Finite Group Databasebeta

← #20243583

Subgroups — #20243583

Order 6016.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×C4⋊Dic47C211yesmaximal, characteristic
2C2×#13093956C212yesmaximal, complemented
3#15688983C211yesmaximal, characteristic
4#15688886C212yesmaximal, complemented
5C2×C22⋊C8×C47C211yesmaximal, characteristic
6C23×Dic47—21no—
7C2×C4⋊Dic47—21no—
8C2×C4⋊Dic47—24no—
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×C22⋊Dic47—21no—
13#13093956—24no—
14C47⋊#95—21no—
15C23×C4×C47C2211yescharacteristic
16C22×C8×C47C2212yes—
17C22⋊C8×C47C414yescomplemented
18C24×C47D411yescharacteristic
19C22×C4×C47—22no—
20C22×C4×C47—22no—
21C22×C4×C47C2×C412yes—
22C22×C4×C47D411yescharacteristic
23C22×C4×C47Q812yes—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—24no—
26C22×Dic47—22no—
27C22×Dic47—21no—
28C22×Dic47—21no—
29C22×Dic47—42no—
30C22×Dic47—42no—
31C2×C8×C47—22no—
32C2×C8×C47—22no—
33C2×C8×C47C2×C414yescomplemented
34C22⋊Dic47—42no—
35C4⋊Dic47—24no—
36C4⋊Dic47—22no—
37C4⋊Dic47—22no—
38C4⋊Dic47—22no—
39C4⋊Dic47D414yes—
40C23×C47—21no—
41C23×C47—21no—
42C23×C47—21no—
43C23×C47—21no—
44C23×C47C4⋊C412yes—
45C23×C47SD1612yes—
46C23×C47SD1612yes—
47C23×C47C2×D411yescharacteristic
48C2×C4×C47—21no—
49C2×C4×C47—21no—
50C2×C4×C47—24no—
51C2×C4×C47—24no—
52C2×C4×C47C4⋊C412yes—
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D412yes—
55C2×C4×C47C2×Q811yescharacteristic
56C2×C4×C47#4112yes—
57C2×Dic47—24no—
58C2×Dic47—48no—
59C2×Dic47—42no—
60C2×Dic47—42no—
61C2×Dic47—41no—
62C2×Dic47—41no—
63C2×Dic47—41no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C8×C47—24no—
68C22×C47—22no—
69C22×C47—22no—
70C22×C47—22no—
71C22×C47—22no—
72C22×C47—22no—
73C22×C47—22no—
74C22×C47#10614yescomplemented
75C22×C47C2×C4⋊C411yescharacteristic
76C22×C47#12011yescharacteristic
77C22×C47#12311yescharacteristic
78C22×C47C2×SD1611yescharacteristic
79C22×C47C2×SD1611yescharacteristic
80C22×C47AGL(1,ℤ/8)11yescharacteristic
81C22×C47#13711yescharacteristic
82C4×C47—22no—
83C4×C47C4×D412yes—
84C4×C47C22⋊Q812yes—
85Dic47—44no—
86Dic47—81no—
87Dic47—81no—
88#1853—471nomaximal, Sylow
89C2×C47—24no—
90C2×C47#38511yescharacteristic
91C2×C47C2×#10611yescharacteristic
92C2×C47#42811yescharacteristic
93C2×C47#44811yescharacteristic
94C2×C47#45011yescharacteristic
95C2×C47#48111yescharacteristic
96C2×C47#48311yescharacteristic
97C22×C4⋊C4—471no—
98C2×#106—472no—
99C2×C22⋊C8D4711yescharacteristic
100#380—471no—
101#340—472no—
102C47#185311yescharacteristic, complemented, Sylow
103C23×C4—941no—
104C23×C4C2×D4711yescharacteristic
105C22×C8C2×D4712yes—
106C2×C4⋊C4—472no—
107C2×C4⋊C4—471no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—944no—
110C2×C4⋊C4—941no—
111C2×C22⋊C4—941no—
112#106—944no—
113C22⋊C8Dic4714yescomplemented
114#95—941no—
115C24D18811yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—944no—
119C22×C4—942no—
120C22×C4—941no—
121C22×C4—941no—
122C22×C4—1882no—
123C22×C4—1882no—
124C22×C4Dic9412yes—
125C22×C4D18811yescharacteristic
126C22×C4C2×Dic4712yes—
127C22×C4C22×D4711yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic4714yescomplemented
131C4⋊C4—474no—
132C4⋊C4—944no—
133C4⋊C4—942no—
134C4⋊C4—942no—
135C4⋊C4—942no—
136C22⋊C4—1882no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23#1062532512yes—
142C23#1062532512yes—
143C23C4⋊Dic4712yes—
144C23C2×D18811yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—944no—
150C2×C4—1881no—
151C2×C4—1881no—
152C2×C4—1881no—
153C2×C4—1881no—
154C2×C4—1881no—
155C2×C4—1881no—
156C2×C4—1888no—
157C2×C4—1882no—
158C2×C4—1882no—
159C2×C4C4⋊Dic4712yes—
160C2×C4C2×Dic9411yescharacteristic
161C2×C4D4×D4712yes—
162C2×C4#1062535212yes—
163C2×C4C22×Dic4711yescharacteristic
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1309395614yescomplemented
172C22C2×C4⋊Dic4711yescharacteristic
173C22#1309399411yescharacteristic
174C22#1309400811yescharacteristic
175C22C2×#1062532511yescharacteristic
176C22C2×#1062532511yescharacteristic
177C22#1309405211yescharacteristic
178C22#1309405711yescharacteristic
179C4—22no—
180C4—3761no—
181C4—3761no—
182C4—1884no—
183C4D4×Dic4712yes—
184C4#1309400112yes—
185C2—24no—
186C2#1568899811yescharacteristic
187C2C2×#1309395611yescharacteristic
188C2#1568916511yescharacteristic
189C2#1568926411yescharacteristic
190C2#1568927611yescharacteristic
191C2#1568944211yescharacteristic
192C2#1568945411yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#1853
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13093956C2semidirect
4. #15688886C2semidirect
17. C22⋊C8×C47C4semidirect
33. C2×C8×C47C2×C4semidirect
74. C22×C47#106semidirect
102. C47#1853semidirect
113. C22⋊C8Dic47semidirect
130. C2×C8C2×Dic47semidirect
171. C22#13093956semidirect