Finite Group Databasebeta

← #13125909

Subgroups — #13125909

Order 1664.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719420C211yesmaximal, characteristic
2#11719402C211yesmaximal, characteristic, complemented
3C13×#490C211yesmaximal, characteristic, complemented
4#11718737C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718444C212yesmaximal, complemented
7#11718437C212yesmaximal, complemented
8#11718428C212yesmaximal, complemented
9#11718423C212yesmaximal, complemented
10#11718376C211yesmaximal, characteristic, complemented
11#11718370C211yesmaximal, characteristic, complemented
12C2×#6129C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C13×#127C2211yescharacteristic
15C13×#125C2211yescharacteristic, complemented
16#88194C2211yescharacteristic
17#88193—22no—
18#88191—22no—
19#88190C2211yescharacteristic
20C2×#6105C2212yes—
21C2×#6105C2212yescomplemented
22C2×Dic52C2212yescomplemented
23C2×#6095C2212yes—
24#88152—22no—
25#88151C2212yes—
26#88144—22no—
27#88141C2212yescomplemented
28#88129C2211yescharacteristic
29#88126C2211yescharacteristic
30#88123C2211yescharacteristic, complemented
31C13×#102C2212yes—
32C13×#102C2212yescomplemented
33C13×#97C2211yescharacteristic, complemented
34#88060C2212yes—
35#88054C2212yescomplemented
36#88050C2212yescomplemented
37#88049C2212yes—
38C4×#1055C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×D4×C13—22no—
41C2×D4×C13C2311yescharacteristic
42C2×D4×C13C2311yescharacteristic
43C2×C22⋊D13—21no—
44C2×C22⋊D13—21no—
45C2×C22⋊D13—22no—
46C22×Dic13—21no—
47#6129—42no—
48D4×D13—42no—
49C2×D52C2311yescharacteristic
50C2×C4×D13C2311yescharacteristic
51C2×Dic26C2312yes—
52C2×Dic26C2311yescharacteristic
53C2×C8×C13C2312yes—
54C13×C4⋊C4—22no—
55C13×C4⋊C4C2312yes—
56C42×C13C2311yescharacteristic
57C22⋊Dic13—22no—
58#6105—42no—
59#6105—42no—
60#6103—22no—
61#6103—22no—
62#6103D412yes—
63C4⋊Dic13—22no—
64C4⋊Dic13—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—22no—
68C4×Dic13C2311yescharacteristic
69C2×#1055C2312yes—
70Dic52—42no—
71#6095—42no—
72#3222—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—21no—
75C22×D13—21no—
76C22×D13—42no—
77C22×D13—82no—
78C22×D13C2×D411yescharacteristic
79D4×C13—22no—
80D4×C13—22no—
81D4×C13—82no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2411yescharacteristic
85C22⋊D13—42no—
86C22⋊D13—42no—
87C22⋊D13—82no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—42no—
91C2×Dic13C2×D412yes—
92C2×Dic13C2×D411yescharacteristic
93D52—22no—
94C4×D13—22no—
95Dic26—22no—
96Dic26—22no—
97Dic26—22no—
98C8×C13—22no—
99#1055—22no—
100#541—131no—
101#535—131no—
102#497—131no—
103#492—131no—
104#490D1311yescharacteristic, complemented
105#488—131no—
106#464—132no—
107#460—132no—
108#452—132no—
109#450—132no—
110#433—131no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13C22×D411yescharacteristic
116C2×D13—21no—
117C2×D13—22no—
118C2×D13—41no—
119C2×D13—42no—
120C2×D13—84no—
121C4×C13—22no—
122C4×C13—42no—
123C4×C13H(5,𝔽2)12yes—
124Dic13—21no—
125Dic13—22no—
126Dic13—42no—
127Dic13—41no—
128C2×#41—131no—
129C22×D4—131no—
130C2×Q16—132no—
131C2×SD16—132no—
132C2×SD16—132no—
133C2×SD16—132no—
134C4⋊Q8—131no—
135#127—131no—
136#127C2×D1311yescharacteristic
137#126—262no—
138#125—262no—
139#125C2×D1311yescharacteristic, complemented
140#124—131no—
141#124—131no—
142C22⋊Q8—132no—
143#121—262no—
144#120—262no—
145C4×Q8—132no—
146#117—131no—
147C4⋊C8—132no—
148#103—132no—
149#102—132no—
150#102C2×D1312yes—
151#102C2×D1312yescomplemented
152C22⋊C8—132no—
153#97C2×D1311yescharacteristic, complemented
154C4×C8—131no—
155C2×C13—81no—
156C2×C13—81no—
157C2×C13#53511yescharacteristic
158C2×C13#57712yes—
159D13—41no—
160D13—81no—
161C24—261no—
162#41—522no—
163C2×Q8—131no—
164C2×Q8—132no—
165C2×D4—22no—
166C2×D4—131no—
167C2×D4—261no—
168C2×D4—262no—
169C2×D4—261no—
170C2×D4—522no—
171C2×D4C22×D1311yescharacteristic
172C2×D4C22×D1311yescharacteristic
173C22×C4—131no—
174C22×C4—261no—
175Q16—522no—
176SD16—522no—
177SD16—522no—
178SD16—522no—
179C2×C8—132no—
180C2×C8C22×D1312yes—
181C4⋊C4—22no—
182C4⋊C4—132no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4C22×D1312yes—
187C22⋊C4—132no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C42—131no—
192C42—262no—
193C42C22×D1311yescharacteristic
194C13#322211yescharacteristic, complemented, Sylow
195C23—21no—
196C23—21no—
197C23—131no—
198C23—261no—
199C23—522no—
200C23—1042no—
201Q8—262no—
202Q8—262no—
203Q8—262no—
204D4—22no—
205D4—22no—
206D4—82no—
207D4—262no—
208D4—522no—
209D4—522no—
210D4—1042no—
211C2×C4—22no—
212C2×C4—132no—
213C2×C4—131no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—522no—
218C2×C4D4×D1312yes—
219C2×C4C23×D1311yescharacteristic
220C8—22no—
221C8—262no—
222C22—42no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22—262no—
227C22—261no—
228C22—522no—
229C22—521no—
230C22—1044no—
231C22C2×D4×D1311yescharacteristic
232C4—22no—
233C4—42no—
234C4—262no—
235C4—261no—
236C4—521no—
237C4—522no—
238C4#8825612yes—
239C2—81no—
240C2—81no—
241C2—521no—
242C2—1041no—
243C2#1171937911yescharacteristic
244C2#1171948012yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#490C2
socleC22×C13C22×D4
prime radical#11719420C2
hypercenter#490D13
hypocenterC13#3222
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #11719402C2semidirect
3. C13×#490C2semidirect
4. #11718737C2semidirect
5. #11718729C2semidirect
6. #11718444C2semidirect
7. #11718437C2semidirect
8. #11718428C2semidirect
9. #11718423C2semidirect
10. #11718376C2semidirect
11. #11718370C2semidirect
15. C13×#125C22semidirect
21. C2×#6105C22semidirect
22. C2×Dic52C22semidirect
27. #88141C22semidirect
30. #88123C22semidirect
32. C13×#102C22semidirect
33. C13×#97C22semidirect
35. #88054C22semidirect
36. #88050C22semidirect
38. C4×#1055C22semidirect
104. #490D13semidirect
139. #125C2×D13semidirect
151. #102C2×D13semidirect
153. #97C2×D13semidirect
194. C13#3222semidirect

Maximal subgroups

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

subgroupindex
#117194202
#117194022
C13×#4902
#117187372
#117187292
#117184442
#117184372
#117184282
#117184232
#117183762
#117183702
#322213