Finite Group Databasebeta

← #20245058

Subgroups — #20245058

Order 6016.

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

normal subgroups only

This group has 270 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#15689686C211yesmaximal, characteristic
2#15689095C212yesmaximal, complemented
3#15688916C211yesmaximal, characteristic, complemented
4#15688915C212yesmaximal, complemented
5C47×#353C211yesmaximal, characteristic, complemented
6C2×#10625352C2211yescharacteristic
7C2×D4×D47C411yescharacteristic, complemented
8#13094020C2211yescharacteristic
9#13094012C411yescharacteristic, complemented
10#13094011C411yescharacteristic, complemented
11#13093996—22no—
12#13093992—22no—
13#13093981C411yescharacteristic, complemented
14#13093980—22no—
15#13093939C2212yescomplemented
16#13093938—22no—
17#127×C47C2211yescharacteristic
18#99×C47C2212yescomplemented
19C23×D47—21no—
20C2×D4×C47—22no—
21C2×D4×C47C2×C411yescharacteristic
22C2×D4×C47C2311yescharacteristic
23C2×C22⋊D47—22no—
24C2×C22⋊D47—21no—
25C2×C22⋊D47D412yes—
26C22×Dic47D412yes—
27#10625352—42no—
28D4×D47—42no—
29C2×D188C2×C411yescharacteristic
30C2×C4×D47C2×C411yescharacteristic
31C2×Dic94C2×C411yescharacteristic
32C22⋊C4×C47—22no—
33C42×C47C2×C411yescharacteristic
34C22⋊Dic47—22no—
35C22⋊Dic47—22no—
36(C2×D47)⋊C4—21no—
37(C2×D47)⋊C4—22no—
38Dic47⋊C4—21no—
39Dic47⋊C4—42no—
40C4×Dic47—42no—
41C4×Dic47C2×C411yescharacteristic
42C23×C47—21no—
43C23×C47C2×D412yes—
44C22×D47—21no—
45C22×D47—42no—
46C22×D47—82no—
47C22×D47C22⋊C411yescharacteristic
48D4×C47—41no—
49D4×C47—41no—
50D4×C47—82no—
51C2×C4×C47—21no—
52C2×C4×C47—42no—
53C2×C4×C47C22×C411yescharacteristic
54C22⋊D47—42no—
55C22⋊D47—42no—
56C22⋊D47—82no—
57C2×Dic47—22no—
58C2×Dic47—22no—
59C2×Dic47—21no—
60C2×Dic47—42no—
61C2×Dic47C22⋊C412yes—
62C2×Dic47C22⋊C411yescharacteristic
63D188—41no—
64C4×D47—22no—
65Dic94—41no—
66C22×C47—22no—
67C22×C47—42no—
68C22×C47—42no—
69C22×C47—41no—
70C22×C47C2×C22⋊C411yescharacteristic
71C2×D47—21no—
72C2×D47—41no—
73C2×D47—42no—
74C2×D47—41no—
75C2×D47—84no—
76C4×C47—21no—
77C4×C47—41no—
78C4×C47—82no—
79Dic47—22no—
80Dic47—41no—
81Dic47—82no—
82Dic47#9912yes—
83#2128—471nomaximal, Sylow
84C2×C47—21no—
85C2×C47—42no—
86C2×C47—81no—
87C2×C47C2×#9911yescharacteristic
88D47—41no—
89D47—81no—
90#535—471no—
91#410—472no—
92#353—471no—
93#353—472no—
94#353D4711yescharacteristic, complemented
95C47#212811yescharacteristic, complemented, Sylow
96C2×#41—471no—
97C22×D4—471no—
98#127—471no—
99#127C2×D4711yescharacteristic
100#124—471no—
101#124—471no—
102#121—942no—
103#120—942no—
104#117—471no—
105#117—942no—
106#99—472no—
107#99—942no—
108#99C2×D4712yescomplemented
109C24—941no—
110#41—1882no—
111C2×Q8—471no—
112C2×D4—22no—
113C2×D4—472no—
114C2×D4—471no—
115C2×D4—941no—
116C2×D4—942no—
117C2×D4—1882no—
118C2×D4C4×D4711yescharacteristic
119C2×D4C22×D4711yescharacteristic
120C22×C4—472no—
121C22×C4—471no—
122C4⋊C4—941no—
123C4⋊C4—1882no—
124C22⋊C4—22no—
125C22⋊C4—942no—
126C22⋊C4—941no—
127C22⋊C4—942no—
128C22⋊C4—942no—
129C42—471no—
130C42—1882no—
131C42C4×D4711yescharacteristic
132C23—21no—
133C23—471no—
134C23—941no—
135C23—3762no—
136C23—1882no—
137C23D4×D4712yes—
138Q8—1881no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—3762no—
143D4—1881no—
144D4—1882no—
145D4—1882no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—471no—
149C2×C4—472no—
150C2×C4—942no—
151C2×C4—942no—
152C2×C4—942no—
153C2×C4—941no—
154C2×C4—1882no—
155C2×C4C2×C4×D4711yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—941no—
161C22—3764no—
162C22—1882no—
163C22—1881no—
164C22—1881no—
165C22C22⋊C4×D4711yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—472no—
170C4—942no—
171C4—3762no—
172C4—1881no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—3761no—
177C2—1881no—
178C2#99×D4711yescharacteristic
subgroupG/H
centerC2#99×D47
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#353C2
socleC2×C47C2×#99
hypercenter#353D47
hypocenterC47#2128
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #15689095C2semidirect
3. #15688916C2semidirect
4. #15688915C2semidirect
5. C47×#353C2semidirect
7. C2×D4×D47C4semidirect
9. #13094012C4semidirect
10. #13094011C4semidirect
13. #13093981C4semidirect
15. #13093939C22semidirect
18. #99×C47C22semidirect
94. #353D47semidirect
95. C47#2128semidirect
108. #99C2×D47semidirect