Finite Group Databasebeta

← #20242374

Subgroups — #20242374

Order 6016.

280 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689434C212yesmaximal, complemented
2#15689048C211yesmaximal, characteristic, complemented
3#15688857C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic, complemented
5C47×#534C211yesmaximal, characteristic
6C2×C4⋊Dic47C2211yescharacteristic, complemented
7C2×C22⋊Dic47—21no—
8#13093957—22no—
9#13093945—22no—
10C22⋊(C47⋊C8)C2212yescomplemented
11C47⋊#95—21no—
12C47⋊#95C2211yescharacteristic, complemented
13C22×D4×C47—21no—
14#123×C47—22no—
15#121×C47—21no—
16#121×C47C2212yes—
17#120×C47—22no—
18C2×C22⋊C4×C47C2211yescharacteristic
19C24×C47—21no—
20C24×C47D411yescharacteristic
21C2×D4×C47—22no—
22C2×D4×C47—22no—
23C2×D4×C47—21no—
24C2×D4×C47—42no—
25C2×D4×C47—42no—
26C2×D4×C47D412yes—
27C22×C4×C47—21no—
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47D412yes—
34C22⋊C4×C47—22no—
35C22⋊C4×C47—22no—
36C22⋊C4×C47—22no—
37C22⋊Dic47—42no—
38C4⋊Dic47—22no—
39C2×C47⋊C8—22no—
40C23×C47—21no—
41C23×C47—21no—
42C23×C47—22no—
43C23×C47—41no—
44C23×C47—41no—
45C23×C47—42no—
46C23×C47—81no—
47C23×C47—81no—
48C23×C47D812yes—
49C23×C47C2×D411yescharacteristic
50D4×C47—42no—
51D4×C47—44no—
52D4×C47—42no—
53D4×C47—42no—
54D4×C47—81no—
55C2×C4×C47—21no—
56C2×C4×C47—22no—
57C2×C4×C47—41no—
58C2×C4×C47—42no—
59C2×C4×C47—41no—
60C2×C4×C47C2×D412yes—
61C2×Dic47—41no—
62C2×Dic47—41no—
63C2×Dic47—41no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C47⋊C8—42no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—22no—
71C22×C47—42no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47—42no—
75C22×C47—42no—
76C22×C47—42no—
77C22×C47—81no—
78C22×C47—84no—
79C22×C47#12011yescharacteristic
80C22×C47C2×D811yescharacteristic
81C22×C47AGL(1,ℤ/8)11yescharacteristic
82C4×C47—22no—
83C4×C47—42no—
84C4×C47—41no—
85Dic47—81no—
86Dic47—81no—
87#1607—471nomaximal, Sylow
88C2×C47—21no—
89C2×C47—21no—
90C2×C47—42no—
91C2×C47—82no—
92C2×C47#44711yescharacteristic
93C2×C47#45511yescharacteristic
94C2×C47#45811yescharacteristic
95#534D4711yescharacteristic
96#480—472no—
97#397—471no—
98#327—472no—
99#323—471no—
100C47#160711yescharacteristic, complemented, Sylow
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C2×D4712yes—
105#120—22no—
106C2×C4⋊C4—471no—
107C2×C22⋊C4—941no—
108C2×C22⋊C4C2×D4711yescharacteristic
109#107—942no—
110#102—942no—
111C22⋊C8—472no—
112#95—471no—
113#95—941no—
114C24—21no—
115C24C22⋊D4711yescharacteristic
116C2×D4—22no—
117C2×D4—22no—
118C2×D4—21no—
119C2×D4—42no—
120C2×D4—42no—
121C2×D4C22⋊D4712yes—
122C22×C4—21no—
123C22×C4—941no—
124C22×C4—941no—
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22×D4711yescharacteristic
127C2×C8—942no—
128C4⋊C4—21no—
129C4⋊C4—942no—
130C4⋊C4C22⋊D4712yes—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C22⋊C4—22no—
134C22⋊C4—1882no—
135C23—21no—
136C23—21no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—42no—
141C23—81no—
142C23—81no—
143C23#1062533412yes—
144C23C2×C22⋊D4711yescharacteristic
145D4—42no—
146D4—44no—
147D4—42no—
148D4—42no—
149D4—81no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—1881no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4C2×C22⋊D4712yes—
162C8—1882no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—81no—
173C22—84no—
174C22#1309399311yescharacteristic
175C22C2×#1062533411yescharacteristic
176C22#1309405011yescharacteristic
177C4—22no—
178C4—42no—
179C4—41no—
180C4—3761no—
181C4—3761no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—82no—
186C2#1568925711yescharacteristic
187C2#1568930111yescharacteristic
188C2#1568931311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#534C2
socleC22×C47#120
hypercenter#534D47
hypocenterC47#1607
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #15689434C2semidirect
2. #15689048C2semidirect
3. #15688857C2semidirect
4. #15688847C2semidirect
6. C2×C4⋊Dic47C22semidirect
10. C22⋊(C47⋊C8)C22semidirect
12. C47⋊#95C22semidirect
100. C47#1607semidirect