Finite Group Databasebeta

← #19133779

Subgroups — #19133779

Order 5504.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583634C211yesmaximal, characteristic
2#14583247C211yesmaximal, characteristic
3#14583181C211yesmaximal, characteristic, complemented
4#14582642C211yesmaximal, characteristic
5Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#14582629C211yesmaximal, characteristic, complemented
7C43×#462C211yesmaximal, characteristic, complemented
8#13063322C2211yescharacteristic
9#13063314—21no—
10#13063313—21no—
11#13063310—22no—
12C4×Dic86C2211yescharacteristic
13C4×D172—21no—
14#13063287—21no—
15#13063256—21no—
16C4⋊(C43⋊C8)C2211yescharacteristic
17#13063248—21no—
18#13063245—22no—
19C4×C43⋊C8C2211yescharacteristic
20C2×Q16×C43—21no—
21C4⋊Q8×C43C2211yescharacteristic
22C4×Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24#103×C43—21no—
25C2×Q8×C43—21no—
26C2×Q8×C43D411yescharacteristic
27C2×D172—21no—
28C2×D172—21no—
29C2×D172D412yes—
30C2×C4×D43—22no—
31C2×Dic86D411yescharacteristic
32Q16×C43—42no—
33C2×C8×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C42×C43—21no—
39C42×C43C2311yescharacteristic
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—22no—
42(C2×D43)⋊C4—22no—
43C4⋊Dic43D411yescharacteristic
44Dic43⋊C4—21no—
45C4×Dic43—21no—
46C2×C43⋊C8—21no—
47C2×C43⋊C8—21no—
48C22×D43—22no—
49Q8×C43—21no—
50Q8×C43—21no—
51Q8×C43—41no—
52Q8×C43—41no—
53C2×C4×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43—41no—
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C2×Dic43—21no—
60C2×Dic43—21no—
61D172—42no—
62D172—41no—
63D172—41no—
64D172—41no—
65D172—41no—
66C4×D43—82no—
67Dic86—21no—
68Dic86—21no—
69C8×C43—41no—
70C43⋊C8—41no—
71C43⋊C8—41no—
72C22×C43#12011yescharacteristic
73C2×D43—42no—
74C2×D43—42no—
75C2×D43—42no—
76C4×C43—21no—
77C4×C43—41no—
78C4×C43—41no—
79C4×C43—81no—
80C4×C43#13511yescharacteristic
81C4×C43#13511yescharacteristic
82C4×C43AGL(1,ℤ/8)11yescharacteristic
83C4×C43#13711yescharacteristic
84Dic43—41no—
85Dic43—41no—
86#1640—431nomaximal, Sylow
87C2×C43#44911yescharacteristic
88C2×C43#45211yescharacteristic
89C2×C43#45511yescharacteristic
90D43—82no—
91#559—431no—
92#486—431no—
93#475—431no—
94#462D4311yescharacteristic, complemented
95#331—431no—
96Q8⋊C8—431no—
97Q8⋊C8—431no—
98C43#164011yescharacteristic, complemented, Sylow
99C2×Q16—21no—
100C4⋊Q8C2×D4311yescharacteristic
101#127—431no—
102#124—861no—
103#124—861no—
104#123—862no—
105C4×Q8—431no—
106C4×Q8C2×D4311yescharacteristic
107C4×D4—861no—
108C4×D4—861no—
109#106—861no—
110C4⋊C8—431no—
111C4⋊C8C2×D4311yescharacteristic
112#103—21no—
113#103—861no—
114#102—862no—
115C4×C8—431no—
116C2×Q8—21no—
117C2×Q8—431no—
118C2×Q8C22⋊D4311yescharacteristic
119C2×D4—432no—
120C2×D4—861no—
121C2×D4—861no—
122C22×C4—862no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—861no—
126C2×C8—861no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—431no—
131C4⋊C4—861no—
132C4⋊C4C22⋊D4311yescharacteristic
133C22⋊C4—862no—
134C22⋊C4—862no—
135C22⋊C4—862no—
136C42—21no—
137C42—861no—
138C42C22×D4311yescharacteristic
139C23—862no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—861no—
145Q8—861no—
146D4—1722no—
147D4—1721no—
148D4—1721no—
149D4—1721no—
150D4—1721no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—861no—
155C2×C4—861no—
156C2×C4—3442no—
157C2×C4D4×D4311yescharacteristic
158C2×C4D4×D4311yescharacteristic
159C2×C4C2×C22⋊D4311yescharacteristic
160C8—41no—
161C8—1721no—
162C8—1721no—
163C22—1722no—
164C22—1722no—
165C22—1722no—
166C22#1306329311yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—1721no—
172C4—1721no—
173C4#1306334511yescharacteristic
174C4#1306334811yescharacteristic
175C4#1306335111yescharacteristic
176C4#1306335711yescharacteristic
177C2—3442no—
178C2#1458304211yescharacteristic
179C2#1458306011yescharacteristic
180C2#1458307511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#462C2
socleC22×C43#120
hypercenter#462D43
hypocenterC43#1640
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #14583181C2semidirect
5. Q8⋊(C43⋊C8)C2semidirect
6. #14582629C2semidirect
7. C43×#462C2semidirect
94. #462D43semidirect
98. C43#1640semidirect