Finite Group Databasebeta

← #16844865

Subgroups — #16844865

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#14521704C211yesmaximal, characteristic
2#14521400C211yesmaximal, characteristic, complemented
3#14521340C211yesmaximal, characteristic, complemented
4#14521339C211yesmaximal, characteristic, complemented
5#14520796C211yesmaximal, characteristic, complemented
6#14520778C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#92495—21no—
9C4×D4×C31C2211yescharacteristic
10#11758515—21no—
11#11758501—21no—
12C4⋊C4×D31—21no—
13#11758460—22no—
14C4×D124C2211yescharacteristic
15#11758446C2211yescharacteristic
16#11758446C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C4×C8×C31C2211yescharacteristic
19#11758420—21no—
20#11758409—21no—
21#11758405—21no—
22#11758404—22no—
23#11758396—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×D4×C31D411yescharacteristic
26C22×C4×C31—21no—
27C2×C22⋊D31—22no—
28#92495—42no—
29#92495—42no—
30C2×D124D411yescharacteristic
31C2×C4×D31—22no—
32C2×C4×D31—21no—
33C2×Dic62—21no—
34C2×Dic62—21no—
35C2×C8×C31—21no—
36C2×C8×C31—21no—
37C4⋊C4×C31D411yescharacteristic
38C22⋊C4×C31—21no—
39C42×C31C2311yescharacteristic
40C22⋊Dic31—22no—
41(C2×D31)⋊C4—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31D412yes—
46C4⋊Dic31D411yescharacteristic
47Dic31⋊C4—22no—
48C2×C31⋊C8—21no—
49C23×C31—21no—
50C22×D31—21no—
51D4×C31—21no—
52D4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C22⋊D31—44no—
60C2×Dic31—21no—
61C2×Dic31—22no—
62C2×Dic31—41no—
63D124—21no—
64D124SD1612yes—
65C4×D31—44no—
66C4×D31—41no—
67C4×D31—41no—
68Dic62—41no—
69Dic62—41no—
70Dic62—42no—
71C8×C31—41no—
72C8×C31—41no—
73C31⋊C8—41no—
74#1635—311nomaximal, Sylow
75C22×C31—41no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31#12011yescharacteristic
79C2×D31—22no—
80C2×D31—41no—
81C2×D31—41no—
82C4×C31—21no—
83C4×C31—41no—
84C4×C31C2×SD1611yescharacteristic
85C4×C31#13511yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87C4×C31#13711yescharacteristic
88Dic31—42no—
89Dic31—41no—
90Dic31—81no—
91#547—311no—
92#487—311no—
93#476—311no—
94#476—311no—
95#332—311no—
96D4⋊C8—311no—
97D4⋊C8D3111yescharacteristic, complemented
98C2×C31—81no—
99C2×C31#45011yescharacteristic
100C2×C31#45211yescharacteristic
101C2×C31#45411yescharacteristic
102D31—42no—
103C2×#41—621no—
104C4⋊Q8—311no—
105C4⋊Q8—311no—
106#123—622no—
107C22⋊Q8—621no—
108#121—621no—
109C4×D4—311no—
110C4×D4C2×D3111yescharacteristic
111C2×C4⋊C4—621no—
112#106—621no—
113#106—621no—
114C4⋊C8—311no—
115C4⋊C8C2×D3111yescharacteristic
116#103—622no—
117#102—621no—
118#102—621no—
119C4×C8C2×D3111yescharacteristic
120C31#163511yescharacteristic, complemented, Sylow
121#41—1242no—
122#41—1242no—
123C2×Q8—621no—
124C2×Q8—621no—
125C2×D4—311no—
126C2×D4—622no—
127C2×D4D12411yescharacteristic
128C22×C4—21no—
129C22×C4—622no—
130C22×C4—621no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—621no—
134C4⋊C4—312no—
135C4⋊C4—311no—
136C4⋊C4—622no—
137C4⋊C4—621no—
138C4⋊C4—621no—
139C4⋊C4—621no—
140C4⋊C4D12411yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—622no—
143C22⋊C4—621no—
144C42C22×D3111yescharacteristic
145C23—21no—
146C23—621no—
147Q8—1242no—
148Q8—1241no—
149Q8—1241no—
150D4—21no—
151D4—21no—
152D4—312no—
153D4—621no—
154D4—1244no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—621no—
159C2×C4—622no—
160C2×C4—1244no—
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—41no—
171C22—41no—
172C22—41no—
173C22—622no—
174C22—1241no—
175C22—1241no—
176C22#1175845911yescharacteristic
177C4—21no—
178C4—41no—
179C4—1242no—
180C4—1241no—
181C4—2481no—
182C4#1175848111yescharacteristic
183C4#1175848611yescharacteristic
184C4#1175848811yescharacteristic
185C4SD16×D3111yescharacteristic
186C2—81no—
187C2—1242no—
188C2#1452120111yescharacteristic
189C2#1452121311yescharacteristic
190C2#1452122311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31#120
prime radical#14521704C2
hypercenterD4⋊C8D31
hypocenterC31#1635
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521400C2semidirect
3. #14521340C2semidirect
4. #14521339C2semidirect
5. #14520796C2semidirect
6. #14520778C2semidirect
7. C31×D4⋊C8C2semidirect
97. D4⋊C8D31semidirect
120. C31#1635semidirect

Maximal subgroups

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

subgroupindex
#145217042
#145214002
#145213402
#145213392
#145207962
#145207782
C31×D4⋊C82
#163531