Finite Group Databasebeta

← #20242511

Subgroups — #20242511

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#15689858C211yesmaximal, characteristic
2#15689496C211yesmaximal, characteristic
3#15689419C211yesmaximal, characteristic, complemented
4#15689418C211yesmaximal, characteristic, complemented
5#15688866C211yesmaximal, characteristic
6#15688855C211yesmaximal, characteristic, complemented
7C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625325—22no—
9#13094024C2211yescharacteristic
10#13094021C2211yescharacteristic
11#13094013—21no—
12#13094012—21no—
13#13094009—22no—
14C4×Dic94C2211yescharacteristic
15C4×D188—21no—
16#13093986—21no—
17#13093958—21no—
18#13093957—21no—
19C4⋊(C47⋊C8)C2211yescharacteristic
20#13093949—21no—
21#13093948—21no—
22C4×Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47D411yescharacteristic
26C2×D188—21no—
27C2×D188—21no—
28C2×D188D412yes—
29C2×C4×D47—22no—
30C2×Dic94—21no—
31C2×Dic94D411yescharacteristic
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47D411yescharacteristic
36C42×C47—21no—
37C42×C47C2311yescharacteristic
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—22no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47#10625325—44no—
48C22×D47—22no—
49Q8×C47—21no—
50Q8×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47—21no—
57C2×Dic47—21no—
58C2×Dic47—41no—
59D188—42no—
60D188—41no—
61D188—41no—
62D188—41no—
63D188—41no—
64C4×D47—82no—
65Dic94—21no—
66Dic94—21no—
67Dic94—42no—
68C8×C47—22no—
69C8×C47—41no—
70C47⋊C8—41no—
71C22×C47#12011yescharacteristic
72C2×D47—42no—
73C2×D47—42no—
74C2×D47—42no—
75C4×C47—21no—
76C4×C47—41no—
77C4×C47—41no—
78C4×C47#13511yescharacteristic
79C4×C47#13511yescharacteristic
80C4×C47#13711yescharacteristic
81C4×C47#13711yescharacteristic
82Dic47—41no—
83Dic47—41no—
84Dic47—81no—
85#1630—471nomaximal, Sylow
86C2×C47#45211yescharacteristic
87C2×C47#45211yescharacteristic
88C2×C47#45311yescharacteristic
89D47—82no—
90#559—471no—
91#492—471no—
92#477—471no—
93#477—471no—
94#331—471no—
95Q8⋊C8—471no—
96Q8⋊C8D4711yescharacteristic, complemented
97C47#163011yescharacteristic, complemented, Sylow
98C2×SD16—942no—
99C4⋊Q8—471no—
100#127—471no—
101#124—941no—
102#124—941no—
103#123—942no—
104C4×Q8—471no—
105C4×Q8C2×D4711yescharacteristic
106C4×D4—941no—
107C4×D4—941no—
108#107—941no—
109#107—941no—
110C4⋊C8—471no—
111C4⋊C8C2×D4711yescharacteristic
112#103—941no—
113#103—941no—
114C4×C8C2×D4711yescharacteristic
115C2×Q8—471no—
116C2×Q8—941no—
117C2×Q8D18811yescharacteristic
118C2×D4—472no—
119C2×D4—941no—
120C2×D4—941no—
121C22×C4—942no—
122SD16—1884no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—941no—
126C4⋊C4—21no—
127C4⋊C4—471no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4D18811yescharacteristic
132C22⋊C4—942no—
133C22⋊C4—942no—
134C22⋊C4—942no—
135C42—21no—
136C42—941no—
137C42C22×D4711yescharacteristic
138C23—942no—
139Q8—21no—
140Q8—21no—
141Q8—941no—
142Q8—941no—
143Q8—1882no—
144D4—1882no—
145D4—1881no—
146D4—1881no—
147D4—1881no—
148D4—1881no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—941no—
152C2×C4—941no—
153C2×C4—3762no—
154C2×C4—1881no—
155C2×C4C2×D18811yescharacteristic
156C2×C4D4×D4711yescharacteristic
157C2×C4D4×D4711yescharacteristic
158C8—22no—
159C8—41no—
160C8—1881no—
161C22—1882no—
162C22—1882no—
163C22—1882no—
164C22#1309399411yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—3761no—
169C4—1881no—
170C4—1881no—
171C4#1309404511yescharacteristic
172C4#1309404611yescharacteristic
173C4#1309405611yescharacteristic
174C4#1309405711yescharacteristic
175C2—3762no—
176C2#1568928711yescharacteristic
177C2#1568928811yescharacteristic
178C2#1568929211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×Q8⋊C8C2
socleC22×C47#120
hypercenterQ8⋊C8D47
hypocenterC47#1630
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #15689419C2semidirect
4. #15689418C2semidirect
6. #15688855C2semidirect
7. C47×Q8⋊C8C2semidirect
96. Q8⋊C8D47semidirect
97. C47#1630semidirect