Finite Group Databasebeta

← #16844949

Subgroups — #16844949

Order 3968.

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

normal subgroups only

This group has 240 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#14521454C211yesmaximal, characteristic, complemented
3#14521329C211yesmaximal, characteristic, complemented
4#14521255C211yesmaximal, 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—
12C2×#92470—21no—
13C4⋊C4×D31—21no—
14#11758460—22no—
15C4×D124C2211yescharacteristic
16#11758446C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C4×C8×C31C2211yescharacteristic
20#11758420—21no—
21#11758406—22no—
22#11758404—21no—
23#11758395—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⋊Dic31D411yescharacteristic
46C4⋊Dic31D412yes—
47Dic31⋊C4—22no—
48C2×C31⋊C8—21no—
49#92470—42no—
50C23×C31—21no—
51C22×D31—21no—
52D4×C31—21no—
53D4×C31—21no—
54C2×C4×C31—21no—
55C2×C4×C31—41no—
56C2×C4×C31—41no—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C22⋊D31—44no—
61C2×Dic31—21no—
62C2×Dic31—22no—
63C2×Dic31—41no—
64D124—21no—
65D124D812yes—
66C4×D31—44no—
67C4×D31—41no—
68C4×D31—41no—
69Dic62—41no—
70Dic62—41no—
71Dic62—41no—
72Dic62—41no—
73C8×C31—22no—
74C8×C31—41no—
75C31⋊C8—41no—
76#1647—311nomaximal, Sylow
77C22×C31—41no—
78C22×C31—41no—
79C22×C31—41no—
80C22×C31#12011yescharacteristic
81C2×D31—22no—
82C2×D31—41no—
83C2×D31—41no—
84C4×C31—21no—
85C4×C31—41no—
86C4×C31C2×D811yescharacteristic
87C4×C31#13511yescharacteristic
88C4×C31AGL(1,ℤ/8)11yescharacteristic
89C4×C31#13711yescharacteristic
90Dic31—42no—
91Dic31—41no—
92Dic31—81no—
93#547—311no—
94#500—311no—
95#474—311no—
96#461—311no—
97#332—311no—
98D4⋊C8—311no—
99D4⋊C8D3111yescharacteristic, complemented
100C2×C31—81no—
101C2×C31#44711yescharacteristic
102C2×C31#45211yescharacteristic
103C2×C31#45611yescharacteristic
104D31—42no—
105C2×#41—621no—
106C2×SD16—621no—
107C4⋊Q8—311no—
108C4⋊Q8—311no—
109#123—622no—
110C22⋊Q8—621no—
111#121—621no—
112C4×D4—311no—
113C4×D4C2×D3111yescharacteristic
114C2×C4⋊C4—621no—
115#107—622no—
116#107—621no—
117C4⋊C8—311no—
118C4⋊C8C2×D3111yescharacteristic
119#103—621no—
120#102—621no—
121C4×C8C2×D3111yescharacteristic
122C31#164711yescharacteristic, complemented, Sylow
123#41—1242no—
124#41—1242no—
125C2×Q8—621no—
126C2×Q8—621no—
127C2×D4—311no—
128C2×D4—622no—
129C2×D4D12411yescharacteristic
130C22×C4—21no—
131C22×C4—622no—
132C22×C4—621no—
133SD16—1242no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—621no—
137C4⋊C4—311no—
138C4⋊C4—312no—
139C4⋊C4—622no—
140C4⋊C4—621no—
141C4⋊C4—621no—
142C4⋊C4—621no—
143C4⋊C4D12411yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—622no—
146C22⋊C4—621no—
147C42C22×D3111yescharacteristic
148C23—21no—
149C23—621no—
150Q8—1241no—
151Q8—1241no—
152Q8—1241no—
153Q8—1241no—
154D4—21no—
155D4—21no—
156D4—312no—
157D4—621no—
158D4—1244no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—621no—
163C2×C4—622no—
164C2×C4—1244no—
165C2×C4—1241no—
166C2×C4—1241no—
167C2×C4—1241no—
168C2×C4C2×D12411yescharacteristic
169C2×C4D4×D3111yescharacteristic
170C2×C4D4×D3111yescharacteristic
171C8—22no—
172C8—41no—
173C8—1241no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—622no—
178C22—1241no—
179C22—1241no—
180C22#1175845911yescharacteristic
181C4—21no—
182C4—41no—
183C4—1242no—
184C4—1241no—
185C4—2481no—
186C4#1175848111yescharacteristic
187C4#1175848611yescharacteristic
188C4D8×D3111yescharacteristic
189C4#1175849111yescharacteristic
190C2—81no—
191C2—1242no—
192C2#1452118411yescharacteristic
193C2#1452121311yescharacteristic
194C2#1452123311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31#120
prime radical#14521704C2
hypercenterD4⋊C8D31
hypocenterC31#1647
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. #14521454C2semidirect
3. #14521329C2semidirect
4. #14521255C2semidirect
5. #14520796C2semidirect
6. #14520778C2semidirect
7. C31×D4⋊C8C2semidirect
99. D4⋊C8D31semidirect
122. C31#1647semidirect

Maximal subgroups

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

subgroupindex
#145217042
#145214542
#145213292
#145212552
#145207962
#145207782
C31×D4⋊C82
#164731