Finite Group Databasebeta

← D13⋊#354 #13131105

Subgroups — D13⋊#354 #13131105

Order 1664.

284 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D13×#124C211yesmaximal, characteristic
2D13⋊#99C212yesmaximal
3#11718300C212yesmaximal, complemented
4#11718226C212yesmaximal, complemented
5C2×Q8×D13C411yescharacteristic, complemented
6C2×D4×D13C2211yescharacteristic
7C2×C22⋊#261—22no—
8C13×#124C411yescharacteristic, complemented
9#88201C2211yescharacteristic
10#88190C411yescharacteristic, complemented
11#88139—22no—
12C22⋊C4×D13—22no—
13#88129C2211yescharacteristic
14C42×D13C411yescharacteristic, complemented
15#88119—22no—
16#88107C2214yes—
17C23×D13D412yes—
18C22×#261—42no—
19C2×Q8×C13C2×C411yescharacteristic, complemented
20C2×D4×C13C2×C411yescharacteristic
21C2×C22⋊D13D412yes—
22Q8×D13—41no—
23Q8×D13—41no—
24D4×D13—41no—
25D4×D13—41no—
26C2×D52C2311yescharacteristic
27C2×C4×D13—21no—
28C2×C4×D13—21no—
29C2×C4×D13C2×C411yescharacteristic
30C2×Dic26—21no—
31C2×Dic26C2×C411yescharacteristic, complemented
32C22⋊#261—24no—
33C22⋊#261—42no—
34C13×C22⋊C4—22no—
35C42×C13C2×C411yescharacteristic, complemented
36C22⋊Dic13—22no—
37#6103—22no—
38#6103—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic, complemented
41C2×#354—131nomaximal, Sylow
42C23×C13C22⋊C412yes—
43C22×D13—22no—
44C22×D13—22no—
45C22×D13—44no—
46C22×D13C22⋊C411yescharacteristic
47C22×D13C2×D412yes—
48C2×#261—44no—
49C2×#261—84no—
50Q8×C13—41no—
51D4×C13—41no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13C22×C411yescharacteristic
55C22⋊D13—42no—
56C2×Dic13—21no—
57C2×Dic13—21no—
58C2×Dic13C22⋊C411yescharacteristic
59D52—41no—
60C4×D13—21no—
61C4×D13—21no—
62C4×D13—42no—
63C4×D13—41no—
64C4×D13—41no—
65Dic26—42no—
66Dic26—41no—
67C2×#124—131no—
68C2×#99—132no—
69#354—132no—
70#354—132no—
71C22×C13—22no—
72C22×C13—42no—
73C22×C13C2×C22⋊C411yescharacteristic
74C2×D13—22no—
75C2×D13—22no—
76C2×D13—44no—
77C2×D13—42no—
78C2×D13—82no—
79C2×D13#9911yescharacteristic
80C2×D13#9911yescharacteristic
81#261—84no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13—41no—
85Dic13—21no—
86Dic13—41no—
87Dic13—41no—
88C22×Q8—131no—
89C22×D4—131no—
90#124—131no—
91#124—131no—
92#124—131no—
93#124—262no—
94#124#26111yescharacteristic, complemented
95C2×C22⋊C4—262no—
96C2×C22⋊C4—262no—
97C2×C42—131no—
98#99—134no—
99#99—262no—
100C2×C13—21no—
101C2×C13—42no—
102C2×C13C2×#9911yescharacteristic
103D13—21no—
104D13—42no—
105D13#35412yescomplemented
106C24—132no—
107C2×Q8—131no—
108C2×Q8—261no—
109C2×Q8—521no—
110C2×Q8—521no—
111C2×Q8C2×#26111yescharacteristic, complemented
112C2×D4—132no—
113C2×D4—131no—
114C2×D4—521no—
115C2×D4—521no—
116C2×D4C2×#26111yescharacteristic
117C22×C4—131no—
118C22×C4—261no—
119C22×C4—261no—
120C22×C4—522no—
121C22⋊C4—22no—
122C22⋊C4—262no—
123C22⋊C4—262no—
124C22⋊C4—262no—
125C22⋊C4—264no—
126C22⋊C4—522no—
127C42—131no—
128C42—261no—
129C42C2×#26111yescharacteristic, complemented
130C13C2×#35411yescharacteristic, complemented, Sylow
131C23—131no—
132C23—132no—
133C23—262no—
134C23—262no—
135C23—524no—
136C23C22⋊#26112yes—
137Q8—41no—
138Q8—521no—
139Q8—522no—
140D4—41no—
141D4—521no—
142D4—522no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—131no—
146C2×C4—261no—
147C2×C4—261no—
148C2×C4—261no—
149C2×C4—261no—
150C2×C4—521no—
151C2×C4—521no—
152C2×C4—522no—
153C2×C4—524no—
154C2×C4—1044no—
155C2×C4C22×#26111yescharacteristic
156C22—22no—
157C22—42no—
158C22—131no—
159C22—131no—
160C22—262no—
161C22—262no—
162C22—522no—
163C22—524no—
164C22—1042no—
165C22C2×C22⋊#26111yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—261no—
170C4—521no—
171C4—521no—
172C4—1044no—
173C2—21no—
174C2—42no—
175C2—132no—
176C2—261no—
177C2—522no—
178C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC2×C13C2×#99
prime radicalC2×D4×D13C22
cosocleC2×D52C23
hypercenter#124#261
hypocenterC13C2×#354
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #11718300C2semidirect
4. #11718226C2semidirect
5. C2×Q8×D13C4semidirect
8. C13×#124C4semidirect
10. #88190C4semidirect
14. C42×D13C4semidirect
19. C2×Q8×C13C2×C4semidirect
31. C2×Dic26C2×C4semidirect
35. C42×C13C2×C4semidirect
40. C4×Dic13C2×C4semidirect
94. #124#261semidirect
105. D13#354semidirect
111. C2×Q8C2×#261semidirect
129. C42C2×#261semidirect
130. C13C2×#354semidirect

Maximal subgroups

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

subgroupindex
D13×#1242
D13⋊#992
#117183002
#117182262
C2×#35413