Finite Group Databasebeta

← #13131133

Subgroups — #13131133

Order 1664.

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

normal subgroups only

This group has 230 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
1#11719231C211yesmaximal, characteristic
2C2×#88113C212yesmaximal, complemented
3#11718228C212yesmaximal, complemented
4#11718227C212yesmaximal, complemented
5C2×#6127C411yescharacteristic
6C22×Dic26C2211yescharacteristic
7C2×#6122—22no—
8C13×#117C411yescharacteristic
9#88151—22no—
10#88140—22no—
11#88129C411yescharacteristic
12#88129C2211yescharacteristic
13#88123C411yescharacteristic
14#88123C2211yescharacteristic
15#88113—22no—
16#88113C2214yes—
17C22×C4×C13C2×C411yescharacteristic
18C2×C22⋊D13—21no—
19C22×Dic13D412yes—
20#6127—42no—
21C2×D52C2×C411yescharacteristic
22C2×C4×D13—21no—
23C2×Dic26—42no—
24C2×Dic26C2×C411yescharacteristic
25C2×Dic26C2×C411yescharacteristic
26C2×Dic26D412yes—
27C2×Dic26C2311yescharacteristic
28#6122—24no—
29#6122—42no—
30C2×#1057—42no—
31C13×C4⋊C4—21no—
32C13×C22⋊C4—21no—
33C42×C13C2×C411yescharacteristic
34C42×C13C2×C411yescharacteristic
35#6103—22no—
36#6103—22no—
37C4⋊Dic13—22no—
38C4⋊Dic13—22no—
39#2133—131nomaximal, Sylow
40C23×C13C22⋊C411yescharacteristic
41C22×D13—21no—
42C2×C4×C13—22no—
43C2×C4×C13—21no—
44C2×C4×C13—21no—
45C2×C4×C13C22⋊C411yescharacteristic
46C2×C4×C13C22×C411yescharacteristic
47C22⋊D13—42no—
48C2×Dic13—22no—
49C2×Dic13—22no—
50C2×Dic13—21no—
51C2×Dic13C22⋊C412yes—
52C2×Dic13C2×D412yes—
53D52—41no—
54C4×D13—42no—
55Dic26—41no—
56Dic26—42no—
57Dic26—41no—
58Dic26—41no—
59#1057—44no—
60#536—131no—
61C2×#101—132no—
62#356—132no—
63#355—132no—
64C22×C13—41no—
65C22×C13#9912yes—
66C22×C13C2×C22⋊C411yescharacteristic
67C2×D13—42no—
68C2×D13—41no—
69C4×C13—21no—
70C4×C13—21no—
71C4×C13—41no—
72C4×C13—41no—
73Dic13—22no—
74Dic13—22no—
75Dic13—41no—
76C2×#41—131no—
77C22×Q8—131no—
78C2×M16—262no—
79C4⋊Q8—131no—
80C4⋊Q8—131no—
81#124—131no—
82#124—131no—
83#123—262no—
84C22⋊Q8—262no—
85#117#26111yescharacteristic
86#101—134no—
87#101—262no—
88C2×C13—21no—
89C2×C13—22no—
90C2×C13C2×#9911yescharacteristic
91D13—81no—
92#41—522no—
93C2×Q8—132no—
94C2×Q8—131no—
95C2×Q8—131no—
96C2×Q8—131no—
97C2×Q8—522no—
98C2×D4—131no—
99C2×D4—261no—
100C22×C4—132no—
101C22×C4—261no—
102C22×C4C2×#26111yescharacteristic
103M16—264no—
104M16—522no—
105C2×C8—522no—
106C4⋊C4—21no—
107C4⋊C4—262no—
108C4⋊C4—262no—
109C22⋊C4—21no—
110C22⋊C4—262no—
111C22⋊C4—262no—
112C42C2×#26111yescharacteristic
113C42C2×#26111yescharacteristic
114C13#213311yescharacteristic, complemented, Sylow
115C23—261no—
116C23C22⋊#26111yescharacteristic
117Q8—522no—
118Q8—521no—
119Q8—521no—
120Q8—521no—
121D4—521no—
122D4—522no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—132no—
127C2×C4—132no—
128C2×C4—262no—
129C2×C4—262no—
130C2×C4—261no—
131C2×C4—522no—
132C2×C4C22⋊#26111yescharacteristic
133C2×C4C22×#26111yescharacteristic
134C8—524no—
135C22—41no—
136C22—522no—
137C22—521no—
138C22#8810712yes—
139C22C2×C22⋊#26111yescharacteristic
140C4—21no—
141C4—21no—
142C4—41no—
143C4—41no—
144C4—262no—
145C4—262no—
146C4—521no—
147C2—21no—
148C2—22no—
149C2—1041no—
150C2C2×#8810711yescharacteristic
subgroupG/H
centerC2C2×#88107
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#117C4
socleC2×C13C2×#99
prime radicalC2×#6127C4
cosocleC2×Dic26C23
hypercenter#117#261
hypocenterC13#2133
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#88113C2semidirect
3. #11718228C2semidirect
4. #11718227C2semidirect
114. C13#2133semidirect

Maximal subgroups

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

subgroupindex
#117192312
C2×#881132
#117182282
#117182272
#213313