Finite Group Databasebeta

← #13131136

Subgroups — #13131136

Order 1664.

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

normal subgroups only

This group has 262 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#11719420C211yesmaximal, characteristic
2#11719148C212yesmaximal, complemented
3#11718295C212yesmaximal, complemented
4#11718228C212yesmaximal, complemented
5C2×#6129C2211yescharacteristic
6C2×D4×D13C411yescharacteristic
7C2×#6122—22no—
8C13×#127C411yescharacteristic
9#88194C411yescharacteristic
10#88193—22no—
11#88191—22no—
12#88190C2211yescharacteristic
13#88129C2211yescharacteristic
14#88126C411yescharacteristic
15#88121—22no—
16#88113C2214yescomplemented
17C23×D13—21no—
18C2×D4×C13—22no—
19C2×D4×C13C2×C411yescharacteristic
20C2×D4×C13C2×C411yescharacteristic
21C2×C22⋊D13—22no—
22C2×C22⋊D13—21no—
23C2×C22⋊D13D412yes—
24C22×Dic13D412yes—
25#6129—42no—
26D4×D13—42no—
27C2×D52C2×C411yescharacteristic
28C2×C4×D13C2×C411yescharacteristic
29C2×Dic26C2311yescharacteristic
30#6122—24no—
31#6122—42no—
32C2×#1057—42no—
33C42×C13C2×C411yescharacteristic
34C22⋊Dic13—22no—
35#6103—21no—
36#6103—22no—
37#6101—21no—
38C4×Dic13C2×C411yescharacteristic
39#2134—131nomaximal, Sylow
40C23×C13—21no—
41C23×C13C22⋊C412yes—
42C22×D13—21no—
43C22×D13—42no—
44C22×D13—82no—
45C22×D13C22⋊C411yescharacteristic
46D4×C13—41no—
47D4×C13—41no—
48D4×C13—82no—
49C2×C4×C13—21no—
50C2×C4×C13C22×C411yescharacteristic
51C22⋊D13—42no—
52C22⋊D13—42no—
53C22⋊D13—82no—
54C2×Dic13—22no—
55C2×Dic13—22no—
56C2×Dic13—21no—
57C2×Dic13C22⋊C411yescharacteristic
58C2×Dic13C2×D412yes—
59D52—41no—
60C4×D13—22no—
61Dic26—41no—
62#1057—44no—
63#535—131no—
64#413—132no—
65#355—132no—
66#355—132no—
67C22×C13—22no—
68C22×C13—42no—
69C22×C13—42no—
70C22×C13—41no—
71C22×C13C2×C22⋊C411yescharacteristic
72C2×D13—21no—
73C2×D13—41no—
74C2×D13—42no—
75C2×D13—41no—
76C2×D13—84no—
77C4×C13—21no—
78C4×C13—41no—
79Dic13—22no—
80Dic13—41no—
81Dic13#9912yes—
82C2×#41—131no—
83C22×D4—131no—
84C2×M16—262no—
85#127—131no—
86#127#26111yescharacteristic
87#124—131no—
88#124—131no—
89#121—262no—
90#120—262no—
91#117—131no—
92#101—134no—
93#100—262no—
94C2×C13—21no—
95C2×C13—42no—
96C2×C13—81no—
97C2×C13C2×#9911yescharacteristic
98D13—41no—
99D13—81no—
100C24—261no—
101#41—522no—
102C2×Q8—131no—
103C2×D4—22no—
104C2×D4—132no—
105C2×D4—131no—
106C2×D4—261no—
107C2×D4—262no—
108C2×D4—522no—
109C2×D4C2×#26111yescharacteristic
110C2×D4C2×#26111yescharacteristic
111C22×C4—132no—
112C22×C4—131no—
113M16—264no—
114M16—522no—
115C2×C8—522no—
116C4⋊C4—261no—
117C22⋊C4—262no—
118C22⋊C4—261no—
119C22⋊C4—262no—
120C42—131no—
121C42C2×#26111yescharacteristic
122C13#213411yescharacteristic, complemented, Sylow
123C23—21no—
124C23—131no—
125C23—261no—
126C23—522no—
127C23—1042no—
128C23C22⋊#26112yes—
129Q8—521no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—521no—
134D4—522no—
135D4—522no—
136D4—1042no—
137C2×C4—21no—
138C2×C4—131no—
139C2×C4—132no—
140C2×C4—262no—
141C2×C4—262no—
142C2×C4—262no—
143C2×C4—261no—
144C2×C4C22×#26111yescharacteristic
145C8—524no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—261no—
151C22—521no—
152C22—522no—
153C22—521no—
154C22—1044no—
155C22C2×C22⋊#26111yescharacteristic
156C4—21no—
157C4—41no—
158C4—132no—
159C4—262no—
160C4—521no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—521no—
165C2—1041no—
166C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#127C4
socleC2×C13C2×#99
prime radical#11719420C2
cosocleC2×Dic26C23
hypercenter#127#261
hypocenterC13#2134
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. #11718228C2semidirect
16. #88113C22semidirect
122. C13#2134semidirect

Maximal subgroups

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

subgroupindex
#117194202
#117191482
#117182952
#117182282
#213413