Finite Group Databasebeta

← #16844863

Subgroups — #16844863

Order 3968.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#14521702C211yesmaximal, characteristic
2#14521401C211yesmaximal, characteristic, complemented
3#14521340C211yesmaximal, characteristic, complemented
4#14521340C211yesmaximal, characteristic, complemented
5#14520776C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic, complemented
7C31×#332C211yesmaximal, characteristic, complemented
8C2×#92499—21no—
9C31×C4⋊Q8C2211yescharacteristic
10#11758523—21no—
11#11758472—21no—
12#11758471—22no—
13C4⋊C4×D31—21no—
14C4×D124C2211yescharacteristic
15C4×D124C2211yescharacteristic
16#11758446C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19#11758409—21no—
20#11758409—21no—
21#11758405—21no—
22#11758405—21no—
23#11758398—22no—
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31—21no—
26#92499—42no—
27#92499—42no—
28C2×D124—22no—
29C2×D124D411yescharacteristic
30C2×D124D411yescharacteristic
31C2×C4×D31—22no—
32C2×C4×D31—21no—
33C2×C4×D31—21no—
34C2×Dic62—21no—
35C2×C8×C31—21no—
36C2×C8×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31D412yes—
39C42×C31C2311yescharacteristic
40(C2×D31)⋊C4—22no—
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43C4⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31D411yescharacteristic
46C4⋊Dic31D411yescharacteristic
47Dic31⋊C4—22no—
48C2×C31⋊C8—21no—
49C22×D31—21no—
50C22×D31—21no—
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—41no—
60D124—21no—
61D124—21no—
62D124—21no—
63D124—44no—
64D124SD1612yes—
65C4×D31—44no—
66C4×D31—41no—
67C4×D31—41no—
68C4×D31—41no—
69C4×D31—41no—
70Dic62—42no—
71C8×C31—41no—
72C8×C31—41no—
73C31⋊C8—41no—
74#1635—311nomaximal, Sylow
75C22×C31#12011yescharacteristic
76C2×D31—22no—
77C2×D31—41no—
78C2×D31—41no—
79C2×D31—41no—
80C2×D31—41no—
81C2×D31—41no—
82C4×C31—21no—
83C4×C31—42no—
84C4×C31C2×SD1611yescharacteristic
85C4×C31#13511yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87C4×C31#13711yescharacteristic
88Dic31—41no—
89Dic31—41no—
90Dic31—81no—
91#547—311no—
92#487—311no—
93#476—311no—
94#476—311no—
95#332D3111yescharacteristic, complemented
96D4⋊C8—311no—
97D4⋊C8—311no—
98C2×C31#45011yescharacteristic
99C2×C31#45211yescharacteristic
100C2×C31#45411yescharacteristic
101D31—42no—
102D31—81no—
103C2×#41—621no—
104C4⋊Q8—311no—
105C4⋊Q8C2×D3111yescharacteristic
106#123—622no—
107C22⋊Q8—621no—
108#121—621no—
109C4×D4—311no—
110C4×D4—311no—
111C2×C4⋊C4—621no—
112#106—621no—
113#106—621no—
114C4⋊C8C2×D3111yescharacteristic
115C4⋊C8C2×D3111yescharacteristic
116#103—622no—
117#102—621no—
118#102—621no—
119C4×C8—311no—
120C31#163511yescharacteristic, complemented, Sylow
121#41—1242no—
122#41—1242no—
123C2×Q8—21no—
124C2×Q8—621no—
125C2×D4—311no—
126C2×D4—311no—
127C2×D4—622no—
128C22×C4—622no—
129C22×C4—621no—
130C22×C4—621no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—621no—
134C4⋊C4—21no—
135C4⋊C4—311no—
136C4⋊C4—311no—
137C4⋊C4—622no—
138C4⋊C4—621no—
139C4⋊C4—621no—
140C4⋊C4D12412yes—
141C22⋊C4—622no—
142C22⋊C4—621no—
143C22⋊C4—621no—
144C42C22×D3111yescharacteristic
145C23—621no—
146C23—621no—
147Q8—41no—
148Q8—41no—
149Q8—1242no—
150D4—312no—
151D4—621no—
152D4—621no—
153D4—621no—
154D4—1244no—
155C2×C4—22no—
156C2×C4—621no—
157C2×C4—621no—
158C2×C4—1244no—
159C2×C4—1241no—
160C2×C4—1241no—
161C2×C4—1241no—
162C2×C4—1241no—
163C2×C4—1241no—
164C2×C4C2×D12411yescharacteristic
165C2×C4D4×D3111yescharacteristic
166C2×C4D4×D3111yescharacteristic
167C8—41no—
168C8—41no—
169C8—1241no—
170C22—622no—
171C22—1241no—
172C22—1241no—
173C22—1241no—
174C22—1241no—
175C22—1241no—
176C22#1175845911yescharacteristic
177C4—21no—
178C4—42no—
179C4—1241no—
180C4—1241no—
181C4—2481no—
182C4#1175848811yescharacteristic
183C4SD16×D3111yescharacteristic
184C4#1175849311yescharacteristic
185C4#1175849511yescharacteristic
186C2—1242no—
187C2—2481no—
188C2#1452120111yescharacteristic
189C2#1452121411yescharacteristic
190C2#1452122411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31#120
prime radical#14521702C2
hypercenter#332D31
hypocenterC31#1635
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14521401C2semidirect
3. #14521340C2semidirect
4. #14521340C2semidirect
5. #14520776C2semidirect
6. #14520776C2semidirect
7. C31×#332C2semidirect
95. #332D31semidirect
120. C31#1635semidirect

Maximal subgroups

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

subgroupindex
#145217022
#145214012
#145213402
#145207762
C31×#3322
#163531