Finite Group Databasebeta

← #19136263

Subgroups — #19136263

Order 5504.

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#14583467C211yesmaximal, characteristic
2#99×D43C212yesmaximal, complemented
3#14582694C211yesmaximal, characteristic, complemented
4#14582691C212yesmaximal, complemented
5C43×#354C211yesmaximal, characteristic, complemented
6C2×#10621902C411yescharacteristic, complemented
7C2×D4×D43C2211yescharacteristic
8#13063322C411yescharacteristic, complemented
9#13063321C2211yescharacteristic
10#13063314C411yescharacteristic, complemented
11#13063298—22no—
12#13063295—22no—
13#13063282C411yescharacteristic, complemented
14C22⋊C4×D43—22no—
15#13063240C2212yes—
16#13063239—22no—
17#124×C43C2211yescharacteristic
18#99×C43C2212yes—
19C23×D43D412yes—
20C2×Q8×C43C2×C411yescharacteristic, complemented
21C2×D4×C43C2311yescharacteristic
22C2×C22⋊D43—22no—
23C2×C22⋊D43D412yes—
24#10621902—42no—
25D4×D43—42no—
26C2×D172—21no—
27C2×D172—22no—
28C2×D172C2×C411yescharacteristic
29C2×D172C2×C411yescharacteristic, complemented
30C2×C4×D43—21no—
31C2×C4×D43—42no—
32C2×C4×D43C2×C411yescharacteristic
33C22⋊C4×C43—22no—
34C22⋊C4×C43—22no—
35C42×C43C2×C411yescharacteristic, complemented
36C22⋊Dic43—22no—
37(C2×D43)⋊C4—21no—
38(C2×D43)⋊C4—22no—
39(C2×D43)⋊C4—42no—
40Dic43⋊C4—21no—
41C4×Dic43C2×C411yescharacteristic, complemented
42C23×C43C2×D412yes—
43C22×D43—22no—
44C22×D43—22no—
45C22×D43—21no—
46C22×D43—82no—
47C22×D43C22⋊C412yes—
48C22×D43C22⋊C411yescharacteristic
49Q8×C43—41no—
50D4×C43—41no—
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—42no—
54C2×C4×C43C22×C411yescharacteristic
55C22⋊D43—42no—
56C22⋊D43—82no—
57C2×Dic43—21no—
58C2×Dic43—42no—
59C2×Dic43C22⋊C411yescharacteristic
60D172—41no—
61D172—41no—
62D172—42no—
63D172—82no—
64C4×D43—22no—
65C4×D43—42no—
66C4×D43—84no—
67C22×C43—22no—
68C22×C43—42no—
69C22×C43C2×C22⋊C411yescharacteristic
70C2×D43—22no—
71C2×D43—41no—
72C2×D43—44no—
73C2×D43—42no—
74C2×D43—42no—
75C2×D43—41no—
76C2×D43—82no—
77C2×D43#9912yes—
78C4×C43—21no—
79C4×C43—41no—
80C4×C43—41no—
81C4×C43—82no—
82Dic43—21no—
83Dic43—41no—
84Dic43—82no—
85#2127—431nomaximal, Sylow
86C2×C43—21no—
87C2×C43—42no—
88C2×C43C2×#9911yescharacteristic
89D43—22no—
90D43—42no—
91D43—81no—
92#535—431no—
93C2×#99—432no—
94#354—431no—
95#354D4311yescharacteristic, complemented
96#353—432no—
97C43#212711yescharacteristic, complemented, Sylow
98C2×#41—431no—
99C22×D4—431no—
100#127—431no—
101#127—431no—
102#124—431no—
103#124C2×D4311yescharacteristic
104#121—862no—
105#120—862no—
106#117—431no—
107C2×C22⋊C4—862no—
108#99—432no—
109#99—862no—
110#99C2×D4312yes—
111C24—432no—
112#41—1722no—
113C2×Q8C4×D4311yescharacteristic, complemented
114C2×D4—432no—
115C2×D4—431no—
116C2×D4—431no—
117C2×D4—862no—
118C2×D4—861no—
119C2×D4—862no—
120C2×D4—1722no—
121C2×D4C22×D4311yescharacteristic
122C22×C4—431no—
123C22×C4—861no—
124C22×C4—1722no—
125C4⋊C4—861no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—861no—
129C22⋊C4—862no—
130C22⋊C4—862no—
131C22⋊C4—1722no—
132C42—431no—
133C42C4×D4311yescharacteristic, complemented
134C23—431no—
135C23—432no—
136C23—862no—
137C23—862no—
138C23—861no—
139C23—3442no—
140C23D4×D4312yes—
141Q8—41no—
142D4—41no—
143D4—3442no—
144D4—3442no—
145D4—1721no—
146D4—1721no—
147D4—1722no—
148D4—1722no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—431no—
153C2×C4—862no—
154C2×C4—861no—
155C2×C4—3444no—
156C2×C4—1722no—
157C2×C4—1722no—
158C2×C4C2×C4×D4311yescharacteristic
159C22—22no—
160C22—42no—
161C22—432no—
162C22—862no—
163C22—3442no—
164C22—1721no—
165C22—1722no—
166C22—1722no—
167C22—1724no—
168C22—1721no—
169C22C22⋊C4×D4311yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—861no—
175C4—3442no—
176C4—1721no—
177C2—21no—
178C2—42no—
179C2—862no—
180C2—3441no—
181C2—1722no—
182C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#354C2
socleC2×C43C2×#99
hypercenter#354D43
hypocenterC43#2127
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D43C2semidirect
3. #14582694C2semidirect
4. #14582691C2semidirect
5. C43×#354C2semidirect
6. C2×#10621902C4semidirect
8. #13063322C4semidirect
10. #13063314C4semidirect
13. #13063282C4semidirect
20. C2×Q8×C43C2×C4semidirect
29. C2×D172C2×C4semidirect
35. C42×C43C2×C4semidirect
41. C4×Dic43C2×C4semidirect
95. #354D43semidirect
97. C43#2127semidirect
113. C2×Q8C4×D43semidirect
133. C42C4×D43semidirect