Finite Group Databasebeta

← #13127064

Subgroups — #13127064

Order 1664.

448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719437C211yesmaximal, characteristic, complemented
2D4×D52C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic, complemented
6#11718547C212yesmaximal, complemented
7#11718546C212yesmaximal, complemented
8#11718509C211yesmaximal, characteristic, complemented
9#11718499C211yesmaximal, characteristic, complemented
10#11718437C212yesmaximal, complemented
11#11718431C212yesmaximal, complemented
12C2×D4×D13C2212yes—
13C22×D52—21no—
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C4×D4×C13C2211yescharacteristic
16#88201—21no—
17Q8×Dic13—21no—
18C2×#6105C2211yescharacteristic
19#88184—21no—
20C2×#6095C2212yescomplemented
21C2×#6094C2212yescomplemented
22#88152—22no—
23#88151C2212yescomplemented
24#88149C2212yes—
25#88146C2212yescomplemented
26#88136—22no—
27#88128C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×Dic26C2211yescharacteristic, complemented
30C13×#107C2212yescomplemented
31C13×C4⋊C8C2211yescharacteristic, complemented
32C13×#102C2212yes—
33#88072C2211yescharacteristic
34#88061C2212yescomplemented
35#88060C2212yescomplemented
36#88050C2211yescharacteristic, complemented
37#88049C2212yescomplemented
38#88049C2212yescomplemented
39#88048C2211yescharacteristic, complemented
40C4×#1055C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×Q8×C13—21no—
43C2×D4×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C2×C22⋊D13—22no—
46D4×D13—24no—
47D4×D13—42no—
48C2×D52—22no—
49C2×D52—21no—
50C2×D52—21no—
51C2×D52—44no—
52C2×D52D411yescharacteristic
53C2×D52C2312yes—
54C2×C4×D13C2312yes—
55C2×Dic26C2311yescharacteristic
56C2×C8×C13C2312yes—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C13×C4⋊C4C2311yescharacteristic
60C13×C22⋊C4—21no—
61C42×C13C2311yescharacteristic
62#6105—22no—
63#6103—22no—
64#6103—22no—
65#6103—22no—
66#6103D412yes—
67C4⋊Dic13—22no—
68C4⋊Dic13D411yescharacteristic
69C4⋊Dic13C2311yescharacteristic
70#6101—21no—
71C4×Dic13—21no—
72C4×Dic13—22no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75#6095—42no—
76#6094—42no—
77#3324—131nomaximal, Sylow
78C23×C13—21no—
79C22×D13—22no—
80C22×D13—44no—
81C22×D13—44no—
82C22×D13—82no—
83C22×D13C2×D412yes—
84Q8×C13—42no—
85D4×C13—21no—
86D4×C13#4112yes—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—42no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2411yescharacteristic
93C22⋊D13—44no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13C2×D412yes—
97D52—22no—
98D52—22no—
99D52—22no—
100D52—44no—
101D52—42no—
102D52—81no—
103C4×D13—22no—
104C4×D13—22no—
105Dic26—21no—
106Dic26—21no—
107C8×C13—22no—
108#1055—21no—
109#1055—21no—
110#556—131no—
111D42—131no—
112#486—131no—
113#482—132no—
114#474D1311yescharacteristic, complemented
115#468—132no—
116#460—131no—
117#450—132no—
118C4×SD16—131no—
119#436—131no—
120#418—132no—
121C22×C13—22no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13C22×D411yescharacteristic
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—42no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—88no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—42no—
135C4×C13AGL(1,ℤ/8)12yes—
136C4×C13C2×#4111yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—22no—
139Dic13—41no—
140Dic13—41no—
141C22×D4—132no—
142C22×D4—261no—
143C2×SD16—131no—
144C2×SD16—132no—
145C2×M16—132no—
146C4⋊Q8C2×D1311yescharacteristic, complemented
147#127—131no—
148#126—262no—
149#124—261no—
150C22⋊Q8—132no—
151#121—132no—
152#121—261no—
153#120—262no—
154C4×Q8—131no—
155C4×Q8—261no—
156C4×D4—131no—
157C4×D4C2×D1311yescharacteristic
158#117—132no—
159#107C2×D1312yescomplemented
160#106—131no—
161C4⋊C8C2×D1311yescharacteristic, complemented
162#103—131no—
163#102—131no—
164#102—132no—
165#102—132no—
166#102—132no—
167#102C2×D1312yes—
168C22⋊C8—132no—
169C4×C8—131no—
170C2×C13—42no—
171C2×C13#54611yescharacteristic
172C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C13#57711yescharacteristic
174D13—42no—
175D13—82no—
176C24—262no—
177C2×Q8—21no—
178C2×Q8—131no—
179C2×D4—131no—
180C2×D4—132no—
181C2×D4—262no—
182C2×D4—262no—
183C2×D4—264no—
184C2×D4—261no—
185C2×D4—261no—
186C2×D4—524no—
187C2×D4—522no—
188C2×D4C22×D1311yescharacteristic
189C22×C4—21no—
190C22×C4—132no—
191SD16—262no—
192SD16—522no—
193M16—522no—
194C2×C8—131no—
195C2×C8—131no—
196C2×C8C22×D1312yes—
197C4⋊C4—21no—
198C4⋊C4—131no—
199C4⋊C4—131no—
200C4⋊C4—262no—
201C4⋊C4—261no—
202C4⋊C4C22×D1312yes—
203C4⋊C4C22×D1311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—132no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4—262no—
209C42—262no—
210C42—261no—
211C42C22×D1311yescharacteristic
212C13#332411yescharacteristic, complemented, Sylow
213C23—21no—
214C23—132no—
215C23—262no—
216C23—524no—
217C23—524no—
218C23—1042no—
219Q8—42no—
220Q8—261no—
221Q8—261no—
222D4—21no—
223D4—262no—
224D4—262no—
225D4—262no—
226D4—524no—
227D4—524no—
228D4—522no—
229D4—1041no—
230D4#613112yes—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—132no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4D4×D1311yescharacteristic
240C2×C4D4×D1311yescharacteristic
241C2×C4C23×D1311yescharacteristic
242C8—22no—
243C8—261no—
244C8—261no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—262no—
249C22—262no—
250C22—262no—
251C22—522no—
252C22—522no—
253C22—522no—
254C22—1048no—
255C22C2×D4×D1311yescharacteristic
256C4—21no—
257C4—41no—
258C4—42no—
259C4—262no—
260C4—521no—
261C4—521no—
262C4#8816512yes—
263C4C2×#613111yescharacteristic
264C4#8825611yescharacteristic
265C2—42no—
266C2—522no—
267C2—1042no—
268C2#1171933511yescharacteristic
269C2C2×#8816511yescharacteristic
270C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalD4×D52C2
hypercenter#474D13
hypocenterC13#3324
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
3. C13×#474C2semidirect
4. #11718749C2semidirect
5. C4×#6105C2semidirect
6. #11718547C2semidirect
7. #11718546C2semidirect
8. #11718509C2semidirect
9. #11718499C2semidirect
10. #11718437C2semidirect
11. #11718431C2semidirect
14. C13×C4⋊Q8C22semidirect
20. C2×#6095C22semidirect
21. C2×#6094C22semidirect
23. #88151C22semidirect
25. #88146C22semidirect
29. C4×Dic26C22semidirect
30. C13×#107C22semidirect
31. C13×C4⋊C8C22semidirect
34. #88061C22semidirect
35. #88060C22semidirect
36. #88050C22semidirect
37. #88049C22semidirect
38. #88049C22semidirect
39. #88048C22semidirect
40. C4×#1055C22semidirect
114. #474D13semidirect
146. C4⋊Q8C2×D13semidirect
159. #107C2×D13semidirect
161. C4⋊C8C2×D13semidirect
212. C13#3324semidirect

Maximal subgroups

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

subgroupindex
#117194372
D4×D522
C13×#4742
#117187492
C4×#61052
#117185472
#117185462
#117185092
#117184992
#117184372
#117184312
#332413