Finite Group Databasebeta

← #13130255

Subgroups — #13130255

Order 1664.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#11719061C211yesmaximal, characteristic, complemented
3#11719054C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal, complemented
5#11718240C212yesmaximal, complemented
6C2×#6127—21no—
7C4×D4×C13C411yescharacteristic, complemented
8#88194C411yescharacteristic, complemented
9#88192C2211yescharacteristic
10C4×C22⋊D13—21no—
11#88149C2211yescharacteristic
12#88142C411yescharacteristic, complemented
13#88139—21no—
14#88138—21no—
15C4×D52C411yescharacteristic, complemented
16C42×D13C2211yescharacteristic
17(C2×#261)⋊C4—21no—
18(C2×#261)⋊C4—21no—
19(C2×#261)⋊C4C2212yes—
20#88111C2212yes—
21#88110—21no—
22C4⋊#1057—21no—
23C22×#261—22no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13—21no—
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28C2×C22⋊D13—21no—
29#6127—44no—
30C2×D52—21no—
31C2×D52C2×C411yescharacteristic
32C2×C4×D13—21no—
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13C2311yescharacteristic
36C2×Dic26—21no—
37C2×#1057—22no—
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C22⋊C4—21no—
40C42×C13C2×C411yescharacteristic
41C22⋊Dic13—21no—
42#6103—21no—
43#6103—21no—
44C4⋊Dic13C2×C411yescharacteristic
45#6101—21no—
46C4×Dic13C2×C411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49#1514—131nomaximal, Sylow
50C23×C13—21no—
51C22×D13—21no—
52C22×D13C2×D411yescharacteristic
53C2×#261—42no—
54C2×#261—42no—
55C2×#261—42no—
56D4×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13—42no—
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22⋊C411yescharacteristic
61C2×C4×C13C22×C411yescharacteristic
62C22⋊D13—42no—
63C22⋊D13—42no—
64C22⋊D13—42no—
65C2×Dic13—21no—
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C2×Dic13C2×D411yescharacteristic
69D52—41no—
70D52—42no—
71C4×D13—22no—
72C4×D13—41no—
73C4×D13—41no—
74C4×D13—42no—
75Dic26—42no—
76#1057—42no—
77#532—131no—
78#432—131no—
79#383—131no—
80#327—132no—
81#327—132no—
82C22×C13—41no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13C2×C22⋊C411yescharacteristic
86C2×D13—21no—
87C2×D13—21no—
88C2×D13—41no—
89C2×D13—41no—
90C2×D13—41no—
91C2×D13AGL(1,ℤ/8)12yes—
92#261—82no—
93C4×C13—21no—
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—41no—
97Dic13—21no—
98Dic13—21no—
99Dic13—21no—
100Dic13—41no—
101C2×#41—261no—
102C4⋊Q8—131no—
103#127—131no—
104#124—261no—
105#121—131no—
106#121—131no—
107#121—261no—
108C4×D4—131no—
109C4×D4—261no—
110C4×D4#26111yescharacteristic, complemented
111C2×C42—131no—
112C4⋊C8—261no—
113C22⋊C8—132no—
114#97—261no—
115#95—132no—
116#95—261no—
117#95—261no—
118C2×C13—81no—
119C2×C13#41011yescharacteristic
120C2×C13#41811yescharacteristic
121C2×C13#42111yescharacteristic
122D13—22no—
123D13—81no—
124#41—524no—
125C2×Q8—261no—
126C2×D4—131no—
127C2×D4—261no—
128C2×D4—261no—
129C2×D4—261no—
130C2×D4—261no—
131C2×D4C2×#26111yescharacteristic
132C22×C4—21no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—261no—
137C22×C4—262no—
138C2×C8—262no—
139C4⋊C4—131no—
140C4⋊C4—261no—
141C4⋊C4C2×#26111yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—261no—
144C22⋊C4—261no—
145C22⋊C4—261no—
146C42—131no—
147C42—131no—
148C42—131no—
149C42C2×#26111yescharacteristic
150C13#151411yescharacteristic, complemented, Sylow
151C23—21no—
152C23—131no—
153C23—261no—
154Q8—522no—
155D4—41no—
156D4—521no—
157D4—522no—
158D4—522no—
159D4—522no—
160D4—522no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—131no—
164C2×C4—131no—
165C2×C4—131no—
166C2×C4—262no—
167C2×C4—261no—
168C2×C4—521no—
169C2×C4—521no—
170C2×C4—522no—
171C2×C4—522no—
172C2×C4—522no—
173C2×C4—522no—
174C2×C4C22⋊#26111yescharacteristic
175C2×C4C22⋊#26111yescharacteristic
176C2×C4C22×#26111yescharacteristic
177C8—522no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—132no—
182C22—261no—
183C22—261no—
184C22—521no—
185C22—521no—
186C22—521no—
187C22C2×C22⋊#26111yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—261no—
193C4—261no—
194C4—261no—
195C4—521no—
196C4—1042no—
197C2—81no—
198C2—262no—
199C2—1041no—
200C2#1171911611yescharacteristic
201C2#1171913811yescharacteristic
202C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radical#11719253C2
cosocleC2×C4×D13C23
hypercenterC4×D4#261
hypocenterC13#1514
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. #11719061C2semidirect
3. #11719054C2semidirect
4. #11718292C2semidirect
5. #11718240C2semidirect
7. C4×D4×C13C4semidirect
8. #88194C4semidirect
12. #88142C4semidirect
15. C4×D52C4semidirect
110. C4×D4#261semidirect
150. C13#1514semidirect

Maximal subgroups

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

subgroupindex
#117192532
#117190612
#117190542
#117182922
#117182402
#151413