Finite Group Databasebeta

← #20245056

Subgroups — #20245056

Order 6016.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689691C211yesmaximal, characteristic
2#99×D47C212yesmaximal, complemented
3#15688918C211yesmaximal, characteristic, complemented
4#15688915C212yesmaximal, complemented
5C47×#354C211yesmaximal, characteristic, complemented
6C2×#10625354C411yescharacteristic, complemented
7C2×D4×D47C2211yescharacteristic
8#13094021C411yescharacteristic, complemented
9#13094020C2211yescharacteristic
10#13094013C411yescharacteristic, complemented
11#13093997—22no—
12#13093994—22no—
13#13093981C411yescharacteristic, complemented
14C22⋊C4×D47—22no—
15#13093939C2212yes—
16#13093938—22no—
17#124×C47C2211yescharacteristic
18#99×C47C2212yes—
19C23×D47D412yes—
20C2×Q8×C47C2×C411yescharacteristic, complemented
21C2×D4×C47C2311yescharacteristic
22C2×C22⋊D47—22no—
23C2×C22⋊D47D412yes—
24#10625354—42no—
25D4×D47—42no—
26C2×D188—21no—
27C2×D188—22no—
28C2×D188C2×C411yescharacteristic
29C2×D188C2×C411yescharacteristic, complemented
30C2×C4×D47—21no—
31C2×C4×D47—42no—
32C2×C4×D47C2×C411yescharacteristic
33C22⋊C4×C47—22no—
34C22⋊C4×C47—22no—
35C42×C47C2×C411yescharacteristic, complemented
36C22⋊Dic47—22no—
37(C2×D47)⋊C4—21no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—42no—
40Dic47⋊C4—21no—
41C4×Dic47C2×C411yescharacteristic, complemented
42C23×C47C2×D412yes—
43C22×D47—22no—
44C22×D47—22no—
45C22×D47—21no—
46C22×D47—82no—
47C22×D47C22⋊C412yes—
48C22×D47C22⋊C411yescharacteristic
49Q8×C47—41no—
50D4×C47—41no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—42no—
54C2×C4×C47C22×C411yescharacteristic
55C22⋊D47—42no—
56C22⋊D47—82no—
57C2×Dic47—21no—
58C2×Dic47—42no—
59C2×Dic47C22⋊C411yescharacteristic
60D188—41no—
61D188—41no—
62D188—42no—
63D188—82no—
64C4×D47—22no—
65C4×D47—42no—
66C4×D47—84no—
67C22×C47—22no—
68C22×C47—42no—
69C22×C47C2×C22⋊C411yescharacteristic
70C2×D47—22no—
71C2×D47—41no—
72C2×D47—44no—
73C2×D47—42no—
74C2×D47—42no—
75C2×D47—41no—
76C2×D47—82no—
77C2×D47#9912yes—
78C4×C47—21no—
79C4×C47—41no—
80C4×C47—41no—
81C4×C47—82no—
82Dic47—21no—
83Dic47—41no—
84Dic47—82no—
85#2127—471nomaximal, Sylow
86C2×C47—21no—
87C2×C47—42no—
88C2×C47C2×#9911yescharacteristic
89D47—22no—
90D47—42no—
91D47—81no—
92#535—471no—
93C2×#99—472no—
94#354—471no—
95#354D4711yescharacteristic, complemented
96#353—472no—
97C47#212711yescharacteristic, complemented, Sylow
98C2×#41—471no—
99C22×D4—471no—
100#127—471no—
101#127—471no—
102#124—471no—
103#124C2×D4711yescharacteristic
104#121—942no—
105#120—942no—
106#117—471no—
107C2×C22⋊C4—942no—
108#99—472no—
109#99—942no—
110#99C2×D4712yes—
111C24—472no—
112#41—1882no—
113C2×Q8C4×D4711yescharacteristic, complemented
114C2×D4—472no—
115C2×D4—471no—
116C2×D4—471no—
117C2×D4—942no—
118C2×D4—941no—
119C2×D4—942no—
120C2×D4—1882no—
121C2×D4C22×D4711yescharacteristic
122C22×C4—471no—
123C22×C4—941no—
124C22×C4—1882no—
125C4⋊C4—941no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—941no—
129C22⋊C4—942no—
130C22⋊C4—942no—
131C22⋊C4—1882no—
132C42—471no—
133C42C4×D4711yescharacteristic, complemented
134C23—471no—
135C23—472no—
136C23—942no—
137C23—942no—
138C23—941no—
139C23—3762no—
140C23D4×D4712yes—
141Q8—41no—
142D4—41no—
143D4—3762no—
144D4—3762no—
145D4—1881no—
146D4—1881no—
147D4—1882no—
148D4—1882no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—471no—
153C2×C4—942no—
154C2×C4—941no—
155C2×C4—3764no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4C2×C4×D4711yescharacteristic
159C22—22no—
160C22—42no—
161C22—472no—
162C22—942no—
163C22—3762no—
164C22—1881no—
165C22—1882no—
166C22—1882no—
167C22—1884no—
168C22—1881no—
169C22C22⋊C4×D4711yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—941no—
175C4—3762no—
176C4—1881no—
177C2—21no—
178C2—42no—
179C2—942no—
180C2—3761no—
181C2—1882no—
182C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#354C2
socleC2×C47C2×#99
hypercenter#354D47
hypocenterC47#2127
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D47C2semidirect
3. #15688918C2semidirect
4. #15688915C2semidirect
5. C47×#354C2semidirect
6. C2×#10625354C4semidirect
8. #13094021C4semidirect
10. #13094013C4semidirect
13. #13093981C4semidirect
20. C2×Q8×C47C2×C4semidirect
29. C2×D188C2×C4semidirect
35. C42×C47C2×C4semidirect
41. C4×Dic47C2×C4semidirect
95. #354D47semidirect
97. C47#2127semidirect
113. C2×Q8C4×D47semidirect
133. C42C4×D47semidirect