Finite Group Databasebeta

← #20242674

Subgroups — #20242674

Order 6016.

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#15689778C211yesmaximal, characteristic
2#15689521C211yesmaximal, characteristic, complemented
3#15689404C211yesmaximal, characteristic, complemented
4#15689328C211yesmaximal, characteristic, complemented
5#15688870C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9C2×#10625335—21no—
10#13094024C2211yescharacteristic
11#13094024C2211yescharacteristic
12#13094006—22no—
13#13094003—21no—
14#13093995—21no—
15C4×D188C2211yescharacteristic
16C4⋊C4×D47—21no—
17#13093958—21no—
18#13093956—22no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093947—21no—
21#13093946—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C2×C22⋊D47—22no—
28#10625350—42no—
29#10625350—42no—
30C2×D188D411yescharacteristic
31C2×C4×D47—22no—
32C2×C4×D47—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C22⋊C4×C47—21no—
39C42×C47C2311yescharacteristic
40C22⋊Dic47—22no—
41#10625335—42no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47D412yes—
47C4⋊Dic47D411yescharacteristic
48Dic47⋊C4—22no—
49C2×C47⋊C8—21no—
50C23×C47—21no—
51C22×D47—21no—
52D4×C47—21no—
53D4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C22⋊D47—44no—
61C2×Dic47—21no—
62C2×Dic47—22no—
63C2×Dic47—41no—
64D188—21no—
65D188SD1612yescomplemented
66C4×D47—44no—
67C4×D47—41no—
68C4×D47—41no—
69Dic94—41no—
70Dic94—41no—
71Dic94—41no—
72Dic94—41no—
73C8×C47—22no—
74C8×C47—41no—
75C47⋊C8—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47#12011yescharacteristic
80C2×D47—22no—
81C2×D47—41no—
82C2×D47—41no—
83C4×C47—21no—
84C4×C47—41no—
85C4×C47C2×SD1611yescharacteristic
86C4×C47#13511yescharacteristic
87C4×C47AGL(1,ℤ/8)11yescharacteristic
88C4×C47AGL(1,ℤ/8)11yescharacteristic
89Dic47—41no—
90Dic47—42no—
91Dic47—81no—
92#1654—471nomaximal, Sylow
93C2×C47—81no—
94C2×C47#44911yescharacteristic
95C2×C47#45011yescharacteristic
96C2×C47#45611yescharacteristic
97D47—42no—
98#547—471no—
99#498—471no—
100#474—471no—
101#461—471no—
102#332—471no—
103D4⋊C8—471no—
104D4⋊C8D4711yescharacteristic, complemented
105C47#165411yescharacteristic, complemented, Sylow
106C2×#41—941no—
107C2×SD16—941no—
108C4⋊Q8—471no—
109C4⋊Q8—471no—
110#123—942no—
111C22⋊Q8—941no—
112#121—941no—
113C4×D4—471no—
114C4×D4C2×D4711yescharacteristic
115C2×C4⋊C4—941no—
116#107—941no—
117#106—942no—
118C4⋊C8—471no—
119C4⋊C8C2×D4711yescharacteristic
120#103—941no—
121#102—941no—
122C4×C8C2×D4711yescharacteristic
123#41—1882no—
124#41—1882no—
125C2×Q8—941no—
126C2×Q8—941no—
127C2×D4—471no—
128C2×D4—942no—
129C2×D4D18811yescharacteristic
130C22×C4—21no—
131C22×C4—942no—
132C22×C4—941no—
133SD16—1882no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—941no—
137C4⋊C4—472no—
138C4⋊C4—471no—
139C4⋊C4—942no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4D18811yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—942no—
146C22⋊C4—941no—
147C42C22×D4711yescharacteristic
148C23—21no—
149C23—941no—
150Q8—1881no—
151Q8—1881no—
152Q8—1881no—
153Q8—1881no—
154D4—21no—
155D4—21no—
156D4—472no—
157D4—941no—
158D4—1884no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—941no—
163C2×C4—942no—
164C2×C4—1884no—
165C2×C4—1881no—
166C2×C4—1881no—
167C2×C4—1881no—
168C2×C4C2×D18811yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C2×C4D4×D4711yescharacteristic
171C8—22no—
172C8—41no—
173C8—1881no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—942no—
178C22—1881no—
179C22—1881no—
180C22#1309399411yescharacteristic
181C4—21no—
182C4—41no—
183C4—3761no—
184C4—1881no—
185C4—1882no—
186C4SD16×D4711yescharacteristic
187C4#1309404611yescharacteristic
188C4#1309404811yescharacteristic
189C4#1309405211yescharacteristic
190C2—81no—
191C2—1882no—
192C2#1568927011yescharacteristic
193C2#1568927511yescharacteristic
194C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1654
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689521C2semidirect
3. #15689404C2semidirect
4. #15689328C2semidirect
5. #15688870C2semidirect
6. #15688852C2semidirect
7. C47×D4⋊C8C2semidirect
65. D188SD16semidirect
104. D4⋊C8D47semidirect
105. C47#1654semidirect