Finite Group Databasebeta

← #13130248

Subgroups — #13130248

Order 1664.

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

normal subgroups only

This group has 222 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#11719385C211yesmaximal, characteristic
2#11719060C211yesmaximal, characteristic, complemented
3#11719054C211yesmaximal, characteristic, complemented
4#11718298C212yesmaximal, complemented
5#11718292C212yesmaximal
6C2×C4⋊#261—21no—
7C13×#124C411yescharacteristic, complemented
8#88200C2211yescharacteristic
9Q8×Dic13C411yescharacteristic, complemented
10#88192C2211yescharacteristic
11D4×Dic13C411yescharacteristic, complemented
12#88137—21no—
13#88135—21no—
14#88133—21no—
15#88131—21no—
16C42×D13C2211yescharacteristic
17#88124C411yescharacteristic, complemented
18(C2×#261)⋊C4—21no—
19(C2×#261)⋊C4C2212yes—
20#88111C2212yes—
21#88110—21no—
22C4⋊#1057—21no—
23C22×#261—22no—
24C2×Q8×C13C2×C411yescharacteristic
25C2×D4×C13C2×C411yescharacteristic
26C2×C22⋊D13—21no—
27C22×Dic13—21no—
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13C2311yescharacteristic
31C2×#1057—22no—
32C4⋊#261—42no—
33C13×C22⋊C4—21no—
34C13×C22⋊C4—21no—
35C42×C13C2×C411yescharacteristic
36C22⋊Dic13—21no—
37C22⋊Dic13—21no—
38#6103—21no—
39C4⋊Dic13—21no—
40C4⋊Dic13C2×C411yescharacteristic
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43#6101—21no—
44#6101—21no—
45C4×Dic13—21no—
46C4×Dic13C2×C411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13D411yescharacteristic
49#1512—131nomaximal, Sylow
50C23×C13—21no—
51C22×D13C2×D411yescharacteristic
52C2×#261—42no—
53C2×#261—42no—
54C2×#261—42no—
55Q8×C13—41no—
56D4×C13—41no—
57C2×C4×C13—21no—
58C2×C4×C13C22⋊C411yescharacteristic
59C2×C4×C13C22⋊C411yescharacteristic
60C2×C4×C13C22×C411yescharacteristic
61C22⋊D13—41no—
62C22⋊D13—41no—
63C2×Dic13—21no—
64C2×Dic13—21no—
65C2×Dic13—42no—
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C2×Dic13C2×D411yescharacteristic
69C4×D13—21no—
70C4×D13—21no—
71C4×D13—41no—
72C4×D13—41no—
73#1057—42no—
74#529—131no—
75#432—131no—
76#382—131no—
77#328—132no—
78#327—132no—
79C22×C13—41no—
80C22×C13—41no—
81C22×C13—41no—
82C22×C13C2×C22⋊C411yescharacteristic
83C2×D13—21no—
84C2×D13—21no—
85C2×D13AGL(1,ℤ/8)11yescharacteristic
86C2×D13#13711yescharacteristic
87#261—82no—
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—21no—
91C4×C13—41no—
92Dic13—21no—
93Dic13—21no—
94Dic13—21no—
95Dic13—41no—
96Dic13—41no—
97#126—261no—
98#125—131no—
99#124#26111yescharacteristic, complemented
100#123—261no—
101C22⋊Q8—131no—
102#121—131no—
103C4×Q8—131no—
104C4×D4—131no—
105C4×D4—261no—
106#117—261no—
107C2×C4⋊C4—261no—
108C2×C42—131no—
109C4⋊C8—261no—
110C22⋊C8—132no—
111#97—261no—
112#95—132no—
113#95—261no—
114C2×C13—81no—
115C2×C13#41011yescharacteristic
116C2×C13#41711yescharacteristic
117C2×C13#42111yescharacteristic
118D13—21no—
119D13—21no—
120C2×Q8C2×#26111yescharacteristic
121C2×D4—261no—
122C2×D4C2×#26111yescharacteristic
123C22×C4—131no—
124C22×C4—131no—
125C22×C4—131no—
126C22×C4—261no—
127C22×C4—262no—
128C2×C8—262no—
129C4⋊C4—131no—
130C4⋊C4—131no—
131C4⋊C4—261no—
132C4⋊C4—261no—
133C4⋊C4—261no—
134C4⋊C4—261no—
135C4⋊C4—522no—
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—261no—
139C22⋊C4—261no—
140C22⋊C4—261no—
141C42—131no—
142C42—131no—
143C42—131no—
144C42—261no—
145C42C2×#26111yescharacteristic
146C13#151211yescharacteristic, complemented, Sylow
147C23—21no—
148C23—131no—
149Q8—41no—
150D4—41no—
151D4—521no—
152D4—521no—
153C2×C4—21no—
154C2×C4—131no—
155C2×C4—131no—
156C2×C4—131no—
157C2×C4—261no—
158C2×C4—261no—
159C2×C4—261no—
160C2×C4—261no—
161C2×C4—521no—
162C2×C4—521no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4—522no—
166C2×C4—522no—
167C2×C4C22⋊#26111yescharacteristic
168C2×C4C22⋊#26111yescharacteristic
169C2×C4C22×#26111yescharacteristic
170C8—522no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—131no—
175C22—131no—
176C22—261no—
177C22—261no—
178C22C2×C22⋊#26111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—261no—
184C4—261no—
185C4—261no—
186C4—521no—
187C4—521no—
188C4—1042no—
189C2—81no—
190C2—261no—
191C2—261no—
192C2#1171914211yescharacteristic
193C2#1171916411yescharacteristic
194C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC22×C13C2×C22⋊C4
prime radical#88192C22
cosocleC2×C4×D13C23
hypercenter#124#261
hypocenterC13#1512
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11719060C2semidirect
3. #11719054C2semidirect
4. #11718298C2semidirect
7. C13×#124C4semidirect
9. Q8×Dic13C4semidirect
11. D4×Dic13C4semidirect
17. #88124C4semidirect
99. #124#261semidirect
146. C13#1512semidirect

Maximal subgroups

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

subgroupindex
#117193852
#117190602
#117190542
#117182982
#117182922
#151213