Finite Group Databasebeta

← #13114058

Subgroups — #13114058

Order 1664.

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

normal subgroups only

This group has 200 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
1#11719427C211yesmaximal, characteristic
2#11718742C211yesmaximal, characteristic
3#11718512C211yesmaximal, characteristic
4#11718510C211yesmaximal, characteristic
5C13×#333C211yesmaximal, characteristic
6#11718076C211yesmaximal, characteristic
7#11718076C211yesmaximal, characteristic
8C13×C4⋊Q8C2211yescharacteristic
9#88198—22no—
10C2×Dic52—21no—
11#88142—21no—
12#88142—21no—
13#88141—21no—
14#88141—21no—
15#88123C2211yescharacteristic
16C4×Dic26C2211yescharacteristic
17C4×Dic26C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20#88075—22no—
21#88057—21no—
22#88056—21no—
23#88056—21no—
24C4×#1055C2211yescharacteristic
25C2×Q8×C13D412yes—
26C2×Dic26—21no—
27C2×Dic26—22no—
28C2×Dic26D411yescharacteristic
29C2×Dic26D411yescharacteristic
30C2×C8×C13—21no—
31C2×C8×C13—21no—
32C13×C4⋊C4—21no—
33C13×C4⋊C4—21no—
34C42×C13C2311yescharacteristic
35C4⋊Dic13—21no—
36C4⋊Dic13—21no—
37C4⋊Dic13D411yescharacteristic
38C4⋊Dic13D411yescharacteristic
39#6101—22no—
40#6101—22no—
41#6101—21no—
42#6101—21no—
43C4×Dic13—22no—
44C4×Dic13—21no—
45C4×Dic13—21no—
46C2×#1055—21no—
47Dic52—42no—
48#1645—131nomaximal, Sylow
49Q8×C13—42no—
50C2×C4×C13—22no—
51C2×C4×C13C2×D411yescharacteristic
52C2×C4×C13C2×D411yescharacteristic
53C2×C4×C13C2×D411yescharacteristic
54C2×Dic13—21no—
55C2×Dic13—21no—
56C2×Dic13—21no—
57C2×Dic13—21no—
58C2×Dic13—41no—
59Dic26—21no—
60Dic26—21no—
61Dic26—41no—
62Dic26—41no—
63Dic26—82no—
64Dic26SD1612yes—
65Dic26Q1612yescomplemented
66C8×C13—41no—
67C8×C13—41no—
68#1055—41no—
69Q82—131no—
70#487—131no—
71#475—131no—
72#462—131no—
73#333D1311yescharacteristic
74Q8⋊C8—131no—
75Q8⋊C8—131no—
76C22×C13#12011yescharacteristic
77C4×C13—21no—
78C4×C13—42no—
79C4×C13C2×SD1611yescharacteristic
80C4×C13C2×Q1611yescharacteristic
81C4×C13#13711yescharacteristic
82C4×C13#13711yescharacteristic
83Dic13—22no—
84Dic13—22no—
85Dic13—41no—
86Dic13—41no—
87Dic13—81no—
88C2×Q16—261no—
89C4⋊Q8—131no—
90C4⋊Q8—261no—
91C4⋊Q8—261no—
92C4⋊Q8—262no—
93C4⋊Q8C2×D1311yescharacteristic
94C4×Q8—131no—
95C4×Q8—131no—
96C4×Q8—261no—
97C4×Q8—261no—
98#106—261no—
99C4⋊C8C2×D1311yescharacteristic
100C4⋊C8C2×D1311yescharacteristic
101#103—261no—
102#103—261no—
103#103—262no—
104C4×C8—131no—
105C2×C13#44811yescharacteristic
106C2×C13#45111yescharacteristic
107C2×C13#45511yescharacteristic
108C2×Q8—131no—
109C2×Q8—131no—
110C2×Q8—262no—
111C2×Q8—261no—
112C2×Q8D5212yes—
113Q16—522no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—261no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—131no—
120C4⋊C4—131no—
121C4⋊C4—262no—
122C4⋊C4—262no—
123C4⋊C4—261no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C42—262no—
128C42—261no—
129C42—261no—
130C42C22×D1311yescharacteristic
131C13#164511yescharacteristic, complemented, Sylow
132Q8—42no—
133Q8—132no—
134Q8—132no—
135Q8—261no—
136Q8—261no—
137Q8—521no—
138Q8—521no—
139Q8—1042no—
140C2×C4—22no—
141C2×C4—261no—
142C2×C4—261no—
143C2×C4—261no—
144C2×C4—261no—
145C2×C4—521no—
146C2×C4C2×D5211yescharacteristic
147C2×C4D4×D1311yescharacteristic
148C2×C4D4×D1311yescharacteristic
149C8—41no—
150C8—41no—
151C8—521no—
152C22#8813611yescharacteristic
153C4—21no—
154C4—42no—
155C4—262no—
156C4—262no—
157C4—521no—
158C4—521no—
159C4—1041no—
160C4SD16×D1311yescharacteristic
161C4#8816911yescharacteristic
162C4Q16×D1311yescharacteristic
163C4#8817211yescharacteristic
164C2#1171840711yescharacteristic
165C2#1171846711yescharacteristic
166C2#1171846911yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#333C2
socle, prime radicalC22×C13#120
hypercenter#333D13
hypocenterC13#1645
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
65. Dic26Q16semidirect
131. C13#1645semidirect

Maximal subgroups

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

subgroupindex
#117194272
#117187422
#117185122
#117185102
C13×#3332
#117180762
#164513