Finite Group Databasebeta

← #16777732

Subgroups — #16777732

Order 3328.

302 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 38 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#13129760C212yesmaximal
2#13114910C211yesmaximal, characteristic
3C22×C13×C22⋊C4C411yescharacteristic
4#11718908C411yescharacteristic
5#11718908C2211yescharacteristic
6#11718305—22no—
7#11718118—22no—
8C25×C13C2×C411yescharacteristic
9C23×C4×C13—21no—
10C2×C13×C22⋊C4—21no—
11C2×C13×C22⋊C4—41no—
12C2×C13×C22⋊C4—41no—
13C2×C13×C22⋊C4C812yescomplemented
14C2×C22⋊Dic13—21no—
15C2×C22⋊Dic13—41no—
16C2×C22⋊Dic13—41no—
17C2×C22⋊Dic13D412yes—
18C22⋊#1057—42no—
19#7349—131nomaximal, Sylow
20C24×C13—21no—
21C24×C13—21no—
22C24×C13—42no—
23C24×C13—82no—
24C24×C13C22⋊C411yescharacteristic
25C24×C13C2×C811yescharacteristic
26C24×C13M1611yescharacteristic
27C22×C4×C13—22no—
28C22×C4×C13—41no—
29C22×C4×C13—41no—
30C22×C4×C13—82no—
31C22×Dic13—22no—
32C22×Dic13—41no—
33C2×#1057—82no—
34C13×C22⋊C4—41no—
35C13×C22⋊C4—41no—
36C13×C22⋊C4—42no—
37C22⋊Dic13—42no—
38C22⋊Dic13—42no—
39C22⋊Dic13—82no—
40C22⋊Dic13—82no—
41#1819—131no—
42#1316—132no—
43C23×C13—21no—
44C23×C13—22no—
45C23×C13—21no—
46C23×C13—42no—
47C23×C13—41no—
48C23×C13—42no—
49C23×C13—42no—
50C23×C13—42no—
51C23×C13—41no—
52C23×C13—42no—
53C23×C13—81no—
54C23×C13—81no—
55C23×C13—81no—
56C23×C13—81no—
57C23×C13—84no—
58C23×C13—84no—
59C23×C13C22⋊C811yescharacteristic
60C23×C13#9911yescharacteristic
61C23×C13#10011yescharacteristic
62C2×C4×C13—42no—
63C2×C4×C13—82no—
64C2×C4×C13—82no—
65C2×C4×C13—82no—
66C2×Dic13—42no—
67C2×Dic13—82no—
68C2×Dic13—81no—
69C2×Dic13—82no—
70#1057—162no—
71C22×C22⋊C4#26111yescharacteristic
72#379—131no—
73#379—131no—
74#342—262no—
75#323—262no—
76C22×C13—22no—
77C22×C13—21no—
78C22×C13—21no—
79C22×C13—41no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13—41no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13—42no—
86C22×C13—42no—
87C22×C13—41no—
88C22×C13—41no—
89C22×C13—82no—
90C22×C13—84no—
91C22×C13—84no—
92C22×C13—82no—
93C22×C13#32311yescharacteristic
94C22×C13#35212yes—
95C4×C13—82no—
96Dic13—82no—
97Dic13—161no—
98C25C2×#26111yescharacteristic
99C23×C4—21no—
100C2×C22⋊C4—21no—
101C2×C22⋊C4—41no—
102C2×C22⋊C4—41no—
103C2×C22⋊C4—132no—
104C2×C22⋊C4—261no—
105C2×C22⋊C4—521no—
106C2×C22⋊C4—521no—
107C2×C22⋊C4#105712yescomplemented
108C22⋊C8—522no—
109C2×C13—22no—
110C2×C13—21no—
111C2×C13—41no—
112C2×C13—42no—
113C2×C13—41no—
114C2×C13—81no—
115C2×C13#131711yescharacteristic
116C24—21no—
117C24—21no—
118C24—42no—
119C24—82no—
120C24C2×#105711yescharacteristic
121C24#612211yescharacteristic
122C24C22⋊#26111yescharacteristic
123C22×C4—22no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4—82no—
127C22×C4—262no—
128C22×C4—521no—
129C2×C8—1042no—
130C22⋊C4—41no—
131C22⋊C4—41no—
132C22⋊C4—42no—
133C22⋊C4—522no—
134C22⋊C4—522no—
135C22⋊C4—1042no—
136C22⋊C4—1042no—
137C13#734911yescharacteristic, complemented, Sylow
138C23—21no—
139C23—22no—
140C23—21no—
141C23—42no—
142C23—41no—
143C23—42no—
144C23—42no—
145C23—42no—
146C23—41no—
147C23—42no—
148C23—81no—
149C23—81no—
150C23—81no—
151C23—81no—
152C23—84no—
153C23—84no—
154C23#8811911yescharacteristic
155C23C22⋊#105711yescharacteristic
156C23#8812111yescharacteristic
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—82no—
161C2×C4—522no—
162C2×C4—1042no—
163C2×C4—1041no—
164C2×C4—1042no—
165C8—2082no—
166C22—22no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22—82no—
180C22—84no—
181C22—84no—
182C22—82no—
183C22#1171828812yes—
184C22#1171830511yescharacteristic
185C4—82no—
186C4—1042no—
187C4—2081no—
188C2—21no—
189C2—22no—
190C2—41no—
191C2—42no—
192C2—41no—
193C2—81no—
194C2#1312976211yescharacteristic
subgroupG/H
centerC2#13129762
commutatorC24×C13C2×C8
FrattiniC25C2×#261
FittingC22×C13×C22⋊C4C4
socleC2×C13#1317
prime radicalC25×C13C2×C4
cosocle#11718908C22
hypercenterC22×C22⋊C4#261
hypocenterC13#7349
LCSG ▷ C24×C13 ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
13. C2×C13×C22⋊C4C8semidirect
107. C2×C22⋊C4#1057semidirect
137. C13#7349semidirect

Maximal subgroups

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

subgroupindex
#131297602
#131149102
#734913