Finite Group Databasebeta

← #19136261

Subgroups — #19136261

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#14583462C211yesmaximal, characteristic
2#99×D43C212yesmaximal, complemented
3#14582693C212yesmaximal, complemented
4#14582692C211yesmaximal, characteristic, complemented
5C43×#353C211yesmaximal, characteristic, complemented
6C2×#10621900C411yescharacteristic, complemented
7C2×D4×D43C2211yescharacteristic
8#13063321C411yescharacteristic, complemented
9#13063313C411yescharacteristic, complemented
10#13063312C2211yescharacteristic
11#13063297—22no—
12#13063293—22no—
13#13063282C411yescharacteristic, complemented
14C22⋊C4×D43—22no—
15#13063240C2212yes—
16#13063239—22no—
17#127×C43C2211yescharacteristic
18#99×C43C2212yes—
19C23×D43D412yes—
20C2×D4×C43—22no—
21C2×D4×C43C2×C411yescharacteristic, complemented
22C2×D4×C43C2311yescharacteristic
23C2×C22⋊D43—21no—
24C2×C22⋊D43—22no—
25C2×C22⋊D43D412yes—
26C22×Dic43—21no—
27#10621900—42no—
28D4×D43—42no—
29C2×D172C2×C411yescharacteristic
30C2×C4×D43—42no—
31C2×C4×D43C2×C411yescharacteristic
32C2×Dic86C2×C411yescharacteristic, complemented
33C22⋊C4×C43—22no—
34C42×C43C2×C411yescharacteristic, complemented
35C22⋊Dic43—22no—
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×C43—21no—
43C23×C43C2×D412yes—
44C22×D43—22no—
45C22×D43—22no—
46C22×D43—82no—
47C22×D43C22⋊C412yes—
48C22×D43C22⋊C411yescharacteristic
49D4×C43—41no—
50D4×C43—41no—
51D4×C43—82no—
52C2×C4×C43—21no—
53C2×C4×C43—42no—
54C2×C4×C43C22×C411yescharacteristic
55C22⋊D43—42no—
56C22⋊D43—42no—
57C22⋊D43—82no—
58C2×Dic43—21no—
59C2×Dic43—21no—
60C2×Dic43—42no—
61C2×Dic43—42no—
62C2×Dic43C22⋊C411yescharacteristic
63D172—41no—
64C4×D43—22no—
65C4×D43—84no—
66Dic86—41no—
67C22×C43—22no—
68C22×C43—42no—
69C22×C43—42no—
70C22×C43—41no—
71C22×C43C2×C22⋊C411yescharacteristic
72C2×D43—22no—
73C2×D43—41no—
74C2×D43—44no—
75C2×D43—42no—
76C2×D43—82no—
77C2×D43#9912yes—
78C4×C43—21no—
79C4×C43—41no—
80C4×C43—82no—
81Dic43—21no—
82Dic43—41no—
83Dic43—41no—
84Dic43—82no—
85#2127—431nomaximal, Sylow
86C2×C43—21no—
87C2×C43—42no—
88C2×C43—81no—
89C2×C43C2×#9911yescharacteristic
90D43—22no—
91D43—42no—
92#535—431no—
93C2×#99—432no—
94#354—432no—
95#353—431no—
96#353D4311yescharacteristic, complemented
97C43#212711yescharacteristic, complemented, Sylow
98C2×#41—431no—
99C22×D4—431no—
100#127—431no—
101#127C2×D4311yescharacteristic
102#124—431no—
103#124—431no—
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×Q8—431no—
114C2×D4—22no—
115C2×D4—432no—
116C2×D4—431no—
117C2×D4—862no—
118C2×D4—861no—
119C2×D4—1722no—
120C2×D4C4×D4311yescharacteristic, complemented
121C2×D4C22×D4311yescharacteristic
122C22×C4—431no—
123C22×C4—861no—
124C22×C4—1722no—
125C4⋊C4—861no—
126C22⋊C4—22no—
127C22⋊C4—861no—
128C22⋊C4—862no—
129C22⋊C4—862no—
130C22⋊C4—862no—
131C22⋊C4—1722no—
132C42—431no—
133C42C4×D4311yescharacteristic, complemented
134C23—21no—
135C23—431no—
136C23—432no—
137C23—862no—
138C23—862no—
139C23—3442no—
140C23D4×D4312yes—
141Q8—1721no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—3442no—
146D4—1721no—
147D4—1722no—
148D4—1722no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—431no—
152C2×C4—862no—
153C2×C4—861no—
154C2×C4—861no—
155C2×C4—3444no—
156C2×C4—1722no—
157C2×C4—1722no—
158C2×C4C2×C4×D4311yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—432no—
164C22—862no—
165C22—3442no—
166C22—1721no—
167C22—1722no—
168C22—1724no—
169C22C22⋊C4×D4311yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—861no—
174C4—3442no—
175C4—1721no—
176C4—1721no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—862no—
181C2—1722no—
182C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#353C2
socleC2×C43C2×#99
hypercenter#353D43
hypocenterC43#2127
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. #99×D43C2semidirect
3. #14582693C2semidirect
4. #14582692C2semidirect
5. C43×#353C2semidirect
6. C2×#10621900C4semidirect
8. #13063321C4semidirect
9. #13063313C4semidirect
13. #13063282C4semidirect
21. C2×D4×C43C2×C4semidirect
32. C2×Dic86C2×C4semidirect
34. C42×C43C2×C4semidirect
41. C4×Dic43C2×C4semidirect
96. #353D43semidirect
97. C43#2127semidirect
120. C2×D4C4×D43semidirect
133. C42C4×D43semidirect