Finite Group Databasebeta

← #13126752

Subgroups — #13126752

Order 1664.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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
2#11719431C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718751C211yesmaximal, characteristic, complemented
5#11718748C211yesmaximal, characteristic, complemented
6#11718476C212yesmaximal, complemented
7#11718474C212yesmaximal, complemented
8#11718471C212yesmaximal, complemented
9#11718465C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×#6131C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15#88201—21no—
16#88200C2212yes—
17Q8×Dic13—21no—
18C2×#6107C2212yes—
19C2×#6095C2211yescharacteristic
20C2×C8×D13C2212yes—
21#88152—22no—
22#88151C2212yes—
23#88149—21no—
24#88148—22no—
25#88146C2212yes—
26C4⋊C4×D13—21no—
27C4×D52C2211yescharacteristic
28C4×D52C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×#103C2212yes—
31C13×#103C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88075C2212yes—
34#88061C2211yescharacteristic
35#88060C2212yes—
36#88057C2211yescharacteristic
37#88056C2211yescharacteristic
38#88049C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43#6131—24no—
44#6131—42no—
45C2×D52—22no—
46C2×D52D411yescharacteristic
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×C4×D13C2312yes—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2311yescharacteristic
53C2×C8×C13C2311yescharacteristic
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C42×C13C2311yescharacteristic
59#6107—42no—
60#6103—22no—
61#6103—22no—
62#6103—22no—
63#6103—21no—
64#6103D412yes—
65C4⋊Dic13—22no—
66C4⋊Dic13D411yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69#6101—21no—
70#6101—22no—
71C4×Dic13—21no—
72C4×Dic13—22no—
73C2×#1055C2312yes—
74#6095—22no—
75C8×D13—42no—
76#3302—131nomaximal, Sylow
77C22×D13—21no—
78C22×D13C2×D412yes—
79Q8×C13—22no—
80Q8×C13—22no—
81Q8×C13—42no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91D52—22no—
92D52—21no—
93D52—44no—
94D52#4112yes—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—44no—
98C4×D13—42no—
99Dic26—21no—
100Dic26—21no—
101C8×C13—21no—
102C8×C13—21no—
103#1055—22no—
104#556—131no—
105#547—131no—
106#487D1311yescharacteristic, complemented
107#485—132no—
108#474—131no—
109#467—132no—
110#462—131no—
111#452—132no—
112C4×SD16—131no—
113C8×D4—131no—
114#416—132no—
115C22×C13C22×D411yescharacteristic
116C2×D13—22no—
117C2×D13—22no—
118C2×D13—22no—
119C2×D13—22no—
120C2×D13—41no—
121C2×D13—41no—
122C4×C13—21no—
123C4×C13—42no—
124C4×C13—42no—
125C4×C13#13512yes—
126C4×C13C2×#4111yescharacteristic
127C4×C13H(5,𝔽2)11yescharacteristic
128Dic13—22no—
129Dic13—41no—
130Dic13—41no—
131Dic13—41no—
132C2×#41—132no—
133C2×Q16—132no—
134C2×SD16—131no—
135C22×C8—132no—
136C4⋊Q8C2×D1311yescharacteristic
137C4⋊Q8C2×D1311yescharacteristic
138#126—262no—
139#124—261no—
140#123—262no—
141C22⋊Q8—132no—
142C22⋊Q8—132no—
143#121—261no—
144C4×Q8—131no—
145C4×Q8—261no—
146C4×D4—131no—
147C4×D4—131no—
148#117—132no—
149C2×C4⋊C4—261no—
150#107—132no—
151#106—131no—
152C4⋊C8—131no—
153#103—132no—
154#103—131no—
155#103C2×D1312yes—
156#103C2×D1312yes—
157#102—131no—
158#102—132no—
159C22⋊C8—132no—
160C4×C8C2×D1311yescharacteristic
161C2×C13#54611yescharacteristic
162C2×C13C2×#13511yescharacteristic
163C2×C13#57811yescharacteristic
164D13—42no—
165D13—42no—
166#41—264no—
167#41—522no—
168C2×Q8—21no—
169C2×Q8—131no—
170C2×Q8C22×D1312yes—
171C2×D4—131no—
172C2×D4—131no—
173C2×D4—262no—
174C22×C4—132no—
175C22×C4—262no—
176C22×C4—261no—
177Q16—522no—
178SD16—262no—
179C2×C8—132no—
180C2×C8—522no—
181C2×C8C22×D1311yescharacteristic
182C2×C8C22×D1311yescharacteristic
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—131no—
187C4⋊C4—131no—
188C4⋊C4—131no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4C22×D1312yes—
193C22⋊C4—132no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—261no—
198C42—262no—
199C42—261no—
200C42C22×D1311yescharacteristic
201C13#330211yescharacteristic, complemented, Sylow
202C23—132no—
203C23—261no—
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—261no—
208Q8—261no—
209D4—132no—
210D4—262no—
211D4—261no—
212D4—524no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—132no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—524no—
222C2×C4—522no—
223C2×C4D4×D1311yescharacteristic
224C2×C4D4×D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—21no—
227C8—21no—
228C8—262no—
229C22—262no—
230C22—262no—
231C22—262no—
232C22—262no—
233C22—521no—
234C22—521no—
235C22C2×D4×D1311yescharacteristic
236C4—21no—
237C4—42no—
238C4—42no—
239C4—262no—
240C4—521no—
241C4—521no—
242C4—521no—
243C4#8817012yes—
244C4#41×D1311yescharacteristic
245C4#8825611yescharacteristic
246C2—522no—
247C2—522no—
248C2#1171938111yescharacteristic
249C2C2×#8817011yescharacteristic
250C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radical#11719431C2
hypercenter#487D13
hypocenterC13#3302
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
3. C13×#487C2semidirect
4. #11718751C2semidirect
5. #11718748C2semidirect
6. #11718476C2semidirect
7. #11718474C2semidirect
8. #11718471C2semidirect
9. #11718465C2semidirect
10. C4×#6095C2semidirect
11. C8×D52C2semidirect
106. #487D13semidirect
201. C13#3302semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117194312
C13×#4872
#117187512
#117187482
#117184762
#117184742
#117184712
#117184652
C4×#60952
C8×D522
#330213