Finite Group Databasebeta

← #16844822

Subgroups — #16844822

Order 3968.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521773C211yesmaximal, characteristic, complemented
2#14521397C211yesmaximal, characteristic, complemented
3#14521250C211yesmaximal, characteristic, complemented
4#14521245C211yesmaximal, characteristic
5#14520779C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic, complemented
7C31×#332C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9#11758524—21no—
10Q8×Dic31—21no—
11C2×D248—21no—
12C2×#92470—21no—
13#11758475—22no—
14#11758474—21no—
15#11758469—21no—
16#11758451C2211yescharacteristic
17C4×D124C2211yescharacteristic
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C31×C4⋊C8C2211yescharacteristic
21#11758409—21no—
22#11758409—21no—
23#11758397—22no—
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×D124—21no—
27C2×D124—21no—
28C2×D124—21no—
29C2×D124D411yescharacteristic
30C2×C4×D31—21no—
31C2×Dic62D411yescharacteristic
32C2×C8×C31—21no—
33C2×C8×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31D412yes—
36C42×C31C2311yescharacteristic
37(C2×D31)⋊C4—22no—
38(C2×D31)⋊C4—22no—
39(C2×D31)⋊C4—21no—
40C4⋊Dic31—22no—
41C4⋊Dic31D411yescharacteristic
42C4⋊Dic31D411yescharacteristic
43Dic31⋊C4—21no—
44C4×Dic31—22no—
45C4×Dic31—21no—
46C2×C31⋊C8—21no—
47D248—42no—
48#92470—42no—
49C22×D31—21no—
50C22×D31—41no—
51Q8×C31—41no—
52Q8×C31—41no—
53C2×C4×C31—22no—
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×Dic31—21no—
58C2×Dic31—21no—
59C2×Dic31—21no—
60D124—21no—
61D124—21no—
62D124—42no—
63D124—41no—
64D124—41no—
65D124—41no—
66D124—41no—
67C4×D31—41no—
68C4×D31—41no—
69Dic62—21no—
70Dic62—21no—
71C8×C31—41no—
72C8×C31—41no—
73C31⋊C8—41no—
74#1628—311nomaximal, Sylow
75C22×C31#12011yescharacteristic
76C2×D31—41no—
77C2×D31—41no—
78C2×D31—41no—
79C2×D31—81no—
80C2×D31—81no—
81C2×D31—81no—
82C4×C31—21no—
83C4×C31—42no—
84C4×C31#13511yescharacteristic
85C4×C31#13511yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87C4×C31AGL(1,ℤ/8)11yescharacteristic
88Dic31—41no—
89Dic31—41no—
90Dic31—41no—
91#556—311no—
92#486—311no—
93#460—311no—
94#459—311no—
95#332D3111yescharacteristic, complemented
96Q8⋊C8—311no—
97D4⋊C8—311no—
98C2×C31#44911yescharacteristic
99C2×C31#44911yescharacteristic
100C2×C31#45411yescharacteristic
101D31—81no—
102D31—161no—
103C2×SD16—621no—
104C2×D8—621no—
105C4⋊Q8C2×D3111yescharacteristic
106#127—311no—
107#126—622no—
108#124—621no—
109C22⋊Q8—621no—
110C4×Q8—311no—
111C4×Q8—621no—
112C4×D4—311no—
113#117—621no—
114C4⋊C8C2×D3111yescharacteristic
115C4⋊C8C2×D3111yescharacteristic
116#102—621no—
117#102—621no—
118#102—622no—
119C4×C8—311no—
120C31#162811yescharacteristic, complemented, Sylow
121C2×Q8—21no—
122C2×Q8—311no—
123C2×D4—311no—
124C2×D4—621no—
125C2×D4—621no—
126C2×D4—621no—
127C22×C4—621no—
128SD16—1242no—
129D8—1242no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—621no—
133C4⋊C4—21no—
134C4⋊C4—311no—
135C4⋊C4—311no—
136C4⋊C4—622no—
137C4⋊C4—621no—
138C4⋊C4D12412yes—
139C22⋊C4—622no—
140C22⋊C4—622no—
141C22⋊C4—621no—
142C42—622no—
143C42—621no—
144C42C22×D3111yescharacteristic
145C23—621no—
146C23—1241no—
147Q8—41no—
148Q8—41no—
149Q8—621no—
150Q8—621no—
151D4—621no—
152D4—621no—
153D4—1242no—
154D4—1241no—
155D4—1241no—
156D4—1241no—
157D4—1241no—
158C2×C4—22no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—621no—
162C2×C4—1241no—
163C2×C4—1241no—
164C2×C4C2×D12411yescharacteristic
165C2×C4D4×D3111yescharacteristic
166C2×C4D4×D3111yescharacteristic
167C8—41no—
168C8—41no—
169C8—1241no—
170C22—1241no—
171C22—1241no—
172C22—1241no—
173C22—2481no—
174C22—2481no—
175C22—2481no—
176C22#1175845911yescharacteristic
177C4—21no—
178C4—42no—
179C4—1241no—
180C4—1241no—
181C4—1241no—
182C4#1175848811yescharacteristic
183C4#1175849111yescharacteristic
184C4#1175849311yescharacteristic
185C4#1175849611yescharacteristic
186C2—4961no—
187C2—2481no—
188C2#1452119511yescharacteristic
189C2#1452119711yescharacteristic
190C2#1452122411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31#120
prime radical#14521245C2
hypercenter#332D31
hypocenterC31#1628
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14521773C2semidirect
2. #14521397C2semidirect
3. #14521250C2semidirect
5. #14520779C2semidirect
6. #14520776C2semidirect
7. C31×#332C2semidirect
95. #332D31semidirect
120. C31#1628semidirect

Maximal subgroups

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

subgroupindex
#145217732
#145213972
#145212502
#145212452
#145207792
#145207762
C31×#3322
#162831