Finite Group Databasebeta

← #19145803

Subgroups — #19145803

Order 5504.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583456C211yesmaximal, characteristic
2C2×#13063317C211yesmaximal, characteristic
3#14583308C212yesmaximal, complemented
4#14583268C212yesmaximal, complemented
5#14583235C212yesmaximal
6#14583230C212yesmaximal
7#14583207C214yesmaximal, complemented
8C43×#432C211yesmaximal, characteristic
9#13063325C2211yescharacteristic
10#13063325C2211yescharacteristic
11#13063317—21no—
12#13063317—21no—
13#13063317—21no—
14#13063317C2212yes—
15#13063317C2212yes—
16#13063304—21no—
17#13063304C2212yes—
18C4×Dic86—21no—
19C4×Dic86C2212yes—
20#13063284—21no—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊Dic43C2211yescharacteristic
23C2×Dic43⋊C4—21no—
24C2×Dic43⋊C4—21no—
25#13063259C2214yes—
26#13063257C2214yes—
27#13063250C2214yes—
28#13063250C2214yes—
29C2×C42×C43C2211yescharacteristic
30C4⋊C8×C43C2212yes—
31C22⋊C8×C43C2212yes—
32#97×C43C2212yes—
33C22×C4×C43D411yescharacteristic
34C22×C4×C43D411yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C22×Dic43—21no—
37C22×Dic43—21no—
38C2×Dic86—21no—
39C2×Dic86C2312yes—
40C2×C8×C43C2314yes—
41C42×C43D411yescharacteristic
42C42×C43D411yescharacteristic
43C42×C43C2311yescharacteristic
44C42×C43C2311yescharacteristic
45C22⋊Dic43—22no—
46C4⋊Dic43—21no—
47C4⋊Dic43—21no—
48C4⋊Dic43—21no—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43C2312yes—
52C4⋊Dic43C2312yes—
53C4⋊Dic43C2312yes—
54Dic43⋊C4—22no—
55Dic43⋊C4—22no—
56Dic43⋊C4—22no—
57Dic43⋊C4—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60C4×Dic43—22no—
61C23×C43C2×D411yescharacteristic
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—41no—
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2411yescharacteristic
71C2×Dic43—22no—
72C2×Dic43—22no—
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43—42no—
76C2×Dic43—42no—
77Dic86—24no—
78Dic86—42no—
79C8×C43—24no—
80C22×C43—21no—
81C22×C43—21no—
82C22×C43#13712yes—
83C22×C43C22×D411yescharacteristic
84C4×C43—21no—
85C4×C43—21no—
86C4×C43—21no—
87C4×C43—21no—
88C4×C43—21no—
89C4×C432−1+412yes—
90Dic43—42no—
91Dic43—42no—
92Dic43—42no—
93Dic43—42no—
94#3236—431nomaximal, Sylow
95C2×C43—22no—
96C2×C43#53611yescharacteristic
97C2×C43C2×#13711yescharacteristic
98C2×C43#57511yescharacteristic
99#533—431no—
100C2×#125—431no—
101#501—432no—
102#491—432no—
103#484—432no—
104#483—432no—
105#479—434no—
106#432D4311yescharacteristic
107C43#323611yescharacteristic, complemented, Sylow
108C4⋊Q8—431no—
109C4⋊Q8—431no—
110#125—432no—
111#125—432no—
112#125—861no—
113#125—861no—
114#125—861no—
115C22⋊Q8—432no—
116C22⋊Q8—861no—
117C4×Q8—432no—
118C4×Q8—861no—
119#117—861no—
120C2×C4⋊C4—431no—
121C2×C4⋊C4—431no—
122C2×C4⋊C4—861no—
123C2×C4⋊C4—861no—
124C2×C42C2×D4311yescharacteristic
125#107—434no—
126#106—434no—
127C4⋊C8C2×D4312yes—
128#103—434no—
129#103—434no—
130C22⋊C8C2×D4312yes—
131#97C2×D4312yes—
132C2×Q8—432no—
133C2×Q8—861no—
134C22×C4—861no—
135C22×C4—861no—
136C22×C4D17211yescharacteristic
137C22×C4D17211yescharacteristic
138C22×C4C22×D4311yescharacteristic
139C2×C8C22×D4314yes—
140C4⋊C4—432no—
141C4⋊C4—432no—
142C4⋊C4—432no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4—862no—
146C4⋊C4—862no—
147C4⋊C4—862no—
148C4⋊C4—862no—
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—862no—
152C4⋊C4—862no—
153C4⋊C4—861no—
154C22⋊C4—862no—
155C42—862no—
156C42D17211yescharacteristic
157C42D17211yescharacteristic
158C42C22×D4311yescharacteristic
159C42C22×D4311yescharacteristic
160C23C2×D17211yescharacteristic
161Q8—864no—
162Q8—1722no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—862no—
167C2×C4—862no—
168C2×C4—862no—
169C2×C4—862no—
170C2×C4—1722no—
171C2×C4—1722no—
172C2×C4C2×D17211yescharacteristic
173C2×C4C2×D17211yescharacteristic
174C2×C4C2×D17211yescharacteristic
175C2×C4C2×D17211yescharacteristic
176C2×C4C2×D17211yescharacteristic
177C2×C4C23×D4311yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1306335812yes—
182C22C22×D17211yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—1722no—
189C4—1722no—
190C4—1722no—
191C4—1722no—
192C4#1306337212yes—
193C2—22no—
194C2#1458347511yescharacteristic
195C2C2×#1306335811yescharacteristic
196C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3236
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #14583308C2semidirect
4. #14583268C2semidirect
7. #14583207C2semidirect
107. C43#3236semidirect