Finite Group Databasebeta

← #13131116

Subgroups — #13131116

Order 1664.

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

normal subgroups only

This group has 270 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#11719379C211yesmaximal, characteristic
2#11719156C212yesmaximal, complemented
3#11718294C212yesmaximal, complemented
4#11718225C212yesmaximal, complemented
5C2×#6131C2211yescharacteristic
6C2×D4×D13C411yescharacteristic, complemented
7#88237—22no—
8C13×#124C411yescharacteristic, complemented
9#88201C411yescharacteristic, complemented
10#88194C2211yescharacteristic
11#88138—22no—
12#88136—22no—
13#88128C2211yescharacteristic
14#88126C411yescharacteristic, complemented
15#88107—22no—
16#88107C2214yescomplemented
17C23×D13—21no—
18C2×Q8×C13C2×C411yescharacteristic
19C2×D4×C13C2×C411yescharacteristic
20C2×C22⋊D13—22no—
21C2×C22⋊D13—21no—
22#6131—42no—
23D4×D13—42no—
24C2×D52—22no—
25C2×D52C2×C411yescharacteristic
26C2×D52D412yes—
27C2×D52C2311yescharacteristic
28C2×C4×D13C2×C411yescharacteristic
29C2×C4×D13D412yes—
30C22⋊#261—24no—
31C4⋊#261—42no—
32C4×#261—42no—
33C13×C22⋊C4—22no—
34C42×C13C2×C411yescharacteristic
35#6103—21no—
36#6103—22no—
37#6101—21no—
38C4×Dic13C2×C411yescharacteristic
39#2128—131nomaximal, Sylow
40C23×C13—21no—
41C22×D13—21no—
42C22×D13—42no—
43C22×D13—82no—
44C22×D13C22⋊C411yescharacteristic
45C22×D13C2×D412yes—
46C2×#261—44no—
47Q8×C13—41no—
48D4×C13—41no—
49C2×C4×C13—21no—
50C2×C4×C13C22⋊C412yes—
51C2×C4×C13C22×C411yescharacteristic
52C22⋊D13—42no—
53C22⋊D13—82no—
54C2×Dic13—21no—
55C2×Dic13C22⋊C411yescharacteristic
56D52—42no—
57D52—41no—
58D52—41no—
59D52—82no—
60C4×D13—22no—
61C4×D13—22no—
62C4×D13—22no—
63#535—131no—
64#410—132no—
65#353—132no—
66#353—132no—
67C22×C13—42no—
68C22×C13—41no—
69C22×C13C2×C22⋊C411yescharacteristic
70C2×D13—22no—
71C2×D13—21no—
72C2×D13—42no—
73C2×D13—41no—
74C2×D13—42no—
75C2×D13—41no—
76C2×D13—84no—
77#261—84no—
78C4×C13—21no—
79C4×C13—22no—
80C4×C13—41no—
81Dic13—41no—
82Dic13#9912yes—
83C2×#41—131no—
84C22×D4—131no—
85#127—131no—
86#127—131no—
87#124—131no—
88#124#26111yescharacteristic, complemented
89#121—262no—
90#120—262no—
91#117—131no—
92#117—262no—
93#99—134no—
94#99—262no—
95C2×C13—21no—
96C2×C13—81no—
97C2×C13C2×#9911yescharacteristic
98D13—42no—
99D13—41no—
100D13—81no—
101C24—261no—
102#41—522no—
103C2×Q8C2×#26111yescharacteristic
104C2×D4—132no—
105C2×D4—131no—
106C2×D4—131no—
107C2×D4—262no—
108C2×D4—261no—
109C2×D4—262no—
110C2×D4—522no—
111C2×D4C2×#26111yescharacteristic
112C22×C4—132no—
113C22×C4—131no—
114C4⋊C4—261no—
115C4⋊C4—522no—
116C22⋊C4—22no—
117C22⋊C4—261no—
118C22⋊C4—262no—
119C22⋊C4—264no—
120C42—131no—
121C42—522no—
122C42C2×#26111yescharacteristic
123C13#212811yescharacteristic, complemented, Sylow
124C23—21no—
125C23—132no—
126C23—131no—
127C23—261no—
128C23—522no—
129C23—1042no—
130Q8—41no—
131D4—41no—
132D4—522no—
133D4—521no—
134D4—521no—
135D4—522no—
136D4—1042no—
137D4—1042no—
138C2×C4—21no—
139C2×C4—131no—
140C2×C4—262no—
141C2×C4—262no—
142C2×C4—262no—
143C2×C4—261no—
144C2×C4—524no—
145C2×C4C22⋊#26112yes—
146C2×C4C22×#26111yescharacteristic
147C22—42no—
148C22—41no—
149C22—262no—
150C22—261no—
151C22—522no—
152C22—521no—
153C22—522no—
154C22—521no—
155C22—1044no—
156C22C2×C22⋊#26111yescharacteristic
157C4—22no—
158C4—21no—
159C4—41no—
160C4—132no—
161C4—521no—
162C4—1044no—
163C2—21no—
164C2—81no—
165C2—522no—
166C2—521no—
167C2—1041no—
168C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC2×C13C2×#99
prime radical#11719379C2
cosocleC2×D52C23
hypercenter#124#261
hypocenterC13#2128
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11719156C2semidirect
3. #11718294C2semidirect
4. #11718225C2semidirect
6. C2×D4×D13C4semidirect
8. C13×#124C4semidirect
9. #88201C4semidirect
14. #88126C4semidirect
16. #88107C22semidirect
88. #124#261semidirect
123. C13#2128semidirect

Maximal subgroups

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

subgroupindex
#117193792
#117191562
#117182942
#117182252
#212813