Finite Group Databasebeta

← #16777558

Subgroups — #16777558

Order 3328.

402 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C4×#88107C212yesmaximal
2#13115634C211yesmaximal, characteristic
3C2×C4×D52C2211yescharacteristic
4C4×C22⋊#261—22no—
5C2×#88107—22no—
6C2×C13×#97C411yescharacteristic, complemented
7C2×#88060—22no—
8C2×C4⋊#1055C411yescharacteristic, complemented
9#11718289C414yescomplemented
10C22×D52D411yescharacteristic
11C22×C4×D13D412yes—
12C2×C22⋊#261—24no—
13C2×C4×#261—42no—
14C22×C8×C13—21no—
15C2×C42×C13C2×C411yescharacteristic
16C2×#6103C2×C412yes—
17C2×C4⋊Dic13Q811yescharacteristic
18C22×#1055—21no—
19C4×D52—41no—
20C4×D52—41no—
21(C2×#261)⋊C4—42no—
22#88107—28no—
23C13×#97—41no—
24#88060—44no—
25C4⋊#1055—41no—
26#7283—131nomaximal, Sylow
27C23×D13C22⋊C412yes—
28C22×#261—44no—
29C22×C4×C13C4211yescharacteristic
30C22×C4×C13C22⋊C411yescharacteristic
31C22×C4×C13C4⋊C411yescharacteristic
32C22×Dic13C4⋊C412yes—
33C2×D52—24no—
34C2×D52—41no—
35C2×C4×D13—22no—
36C2×C4×D13—22no—
37C2×C4×D13—42no—
38C2×C4×D13—42no—
39C22⋊#261—28no—
40C22⋊#261—44no—
41C4×#261—82no—
42C4×#261—82no—
43C2×C8×C13—22no—
44C2×C8×C13—41no—
45C2×C8×C13—41no—
46C42×C13—21no—
47C42×C13—21no—
48#6103—42no—
49C4⋊Dic13—41no—
50C2×#1055—42no—
51C2×#1055—41no—
52#1955—131no—
53C4×#99—132no—
54C23×C13#9511yescharacteristic
55C22×D13—22no—
56C22×D13—22no—
57C22×D13—42no—
58C22×D13—42no—
59C22×D13#10414yes—
60C2×#261—48no—
61C2×#261—84no—
62C2×#261—84no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—41no—
69C2×C4×C13#9911yescharacteristic
70C2×C4×C13#9911yescharacteristic
71C2×Dic13—22no—
72C2×Dic13—42no—
73D52—44no—
74C4×D13—42no—
75C4×D13—42no—
76C4×D13—82no—
77C8×C13—42no—
78#1055—81no—
79C2×C4×D4—131no—
80C2×C4⋊C8—131no—
81C2×#99—262no—
82C2×C22⋊C8—262no—
83C2×#97#26111yescharacteristic, complemented
84C4×C22⋊C4—262no—
85#342—134no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13#33912yes—
89C22×C13#34211yescharacteristic
90C2×D13—24no—
91C2×D13—42no—
92C2×D13—42no—
93C2×D13—44no—
94C2×D13—82no—
95#261—88no—
96C4×C13—21no—
97C4×C13—41no—
98C4×C13—41no—
99C4×C13#35311yescharacteristic
100C4×C13#35411yescharacteristic
101Dic13—42no—
102C22×D4—131no—
103C23×C4—132no—
104C22×C8—21no—
105C22×C8—261no—
106C4×D4—521no—
107C4×D4—521no—
108C2×C4⋊C4—131no—
109C2×C22⋊C4—132no—
110C2×C22⋊C4—264no—
111C2×C42—522no—
112C2×C42C2×#26111yescharacteristic
113C4⋊C8—521no—
114#99—268no—
115C22⋊C8—524no—
116#97—41no—
117#95—522no—
118C2×C13—22no—
119C2×C13#129711yescharacteristic
120C2×C13#139111yescharacteristic
121C2×C13#139311yescharacteristic
122D13—44no—
123C24—132no—
124C2×D4—264no—
125C2×D4—521no—
126C22×C4—132no—
127C22×C4—262no—
128C22×C4—262no—
129C22×C4—522no—
130C22×C4—522no—
131C22×C4—524no—
132C22×C4C4×#26111yescharacteristic
133C22×C4C4⋊#26111yescharacteristic
134C22×C4C22⋊#26111yescharacteristic
135C2×C8—22no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—522no—
139C2×C8—521no—
140C4⋊C4—521no—
141C22⋊C4—268no—
142C22⋊C4—522no—
143C22⋊C4—524no—
144C42—21no—
145C42—21no—
146C42—1042no—
147C42—1042no—
148C13#728311yescharacteristic, complemented, Sylow
149C23—134no—
150C23—262no—
151C23—262no—
152C23—522no—
153C23—522no—
154C23(C2×#261)⋊C411yescharacteristic
155D4—524no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—262no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4—528no—
167C2×C4—1042no—
168C2×C4—1044no—
169C2×C4—1044no—
170C2×C4#8810711yescharacteristic
171C2×C4#8811911yescharacteristic
172C8—42no—
173C8—1041no—
174C22—21no—
175C22—21no—
176C22—264no—
177C22—524no—
178C22—522no—
179C22—522no—
180C22—1042no—
181C22#1171827212yes—
182C22#1171828911yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—522no—
187C4—1048no—
188C4#1171822511yescharacteristic
189C4#1171822611yescharacteristic
190C2—22no—
191C2—524no—
192C2#1312971611yescharacteristic
193C2#1312992511yescharacteristic
194C2#1312993011yescharacteristic
subgroupG/H
centerC2×C4#88107
commutatorC22×C4×C13C42
FrattiniC2×C42C2×#261
FittingC2×C13×#97C4
socleC22×C13#342
prime radicalC22×D52D4
cosocleC2×C4×D52C22
hypercenterC2×#97#261
hypocenterC13#7283
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
6. C2×C13×#97C4semidirect
8. C2×C4⋊#1055C4semidirect
9. #11718289C4semidirect
83. C2×#97#261semidirect
148. C13#7283semidirect

Maximal subgroups

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

subgroupindex
C4×#881072
#131156342
#728313