Finite Group Databasebeta

← #19134668

Subgroups — #19134668

Order 5504.

504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C22⋊C4×D43C211yesmaximal, characteristic
2#14582754C212yesmaximal
3#14582666C211yesmaximal, characteristic, complemented
4#14582665C212yesmaximal, complemented
5C43×#342C211yesmaximal, characteristic, complemented
6C24×D43C2211yescharacteristic
7C22×C4×D43C412yescomplemented
8C2×C22⋊Dic43C2212yes—
9C2×C22⋊Dic43C2211yescharacteristic
10C2×(C2×D43)⋊C4—24no—
11C2×(C2×D43)⋊C4C412yescomplemented
12C22⋊C4×D43—24no—
13C2×C22⋊C4×C43C2212yes—
14C2×C22⋊C4×C43C2211yescharacteristic
15C24×C43C2311yescharacteristic
16C23×D43—22no—
17C23×D43—21no—
18C23×D43—21no—
19C23×D43—44no—
20C23×D43C2×C411yescharacteristic
21C23×D43C2×C411yescharacteristic
22C23×D43D414yes—
23C22×C4×C43—22no—
24C22×C4×C43C2×C412yes—
25C22×Dic43—22no—
26C22×Dic43C2×C412yes—
27C2×C4×D43—22no—
28C2×C4×D43—22no—
29C2×C4×D43—44no—
30C22⋊C4×C43—22no—
31C22⋊C4×C43—22no—
32C22⋊C4×C43—22no—
33C22⋊Dic43—22no—
34C22⋊Dic43—22no—
35C22⋊Dic43—22no—
36(C2×D43)⋊C4—24no—
37(C2×D43)⋊C4—48no—
38C23×C43—42no—
39C23×C43C22×C411yescharacteristic
40C23×C43C2×D412yes—
41C23×C43#4112yes—
42C23×C43#4111yescharacteristic
43C23×C43#4111yescharacteristic
44C22×D43—21no—
45C22×D43—21no—
46C22×D43—24no—
47C22×D43—21no—
48C22×D43—21no—
49C22×D43—24no—
50C22×D43—24no—
51C22×D43—28no—
52C22×D43—42no—
53C22×D43—44no—
54C22×D43—48no—
55C22×D43—44no—
56C22×D43—44no—
57C22×D43C22⋊C412yes—
58C22×D43C22⋊C412yes—
59C2×C4×C43—22no—
60C2×C4×C43—42no—
61C2×C4×C43—44no—
62C2×C4×C43—42no—
63C2×Dic43—22no—
64C2×Dic43—42no—
65C2×Dic43—44no—
66C2×Dic43—42no—
67C4×D43—44no—
68C4×D43—44no—
69C22×C43—22no—
70C22×C43—24no—
71C22×C43—42no—
72C22×C43—41no—
73C22×C43—41no—
74C22×C43C2×C22⋊C411yescharacteristic
75C22×C43#11711yescharacteristic
76C22×C43#11711yescharacteristic
77C22×C43#12312yes—
78C22×C43#12312yes—
79C2×D43—24no—
80C2×D43—24no—
81C2×D43—22no—
82C2×D43—22no—
83C2×D43—22no—
84C2×D43—24no—
85C2×D43—48no—
86C2×D43—48no—
87C2×D43—42no—
88C2×D43—42no—
89C2×D43#9914yes—
90C4×C43—42no—
91C4×C43—82no—
92Dic43—42no—
93Dic43—82no—
94#1819—431nomaximal, Sylow
95C2×C43—22no—
96C2×C43—22no—
97C2×C43—21no—
98C2×C43—21no—
99C2×C43#38111yescharacteristic
100C2×C43C2×#9912yes—
101D43—24no—
102D43—42no—
103C22×C22⋊C4—431no—
104#379—432no—
105#342—432no—
106#342—431no—
107#342D4311yescharacteristic, complemented
108C43#181911yescharacteristic, complemented, Sylow
109C25—431no—
110C23×C4—432no—
111C2×C22⋊C4—431no—
112C2×C22⋊C4—432no—
113C2×C22⋊C4—432no—
114C2×C22⋊C4—864no—
115C2×C22⋊C4—864no—
116C2×C22⋊C4C2×D4312yes—
117C2×C22⋊C4C2×D4311yescharacteristic
118C24—431no—
119C24—434no—
120C24—431no—
121C24—862no—
122C24—861no—
123C24—861no—
124C24—1724no—
125C24C22×D4311yescharacteristic
126C22×C4—22no—
127C22×C4—432no—
128C22×C4—862no—
129C22×C4—862no—
130C22×C4—862no—
131C22×C4—1724no—
132C22×C4C4×D4312yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—864no—
137C22⋊C4—862no—
138C22⋊C4—862no—
139C22⋊C4—862no—
140C22⋊C4—1728no—
141C23—42no—
142C23—432no—
143C23—432no—
144C23—864no—
145C23—868no—
146C23—861no—
147C23—861no—
148C23—861no—
149C23—861no—
150C23—864no—
151C23—864no—
152C23—1722no—
153C23—1724no—
154C23—1728no—
155C23—1724no—
156C23—1724no—
157C23C2×C4×D4311yescharacteristic
158C23#1062189812yes—
159C23D4×D4312yes—
160C23#1062190011yescharacteristic
161C23#1062190211yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—862no—
167C2×C4—1724no—
168C2×C4—1724no—
169C2×C4—1724no—
170C2×C4—1722no—
171C2×C4—1722no—
172C22—22no—
173C22—24no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—434no—
178C22—864no—
179C22—864no—
180C22—862no—
181C22—862no—
182C22—864no—
183C22—862no—
184C22—1728no—
185C22—1728no—
186C22—1722no—
187C22—1722no—
188C22C22⋊C4×D4311yescharacteristic
189C22#1306328211yescharacteristic
190C22#1306328311yescharacteristic
191C22#1306330712yes—
192C22#1306331012yes—
193C4—42no—
194C4—82no—
195C4—3442no—
196C4—1722no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—864no—
202C2—1722no—
203C2#1458276111yescharacteristic
204C2#99×D4312yes—
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43C2×C22⋊C4
hypercenter#342D43
hypocenterC43#1819
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #14582666C2semidirect
4. #14582665C2semidirect
5. C43×#342C2semidirect
7. C22×C4×D43C4semidirect
11. C2×(C2×D43)⋊C4C4semidirect
107. #342D43semidirect
108. C43#1819semidirect