Finite Group Databasebeta

← #16848335

Subgroups — #16848335

Order 3968.

600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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×#11758503C211yesmaximal, characteristic
2C2×#11758503C211yesmaximal, characteristic
3#14520945C214yesmaximal, complemented
4#14520922C214yesmaximal
5#14520918C212yesmaximal, complemented
6#14520914C212yesmaximal, complemented
7C22×C4⋊C4×C31C211yesmaximal, characteristic
8C23×C4×C31C2212yes—
9C23×C4×C31C2211yescharacteristic
10C2×C4⋊C4×C31—24no—
11C2×C4⋊C4×C31C2212yes—
12C2×C4⋊C4×C31C2212yes—
13C2×C22⋊Dic31C2212yes—
14C2×C22⋊Dic31C2212yes—
15#11758503—24no—
16#11758503C418yescomplemented
17C2×C4⋊Dic31C2211yescharacteristic
18C2×C4⋊Dic31C2211yescharacteristic
19C2×C4⋊Dic31C2212yes—
20C2×Dic31⋊C4C2218yes—
21C2×C4×Dic31C2212yes—
22C2×C4×Dic31C2212yes—
23C31⋊#95C2218yes—
24C24×C31C2311yescharacteristic
25C22×C4×C31—24no—
26C22×C4×C31—44no—
27C22×C4×C31C2×C414yes—
28C22×C4×C31D414yes—
29C22×C4×C31Q814yes—
30C22×C4×C31C2314yes—
31C22×C4×C31C2311yescharacteristic
32C22×C4×C31C2311yescharacteristic
33C22×Dic31C2312yes—
34C22×Dic31C2312yes—
35C22×Dic31C2314yes—
36C4⋊C4×C31—24no—
37C4⋊C4×C31—24no—
38C22⋊Dic31—24no—
39C22⋊Dic31C2×C418yes—
40C4⋊Dic31—22no—
41C4⋊Dic31—22no—
42C4⋊Dic31C2×C418yescomplemented
43Dic31⋊C4—48no—
44C4×Dic31—24no—
45C4×Dic31C2×C418yescomplemented
46C23×C31—22no—
47C23×C31—22no—
48C23×C31C22×C412yes—
49C23×C31C2×D412yes—
50C23×C31C2×Q812yes—
51C23×C31C2411yescharacteristic
52C2×C4×C31—24no—
53C2×C4×C31—28no—
54C2×C4×C31—48no—
55C2×C4×C31C4⋊C4116yescomplemented
56C2×C4×C31C22×C412yes—
57C2×C4×C31C22×C412yes—
58C2×C4×C31C2×D412yes—
59C2×C4×C31C2×D412yes—
60C2×C4×C31C2×Q812yes—
61C2×C4×C31C2×Q812yes—
62C2×Dic31—24no—
63C2×Dic31—24no—
64C2×Dic31—22no—
65C2×Dic31—22no—
66C2×Dic31—24no—
67C2×Dic31—24no—
68C2×Dic31C22×C418yes—
69#2317—311nomaximal, Sylow
70C22×C31—24no—
71C22×C31—22no—
72C22×C31—22no—
73C22×C31—24no—
74C22×C31C2×C4⋊C414yes—
75C22×C31C23×C411yescharacteristic
76C22×C31C22×D411yescharacteristic
77C22×C31C22×Q811yescharacteristic
78C22×C31H(5,𝔽2)12yes—
79C22×C312−1+412yes—
80C4×C31—44no—
81C4×C31C2×C4⋊C414yes—
82C4×C31C2×C4⋊C414yes—
83Dic31—28no—
84Dic31—42no—
85Dic31—42no—
86C2×#117—311no—
87C2×#117—311no—
88C22×C4⋊C4D3111yescharacteristic
89#389—314no—
90#385—314no—
91#384—312no—
92#382—312no—
93C2×C31—24no—
94C2×C31C22×C4⋊C411yescharacteristic
95C2×C31#52012yes—
96C2×C31#53511yescharacteristic
97C2×C31#53611yescharacteristic
98C2×C31#54412yes—
99C23×C4C2×D3112yes—
100C23×C4C2×D3111yescharacteristic
101#117—318no—
102#117—624no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—312no—
105C2×C4⋊C4—311no—
106C2×C4⋊C4—311no—
107C2×C4⋊C4—318no—
108C2×C4⋊C4C2×D3112yes—
109C2×C4⋊C4C2×D3112yes—
110C2×C22⋊C4—312no—
111C2×C22⋊C4—312no—
112C2×C42—312no—
113C2×C42—312no—
114#95—318no—
115C31#231711yescharacteristic, complemented, Sylow
116C24C22×D3111yescharacteristic
117C22×C4—24no—
118C22×C4—44no—
119C22×C4—314no—
120C22×C4—312no—
121C22×C4—312no—
122C22×C4Dic6214yes—
123C22×C4C4×D3114yes—
124C22×C4C22⋊D3114yes—
125C22×C4C22×D3114yes—
126C22×C4C22×D3111yescharacteristic
127C22×C4C22×D3111yescharacteristic
128C4⋊C4—24no—
129C4⋊C4—24no—
130C4⋊C4—318no—
131C4⋊C4—622no—
132C4⋊C4—622no—
133C4⋊C4—1248no—
134C22⋊C4—318no—
135C22⋊C4—624no—
136C42—318no—
137C42—624no—
138C23—22no—
139C23—22no—
140C23C2×Dic6212yes—
141C23C2×C4×D3112yes—
142C23C2×C22⋊D3112yes—
143C23C23×D3111yescharacteristic
144C2×C4—28no—
145C2×C4—24no—
146C2×C4—48no—
147C2×C4—318no—
148C2×C4—624no—
149C2×C4—624no—
150C2×C4—624no—
151C2×C4—624no—
152C2×C4—622no—
153C2×C4—622no—
154C2×C4Dic31⋊C4116yescomplemented
155C2×C4C2×Dic6212yes—
156C2×C4C2×Dic6212yes—
157C2×C4C2×C4×D3112yes—
158C2×C4C2×C4×D3112yes—
159C2×C4C2×C22⋊D3112yes—
160C2×C4C2×C22⋊D3112yes—
161C22—22no—
162C22—22no—
163C22—24no—
164C22—24no—
165C22C2×Dic31⋊C414yes—
166C22C22×Dic6211yescharacteristic
167C22C22×C4×D3111yescharacteristic
168C22#1175856112yes—
169C22#1175856412yes—
170C22C22×C22⋊D3111yescharacteristic
171C4—44no—
172C4—628no—
173C4—1242no—
174C4—1242no—
175C4C2×Dic31⋊C414yes—
176C4C2×Dic31⋊C414yes—
177C2—24no—
178C2C22×Dic31⋊C411yescharacteristic
179C2#1452153012yes—
180C2#1452161611yescharacteristic
181C2#1452162311yescharacteristic
182C2#1452168012yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC22×C4⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenterC22×C4⋊C4D31
hypocenterC31#2317
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14520945C2semidirect
5. #14520918C2semidirect
6. #14520914C2semidirect
16. #11758503C4semidirect
42. C4⋊Dic31C2×C4semidirect
45. C4×Dic31C2×C4semidirect
55. C2×C4×C31C4⋊C4semidirect
115. C31#2317semidirect
154. C2×C4Dic31⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#117585032
#145209452
#145209222
#145209182
#145209142
C22×C4⋊C4×C312
#231731