Finite Group Databasebeta

← #19133683

Subgroups — #19133683

Order 5504.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583554C211yesmaximal, characteristic, complemented
2#14583245C211yesmaximal, characteristic, complemented
3#14583091C211yesmaximal, characteristic, complemented
4#14582644C211yesmaximal, characteristic, complemented
5D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#14582626C211yesmaximal, characteristic, complemented
7C43×#459C211yesmaximal, characteristic, complemented
8C2×#10621898—21no—
9C2×#10621882—21no—
10#13063325C2211yescharacteristic
11#13063307—22no—
12#13063304—21no—
13#13063296—21no—
14C4×D172C2211yescharacteristic
15C4⋊C4×D43—21no—
16C4⋊(C43⋊C8)C2211yescharacteristic
17#13063246—21no—
18#13063246—22no—
19C4×C43⋊C8C2211yescharacteristic
20C2×D8×C43—21no—
21#127×C43C2211yescharacteristic
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24#102×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43D411yescharacteristic
29C22×C4×C43—21no—
30C2×C22⋊D43—22no—
31#10621898—42no—
32#10621898—42no—
33C2×D172D411yescharacteristic
34C2×C4×D43—22no—
35C2×C4×D43—21no—
36C2×Dic86—21no—
37D8×C43—42no—
38C2×C8×C43—21no—
39C4⋊C4×C43D411yescharacteristic
40C22⋊C4×C43—21no—
41C42×C43C2311yescharacteristic
42C22⋊Dic43—22no—
43#10621882—42no—
44(C2×D43)⋊C4—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43D411yescharacteristic
47C4⋊Dic43D412yes—
48Dic43⋊C4—22no—
49C2×C43⋊C8—21no—
50C2×C43⋊C8—21no—
51C23×C43—21no—
52C23×C43—41no—
53C22×D43—21no—
54D4×C43—21no—
55D4×C43—21no—
56D4×C43—42no—
57D4×C43—41no—
58D4×C43—41no—
59D4×C43—41no—
60D4×C43—41no—
61C2×C4×C43—21no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C22⋊D43—44no—
68C2×Dic43—21no—
69C2×Dic43—22no—
70D172—21no—
71D172D812yescomplemented
72C4×D43—44no—
73C4×D43—41no—
74C4×D43—41no—
75Dic86—41no—
76Dic86—41no—
77C8×C43—41no—
78C43⋊C8—41no—
79C43⋊C8—41no—
80C22×C43—41no—
81C22×C43—41no—
82C22×C43—41no—
83C22×C43—81no—
84C22×C43—81no—
85C22×C43—81no—
86C22×C43#12011yescharacteristic
87C2×D43—22no—
88C2×D43—41no—
89C2×D43—41no—
90C4×C43—21no—
91C4×C43—41no—
92C4×C43C2×D811yescharacteristic
93C4×C43#13511yescharacteristic
94C4×C43AGL(1,ℤ/8)11yescharacteristic
95C4×C43AGL(1,ℤ/8)11yescharacteristic
96Dic43—42no—
97Dic43—41no—
98#1625—431nomaximal, Sylow
99C2×C43—81no—
100C2×C43—161no—
101C2×C43#44711yescharacteristic
102C2×C43#44911yescharacteristic
103C2×C43#45411yescharacteristic
104D43—42no—
105#547—431no—
106#486—431no—
107#459—431no—
108#459D4311yescharacteristic, complemented
109#332—431no—
110D4⋊C8—431no—
111D4⋊C8—431no—
112C43#162511yescharacteristic, complemented, Sylow
113C2×#41—861no—
114C2×D8—21no—
115C2×D8—861no—
116C4⋊Q8—431no—
117#127C2×D4311yescharacteristic
118#123—862no—
119C22⋊Q8—861no—
120#121—861no—
121C4×D4—431no—
122C4×D4C2×D4311yescharacteristic
123C2×C4⋊C4—861no—
124C4⋊C8—431no—
125C4⋊C8C2×D4311yescharacteristic
126#102—21no—
127#102—861no—
128#102—862no—
129C4×C8—431no—
130#41—1722no—
131#41—1722no—
132C2×Q8—861no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—431no—
137C2×D4—862no—
138C2×D4C22⋊D4311yescharacteristic
139C22×C4—21no—
140C22×C4—862no—
141C22×C4—861no—
142D8—42no—
143D8—1722no—
144C2×C8—21no—
145C2×C8—861no—
146C2×C8—861no—
147C4⋊C4—431no—
148C4⋊C4—432no—
149C4⋊C4—862no—
150C4⋊C4—861no—
151C4⋊C4C22⋊D4311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—862no—
154C22⋊C4—861no—
155C42C22×D4311yescharacteristic
156C23—21no—
157C23—41no—
158C23—861no—
159Q8—1721no—
160Q8—1721no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—432no—
169D4—861no—
170D4—1724no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—861no—
175C2×C4—862no—
176C2×C4—1724no—
177C2×C4—1721no—
178C2×C4—1721no—
179C2×C4D4×D4311yescharacteristic
180C2×C4D4×D4311yescharacteristic
181C2×C4C2×C22⋊D4311yescharacteristic
182C8—41no—
183C8—1721no—
184C8—1721no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—862no—
192C22—1721no—
193C22—1721no—
194C22#1306329311yescharacteristic
195C4—21no—
196C4—41no—
197C4—1721no—
198C4—1722no—
199C4D8×D4311yescharacteristic
200C4#1306334511yescharacteristic
201C4#1306334911yescharacteristic
202C4#1306335111yescharacteristic
203C2—81no—
204C2—161no—
205C2—1722no—
206C2#1458303111yescharacteristic
207C2#1458304211yescharacteristic
208C2#1458307011yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#459C2
socleC22×C43#120
hypercenter#459D43
hypocenterC43#1625
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14583554C2semidirect
2. #14583245C2semidirect
3. #14583091C2semidirect
4. #14582644C2semidirect
5. D4⋊(C43⋊C8)C2semidirect
6. #14582626C2semidirect
7. C43×#459C2semidirect
71. D172D8semidirect
108. #459D43semidirect
112. C43#1625semidirect