Finite Group Databasebeta

← D13×#356 #13116515

Subgroups — D13×#356 #13116515

Order 1664.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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
3C13×#356C211yesmaximal, characteristic, complemented
4#11718140C211yesmaximal, characteristic, complemented
5#11718070C212yesmaximal, complemented
6C2×Q8×D13C411yescharacteristic
7C2×Q8×D13C2211yescharacteristic
8C13×C4⋊Q8C2211yescharacteristic
9#88198C411yescharacteristic
10#88198C2211yescharacteristic
11M16×D13—22no—
12C4⋊C4×D13—22no—
13#88142—22no—
14C42×D13C411yescharacteristic
15#88123C411yescharacteristic
16C13×#101C2212yes—
17#88076C2212yes—
18#88064—22no—
19C2×Q8×C13C2×C411yescharacteristic
20C2×Q8×C13C2311yescharacteristic
21Q8×D13—41no—
22Q8×D13—41no—
23Q8×D13—41no—
24Q8×D13—41no—
25C2×C4×D13—21no—
26C2×C4×D13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D412yes—
29C2×Dic26—21no—
30C2×Dic26C2×C411yescharacteristic
31C2×Dic26C2×C411yescharacteristic
32C2×Dic26D412yes—
33C13×M16—22no—
34C13×C4⋊C4—22no—
35C42×C13C2×C411yescharacteristic
36C4⋊Dic13—22no—
37#6101—22no—
38#6101—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic
41#6099—22no—
42#6094—42no—
43C8×D13—42no—
44C2×#356—131nomaximal, Sylow
45C22×D13C22⋊C411yescharacteristic
46Q8×C13—41no—
47Q8×C13—41no—
48C2×C4×C13—21no—
49C2×C4×C13—21no—
50C2×C4×C13C22×C411yescharacteristic
51C2×C4×C13C2×D412yes—
52C2×Dic13—21no—
53C2×Dic13—21no—
54C2×Dic13C22⋊C411yescharacteristic
55C2×Dic13C22⋊C412yes—
56C4×D13—24no—
57C4×D13—22no—
58C4×D13—22no—
59C4×D13—21no—
60C4×D13—21no—
61C4×D13—41no—
62C4×D13—41no—
63Dic26—41no—
64Dic26—42no—
65Dic26—42no—
66Dic26—41no—
67C8×C13—42no—
68#1055—42no—
69C2×C4⋊Q8—131no—
70C2×#101—132no—
71#356—131no—
72#356—132no—
73#356D1311yescharacteristic, direct product factor
74C22×C13C2×C22⋊C411yescharacteristic
75C2×D13—22no—
76C2×D13#9911yescharacteristic
77C2×D13#9911yescharacteristic
78C4×C13—22no—
79C4×C13—22no—
80C4×C13—21no—
81C4×C13—41no—
82Dic13—22no—
83Dic13—21no—
84Dic13—22no—
85Dic13—41no—
86C22×Q8—131no—
87C22×Q8—131no—
88C2×M16—262no—
89C4⋊Q8—131no—
90C4⋊Q8—131no—
91C4⋊Q8—131no—
92C4⋊Q8—262no—
93C4⋊Q8C2×D1311yescharacteristic
94C2×C4⋊C4—262no—
95C2×C42—131no—
96#101—132no—
97#101—262no—
98#101C2×D1312yes—
99C2×C13—21no—
100C2×C13C2×#9911yescharacteristic
101D13—21no—
102D13#35612yesdirect product factor
103C2×Q8—131no—
104C2×Q8—132no—
105C2×Q8—131no—
106C2×Q8—261no—
107C2×Q8—521no—
108C2×Q8—521no—
109C2×Q8—521no—
110C2×Q8—521no—
111C2×Q8C4×D1311yescharacteristic
112C2×Q8C22×D1311yescharacteristic
113C22×C4—131no—
114C22×C4—132no—
115C22×C4—261no—
116C22×C4—261no—
117M16—22no—
118M16—262no—
119M16—522no—
120C2×C8—522no—
121C4⋊C4—22no—
122C4⋊C4—262no—
123C4⋊C4—262no—
124C4⋊C4—262no—
125C42—131no—
126C42—261no—
127C42C4×D1311yescharacteristic
128C13C2×#35611yescharacteristic, complemented, Sylow
129C23—131no—
130Q8—41no—
131Q8—41no—
132Q8—522no—
133Q8—521no—
134Q8—521no—
135Q8—522no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—131no—
139C2×C4—132no—
140C2×C4—262no—
141C2×C4—262no—
142C2×C4—261no—
143C2×C4—261no—
144C2×C4—264no—
145C2×C4—261no—
146C2×C4—261no—
147C2×C4—521no—
148C2×C4—521no—
149C2×C4C2×C4×D1311yescharacteristic
150C2×C4D4×D1312yes—
151C8—42no—
152C8—522no—
153C22—131no—
154C22—131no—
155C22—262no—
156C22C22⋊C4×D1311yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—41no—
161C4—262no—
162C4—262no—
163C4—261no—
164C4—521no—
165C2—21no—
166C2—132no—
167C2—261no—
168C2D13×#9911yescharacteristic
subgroupG/H
centerC2D13×#99
commutatorC2×C4×C13C22×C4
FrattiniC2×Q8C22×D13
FittingC13×#356C2
socleC2×C13C2×#99
prime radicalC22×D13C22⋊C4
cosocleC2×Q8×C13C23
hypercenter#356D13
hypocenterC13C2×#356
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. C13×#356C2semidirect
4. #11718140C2semidirect
5. #11718070C2semidirect
73. #356D13direct (N × H)
102. D13#356direct (N × H)
128. 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
C13×#3562
#117181402
#117180702
C2×#35613