Finite Group Databasebeta

← #19133615

Subgroups — #19133615

Order 5504.

288 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 57 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#14583215C212yesmaximal, complemented
2#14582835C211yesmaximal, characteristic, complemented
3#14582633C212yesmaximal, complemented
4#14582623C211yesmaximal, characteristic, complemented
5C43×#534C211yesmaximal, characteristic
6C2×C4⋊Dic43C2211yescharacteristic, complemented
7C2×Dic43⋊C4—21no—
8C2×C22⋊Dic43—21no—
9#13063256—22no—
10#13063246—22no—
11C22⋊(C43⋊C8)C2212yescomplemented
12C43⋊#95C2211yescharacteristic, complemented
13C22×D4×C43—21no—
14#123×C43—22no—
15#121×C43—21no—
16#121×C43C2212yes—
17#120×C43—22no—
18C2×C22⋊C4×C43C2211yescharacteristic
19C24×C43—21no—
20C24×C43D411yescharacteristic
21C2×D4×C43—22no—
22C2×D4×C43—21no—
23C2×D4×C43—22no—
24C2×D4×C43—42no—
25C2×D4×C43—42no—
26C2×D4×C43D412yes—
27C22×C4×C43—21no—
28C22×C4×C43D411yescharacteristic
29C22×C4×C43C2311yescharacteristic
30C22×Dic43—21no—
31C22×Dic43—21no—
32C4⋊C4×C43—21no—
33C4⋊C4×C43D412yes—
34C22⋊C4×C43—22no—
35C22⋊C4×C43—22no—
36C22⋊C4×C43—22no—
37C22⋊Dic43—42no—
38C4⋊Dic43—22no—
39Dic43⋊C4—42no—
40C2×C43⋊C8—22no—
41C23×C43—21no—
42C23×C43—21no—
43C23×C43—22no—
44C23×C43—41no—
45C23×C43—41no—
46C23×C43—42no—
47C23×C43—81no—
48C23×C43—81no—
49C23×C43SD1612yes—
50C23×C43C2×D411yescharacteristic
51D4×C43—42no—
52D4×C43—44no—
53D4×C43—42no—
54D4×C43—42no—
55D4×C43—81no—
56C2×C4×C43—21no—
57C2×C4×C43—22no—
58C2×C4×C43—41no—
59C2×C4×C43—42no—
60C2×C4×C43—41no—
61C2×C4×C43C2×D412yes—
62C2×Dic43—22no—
63C2×Dic43—41no—
64C2×Dic43—41no—
65C2×Dic43—41no—
66C2×Dic43—41no—
67C2×Dic43—41no—
68C43⋊C8—42no—
69C22×C43—21no—
70C22×C43—21no—
71C22×C43—22no—
72C22×C43—42no—
73C22×C43—41no—
74C22×C43—41no—
75C22×C43—42no—
76C22×C43—42no—
77C22×C43—42no—
78C22×C43—81no—
79C22×C43—84no—
80C22×C43#12011yescharacteristic
81C22×C43C2×SD1611yescharacteristic
82C22×C43AGL(1,ℤ/8)11yescharacteristic
83C4×C43—22no—
84C4×C43—42no—
85C4×C43—41no—
86Dic43—42no—
87Dic43—81no—
88#1613—431nomaximal, Sylow
89C2×C43—21no—
90C2×C43—21no—
91C2×C43—42no—
92C2×C43—82no—
93C2×C43#45011yescharacteristic
94C2×C43#45311yescharacteristic
95C2×C43#45811yescharacteristic
96#534D4311yescharacteristic
97#481—432no—
98#399—431no—
99#327—432no—
100#323—431no—
101C43#161311yescharacteristic, complemented, Sylow
102C22×D4—21no—
103#123—22no—
104#121—21no—
105#121C2×D4312yes—
106#120—22no—
107C2×C4⋊C4—431no—
108C2×C4⋊C4—861no—
109C2×C22⋊C4—861no—
110C2×C22⋊C4C2×D4311yescharacteristic
111#106—862no—
112#102—862no—
113C22⋊C8—432no—
114#95—431no—
115C24—21no—
116C24C22⋊D4311yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—42no—
121C2×D4—42no—
122C2×D4C22⋊D4312yes—
123C22×C4—21no—
124C22×C4—861no—
125C22×C4—861no—
126C22×C4C22⋊D4311yescharacteristic
127C22×C4C22×D4311yescharacteristic
128C2×C8—862no—
129C4⋊C4—21no—
130C4⋊C4—862no—
131C4⋊C4—1722no—
132C4⋊C4C22⋊D4312yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—1722no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23#1062188312yes—
146C23C2×C22⋊D4311yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—862no—
158C2×C4—1721no—
159C2×C4—1721no—
160C2×C4—1721no—
161C2×C4—1721no—
162C2×C4—1721no—
163C2×C4C2×C22⋊D4312yes—
164C8—1722no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22#1306329411yescharacteristic
177C22C2×#1062188311yescharacteristic
178C22#1306335111yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—3441no—
183C4—1722no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2#1458305011yescharacteristic
189C2#1458306711yescharacteristic
190C2#1458308911yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#534C2
socleC22×C43#120
hypercenter#534D43
hypocenterC43#1613
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14583215C2semidirect
2. #14582835C2semidirect
3. #14582633C2semidirect
4. #14582623C2semidirect
6. C2×C4⋊Dic43C22semidirect
11. C22⋊(C43⋊C8)C22semidirect
12. C43⋊#95C22semidirect
101. C43#1613semidirect