Finite Group Databasebeta

← #13131128

Subgroups — #13131128

Order 1664.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#11719421C211yesmaximal, characteristic
2#11719148C212yesmaximal, complemented
3#11718295C212yesmaximal, complemented
4#11718227C212yesmaximal, complemented
5C2×#6129C411yescharacteristic
6C2×#6129C2211yescharacteristic
7C2×#6122—22no—
8C13×#127C411yescharacteristic
9#88192—22no—
10#88190C411yescharacteristic
11#88190C2211yescharacteristic
12D4×Dic13—22no—
13C42×D13C411yescharacteristic
14#88123C2211yescharacteristic
15#88121—22no—
16#88113C2214yes—
17C2×D4×C13—22no—
18C2×D4×C13C2×C411yescharacteristic
19C2×D4×C13C2×C411yescharacteristic
20C2×C22⋊D13—21no—
21C2×C22⋊D13D412yes—
22C22×Dic13—21no—
23C22×Dic13D412yes—
24#6129—41no—
25#6129—41no—
26#6129—41no—
27#6129—41no—
28C2×C4×D13—21no—
29C2×C4×D13C2×C411yescharacteristic
30C2×Dic26C2×C411yescharacteristic
31C2×Dic26C2311yescharacteristic
32#6122—24no—
33#6122—42no—
34C2×#1057—42no—
35C42×C13C2×C411yescharacteristic
36C22⋊Dic13—22no—
37C22⋊Dic13—22no—
38C4⋊Dic13—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic
41#2132—131nomaximal, Sylow
42C23×C13—21no—
43C23×C13C22⋊C412yes—
44C22×D13C22⋊C411yescharacteristic
45D4×C13—41no—
46D4×C13—44no—
47D4×C13—41no—
48C2×C4×C13—21no—
49C2×C4×C13C22×C411yescharacteristic
50C22⋊D13—42no—
51C22⋊D13—42no—
52C2×Dic13—22no—
53C2×Dic13—22no—
54C2×Dic13—21no—
55C2×Dic13—21no—
56C2×Dic13—41no—
57C2×Dic13—41no—
58C2×Dic13C22⋊C411yescharacteristic
59C2×Dic13C2×D412yes—
60C4×D13—21no—
61C4×D13—21no—
62C4×D13—42no—
63Dic26—41no—
64Dic26—41no—
65#1057—44no—
66#532—131no—
67#413—132no—
68#356—132no—
69#355—132no—
70C22×C13—22no—
71C22×C13—42no—
72C22×C13—42no—
73C22×C13—41no—
74C22×C13C2×C22⋊C411yescharacteristic
75C2×D13—21no—
76C2×D13—41no—
77C4×C13—22no—
78C4×C13—21no—
79Dic13—22no—
80Dic13—41no—
81Dic13—41no—
82Dic13#9911yescharacteristic
83Dic13#9911yescharacteristic
84C2×#41—131no—
85C2×#41—131no—
86C2×M16—262no—
87C4⋊Q8—131no—
88#127#26111yescharacteristic
89#124—131no—
90#124—131no—
91#121—262no—
92C4×D4—262no—
93C2×C42—131no—
94#101—134no—
95#100—262no—
96C2×C13—21no—
97C2×C13—42no—
98C2×C13—81no—
99C2×C13C2×#9911yescharacteristic
100D13—41no—
101#41—521no—
102#41—521no—
103#41—521no—
104#41—521no—
105C2×Q8—131no—
106C2×Q8—131no—
107C2×D4—22no—
108C2×D4—132no—
109C2×D4—261no—
110C2×D4C2×#26111yescharacteristic
111C2×D4C2×#26111yescharacteristic
112C22×C4—132no—
113C22×C4—131no—
114C22×C4—261no—
115C22×C4—261no—
116M16—264no—
117M16—522no—
118C2×C8—522no—
119C4⋊C4—262no—
120C22⋊C4—262no—
121C22⋊C4—262no—
122C42—131no—
123C42—261no—
124C42C2×#26111yescharacteristic
125C13#213211yescharacteristic, complemented, Sylow
126C23—21no—
127C23—131no—
128C23C22⋊#26112yes—
129Q8—521no—
130Q8—521no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—522no—
135D4—522no—
136C2×C4—21no—
137C2×C4—131no—
138C2×C4—132no—
139C2×C4—261no—
140C2×C4—261no—
141C2×C4—262no—
142C2×C4—262no—
143C2×C4—261no—
144C2×C4—261no—
145C2×C4—522no—
146C2×C4—521no—
147C2×C4—521no—
148C2×C4C22×#26111yescharacteristic
149C8—524no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—261no—
155C22—521no—
156C22C2×C22⋊#26111yescharacteristic
157C4—22no—
158C4—21no—
159C4—131no—
160C4—131no—
161C4—262no—
162C4—521no—
163C4—521no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—521no—
168C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#127C4
socleC2×C13C2×#99
prime radical#11719421C2
cosocleC2×Dic26C23
hypercenter#127#261
hypocenterC13#2132
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11719148C2semidirect
3. #11718295C2semidirect
4. #11718227C2semidirect
125. C13#2132semidirect

Maximal subgroups

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

subgroupindex
#117194212
#117191482
#117182952
#117182272
#213213