Finite Group Databasebeta

← #13126630

Subgroups — #13126630

Order 1664.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719475C212yesmaximal, complemented
2#11719456C212yesmaximal, complemented
3C13×#443C211yesmaximal, characteristic, complemented
4#11718802C212yesmaximal, complemented
5#11718559C212yesmaximal, complemented
6#11718487C212yesmaximal, complemented
7#11718483C212yesmaximal, complemented
8#11718361C211yesmaximal, characteristic, complemented
9#11718354C211yesmaximal, characteristic, complemented
10#88257C2212yes—
11#88256C2212yescomplemented
12C13×#135C2211yescharacteristic
13C13×#131C2212yescomplemented
14#88205C2212yescomplemented
15#88203C2212yes—
16#88172—22no—
17#88170—22no—
18SD16×D13—22no—
19#88165—22no—
20#88163—22no—
21#88163C2212yescomplemented
22#88162—22no—
23#88162C2212yes—
24#88158—22no—
25#88158C2211yescharacteristic
26C2×#6095—22no—
27C2×#6095C2212yescomplemented
28C2×#6095C2212yescomplemented
29#88155C2212yescomplemented
30#88128C2211yescharacteristic
31#88123C2211yescharacteristic, complemented
32C13×#108C2211yescharacteristic, complemented
33C13×#104C2212yescomplemented
34C4×C8×C13C2211yescharacteristic, complemented
35#88064C2212yescomplemented
36#88063C2212yescomplemented
37#88059C2211yescharacteristic, complemented
38#88045C2212yescomplemented
39C13×#41C2312yes—
40#6131—22no—
41Q8×D13—22no—
42#6129—22no—
43#6129—42no—
44D4×D13—22no—
45D4×D13—42no—
46#6127—22no—
47#6127—22no—
48#6127C2312yes—
49C2×D52—22no—
50C2×D52—41no—
51C2×D52C2312yes—
52C2×Dic26—22no—
53C2×Dic26C2312yes—
54C13×Q16D411yescharacteristic, complemented
55C13×SD16D412yescomplemented
56C13×D8D411yescharacteristic, complemented
57C13×M16—22no—
58C13×M16C2312yes—
59C2×C8×C13—22no—
60C2×C8×C13C2311yescharacteristic
61C2×C8×C13C2311yescharacteristic
62C42×C13C2311yescharacteristic
63#6107—22no—
64#6106—22no—
65#6105—22no—
66#6104—22no—
67C4⋊Dic13—41no—
68#6099C2312yes—
69Dic52—22no—
70Dic52D411yescharacteristic, complemented
71D104—22no—
72D104D411yescharacteristic, complemented
73#6095—22no—
74#6095—22no—
75#6095—22no—
76#6095—22no—
77#6095—22no—
78#6095—22no—
79#6095D412yescomplemented
80#6094—22no—
81C8×D13—22no—
82#3291—131nomaximal, Sylow
83C22×D13—22no—
84C22×D13—42no—
85Q8×C13C2×D412yes—
86D4×C13—22no—
87D4×C13C2×D412yes—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—22no—
92C22⋊D13—42no—
93C22⋊D13—42no—
94C2×Dic13—22no—
95C2×Dic13—42no—
96D52—22no—
97D52—22no—
98D52—42no—
99D52—82no—
100D52C2×D412yes—
101C4×D13—22no—
102C4×D13—42no—
103C4×D13—42no—
104Dic26—22no—
105Dic26—22no—
106Dic26—42no—
107Dic26C2×D412yes—
108C8×C13—22no—
109C8×C13C2×D411yescharacteristic
110C8×C13C2×D411yescharacteristic
111C8×C13C2×D411yescharacteristic
112C8×C13C2×D411yescharacteristic
113#1055—22no—
114#577—132no—
115#577—132no—
116#492—131no—
117#471—132no—
118#471—132no—
119#456—132no—
120#453—132no—
121#443—131no—
122#443D1311yescharacteristic, complemented
123C22×C13—22no—
124C22×C13H(5,𝔽2)11yescharacteristic
125C2×D13—22no—
126C2×D13—42no—
127C2×D13—82no—
128C2×D13—162no—
129C4×C13—22no—
130C4×C13—22no—
131C4×C13C22×D411yescharacteristic
132C4×C13C22×D411yescharacteristic
133Dic13—22no—
134Dic13—42no—
1352−1+4—132no—
136H(5,𝔽2)—132no—
137#137—132no—
138#137—132no—
139#137—262no—
140#137—262no—
141AGL(1,ℤ/8)—132no—
142AGL(1,ℤ/8)—132no—
143AGL(1,ℤ/8)—262no—
144AGL(1,ℤ/8)—262no—
145#135—131no—
146#135—262no—
147#135—262no—
148#135C2×D1311yescharacteristic
149C2×SD16—132no—
150C2×SD16—132no—
151C2×SD16—262no—
152C2×SD16—262no—
153#131—132no—
154#131C2×D1312yescomplemented
155C4⋊Q8—131no—
156#127—131no—
157#108—131no—
158#108C2×D1311yescharacteristic, complemented
159#104—132no—
160#104C2×D1312yescomplemented
161#101—132no—
162#100—132no—
163C4×C8C2×D1311yescharacteristic, complemented
164C2×C13—21no—
165C2×C13—42no—
166C2×C13D4211yescharacteristic
167D13—42no—
168D13—82no—
169#41—132no—
170#41—262no—
171#41—262no—
172#41—262no—
173#41—262no—
174#41—522no—
175#41C22×D1312yes—
176C2×Q8—132no—
177C2×Q8—262no—
178C2×Q8—262no—
179C2×D4—132no—
180C2×D4—262no—
181C2×D4—262no—
182C2×D4—521no—
183C2×D4—522no—
184Q16—131no—
185Q16—262no—
186Q16—262no—
187Q16D5211yescharacteristic, complemented
188SD16—132no—
189SD16—262no—
190SD16—262no—
191SD16—262no—
192SD16—262no—
193SD16—262no—
194SD16—262no—
195SD16—262no—
196SD16—262no—
197SD16D5212yescomplemented
198D8—131no—
199D8—262no—
200D8—262no—
201D8D5211yescharacteristic, complemented
202M16—22no—
203M16—132no—
204M16—262no—
205M16C22×D1312yes—
206C2×C8—22no—
207C2×C8—262no—
208C2×C8C22×D1311yescharacteristic
209C2×C8C22×D1311yescharacteristic
210C4⋊C4—521no—
211C42C22×D1311yescharacteristic
212C13#329111yescharacteristic, complemented, Sylow
213C23—262no—
214C23—522no—
215Q8—132no—
216Q8—262no—
217Q8—262no—
218Q8—522no—
219Q8C2×D5212yes—
220D4—22no—
221D4—132no—
222D4—262no—
223D4—262no—
224D4—262no—
225D4—522no—
226D4—522no—
227D4—522no—
228D4—1042no—
229D4C2×D5212yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4C23×D1311yescharacteristic
238C8—22no—
239C8—262no—
240C8C2×D5211yescharacteristic
241C8C2×D5211yescharacteristic
242C8D4×D1311yescharacteristic
243C8D4×D1311yescharacteristic
244C22—22no—
245C22—262no—
246C22—522no—
247C22—1042no—
248C22—2082no—
249C22#8825611yescharacteristic
250C4—22no—
251C4—22no—
252C4—262no—
253C4—522no—
254C4C22×D5211yescharacteristic
255C4C2×D4×D1311yescharacteristic
256C2—21no—
257C2—42no—
258C2—522no—
259C2—1042no—
260C2D4×D5211yescharacteristic
subgroupG/H
centerC2D4×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#443C2
socleC2×C13D42
hypercenter#443D13
hypocenterC13#3291
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #11719475C2semidirect
2. #11719456C2semidirect
3. C13×#443C2semidirect
4. #11718802C2semidirect
5. #11718559C2semidirect
6. #11718487C2semidirect
7. #11718483C2semidirect
8. #11718361C2semidirect
9. #11718354C2semidirect
11. #88256C22semidirect
13. C13×#131C22semidirect
14. #88205C22semidirect
21. #88163C22semidirect
27. C2×#6095C22semidirect
28. C2×#6095C22semidirect
29. #88155C22semidirect
31. #88123C22semidirect
32. C13×#108C22semidirect
33. C13×#104C22semidirect
34. C4×C8×C13C22semidirect
35. #88064C22semidirect
36. #88063C22semidirect
37. #88059C22semidirect
38. #88045C22semidirect
54. C13×Q16D4semidirect
55. C13×SD16D4semidirect
56. C13×D8D4semidirect
70. Dic52D4semidirect
72. D104D4semidirect
79. #6095D4semidirect
122. #443D13semidirect
154. #131C2×D13semidirect
158. #108C2×D13semidirect
160. #104C2×D13semidirect
163. C4×C8C2×D13semidirect
187. Q16D52semidirect
197. SD16D52semidirect
201. D8D52semidirect
212. C13#3291semidirect

Maximal subgroups

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

subgroupindex
#117194752
#117194562
C13×#4432
#117188022
#117185592
#117184872
#117184832
#117183612
#117183542
#329113