Finite Group Databasebeta

← #20242532

Subgroups — #20242532

Order 6016.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689838C211yesmaximal, characteristic
2#15689502C211yesmaximal, characteristic, complemented
3#15689410C211yesmaximal, characteristic, complemented
4#15688871C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#476C211yesmaximal, characteristic, complemented
8C2×#10625337—22no—
9#13094024C2211yescharacteristic
10#13094010—22no—
11#13093998—21no—
12#13093995—21no—
13C4×D188C2211yescharacteristic
14#13093983—21no—
15#13093982—21no—
16#13093955—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18#13093944—21no—
19C4×C47⋊C8C2211yescharacteristic
20C4⋊Q8×C47C2211yescharacteristic
21C4×D4×C47C2211yescharacteristic
22#106×C47—21no—
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×Q8×C47—21no—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47—21no—
28C2×C22⋊D47—22no—
29C2×D188D411yescharacteristic
30C2×C4×D47—21no—
31C2×Dic94D412yes—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47D411yescharacteristic
36C22⋊C4×C47—21no—
37C42×C47C2311yescharacteristic
38C22⋊Dic47—22no—
39#10625337—44no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47D411yescharacteristic
45C4×Dic47—22no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49C22×D47—21no—
50Q8×C47—42no—
51D4×C47—21no—
52D4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C22⋊D47—82no—
61C2×Dic47—21no—
62C2×Dic47—22no—
63D188—21no—
64D188—21no—
65C4×D47—41no—
66C4×D47—41no—
67Dic94—42no—
68C8×C47—41no—
69C47⋊C8—22no—
70C47⋊C8—41no—
71C22×C47—41no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47#12011yescharacteristic
75C2×D47—41no—
76C2×D47—41no—
77C2×D47—41no—
78C4×C47—21no—
79C4×C47—41no—
80C4×C47—81no—
81C4×C47#13511yescharacteristic
82C4×C47#13511yescharacteristic
83C4×C47#13711yescharacteristic
84C4×C47#13711yescharacteristic
85Dic47—41no—
86Dic47—42no—
87#1634—471nomaximal, Sylow
88C2×C47—81no—
89C2×C47#45211yescharacteristic
90C2×C47#45211yescharacteristic
91C2×C47#45311yescharacteristic
92D47—81no—
93#555—471no—
94#494—471no—
95#476—471no—
96#476D4711yescharacteristic, complemented
97#333—471no—
98D4⋊C8—471no—
99D4⋊C8—471no—
100C47#163411yescharacteristic, complemented, Sylow
101C2×Q16—942no—
102C4⋊Q8—471no—
103C4⋊Q8C2×D4711yescharacteristic
104#124—942no—
105#121—941no—
106#121—941no—
107C4×D4—471no—
108C4×D4C2×D4711yescharacteristic
109#117—941no—
110#117—941no—
111#106—21no—
112#106—941no—
113C4⋊C8—471no—
114C4⋊C8C2×D4711yescharacteristic
115#102—21no—
116#102—941no—
117C4×C8—471no—
118C2×Q8—21no—
119C2×Q8—472no—
120C2×D4—471no—
121C2×D4—942no—
122C2×D4C22⋊D4711yescharacteristic
123C22×C4—21no—
124C22×C4—941no—
125Q16—1884no—
126C2×C8—21no—
127C2×C8—941no—
128C2×C8—941no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—471no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4C22⋊D4711yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—942no—
137C22⋊C4—942no—
138C22⋊C4—941no—
139C42—942no—
140C42C22×D4711yescharacteristic
141C23—21no—
142C23—941no—
143Q8—42no—
144Q8—1882no—
145D4—21no—
146D4—21no—
147D4—941no—
148D4—941no—
149D4—3762no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—941no—
155C2×C4—942no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4D4×D4711yescharacteristic
159C2×C4D4×D4711yescharacteristic
160C2×C4C2×C22⋊D4711yescharacteristic
161C8—41no—
162C8—942no—
163C8—1881no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—1881no—
168C22—1881no—
169C22—1881no—
170C22#1309399211yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—1881no—
175C4—1882no—
176C4#1309404411yescharacteristic
177C4#1309404511yescharacteristic
178C4#1309405311yescharacteristic
179C4#1309405511yescharacteristic
180C2—81no—
181C2—3761no—
182C2#1568928211yescharacteristic
183C2#1568928311yescharacteristic
184C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#476C2
socleC22×C47#120
hypercenter#476D47
hypocenterC47#1634
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #15689502C2semidirect
3. #15689410C2semidirect
4. #15688871C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×#476C2semidirect
96. #476D47semidirect
100. C47#1634semidirect