Finite Group Databasebeta

← #19141502

Subgroups — #19141502

Order 5504.

448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13063318C212yesmaximal
2#14582833C212yesmaximal, complemented
3#14582832C212yesmaximal, complemented
4#14582824C211yesmaximal, characteristic
5#14582796C212yesmaximal, complemented
6#14582781C212yesmaximal, complemented
7#14582771C211yesmaximal, characteristic
8#14582757C212yesmaximal
9C43×#397C211yesmaximal, characteristic
10C23×Dic43C2211yescharacteristic
11#13063318—28no—
12C2×C4⋊Dic43C2212yes—
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2211yescharacteristic
21C2×C4×Dic43C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2211yescharacteristic
30#95×C43C2212yes—
31#95×C43C2211yescharacteristic
32C24×C43C2311yescharacteristic
33C22×C4×C43C2312yes—
34C22×C4×C43C2311yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2312yes—
37C22×Dic43—24no—
38C22×Dic43—41no—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C4⋊C4×C43—41no—
44C22⋊C4×C43—24no—
45C22⋊C4×C43—41no—
46C22⋊Dic43—24no—
47C22⋊Dic43D414yes—
48C4⋊Dic43—24no—
49C4⋊Dic43—41no—
50Dic43⋊C4—24no—
51Dic43⋊C4—24no—
52Dic43⋊C4—24no—
53Dic43⋊C4—24no—
54Dic43⋊C4—42no—
55C4×Dic43—24no—
56C23×C43—22no—
57C23×C43—21no—
58C23×C43—21no—
59C23×C43—22no—
60C23×C43C2×D412yes—
61C23×C43C2411yescharacteristic
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×Dic43—22no—
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—44no—
83C2×Dic43C2×D414yes—
84C2×Dic43#4114yes—
85C22×C43—22no—
86C22×C43—24no—
87C22×C43—42no—
88C22×C43—41no—
89C22×C43—41no—
90C22×C43C22×D411yescharacteristic
91C22×C43C2×#4112yes—
92C22×C43H(5,𝔽2)11yescharacteristic
93C22×C432−1+411yescharacteristic
94C22×C432−1+412yes—
95C4×C43—42no—
96C4×C43—42no—
97C4×C43—41no—
98C4×C43—41no—
99Dic43—24no—
100Dic43—24no—
101Dic43—42no—
102Dic43—42no—
103#2722—431nomaximal, Sylow
104C2×C43—42no—
105C2×C43#53711yescharacteristic
106C2×C43#54112yes—
107C2×C43#54712yes—
108C2×C43#55111yescharacteristic
109C2×C43#56311yescharacteristic
110C2×#126—432no—
111#398—432no—
112#398—432no—
113#397—431no—
114#397D4311yescharacteristic
115#389—432no—
116#387—432no—
117#385—431no—
118#380—432no—
119C43#272211yescharacteristic, complemented, Sylow
120C23×C4—431no—
121#126—868no—
122C2×C4⋊C4—432no—
123C2×C4⋊C4—432no—
124C2×C4⋊C4—432no—
125C2×C4⋊C4—432no—
126C2×C4⋊C4—432no—
127C2×C4⋊C4—432no—
128C2×C4⋊C4—431no—
129C2×C4⋊C4C2×D4311yescharacteristic
130C2×C22⋊C4—431no—
131C2×C22⋊C4—432no—
132C2×C22⋊C4C2×D4312yes—
133C2×C22⋊C4C2×D4311yescharacteristic
134C2×C42—432no—
135#95—432no—
136#95—432no—
137#95—432no—
138#95—432no—
139#95—431no—
140#95C2×D4311yescharacteristic
141#95C2×D4312yes—
142C24C22×D4311yescharacteristic
143C22×C4—432no—
144C22×C4—432no—
145C22×C4—432no—
146C22×C4—432no—
147C22×C4—864no—
148C22×C4—1721no—
149C22×C4C22×D4311yescharacteristic
150C22×C4C22×D4312yes—
151C22×C4C22×D4311yescharacteristic
152C22×C4C22×D4312yes—
153C4⋊C4—41no—
154C4⋊C4—864no—
155C4⋊C4—864no—
156C4⋊C4—864no—
157C4⋊C4—864no—
158C4⋊C4—864no—
159C4⋊C4—1722no—
160C4⋊C4—1721no—
161C22⋊C4—24no—
162C22⋊C4—41no—
163C22⋊C4—434no—
164C22⋊C4—864no—
165C42—864no—
166C23—22no—
167C23—21no—
168C23—21no—
169C23—22no—
170C23D4×D4312yes—
171C23C23×D4311yescharacteristic
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—434no—
183C2×C4—434no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—1724no—
195C22—22no—
196C22—24no—
197C22—41no—
198C22—41no—
199C22—42no—
200C22C2×D4×D4311yescharacteristic
201C22#41×D4312yes—
202C22#1306337011yescharacteristic
203C22#1306337212yes—
204C22#1306337211yescharacteristic
205C4—41no—
206C4—41no—
207C4—42no—
208C4—42no—
209C4—864no—
210C4—864no—
211C4—1722no—
212C4—1722no—
213C2—42no—
214C2#1458347611yescharacteristic
215C2#1458350612yes—
216C2#1458354712yes—
217C2#1458357911yescharacteristic
218C2#1458365211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2722
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #14582833C2semidirect
3. #14582832C2semidirect
5. #14582796C2semidirect
6. #14582781C2semidirect
119. C43#2722semidirect