Finite Group Databasebeta

← D13⋊#356 #13131125

Subgroups — D13⋊#356 #13131125

Order 1664.

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

normal subgroups only

This group has 240 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×C4⋊Q8C211yesmaximal, characteristic
2D13⋊#101C212yesmaximal
3#11718301C212yesmaximal, complemented
4#11718227C212yesmaximal, complemented
5C2×Q8×D13C411yescharacteristic
6C2×Q8×D13C2211yescharacteristic
7D13⋊M16—22no—
8C13×C4⋊Q8C411yescharacteristic
9#88198C411yescharacteristic
10#88198C2211yescharacteristic
11C4⋊C4×D13—22no—
12#88142—22no—
13C42×D13C411yescharacteristic
14#88123C2211yescharacteristic
15#88113—22no—
16#88113C2214yes—
17C2×Q8×C13C2×C411yescharacteristic
18C2×Q8×C13C2×C411yescharacteristic
19Q8×D13—41no—
20Q8×D13—41no—
21Q8×D13—41no—
22Q8×D13—41no—
23C2×C4×D13—21no—
24C2×C4×D13—21no—
25C2×C4×D13C2×C411yescharacteristic
26C2×C4×D13D412yes—
27C2×Dic26—21no—
28C2×Dic26C2×C411yescharacteristic
29C2×Dic26D412yes—
30C2×Dic26C2311yescharacteristic
31#6122—24no—
32#6118—42no—
33D13⋊C8—42no—
34C13×C4⋊C4—22no—
35C42×C13C2×C411yescharacteristic
36C4⋊Dic13—22no—
37#6101—22no—
38#6101—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic
41C2×#356—131nomaximal, Sylow
42C22×D13C22⋊C411yescharacteristic
43Q8×C13—41no—
44Q8×C13—41no—
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13C22⋊C412yes—
48C2×C4×C13C22×C411yescharacteristic
49C2×Dic13—21no—
50C2×Dic13—21no—
51C2×Dic13C22⋊C411yescharacteristic
52C2×Dic13C2×D412yes—
53C4×D13—24no—
54C4×D13—22no—
55C4×D13—22no—
56C4×D13—21no—
57C4×D13—21no—
58C4×D13—41no—
59C4×D13—41no—
60Dic26—42no—
61Dic26—41no—
62Dic26—42no—
63Dic26—41no—
64#1057—44no—
65C2×C4⋊Q8—131no—
66C2×#101—132no—
67#356—132no—
68#356—132no—
69C22×C13C2×C22⋊C411yescharacteristic
70C2×D13—22no—
71C2×D13#9911yescharacteristic
72C2×D13#9911yescharacteristic
73C4×C13—22no—
74C4×C13—21no—
75C4×C13—22no—
76C4×C13—41no—
77Dic13—22no—
78Dic13—22no—
79Dic13—21no—
80Dic13—41no—
81C22×Q8—131no—
82C22×Q8—131no—
83C2×M16—262no—
84C4⋊Q8—131no—
85C4⋊Q8—131no—
86C4⋊Q8—131no—
87C4⋊Q8—262no—
88C4⋊Q8#26111yescharacteristic
89C2×C4⋊C4—262no—
90C2×C42—131no—
91#101—134no—
92#101—262no—
93C2×C13—21no—
94C2×C13C2×#9911yescharacteristic
95D13—21no—
96D13#35612yescomplemented
97C2×Q8—132no—
98C2×Q8—131no—
99C2×Q8—131no—
100C2×Q8—261no—
101C2×Q8—521no—
102C2×Q8—521no—
103C2×Q8—521no—
104C2×Q8—521no—
105C2×Q8C2×#26111yescharacteristic
106C2×Q8C2×#26111yescharacteristic
107C22×C4—132no—
108C22×C4—131no—
109C22×C4—261no—
110C22×C4—261no—
111M16—264no—
112M16—522no—
113C2×C8—522no—
114C4⋊C4—22no—
115C4⋊C4—262no—
116C4⋊C4—262no—
117C4⋊C4—262no—
118C42—131no—
119C42—261no—
120C42C2×#26111yescharacteristic
121C13C2×#35611yescharacteristic, complemented, Sylow
122C23—131no—
123Q8—41no—
124Q8—41no—
125Q8—522no—
126Q8—521no—
127Q8—521no—
128Q8—522no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—131no—
132C2×C4—132no—
133C2×C4—262no—
134C2×C4—262no—
135C2×C4—261no—
136C2×C4—261no—
137C2×C4—264no—
138C2×C4—261no—
139C2×C4—261no—
140C2×C4—521no—
141C2×C4—521no—
142C2×C4C22⋊#26112yes—
143C2×C4C22×#26111yescharacteristic
144C8—524no—
145C22—131no—
146C22—131no—
147C22—262no—
148C22C2×C22⋊#26111yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—262no—
154C4—262no—
155C4—261no—
156C4—521no—
157C2—21no—
158C2—132no—
159C2—261no—
160C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC2×C13C2×#99
prime radicalC22×D13C22⋊C4
cosocleC2×Dic26C23
hypercenterC4⋊Q8#261
hypocenterC13C2×#356
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11718301C2semidirect
4. #11718227C2semidirect
96. D13#356semidirect
121. C13C2×#356semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
D13⋊#1012
#117183012
#117182272
C2×#35613