Finite Group Databasebeta

← #19133746

Subgroups — #19133746

Order 5504.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#14583251C211yesmaximal, characteristic, complemented
2#14583189C211yesmaximal, characteristic, complemented
3#14583189C211yesmaximal, characteristic, complemented
4#14582645C211yesmaximal, characteristic, complemented
5D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
7C43×#547C211yesmaximal, characteristic
8#13063325C2211yescharacteristic
9#13063256—21no—
10#13063256—21no—
11C4⋊(C43⋊C8)C2211yescharacteristic
12C4⋊(C43⋊C8)C2211yescharacteristic
13#13063248—22no—
14#13063246—21no—
15#13063246—21no—
16C4×C43⋊C8C2211yescharacteristic
17C2×#41×C43—21no—
18C4⋊Q8×C43C2211yescharacteristic
19#123×C43—22no—
20C22⋊Q8×C43—21no—
21#121×C43—21no—
22C4×D4×C43C2211yescharacteristic
23C4×D4×C43C2211yescharacteristic
24C2×C4⋊C4×C43—21no—
25#41×C43—42no—
26#41×C43—42no—
27C2×Q8×C43—21no—
28C2×D4×C43—22no—
29C2×D4×C43D411yescharacteristic
30C2×D4×C43D411yescharacteristic
31C22×C4×C43—22no—
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C2×Dic86—21no—
35C4⋊C4×C43—22no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C4⋊C4×C43D411yescharacteristic
39C4⋊C4×C43D412yes—
40C22⋊C4×C43—22no—
41C22⋊C4×C43—21no—
42C22⋊C4×C43—21no—
43C42×C43C2311yescharacteristic
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C2×C43⋊C8—21no—
49C23×C43—21no—
50C23×C43—21no—
51Q8×C43—41no—
52Q8×C43—41no—
53D4×C43—21no—
54D4×C43—21no—
55D4×C43—21no—
56D4×C43—44no—
57D4×C43SD1612yes—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—22no—
61C2×C4×C43—44no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×Dic43—41no—
70Dic86—42no—
71C43⋊C8—41no—
72C43⋊C8—41no—
73C43⋊C8—41no—
74C22×C43—22no—
75C22×C43—41no—
76C22×C43—41no—
77C22×C43—41no—
78C22×C43—41no—
79C22×C43—41no—
80C22×C43#12011yescharacteristic
81C4×C43—21no—
82C4×C43—41no—
83C4×C43—42no—
84C4×C43—41no—
85C4×C43C2×SD1611yescharacteristic
86C4×C43#13511yescharacteristic
87C4×C43AGL(1,ℤ/8)11yescharacteristic
88C4×C43#13711yescharacteristic
89Dic43—81no—
90#1635—431nomaximal, Sylow
91C2×C43—42no—
92C2×C43—81no—
93C2×C43#45011yescharacteristic
94C2×C43#45211yescharacteristic
95C2×C43#45411yescharacteristic
96#547D4311yescharacteristic
97#487—431no—
98#476—431no—
99#476—431no—
100#332—431no—
101D4⋊C8—431no—
102D4⋊C8—431no—
103C43#163511yescharacteristic, complemented, Sylow
104C2×#41—21no—
105C4⋊Q8—431no—
106C4⋊Q8C2×D4311yescharacteristic
107#123—22no—
108C22⋊Q8—21no—
109#121—21no—
110C4×D4C2×D4311yescharacteristic
111C4×D4C2×D4311yescharacteristic
112C2×C4⋊C4—21no—
113#106—861no—
114#106—861no—
115C4⋊C8—431no—
116C4⋊C8—431no—
117#103—862no—
118#102—861no—
119#102—861no—
120C4×C8—431no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—861no—
125C2×D4—22no—
126C2×D4C22⋊D4311yescharacteristic
127C2×D4C22⋊D4311yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—861no—
132C2×C8—861no—
133C2×C8—861no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—861no—
137C4⋊C4—861no—
138C4⋊C4C22⋊D4312yes—
139C4⋊C4C22⋊D4311yescharacteristic
140C4⋊C4C22⋊D4311yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C22×D4311yescharacteristic
145C23—21no—
146C23—21no—
147Q8—41no—
148Q8—41no—
149Q8—1722no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4#1062188312yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1721no—
164C2×C4C2×C22⋊D4311yescharacteristic
165C2×C4C2×C22⋊D4311yescharacteristic
166C2×C4C2×C22⋊D4311yescharacteristic
167C8—1721no—
168C8—1721no—
169C8—1721no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1306329411yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—3441no—
182C4C2×#1062188311yescharacteristic
183C4#1306334511yescharacteristic
184C4#1306335111yescharacteristic
185C4#1306335511yescharacteristic
186C2—42no—
187C2—81no—
188C2#1458305011yescharacteristic
189C2#1458306111yescharacteristic
190C2#1458307211yescharacteristic
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#547C2
socleC22×C43#120
hypercenter#547D43
hypocenterC43#1635
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14583251C2semidirect
2. #14583189C2semidirect
3. #14583189C2semidirect
4. #14582645C2semidirect
5. D4⋊(C43⋊C8)C2semidirect
6. D4⋊(C43⋊C8)C2semidirect
103. C43#1635semidirect