718672C2semidirect
15. #11718670C2semidirect
29. C2×#6105C22semidirect
30. C2×#6105C22semidirect
31. #88180C22semidirect
32. C2×C4⋊Dic13C22semidirect
33. #88178C22semidirect
34. #88178C22semidirect
35. C2×#6099C22semidirect
36. C22×#1055C22semidirect
40. #88124C22semidirect
41. C4×Dic26C22semidirect
45. #88072C22semidirect
46. #88072C22semidirect
47. #88072C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
50. #88072C22semidirect
51. C22⋊#1055C22semidirect
52. C22⋊#1055C22semidirect
53. #88050C22semidirect
54. #88048C22semidirect
55. #88047C22semidirect
56. #88047C22semidirect
57. C4⋊#1055C22semidirect
58. #88043C22semidirect
307. C13#3310semidirect

Maximal subgroups

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

subgroupindex
D42×C132
#117192462
#117188792
#117188762
C2×#880722
#117187362
#117187322
#117187032
#117187022
#117186962
#117186942
#117186792
#117186722
#117186702
#331013