Finite Group Databasebeta

← #13130367

Subgroups — #13130367

Order 1664.

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

normal subgroups only

This group has 246 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
1#11719253C211yesmaximal, characteristic
2#11719055C211yesmaximal, characteristic, complemented
3#11719053C211yesmaximal, characteristic, complemented
4#11718297C212yesmaximal, complemented
5#11718245C212yesmaximal, complemented
6C2×#6127—21no—
7C2×#6118—21no—
8C4×D4×C13C411yescharacteristic
9#88194C2211yescharacteristic
10#88192C411yescharacteristic
11C4×C22⋊D13—21no—
12#88149C411yescharacteristic
13#88142C2211yescharacteristic
14#88139—21no—
15#88138—21no—
16C4×D52C411yescharacteristic
17C42×D13C2211yescharacteristic
18#88112—21no—
19#88112C2212yes—
20#88112C2212yes—
21#88111—21no—
22#88110—21no—
23C2×D4×C13C2×C411yescharacteristic
24C22×C4×C13—21no—
25C2×C22⋊D13—21no—
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28#6127—44no—
29C2×D52—21no—
30C2×D52C2×C411yescharacteristic
31C2×C4×D13—21no—
32C2×C4×D13C2×C411yescharacteristic
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×Dic26—21no—
36C2×#1057—22no—
37C2×#1057—22no—
38#6118—42no—
39C13×C4⋊C4C2×C411yescharacteristic
40C13×C22⋊C4—21no—
41C42×C13C2×C411yescharacteristic
42C22⋊Dic13—21no—
43#6103—21no—
44#6103—21no—
45C4⋊Dic13C2×C411yescharacteristic
46#6101—21no—
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49C4×Dic13C2311yescharacteristic
50#1557—131nomaximal, Sylow
51C23×C13—21no—
52C22×D13—21no—
53C22×D13C22⋊C411yescharacteristic
54D4×C13—41no—
55C2×C4×C13—21no—
56C2×C4×C13—42no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22×C411yescharacteristic
60C22⋊D13—42no—
61C22⋊D13—42no—
62C22⋊D13—41no—
63C22⋊D13—41no—
64C2×Dic13—21no—
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67C2×Dic13C2×D411yescharacteristic
68D52—41no—
69D52—42no—
70C4×D13—21no—
71C4×D13—22no—
72C4×D13—21no—
73C4×D13—41no—
74C4×D13—42no—
75Dic26—42no—
76#1057—42no—
77#1057—42no—
78#532—131no—
79#432—131no—
80#423—131no—
81#332—132no—
82#331—132no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13—41no—
86C22×C13C2×C22⋊C411yescharacteristic
87C2×D13—21no—
88C2×D13—21no—
89C2×D13—21no—
90C2×D13—41no—
91C2×D13—41no—
92C2×D13—41no—
93C4×C13—21no—
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—41no—
97Dic13—21no—
98Dic13—41no—
99Dic13AGL(1,ℤ/8)11yescharacteristic
100Dic13AGL(1,ℤ/8)12yes—
101Dic13#13711yescharacteristic
102C2×#41—261no—
103C2×M16—261no—
104C4⋊Q8—131no—
105#127—131no—
106#124—261no—
107#121—131no—
108#121—131no—
109#121—261no—
110C4×D4—131no—
111C4×D4—261no—
112C4×D4#26111yescharacteristic
113C2×C42—131no—
114C4⋊C8—132no—
115C4⋊C8—132no—
116C4⋊C8—261no—
117C22⋊C8—261no—
118#97—261no—
119C2×C13—81no—
120C2×C13#41311yescharacteristic
121C2×C13#41711yescharacteristic
122C2×C13#41811yescharacteristic
123D13—41no—
124D13—81no—
125#41—524no—
126C2×Q8—261no—
127C2×D4—131no—
128C2×D4—261no—
129C2×D4—261no—
130C2×D4—261no—
131C2×D4—261no—
132C2×D4C2×#26111yescharacteristic
133C22×C4—21no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—261no—
138M16—522no—
139C2×C8—262no—
140C2×C8—262no—
141C4⋊C4—131no—
142C4⋊C4—261no—
143C4⋊C4C2×#26111yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—261no—
146C22⋊C4—261no—
147C22⋊C4—261no—
148C42—131no—
149C42—131no—
150C42—131no—
151C42C2×#26111yescharacteristic
152C13#155711yescharacteristic, complemented, Sylow
153C23—21no—
154C23—131no—
155C23—261no—
156Q8—522no—
157D4—41no—
158D4—521no—
159D4—522no—
160D4—521no—
161D4—521no—
162D4—522no—
163D4—522no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—131no—
167C2×C4—131no—
168C2×C4—131no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—262no—
172C2×C4—261no—
173C2×C4—521no—
174C2×C4—522no—
175C2×C4C22⋊#26111yescharacteristic
176C2×C4C22⋊#26111yescharacteristic
177C2×C4C22×#26111yescharacteristic
178C8—522no—
179C8—522no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—261no—
184C22—261no—
185C22—261no—
186C22—521no—
187C22—521no—
188C22—521no—
189C22C2×C22⋊#26111yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—132no—
195C4—131no—
196C4—131no—
197C4—261no—
198C4—521no—
199C2—81no—
200C2—521no—
201C2—1041no—
202C2#1171913211yescharacteristic
203C2#1171913811yescharacteristic
204C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radical#11719253C2
cosocleC4×Dic13C23
hypercenterC4×D4#261
hypocenterC13#1557
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11719055C2semidirect
3. #11719053C2semidirect
4. #11718297C2semidirect
5. #11718245C2semidirect
152. C13#1557semidirect

Maximal subgroups

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

subgroupindex
#117192532
#117190552
#117190532
#117182972
#117182452
#155713