Finite Group Databasebeta

← #13126774

Subgroups — #13126774

Order 1664.

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

normal subgroups only

This group has 396 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#11719423C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718736C211yesmaximal, characteristic, complemented
6#11718445C212yesmaximal, complemented
7#11718444C212yesmaximal, complemented
8#11718439C212yesmaximal, complemented
9#11718433C212yesmaximal, complemented
10C4×Dic52C211yesmaximal, characteristic, complemented
11C8×D52C211yesmaximal, characteristic, complemented
12C2×#6129C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#127C2211yescharacteristic
15#88201—21no—
16Q8×Dic13—21no—
17#88194—21no—
18#88193—22no—
19#88192C2212yes—
20D4×Dic13—21no—
21C2×#6105C2212yes—
22C2×Dic52C2211yescharacteristic
23C2×C8×D13C2212yes—
24#88152—22no—
25#88151C2212yes—
26#88146C2212yes—
27C4×D52C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C4×Dic26C2211yescharacteristic
30C13×#102C2212yes—
31C13×#102C2212yes—
32C4×C8×C13C2211yescharacteristic
33#88072C2212yes—
34#88060C2212yes—
35#88058C2211yescharacteristic
36#88056C2211yescharacteristic
37#88056C2211yescharacteristic
38#88050C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13C2312yes—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C22×Dic13—22no—
48#6129—24no—
49#6129—42no—
50C2×D52D411yescharacteristic
51C2×C4×D13C2312yes—
52C2×Dic26C2311yescharacteristic
53C2×Dic26C2311yescharacteristic
54C2×C8×C13C2311yescharacteristic
55C2×C8×C13C2311yescharacteristic
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C42×C13C2311yescharacteristic
59C22⋊Dic13—22no—
60#6105—42no—
61#6103—22no—
62#6103—22no—
63#6103D412yes—
64C4⋊Dic13—22no—
65C4⋊Dic13D411yescharacteristic
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68#6101—21no—
69#6101—21no—
70C4×Dic13—21no—
71C4×Dic13—21no—
72C4×Dic13—22no—
73C2×#1055C2312yes—
74Dic52—22no—
75C8×D13—42no—
76#3304—131nomaximal, Sylow
77C23×C13—22no—
78C22×D13C2×D412yes—
79Q8×C13—42no—
80D4×C13—22no—
81D4×C13—22no—
82D4×C13—42no—
83D4×C13—81no—
84C2×C4×C13—22no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C22⋊D13—44no—
89C22⋊D13—82no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—44no—
95C2×Dic13C2×D412yes—
96D52—22no—
97C4×D13—22no—
98C4×D13—22no—
99Dic26—21no—
100Dic26—21no—
101Dic26—21no—
102Dic26#4112yes—
103C8×C13—21no—
104C8×C13—21no—
105#1055—22no—
106#556—131no—
107#550—131no—
108#486D1311yescharacteristic, complemented
109#482—132no—
110#475—131no—
111#465—132no—
112#460—131no—
113#452—132no—
114C4×Q16—131no—
115C8×D4—131no—
116#416—132no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13C22×D411yescharacteristic
121C2×D13—22no—
122C2×D13—22no—
123C2×D13—22no—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13#13512yes—
127C4×C13C2×#4111yescharacteristic
128C4×C13H(5,𝔽2)11yescharacteristic
129Dic13—22no—
130Dic13—22no—
131Dic13—41no—
132Dic13—41no—
133Dic13—41no—
134C2×#41—132no—
135C2×Q16—131no—
136C2×SD16—132no—
137C22×C8—132no—
138C4⋊Q8C2×D1311yescharacteristic
139#127—261no—
140#127C2×D1311yescharacteristic
141#126—262no—
142#124—261no—
143C22⋊Q8—132no—
144#121—132no—
145#121—262no—
146C4×Q8—131no—
147C4×Q8—131no—
148C4×Q8—261no—
149C4×D4—131no—
150C4×D4—261no—
151#117—132no—
152#107—131no—
153#106—132no—
154C4⋊C8—131no—
155#103—131no—
156#103—131no—
157#103—132no—
158#102—132no—
159#102C2×D1312yes—
160#102C2×D1312yes—
161C22⋊C8—132no—
162C4×C8C2×D1311yescharacteristic
163C2×C13—82no—
164C2×C13#54611yescharacteristic
165C2×C13C2×#13511yescharacteristic
166C2×C13#57711yescharacteristic
167D13—42no—
168#41—264no—
169#41—522no—
170C2×Q8—21no—
171C2×Q8—131no—
172C2×Q8—131no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—131no—
176C2×D4—262no—
177C2×D4—262no—
178C2×D4C22×D1312yes—
179C22×C4—132no—
180C22×C4—262no—
181Q16—262no—
182SD16—522no—
183C2×C8—132no—
184C2×C8—522no—
185C2×C8C22×D1311yescharacteristic
186C2×C8C22×D1311yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—131no—
189C4⋊C4—131no—
190C4⋊C4—131no—
191C4⋊C4—262no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4C22×D1312yes—
195C22⋊C4—132no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C22⋊C4—262no—
199C42—262no—
200C42—261no—
201C42—261no—
202C42C22×D1311yescharacteristic
203C13#330411yescharacteristic, complemented, Sylow
204C23—22no—
205C23—132no—
206Q8—42no—
207Q8—132no—
208Q8—261no—
209Q8—261no—
210Q8—261no—
211D4—22no—
212D4—22no—
213D4—42no—
214D4—81no—
215D4—262no—
216D4—524no—
217D4—1042no—
218C2×C4—22no—
219C2×C4—132no—
220C2×C4—261no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—524no—
227C2×C4D4×D1311yescharacteristic
228C2×C4D4×D1311yescharacteristic
229C2×C4C23×D1311yescharacteristic
230C8—21no—
231C8—21no—
232C8—262no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—262no—
237C22—262no—
238C22—262no—
239C22C2×D4×D1311yescharacteristic
240C4—21no—
241C4—42no—
242C4—262no—
243C4—262no—
244C4—521no—
245C4—521no—
246C4—521no—
247C4#8816612yes—
248C4#41×D1311yescharacteristic
249C4#8825611yescharacteristic
250C2—82no—
251C2—522no—
252C2#1171938111yescharacteristic
253C2C2×#8816611yescharacteristic
254C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radical#11719423C2
hypercenter#486D13
hypocenterC13#3304
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
3. C13×#486C2semidirect
4. #11718755C2semidirect
5. #11718736C2semidirect
6. #11718445C2semidirect
7. #11718444C2semidirect
8. #11718439C2semidirect
9. #11718433C2semidirect
10. C4×Dic52C2semidirect
11. C8×D52C2semidirect
108. #486D13semidirect
203. C13#3304semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117194232
C13×#4862
#117187552
#117187362
#117184452
#117184442
#117184392
#117184332
C4×Dic522
C8×D522
#330413