Finite Group Databasebeta

← #19136265

Subgroups — #19136265

Order 5504.

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#14583462C211yesmaximal, characteristic
2#14582871C212yesmaximal, complemented
3#14582692C211yesmaximal, characteristic, complemented
4#14582691C212yesmaximal, complemented
5C43×#353C211yesmaximal, characteristic, complemented
6C2×#10621900C2211yescharacteristic
7C2×D4×D43C411yescharacteristic, complemented
8#13063321C2211yescharacteristic
9#13063313C411yescharacteristic, complemented
10#13063312C411yescharacteristic, complemented
11#13063297—22no—
12#13063293—22no—
13#13063282C411yescharacteristic, complemented
14#13063281—22no—
15#13063240C2212yescomplemented
16#13063239—22no—
17#127×C43C2211yescharacteristic
18#99×C43C2212yescomplemented
19C23×D43—21no—
20C2×D4×C43—22no—
21C2×D4×C43C2×C411yescharacteristic
22C2×D4×C43C2311yescharacteristic
23C2×C22⋊D43—21no—
24C2×C22⋊D43—22no—
25C2×C22⋊D43D412yes—
26C22×Dic43D412yes—
27#10621900—42no—
28D4×D43—42no—
29C2×D172C2×C411yescharacteristic
30C2×C4×D43C2×C411yescharacteristic
31C2×Dic86C2×C411yescharacteristic
32C22⋊C4×C43—22no—
33C42×C43C2×C411yescharacteristic
34C22⋊Dic43—22no—
35C22⋊Dic43—22no—
36(C2×D43)⋊C4—22no—
37(C2×D43)⋊C4—21no—
38Dic43⋊C4—21no—
39Dic43⋊C4—42no—
40C4×Dic43—42no—
41C4×Dic43C2×C411yescharacteristic
42C23×C43—21no—
43C23×C43C2×D412yes—
44C22×D43—21no—
45C22×D43—42no—
46C22×D43—82no—
47C22×D43C22⋊C411yescharacteristic
48D4×C43—41no—
49D4×C43—41no—
50D4×C43—82no—
51C2×C4×C43—21no—
52C2×C4×C43—42no—
53C2×C4×C43C22×C411yescharacteristic
54C22⋊D43—42no—
55C22⋊D43—42no—
56C22⋊D43—82no—
57C2×Dic43—22no—
58C2×Dic43—22no—
59C2×Dic43—21no—
60C2×Dic43—42no—
61C2×Dic43C22⋊C412yes—
62C2×Dic43C22⋊C411yescharacteristic
63D172—41no—
64C4×D43—22no—
65Dic86—41no—
66C22×C43—22no—
67C22×C43—42no—
68C22×C43—42no—
69C22×C43—41no—
70C22×C43C2×C22⋊C411yescharacteristic
71C2×D43—21no—
72C2×D43—41no—
73C2×D43—42no—
74C2×D43—41no—
75C2×D43—84no—
76C4×C43—21no—
77C4×C43—41no—
78C4×C43—82no—
79Dic43—22no—
80Dic43—41no—
81Dic43—82no—
82Dic43#9912yes—
83#2128—431nomaximal, Sylow
84C2×C43—21no—
85C2×C43—42no—
86C2×C43—81no—
87C2×C43C2×#9911yescharacteristic
88D43—41no—
89D43—81no—
90#535—431no—
91#410—432no—
92#353—431no—
93#353—432no—
94#353D4311yescharacteristic, complemented
95C43#212811yescharacteristic, complemented, Sylow
96C2×#41—431no—
97C22×D4—431no—
98#127—431no—
99#127C2×D4311yescharacteristic
100#124—431no—
101#124—431no—
102#121—862no—
103#120—862no—
104#117—431no—
105#117—862no—
106#99—432no—
107#99—862no—
108#99C2×D4312yescomplemented
109C24—861no—
110#41—1722no—
111C2×Q8—431no—
112C2×D4—22no—
113C2×D4—432no—
114C2×D4—431no—
115C2×D4—861no—
116C2×D4—862no—
117C2×D4—1722no—
118C2×D4C4×D4311yescharacteristic
119C2×D4C22×D4311yescharacteristic
120C22×C4—432no—
121C22×C4—431no—
122C4⋊C4—861no—
123C4⋊C4—1722no—
124C22⋊C4—22no—
125C22⋊C4—862no—
126C22⋊C4—861no—
127C22⋊C4—862no—
128C22⋊C4—862no—
129C42—431no—
130C42—1722no—
131C42C4×D4311yescharacteristic
132C23—21no—
133C23—431no—
134C23—861no—
135C23—3442no—
136C23—1722no—
137C23D4×D4312yes—
138Q8—1721no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—3442no—
143D4—1721no—
144D4—1722no—
145D4—1722no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—431no—
149C2×C4—432no—
150C2×C4—862no—
151C2×C4—862no—
152C2×C4—862no—
153C2×C4—861no—
154C2×C4—1722no—
155C2×C4C2×C4×D4311yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—861no—
161C22—3444no—
162C22—1722no—
163C22—1721no—
164C22—1721no—
165C22C22⋊C4×D4311yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—432no—
170C4—862no—
171C4—3442no—
172C4—1721no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—3441no—
177C2—1721no—
178C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#353C2
socleC2×C43C2×#99
hypercenter#353D43
hypocenterC43#2128
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #14582871C2semidirect
3. #14582692C2semidirect
4. #14582691C2semidirect
5. C43×#353C2semidirect
7. C2×D4×D43C4semidirect
9. #13063313C4semidirect
10. #13063312C4semidirect
13. #13063282C4semidirect
15. #13063240C22semidirect
18. #99×C43C22semidirect
94. #353D43semidirect
95. C43#2128semidirect
108. #99C2×D43semidirect