Finite Group Databasebeta

← #19136259

Subgroups — #19136259

Order 5504.

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

normal subgroups only

This group has 258 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#14583448C211yesmaximal, characteristic
2#14582871C212yesmaximal, complemented
3#14582694C211yesmaximal, characteristic, complemented
4#14582691C212yesmaximal, complemented
5C43×#354C211yesmaximal, characteristic, complemented
6C2×#10621902C411yescharacteristic, complemented
7C2×#10621900C2211yescharacteristic
8#13063323C411yescharacteristic, complemented
9#13063321C2211yescharacteristic
10#13063313C411yescharacteristic, complemented
11#13063298—22no—
12(C22⋊D43)⋊C4—22no—
13#13063281—22no—
14C42×D43C411yescharacteristic, complemented
15#13063240C2212yes—
16#13063239—22no—
17#124×C43C2211yescharacteristic
18#99×C43C2212yes—
19C2×Q8×C43C2×C411yescharacteristic
20C2×D4×C43C2311yescharacteristic
21C2×C22⋊D43—22no—
22C2×C22⋊D43D412yes—
23C22×Dic43D412yes—
24#10621902—41no—
25#10621902—41no—
26#10621900—41no—
27#10621900—41no—
28C2×D172—21no—
29C2×D172C2×C411yescharacteristic
30C2×C4×D43—21no—
31C2×C4×D43—21no—
32C2×C4×D43C2×C411yescharacteristic
33C2×Dic86C2×C411yescharacteristic
34C22⋊C4×C43—22no—
35C22⋊C4×C43—22no—
36C42×C43C2×C411yescharacteristic
37C22⋊Dic43—22no—
38(C2×D43)⋊C4—22no—
39Dic43⋊C4—22no—
40Dic43⋊C4—42no—
41C4×Dic43—21no—
42C4×Dic43—42no—
43C4×Dic43C2×C411yescharacteristic
44C23×C43C2×D412yes—
45C22×D43—21no—
46C22×D43C22⋊C411yescharacteristic
47Q8×C43—41no—
48D4×C43—41no—
49C2×C4×C43—21no—
50C2×C4×C43—21no—
51C2×C4×C43—42no—
52C2×C4×C43C22×C411yescharacteristic
53C22⋊D43—42no—
54C22⋊D43—44no—
55C2×Dic43—21no—
56C2×Dic43—22no—
57C2×Dic43—22no—
58C2×Dic43—42no—
59C2×Dic43C22⋊C412yes—
60C2×Dic43C22⋊C411yescharacteristic
61D172—41no—
62D172—42no—
63C4×D43—21no—
64C4×D43—21no—
65C4×D43—42no—
66C4×D43—41no—
67C4×D43—41no—
68Dic86—41no—
69C22×C43—22no—
70C22×C43—42no—
71C22×C43C2×C22⋊C411yescharacteristic
72C2×D43—21no—
73C2×D43—41no—
74C2×D43—42no—
75C2×D43—41no—
76C4×C43—21no—
77C4×C43—41no—
78C4×C43—41no—
79C4×C43—82no—
80Dic43—22no—
81Dic43—22no—
82Dic43—82no—
83Dic43#9911yescharacteristic
84Dic43#9911yescharacteristic
85#2126—431nomaximal, Sylow
86C2×C43—21no—
87C2×C43—42no—
88C2×C43C2×#9911yescharacteristic
89D43—41no—
90D43—81no—
91#532—431no—
92#410—432no—
93#354—431no—
94#354D4311yescharacteristic, complemented
95#353—432no—
96C43#212611yescharacteristic, complemented, Sylow
97C2×#41—431no—
98C2×#41—431no—
99C4⋊Q8—431no—
100#127—431no—
101#124—431no—
102#124C2×D4311yescharacteristic
103#121—862no—
104C4×D4—862no—
105#117—862no—
106C2×C42—431no—
107#99—432no—
108#99—862no—
109#99C2×D4312yes—
110#41—1721no—
111#41—1721no—
112#41—1721no—
113#41—1721no—
114C2×Q8—431no—
115C2×Q8C4×D4311yescharacteristic
116C2×D4—432no—
117C2×D4—431no—
118C2×D4—861no—
119C2×D4—862no—
120C2×D4C22×D4311yescharacteristic
121C22×C4—432no—
122C22×C4—431no—
123C22×C4—861no—
124C22×C4—861no—
125C4⋊C4—862no—
126C4⋊C4—1722no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—862no—
130C22⋊C4—862no—
131C42—431no—
132C42—861no—
133C42—1722no—
134C42C4×D4311yescharacteristic
135C23—431no—
136C23—861no—
137C23D4×D4312yes—
138Q8—41no—
139Q8—1721no—
140D4—41no—
141D4—1721no—
142D4—1722no—
143D4—1722no—
144D4—1724no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—431no—
149C2×C4—432no—
150C2×C4—861no—
151C2×C4—861no—
152C2×C4—862no—
153C2×C4—862no—
154C2×C4—861no—
155C2×C4—1721no—
156C2×C4—1721no—
157C2×C4—1722no—
158C2×C4—1722no—
159C2×C4C2×C4×D4311yescharacteristic
160C22—22no—
161C22—42no—
162C22—861no—
163C22—1722no—
164C22—1721no—
165C22—1721no—
166C22C22⋊C4×D4311yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—431no—
172C4—431no—
173C4—862no—
174C4—862no—
175C4—3442no—
176C2—21no—
177C2—42no—
178C2—3441no—
179C2—1721no—
180C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#354C2
socleC2×C43C2×#99
hypercenter#354D43
hypocenterC43#2126
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. #14582871C2semidirect
3. #14582694C2semidirect
4. #14582691C2semidirect
5. C43×#354C2semidirect
6. C2×#10621902C4semidirect
8. #13063323C4semidirect
10. #13063313C4semidirect
14. C42×D43C4semidirect
94. #354D43semidirect
96. C43#2126semidirect