Finite Group Databasebeta

← #20242710

Subgroups — #20242710

Order 6016.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689867C211yesmaximal, characteristic
2#15689491C211yesmaximal, characteristic, complemented
3#15689485C211yesmaximal, characteristic, complemented
4#15688864C211yesmaximal, characteristic, complemented
5#15688863C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic, complemented
7C47×#489C211yesmaximal, characteristic, complemented
8#13094016C2211yescharacteristic
9#13094012C2211yescharacteristic
10#13094008—21no—
11#13094006—21no—
12#13094001—21no—
13#13094000—21no—
14#13093997—21no—
15#13093996—21no—
16#13093948—21no—
17#13093948—21no—
18#13093947—21no—
19#13093944—21no—
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#124×C47C2211yescharacteristic
24#103×C47—21no—
25#102×C47—21no—
26#97×C47C2211yescharacteristic
27C2×Q8×C47—21no—
28C2×Q8×C47D411yescharacteristic
29C2×D4×C47D411yescharacteristic
30C2×C22⋊D47—21no—
31C2×C22⋊D47—21no—
32C22×Dic47—21no—
33C2×D188D411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94D411yescharacteristic
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C42×C47C2311yescharacteristic
42C22⋊Dic47—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47D411yescharacteristic
48C4⋊Dic47D411yescharacteristic
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47—21no—
55C22×D47—21no—
56Q8×C47—41no—
57Q8×C47—42no—
58D4×C47—41no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C22⋊D47—81no—
65C22⋊D47—81no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—81no—
70D188—41no—
71C4×D47—81no—
72Dic94—41no—
73C8×C47—41no—
74C47⋊C8—41no—
75C47⋊C8—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47#12011yescharacteristic
80C2×D47—41no—
81C2×D47—41no—
82C2×D47—41no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—41no—
87C4×C47—81no—
88Dic47—41no—
89Dic47—41no—
90Dic47—41no—
91#1662—471nomaximal, Sylow
92C2×C47—81no—
93C2×C47#45411yescharacteristic
94C2×C47#45511yescharacteristic
95C2×C47#45511yescharacteristic
96D47—81no—
97#562—471no—
98#491—471no—
99#489—471no—
100#489D4711yescharacteristic, complemented
101#330—471no—
102#329—471no—
103#329—471no—
104C47#166211yescharacteristic, complemented, Sylow
105C4⋊Q8C2×D4711yescharacteristic
106#125—471no—
107#124—471no—
108#124C2×D4711yescharacteristic
109#123—941no—
110#123—941no—
111C22⋊Q8—941no—
112C22⋊Q8—941no—
113#121—941no—
114#121—941no—
115#103—21no—
116#103—941no—
117#103—941no—
118#103—941no—
119#102—21no—
120#102—941no—
121#97—471no—
122#97—471no—
123#97C2×D4711yescharacteristic
124C2×Q8—21no—
125C2×Q8—471no—
126C2×Q8C22⋊D4711yescharacteristic
127C2×D4—471no—
128C2×D4—941no—
129C2×D4—941no—
130C2×D4C22⋊D4711yescharacteristic
131C22×C4—941no—
132C22×C4—941no—
133C2×C8—21no—
134C2×C8—941no—
135C2×C8—941no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—471no—
139C4⋊C4—471no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—941no—
147C22⋊C4—941no—
148C22⋊C4—941no—
149C22⋊C4—941no—
150C42C22×D4711yescharacteristic
151C23—21no—
152C23—941no—
153Q8—41no—
154Q8—42no—
155Q8—1881no—
156D4—41no—
157D4—3761no—
158D4—3761no—
159D4—1881no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—941no—
163C2×C4—941no—
164C2×C4—941no—
165C2×C4—3761no—
166C2×C4—3761no—
167C2×C4D4×D4711yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C2×C4C2×C22⋊D4711yescharacteristic
170C8—41no—
171C8—1881no—
172C8—1881no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—1881no—
177C22—1881no—
178C22—1881no—
179C22#1309399211yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—1881no—
186C4—1881no—
187C4—1881no—
188C2—81no—
189C2—3761no—
190C2#1568929411yescharacteristic
191C2#1568929911yescharacteristic
192C2#1568930011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#489C2
socleC22×C47#120
hypercenter#489D47
hypocenterC47#1662
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #15689491C2semidirect
3. #15689485C2semidirect
4. #15688864C2semidirect
5. #15688863C2semidirect
6. #15688862C2semidirect
7. C47×#489C2semidirect
100. #489D47semidirect
104. C47#1662semidirect