Finite Group Databasebeta

← #13126711

Subgroups — #13126711

Order 1664.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#11719435C211yesmaximal, characteristic
2#11719432C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718751C211yesmaximal, characteristic, complemented
6#11718474C212yesmaximal, complemented
7#11718470C212yesmaximal, complemented
8#11718469C212yesmaximal, complemented
9D13×#103C212yesmaximal, complemented
10C4×Dic52C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic
12C2×Q8×D13C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15#88200—22no—
16#88200C2212yes—
17C2×#6107C2212yes—
18C2×Dic52C2211yescharacteristic
19C2×C8×D13C2212yes—
20#88151C2212yes—
21#88150—22no—
22#88147—21no—
23#88147—21no—
24C4⋊C4×D13C2212yes—
25#88144—21no—
26#88142—21no—
27C4×D52C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×#103C2212yes—
31C13×#103C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88075C2212yes—
34#88060C2212yes—
35#88058C2211yescharacteristic
36#88056C2211yescharacteristic
37#88056C2211yescharacteristic
38#88050C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43Q8×D13—24no—
44Q8×D13—42no—
45C2×D52D411yescharacteristic
46C2×C4×D13—22no—
47C2×C4×D13—22no—
48C2×C4×D13C2312yes—
49C2×Dic26—22no—
50C2×Dic26C2311yescharacteristic
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#6103D412yes—
63C4⋊Dic13—22no—
64C4⋊Dic13D411yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66C4⋊Dic13C2311yescharacteristic
67#6101—21no—
68#6101—21no—
69#6101—22no—
70#6101—22no—
71C4×Dic13—21no—
72C4×Dic13—21no—
73C2×#1055C2312yes—
74Dic52—22no—
75C8×D13—42no—
76#3299—131nomaximal, Sylow
77C22×D13C2×D412yes—
78Q8×C13—22no—
79Q8×C13—22no—
80Q8×C13—81no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91D52Q1614yescomplemented
92C4×D13—22no—
93C4×D13—22no—
94C4×D13—44no—
95C4×D13—82no—
96Dic26—21no—
97Dic26—21no—
98Dic26—21no—
99Dic26—44no—
100Dic26#4112yes—
101C8×C13—21no—
102C8×C13—21no—
103#1055—22no—
104#554—131no—
105D4×Q8—131no—
106#487D1311yescharacteristic, complemented
107#484—132no—
108#477—131no—
109#467—132no—
110#462—131no—
111#451—132no—
112C4×Q16—131no—
113C8×D4—131no—
114C2×#103—132no—
115C22×C13C22×D411yescharacteristic
116C2×D13—22no—
117C2×D13—22no—
118C2×D13C2×Q1614yes—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13—42no—
122C4×C13C2×Q1612yes—
123C4×C13C2×#4111yescharacteristic
124C4×C13H(5,𝔽2)11yescharacteristic
125Dic13—22no—
126Dic13—22no—
127Dic13—41no—
128Dic13—41no—
129Dic13—41no—
130C22×Q8—132no—
131C2×Q16—132no—
132C2×Q16—131no—
133C22×C8—132no—
134C4⋊Q8—261no—
135C4⋊Q8C2×D1311yescharacteristic
136C4⋊Q8C2×D1311yescharacteristic
137#125—261no—
138C22⋊Q8—132no—
139C22⋊Q8—132no—
140C22⋊Q8—262no—
141C22⋊Q8—262no—
142C4×Q8—131no—
143C4×Q8—131no—
144C4×D4—131no—
145C4×D4—261no—
146C4×D4—261no—
147C2×C4⋊C4—132no—
148#107—131no—
149#107—132no—
150C4⋊C8—131no—
151#103—132no—
152#103—131no—
153#103—131no—
154#103—132no—
155#103C2×D1312yes—
156#103C2×D1312yes—
157C22⋊C8—132no—
158C4×C8C2×D1311yescharacteristic
159C2×C13#54611yescharacteristic
160C2×C13C22×Q1611yescharacteristic
161C2×C13#57711yescharacteristic
162D13—24no—
163C2×Q8—21no—
164C2×Q8—131no—
165C2×Q8—131no—
166C2×Q8—262no—
167C2×Q8—264no—
168C2×Q8—522no—
169C2×Q8C22×D1312yes—
170C2×D4—131no—
171C22×C4—132no—
172C22×C4—262no—
173C22×C4—262no—
174Q16—262no—
175Q16—522no—
176C2×C8—132no—
177C2×C8—522no—
178C2×C8C22×D1311yescharacteristic
179C2×C8C22×D1311yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—131no—
184C4⋊C4—131no—
185C4⋊C4—131no—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4C22×D1312yes—
192C22⋊C4—132no—
193C22⋊C4—262no—
194C22⋊C4—262no—
195C42—261no—
196C42—261no—
197C42C22×D1311yescharacteristic
198C13#329911yescharacteristic, complemented, Sylow
199C23—132no—
200Q8—22no—
201Q8—22no—
202Q8—81no—
203Q8—132no—
204Q8—261no—
205Q8—261no—
206Q8—261no—
207Q8—524no—
208D4—134no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—132no—
212C2×C4—261no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—261no—
218C2×C4—524no—
219C2×C4—1042no—
220C2×C4D4×D1311yescharacteristic
221C2×C4D4×D1311yescharacteristic
222C2×C4C23×D1311yescharacteristic
223C8—21no—
224C8—21no—
225C8—262no—
226C22—134no—
227C22—262no—
228C22—262no—
229C22C2×D4×D1311yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—262no—
234C4—262no—
235C4—521no—
236C4—521no—
237C4—521no—
238C4Q16×D1312yes—
239C4#41×D1311yescharacteristic
240C4#8825611yescharacteristic
241C2—264no—
242C2#1171938111yescharacteristic
243C2#1171946711yescharacteristic
244C2C2×Q16×D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#487D13
hypocenterC13#3299
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
3. C13×#487C2semidirect
4. #11718752C2semidirect
5. #11718751C2semidirect
6. #11718474C2semidirect
7. #11718470C2semidirect
8. #11718469C2semidirect
9. D13×#103C2semidirect
10. C4×Dic52C2semidirect
91. D52Q16semidirect
106. #487D13semidirect
198. C13#3299semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117194322
C13×#4872
#117187522
#117187512
#117184742
#117184702
#117184692
D13×#1032
C4×Dic522
C8×D522
#329913