Finite Group Databasebeta

← #19133757

Subgroups — #19133757

Order 5504.

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

normal subgroups only

This group has 228 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#14583564C211yesmaximal, characteristic
2#14583191C211yesmaximal, characteristic, complemented
3#14583186C211yesmaximal, characteristic
4#14582645C211yesmaximal, characteristic, complemented
5#14582631C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic
7C43×#487C211yesmaximal, characteristic, complemented
8C2×Q8×D43—21no—
9#13063324—21no—
10#13063303—22no—
11#13063301—21no—
12C4×Dic86C2211yescharacteristic
13C4×D172C2211yescharacteristic
14#13063287—21no—
15#13063258—21no—
16#13063256—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063248—21no—
20#13063245—21no—
21C4⋊Q8×C43C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23#103×C43—22no—
24C4×C8×C43C2211yescharacteristic
25C2×Q8×C43—21no—
26C2×Q8×C43—21no—
27Q8×D43—42no—
28Q8×D43—42no—
29C2×D172D411yescharacteristic
30C2×C4×D43—22no—
31C2×C4×D43—21no—
32C2×Dic86—22no—
33C2×Dic86D411yescharacteristic
34C2×C8×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43D412yes—
39C42×C43C2311yescharacteristic
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—21no—
42C4⋊Dic43D411yescharacteristic
43C4⋊Dic43D411yescharacteristic
44Dic43⋊C4—22no—
45Dic43⋊C4—21no—
46C4×Dic43—21no—
47C2×C43⋊C8—21no—
48C2×C43⋊C8—21no—
49C22×D43—21no—
50Q8×C43—42no—
51Q8×C43—41no—
52Q8×C43—41no—
53C2×C4×C43—22no—
54C2×C4×C43—41no—
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×Dic43—21no—
59C2×Dic43—21no—
60C2×Dic43—21no—
61D172—21no—
62D172Q1612yes—
63C4×D43—44no—
64C4×D43—41no—
65C4×D43—41no—
66Dic86—21no—
67Dic86—44no—
68Dic86SD1612yes—
69C8×C43—41no—
70C43⋊C8—41no—
71C43⋊C8—41no—
72C22×C43#12011yescharacteristic
73C2×D43—22no—
74C2×D43—41no—
75C2×D43—41no—
76C4×C43—21no—
77C4×C43—42no—
78C4×C43—81no—
79C4×C43C2×SD1611yescharacteristic
80C4×C43C2×Q1611yescharacteristic
81C4×C43AGL(1,ℤ/8)11yescharacteristic
82C4×C43#13711yescharacteristic
83Dic43—22no—
84Dic43—41no—
85Dic43—41no—
86#1637—431nomaximal, Sylow
87C2×C43#45011yescharacteristic
88C2×C43#45111yescharacteristic
89C2×C43#45411yescharacteristic
90D43—42no—
91D4×Q8—431no—
92#487D4311yescharacteristic, complemented
93#477—431no—
94#476—431no—
95#332—431no—
96Q8⋊C8—431no—
97D4⋊C8—431no—
98C43#163711yescharacteristic, complemented, Sylow
99C22×Q8—861no—
100C4⋊Q8—861no—
101C4⋊Q8C2×D4311yescharacteristic
102C4⋊Q8C2×D4311yescharacteristic
103C22⋊Q8—861no—
104C22⋊Q8—862no—
105C4×Q8—431no—
106C4×D4—431no—
107C4×D4—861no—
108#107—861no—
109#106—861no—
110C4⋊C8—431no—
111C4⋊C8—431no—
112#103—22no—
113#103—861no—
114#102—861no—
115C4×C8C2×D4311yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—431no—
119C2×Q8—862no—
120C2×Q8—1722no—
121C2×Q8—1722no—
122C2×D4—431no—
123C22×C4—862no—
124C22×C4—861no—
125C2×C8—21no—
126C2×C8—861no—
127C2×C8—861no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—431no—
132C4⋊C4—431no—
133C4⋊C4—862no—
134C4⋊C4—861no—
135C4⋊C4C22⋊D4312yes—
136C22⋊C4—862no—
137C22⋊C4—861no—
138C42—861no—
139C42C22×D4311yescharacteristic
140C23—861no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—432no—
145Q8—861no—
146Q8—1724no—
147D4—432no—
148D4—861no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—861no—
152C2×C4—861no—
153C2×C4—861no—
154C2×C4—1724no—
155C2×C4—1721no—
156C2×C4—1721no—
157C2×C4D4×D4311yescharacteristic
158C2×C4D4×D4311yescharacteristic
159C2×C4C2×C22⋊D4311yescharacteristic
160C8—41no—
161C8—1721no—
162C8—1721no—
163C22—862no—
164C22—1721no—
165C22—1721no—
166C22#1306329311yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—862no—
171C4—1721no—
172C4—1721no—
173C4SD16×D4311yescharacteristic
174C4Q16×D4311yescharacteristic
175C4#1306335211yescharacteristic
176C4#1306335711yescharacteristic
177C2—1722no—
178C2#1458304811yescharacteristic
179C2#1458305311yescharacteristic
180C2#1458307111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#487C2
socleC22×C43#120
hypercenter#487D43
hypocenterC43#1637
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14583191C2semidirect
4. #14582645C2semidirect
5. #14582631C2semidirect
7. C43×#487C2semidirect
92. #487D43semidirect
98. C43#1637semidirect