Finite Group Databasebeta

← #13131118

Subgroups — #13131118

Order 1664.

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

normal subgroups only

This group has 238 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#11719521C211yesmaximal, characteristic
2#11719116C212yesmaximal
3#11718300C214yesmaximal, complemented
4C22×Q8×C13C411yescharacteristic, complemented
5C2×#6127C2211yescharacteristic
6#88237—22no—
7#88201C2212yes—
8#88200—22no—
9#88198C412yescomplemented
10#88183—22no—
11#88180C411yescharacteristic, complemented
12#88119—22no—
13#88107C2214yes—
14C2×Q8×C13—21no—
15C2×Q8×C13—42no—
16C2×Q8×C13C2×C412yes—
17C22×C4×C13—21no—
18C22×C4×C13C2×C411yescharacteristic
19C2×C22⋊D13D412yes—
20#6127—42no—
21C2×D52C2311yescharacteristic
22C2×C4×D13D412yes—
23C2×Dic26C2×C411yescharacteristic
24C22⋊#261—24no—
25C4⋊#261—42no—
26C4×#261—42no—
27C22⋊Dic13—21no—
28#6103—24no—
29C4⋊Dic13—21no—
30#6101—24no—
31C4×Dic13C2×C412yes—
32#2129—131nomaximal, Sylow
33C23×C13C22⋊C411yescharacteristic
34C22×D13C2×D412yes—
35C2×#261—44no—
36Q8×C13—42no—
37Q8×C13—42no—
38C2×C4×C13—22no—
39C2×C4×C13—22no—
40C2×C4×C13—42no—
41C2×C4×C13C22⋊C411yescharacteristic
42C2×C4×C13C22×C411yescharacteristic
43C22⋊D13—42no—
44C2×Dic13—22no—
45C2×Dic13C22⋊C412yes—
46D52—41no—
47C4×D13—22no—
48C4×D13—22no—
49Dic26—41no—
50#536—131no—
51#410—132no—
52#354—134no—
53C22×C13—21no—
54C22×C13—41no—
55C22×C13C2×C22⋊C411yescharacteristic
56C2×D13—22no—
57C2×D13—42no—
58#261—84no—
59C4×C13—21no—
60C4×C13—42no—
61C4×C13#9912yes—
62Dic13—22no—
63Dic13—42no—
64C2×#41—131no—
65C22×Q8#26111yescharacteristic, complemented
66C4⋊Q8—132no—
67#124—132no—
68#123—262no—
69C22⋊Q8—262no—
70#117—131no—
71#117—262no—
72#99—134no—
73#99—262no—
74C2×C13—21no—
75C2×C13—41no—
76C2×C13C2×#9911yescharacteristic
77D13—42no—
78#41—522no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—131no—
82C2×Q8C2×#26112yes—
83C2×D4—132no—
84C2×D4—131no—
85C22×C4—21no—
86C22×C4—132no—
87C22×C4C2×#26111yescharacteristic
88C4⋊C4—264no—
89C4⋊C4—261no—
90C4⋊C4—522no—
91C22⋊C4—264no—
92C22⋊C4—261no—
93C22⋊C4—264no—
94C42—132no—
95C42—522no—
96C13#212911yescharacteristic, complemented, Sylow
97C23—132no—
98C23C22⋊#26111yescharacteristic
99Q8—42no—
100Q8—42no—
101Q8—521no—
102D4—521no—
103D4—522no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—42no—
107C2×C4—132no—
108C2×C4—262no—
109C2×C4—262no—
110C2×C4—262no—
111C2×C4—524no—
112C2×C4C22⋊#26111yescharacteristic
113C2×C4C22×#26111yescharacteristic
114C22—21no—
115C22—41no—
116C22—262no—
117C22—522no—
118C22C2×C22⋊#26111yescharacteristic
119C4—21no—
120C4—42no—
121C4—262no—
122C4—522no—
123C4—1044no—
124C4#8811912yes—
125C2—21no—
126C2—41no—
127C2—522no—
128C2C2×#8811911yescharacteristic
subgroupG/H
centerC2C2×#88119
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC22×Q8×C13C4
socleC2×C13C2×#99
prime radicalC2×#6127C22
cosocleC2×D52C23
hypercenterC22×Q8#261
hypocenterC13#2129
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #11718300C2semidirect
4. C22×Q8×C13C4semidirect
9. #88198C4semidirect
11. #88180C4semidirect
65. C22×Q8#261semidirect
96. C13#2129semidirect

Maximal subgroups

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

subgroupindex
#117195212
#117191162
#117183002
#212913