Finite Group Databasebeta

← #13115967

Subgroups — #13115967

Order 1664.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#88183C212yesmaximal, complemented
2#11719198C211yesmaximal, characteristic
3C13×#381C211yesmaximal, characteristic, complemented
4C2×#88046C212yesmaximal, complemented
5#11718118C211yesmaximal, characteristic, complemented
6C23×C4×C13C2211yescharacteristic
7C22×C22⋊D13C2212yes—
8C2×C13×C22⋊C4C2211yescharacteristic
9C2×C13×C22⋊C4C2211yescharacteristic
10C2×C22⋊Dic13C2212yes—
11#88184—22no—
12#88183—24no—
13#88183—24no—
14C2×#6103—22no—
15C2×#6101—22no—
16#88140—22no—
17#88136—22no—
18C13×#95—22no—
19#88046—24no—
20C24×C13C2311yescharacteristic
21C23×D13D412yes—
22C22×C4×C13—21no—
23C22×C4×C13—22no—
24C22×C4×C13—22no—
25C22×C4×C13—21no—
26C22×C4×C13—21no—
27C22×C4×C13D412yes—
28C22×C4×C13D412yescomplemented
29C2×C22⋊D13—22no—
30C2×C22⋊D13—22no—
31C2×C22⋊D13—22no—
32C2×C22⋊D13—22no—
33C2×C22⋊D13—22no—
34C2×C22⋊D13—22no—
35C22×Dic13—22no—
36C22×Dic13D412yes—
37C2×D52—22no—
38C13×C22⋊C4—22no—
39C13×C22⋊C4—22no—
40C22⋊Dic13—22no—
41C22⋊Dic13D414yescomplemented
42#6103—24no—
43#6103—28no—
44C4⋊Dic13—22no—
45#6101—28no—
46#2022—131nomaximal, Sylow
47C23×C13—42no—
48C23×C13C2×D412yes—
49C23×C13C2×D411yescharacteristic
50C23×C13C2×D411yescharacteristic
51C23×C13C2×D412yes—
52C23×C13#4111yescharacteristic
53C22×D13—22no—
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—44no—
57C2×C4×C13—24no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—41no—
61C2×C4×C13—42no—
62C2×C4×C13—41no—
63C2×C4×C13—42no—
64C2×C4×C13—42no—
65C2×C4×C13—41no—
66C22⋊D13—42no—
67C22⋊D13—42no—
68C22⋊D13—42no—
69C22⋊D13—42no—
70C2×Dic13—22no—
71C2×Dic13—24no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—44no—
75D52—82no—
76#534—131no—
77C2×#123—132no—
78C2×#99—132no—
79#381D1311yescharacteristic, complemented
80#342—131no—
81C22×C13—24no—
82C22×C13—22no—
83C22×C13—41no—
84C22×C13—42no—
85C22×C13—41no—
86C22×C13#12012yes—
87C22×C13#12011yescharacteristic
88C22×C13#12112yes—
89C22×C13#12111yescharacteristic
90C22×C13#12711yescharacteristic
91C2×D13—44no—
92C2×D13—42no—
93C2×D13—44no—
94C2×D13—82no—
95C4×C13—42no—
96C4×C13—42no—
97C4×C13—81no—
98Dic13—44no—
99Dic13—42no—
100C22×D4—132no—
101C23×C4C2×D1311yescharacteristic
102#123—262no—
103#123—264no—
104#123—264no—
105#121—262no—
106#120—262no—
107C2×C4⋊C4—262no—
108C2×C22⋊C4—132no—
109C2×C22⋊C4—262no—
110C2×C22⋊C4C2×D1311yescharacteristic
111C2×C22⋊C4C2×D1311yescharacteristic
112#99—264no—
113#95—22no—
114C2×C13—22no—
115C2×C13—21no—
116C2×C13—22no—
117C2×C13—21no—
118C2×C13#39211yescharacteristic
119C2×C13#45812yes—
120D13—82no—
121C24—132no—
122C24C22×D1311yescharacteristic
123C2×D4—262no—
124C2×D4—262no—
125C2×D4—262no—
126C2×D4—262no—
127C2×D4—262no—
128C2×D4—262no—
129C2×D4—262no—
130C22×C4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—132no—
136C22×C4—262no—
137C22×C4D5212yescomplemented
138C22×C4C22⋊D1312yes—
139C4⋊C4—268no—
140C4⋊C4—262no—
141C22⋊C4—22no—
142C22⋊C4—22no—
143C22⋊C4—134no—
144C22⋊C4—268no—
145C22⋊C4—264no—
146C22⋊C4—262no—
147C13#202211yescharacteristic, complemented, Sylow
148C23—42no—
149C23—262no—
150C23—262no—
151C23—262no—
152C23—524no—
153C23C2×D5211yescharacteristic
154C23#612711yescharacteristic
155C23D4×D1312yes—
156C23D4×D1312yes—
157C23C2×C22⋊D1311yescharacteristic
158D4—522no—
159D4—522no—
160D4—522no—
161D4—522no—
162D4—1042no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—264no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—524no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—524no—
183C22—524no—
184C22—522no—
185C22—1042no—
186C22#8813612yes—
187C22#8813812yes—
188C22#8818411yescharacteristic
189C22#8819111yescharacteristic
190C22#8819411yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—524no—
195C4—522no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—1042no—
201C2#1171862111yescharacteristic
202C2#1171871412yes—
subgroupG/H
centerC22#88191
commutator, cosocleC24×C13C23
FrattiniC24C22×D13
FittingC13×#381C2
socleC22×C13#120
prime radical#11719198C2
hypercenter#381D13
hypocenterC13#2022
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#88183C2semidirect
3. C13×#381C2semidirect
4. C2×#88046C2semidirect
5. #11718118C2semidirect
28. C22×C4×C13D4semidirect
41. C22⋊Dic13D4semidirect
79. #381D13semidirect
137. C22×C4D52semidirect
147. C13#2022semidirect

Maximal subgroups

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

subgroupindex
C2×#881832
#117191982
C13×#3812
C2×#880462
#117181182
#202213