Finite Group Databasebeta

← #20242384

Subgroups — #20242384

Order 6016.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689722C211yesmaximal, characteristic
2#15689436C211yesmaximal, characteristic
3#15689054C211yesmaximal, characteristic, complemented
4#15688860C211yesmaximal, characteristic, complemented
5#15688858C211yesmaximal, characteristic
6#15688848C211yesmaximal, characteristic, complemented
7C47×#483C211yesmaximal, characteristic, complemented
8#13094019—21no—
9#13094015—21no—
10#13094009—21no—
11#13094008—21no—
12#13094000—21no—
13#13093998C2211yescharacteristic
14(C22⋊D47)⋊C4—21no—
15C2×Dic47⋊C4—21no—
16C2×Dic47⋊C4C2211yescharacteristic
17#13093957—21no—
18#13093944—21no—
19C22⋊(C47⋊C8)C2211yescharacteristic
20C47⋊#95—21no—
21C47⋊#95C2211yescharacteristic
22C22⋊Q8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#106×C47—21no—
25#103×C47—21no—
26C22⋊C8×C47C2211yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33C22×Dic47D411yescharacteristic
34C2×D188D411yescharacteristic
35C2×C4×D47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47D411yescharacteristic
41C22⋊C4×C47—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47D411yescharacteristic
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52Dic47⋊C4—42no—
53C4×Dic47—21no—
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56C22×D47—21no—
57Q8×C47—41no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C22⋊D47—41no—
67C22⋊D47—41no—
68C2×Dic47—22no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77D188—41no—
78C4×D47—81no—
79C8×C47—41no—
80C47⋊C8—41no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47#12011yescharacteristic
84C22×C47#13511yescharacteristic
85C22×C47AGL(1,ℤ/8)11yescharacteristic
86C2×D47—41no—
87C2×D47—41no—
88C2×D47—41no—
89C4×C47—21no—
90C4×C47—21no—
91C4×C47—41no—
92C4×C47—41no—
93C4×C47—81no—
94Dic47—42no—
95Dic47—41no—
96Dic47—41no—
97Dic47—41no—
98#1609—471nomaximal, Sylow
99C2×C47—21no—
100C2×C47—21no—
101C2×C47#44911yescharacteristic
102C2×C47#45611yescharacteristic
103C2×C47#45811yescharacteristic
104D47—81no—
105#539—471no—
106#483D4711yescharacteristic, complemented
107#480—471no—
108#398—471no—
109#328—471no—
110#327—471no—
111#324—471no—
112C47#160911yescharacteristic, complemented, Sylow
113#126—941no—
114#125—941no—
115#123—941no—
116#123—941no—
117C22⋊Q8—941no—
118C22⋊Q8C2×D4711yescharacteristic
119#121—471no—
120C4×D4—941no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—941no—
123C2×C4⋊C4C2×D4711yescharacteristic
124#107—941no—
125#106—21no—
126#103—21no—
127#102—941no—
128C22⋊C8—471no—
129C22⋊C8C2×D4711yescharacteristic
130#95—471no—
131#95—941no—
132C2×Q8C22⋊D4711yescharacteristic
133C2×D4—471no—
134C2×D4—941no—
135C22×C4—21no—
136C22×C4—471no—
137C22×C4—471no—
138C22×C4—941no—
139C22×C4—941no—
140C22×C4C22×D4711yescharacteristic
141C2×C8—21no—
142C2×C8—941no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—471no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4—1882no—
153C4⋊C4C22⋊D4711yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—941no—
156C22⋊C4—941no—
157C22⋊C4—941no—
158C22⋊C4—941no—
159C42—941no—
160C23—941no—
161C23D4×D4711yescharacteristic
162Q8—41no—
163D4—1881no—
164D4—1881no—
165D4—1881no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—942no—
173C2×C4—941no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—941no—
178C2×C4—3761no—
179C2×C4—1881no—
180C2×C4—1881no—
181C2×C4—1881no—
182C2×C4D4×D4711yescharacteristic
183C2×C4C2×C22⋊D4711yescharacteristic
184C8—41no—
185C8—1881no—
186C22—21no—
187C22—21no—
188C22—1881no—
189C22—1881no—
190C22—1881no—
191C22#1309399211yescharacteristic
192C22#1309404511yescharacteristic
193C22#1309405111yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—1882no—
200C4—1881no—
201C4—1881no—
202C4—1881no—
203C2—21no—
204C2—21no—
205C2—3761no—
206C2#1568926711yescharacteristic
207C2#1568930411yescharacteristic
208C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#483C2
socleC22×C47#120
hypercenter#483D47
hypocenterC47#1609
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #15689054C2semidirect
4. #15688860C2semidirect
6. #15688848C2semidirect
7. C47×#483C2semidirect
106. #483D47semidirect
112. C47#1609semidirect