Finite Group Databasebeta

← #13131108

Subgroups — #13131108

Order 1664.

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

normal subgroups only

This group has 258 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#11719373C211yesmaximal, characteristic
2#11719156C212yesmaximal, complemented
3#11718294C212yesmaximal, complemented
4#11718226C212yesmaximal, complemented
5C2×#6131C2211yescharacteristic
6C2×#6129C411yescharacteristic, complemented
7#88237—22no—
8C13×#124C411yescharacteristic, complemented
9#88198C411yescharacteristic, complemented
10#88194C2211yescharacteristic
11#88138—22no—
12#88135—22no—
13#88129C2211yescharacteristic
14C42×D13C411yescharacteristic, complemented
15#88107—22no—
16#88107C2214yes—
17C2×Q8×C13C2×C411yescharacteristic
18C2×D4×C13C2×C411yescharacteristic
19C2×C22⋊D13—21no—
20C2×C22⋊D13—22no—
21C22×Dic13—21no—
22#6131—41no—
23#6131—41no—
24#6129—41no—
25#6129—41no—
26C2×D52D412yes—
27C2×D52C2311yescharacteristic
28C2×C4×D13—21no—
29C2×C4×D13C2×C411yescharacteristic
30C2×C4×D13D412yes—
31C2×Dic26C2×C411yescharacteristic
32C22⋊#261—24no—
33C4⋊#261—42no—
34C4×#261—42no—
35C13×C22⋊C4—22no—
36C42×C13C2×C411yescharacteristic
37#6103—22no—
38#6101—22no—
39C4×Dic13—21no—
40C4×Dic13C2×C411yescharacteristic
41#2126—131nomaximal, Sylow
42C23×C13—21no—
43C22×D13C22⋊C411yescharacteristic
44C22×D13C2×D412yes—
45C2×#261—44no—
46Q8×C13—41no—
47D4×C13—41no—
48C2×C4×C13—21no—
49C2×C4×C13C22⋊C412yes—
50C2×C4×C13C22×C411yescharacteristic
51C22⋊D13—44no—
52C22⋊D13—42no—
53C2×Dic13—21no—
54C2×Dic13—21no—
55C2×Dic13—41no—
56C2×Dic13—41no—
57C2×Dic13C22⋊C411yescharacteristic
58D52—42no—
59D52—41no—
60C4×D13—22no—
61C4×D13—22no—
62C4×D13—21no—
63C4×D13—21no—
64C4×D13—42no—
65Dic26—41no—
66#532—131no—
67#410—132no—
68#354—132no—
69#353—132no—
70C22×C13—42no—
71C22×C13—41no—
72C22×C13C2×C22⋊C411yescharacteristic
73C2×D13—21no—
74C2×D13—22no—
75C2×D13—41no—
76C2×D13—42no—
77#261—84no—
78C4×C13—21no—
79C4×C13—22no—
80C4×C13—41no—
81Dic13—22no—
82Dic13—41no—
83Dic13#9911yescharacteristic
84Dic13#9911yescharacteristic
85C2×#41—131no—
86C2×#41—131no—
87C4⋊Q8—131no—
88#127—131no—
89#124—131no—
90#124#26111yescharacteristic, complemented
91#121—262no—
92C4×D4—262no—
93#117—262no—
94C2×C42—131no—
95#99—134no—
96#99—262no—
97C2×C13—21no—
98C2×C13—81no—
99C2×C13C2×#9911yescharacteristic
100D13—42no—
101D13—41no—
102#41—521no—
103#41—521no—
104#41—521no—
105#41—521no—
106C2×Q8—131no—
107C2×Q8C2×#26111yescharacteristic
108C2×D4—132no—
109C2×D4—131no—
110C2×D4—262no—
111C2×D4—261no—
112C2×D4C2×#26111yescharacteristic
113C22×C4—132no—
114C22×C4—131no—
115C22×C4—261no—
116C22×C4—261no—
117C4⋊C4—262no—
118C4⋊C4—522no—
119C22⋊C4—22no—
120C22⋊C4—262no—
121C22⋊C4—264no—
122C42—131no—
123C42—261no—
124C42—522no—
125C42C2×#26111yescharacteristic
126C13#212611yescharacteristic, complemented, Sylow
127C23—21no—
128C23—132no—
129C23—131no—
130Q8—41no—
131Q8—521no—
132D4—41no—
133D4—522no—
134D4—521no—
135D4—524no—
136D4—522no—
137C2×C4—21no—
138C2×C4—131no—
139C2×C4—262no—
140C2×C4—262no—
141C2×C4—261no—
142C2×C4—261no—
143C2×C4—261no—
144C2×C4—261no—
145C2×C4—522no—
146C2×C4—521no—
147C2×C4—521no—
148C2×C4—524no—
149C2×C4C22⋊#26112yes—
150C2×C4C22×#26111yescharacteristic
151C22—42no—
152C22—41no—
153C22—262no—
154C22—261no—
155C22—521no—
156C22—522no—
157C22C2×C22⋊#26111yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—131no—
162C4—131no—
163C4—262no—
164C4—521no—
165C4—1044no—
166C2—21no—
167C2—81no—
168C2—522no—
169C2—521no—
170C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC2×C13C2×#99
prime radical#11719373C2
cosocleC2×D52C23
hypercenter#124#261
hypocenterC13#2126
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. #11718226C2semidirect
6. C2×#6129C4semidirect
8. C13×#124C4semidirect
9. #88198C4semidirect
14. C42×D13C4semidirect
90. #124#261semidirect
126. C13#2126semidirect

Maximal subgroups

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

subgroupindex
#117193732
#117191562
#117182942
#117182262
#212613