Finite Group Databasebeta

← #19133664

Subgroups — #19133664

Order 5504.

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

normal subgroups only

This group has 236 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#14583610C211yesmaximal, characteristic, complemented
2#14583096C211yesmaximal, characteristic, complemented
3#14583091C211yesmaximal, characteristic
4#14582648C211yesmaximal, characteristic, complemented
5#14582631C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×#492C211yesmaximal, characteristic, complemented
8C2×#10621883—21no—
9C2×#10621882—21no—
10#13063316—21no—
11#13063305—21no—
12#13063301—22no—
13C4×Dic86C2211yescharacteristic
14C4×D172C2211yescharacteristic
15#13063287—21no—
16C4⋊C4×D43—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063246—21no—
20#13063246—21no—
21C2×SD16×C43—22no—
22C4⋊Q8×C43C2211yescharacteristic
23#127×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×Q8×C43D412yes—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D172D411yescharacteristic
30C2×C4×D43—21no—
31C2×C4×D43—22no—
32C2×Dic86D411yescharacteristic
33SD16×C43—44no—
34C2×C8×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C42×C43C2311yescharacteristic
38#10621883—42no—
39#10621882—42no—
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—21no—
42C4⋊Dic43—22no—
43C4⋊Dic43D411yescharacteristic
44C4⋊Dic43D411yescharacteristic
45Dic43⋊C4—22no—
46Dic43⋊C4—21no—
47C4×Dic43—21no—
48C2×C43⋊C8—21no—
49C2×C43⋊C8—21no—
50C23×C43—41no—
51C22×D43—21no—
52Q8×C43—42no—
53D4×C43—42no—
54D4×C43—41no—
55D4×C43—41no—
56D4×C43—41no—
57D4×C43—41no—
58C2×C4×C43—22no—
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65D172—21no—
66D172SD1612yescomplemented
67C4×D43—41no—
68C4×D43—41no—
69C4×D43—82no—
70Dic86—21no—
71Dic86—21no—
72C8×C43—22no—
73C43⋊C8—41no—
74C43⋊C8—41no—
75C22×C43—81no—
76C22×C43—81no—
77C22×C43—81no—
78C22×C43#12011yescharacteristic
79C2×D43—22no—
80C2×D43—41no—
81C2×D43—41no—
82C4×C43—21no—
83C4×C43—42no—
84C4×C43C2×SD1611yescharacteristic
85C4×C43#13511yescharacteristic
86C4×C43AGL(1,ℤ/8)11yescharacteristic
87C4×C43#13711yescharacteristic
88Dic43—41no—
89Dic43—41no—
90Dic43—41no—
91#1622—431nomaximal, Sylow
92C2×C43—161no—
93C2×C43#44811yescharacteristic
94C2×C43#44911yescharacteristic
95C2×C43#45311yescharacteristic
96D43—42no—
97#554—431no—
98#492D4311yescharacteristic, complemented
99#460—431no—
100#459—431no—
101#333—431no—
102Q8⋊C8—431no—
103D4⋊C8—431no—
104C43#162211yescharacteristic, complemented, Sylow
105C2×SD16—22no—
106C2×SD16—861no—
107C2×D8—861no—
108C4⋊Q8C2×D4311yescharacteristic
109#127C2×D4311yescharacteristic
110#125—861no—
111C22⋊Q8—861no—
112C22⋊Q8—862no—
113C4×Q8—431no—
114C4×D4—431no—
115C4×D4—861no—
116C2×C4⋊C4—861no—
117C4⋊C8—431no—
118C4⋊C8—431no—
119#102—861no—
120#102—861no—
121C4×C8C2×D4311yescharacteristic
122C2×Q8—431no—
123C2×Q8C22⋊D4312yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—431no—
128C22×C4—862no—
129C22×C4—861no—
130SD16—44no—
131SD16—1722no—
132D8—1722no—
133C2×C8—21no—
134C2×C8—861no—
135C2×C8—861no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—431no—
139C4⋊C4—431no—
140C4⋊C4—862no—
141C4⋊C4—862no—
142C4⋊C4—861no—
143C22⋊C4—862no—
144C22⋊C4—861no—
145C42—861no—
146C42C22×D4311yescharacteristic
147C23—41no—
148C23—861no—
149Q8—42no—
150Q8—861no—
151Q8—861no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—432no—
158D4—861no—
159C2×C4—22no—
160C2×C4—861no—
161C2×C4—861no—
162C2×C4—861no—
163C2×C4—3442no—
164C2×C4—1721no—
165C2×C4—1721no—
166C2×C4D4×D4311yescharacteristic
167C2×C4D4×D4311yescharacteristic
168C2×C4C2×C22⋊D4311yescharacteristic
169C8—22no—
170C8—1721no—
171C8—1721no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—862no—
176C22—1721no—
177C22—1721no—
178C22#1306329311yescharacteristic
179C4—21no—
180C4—42no—
181C4—1721no—
182C4—1721no—
183C4—1721no—
184C4SD16×D4311yescharacteristic
185C4#1306334611yescharacteristic
186C4#1306335211yescharacteristic
187C4#1306335411yescharacteristic
188C2—161no—
189C2—1722no—
190C2#1458303611yescharacteristic
191C2#1458304311yescharacteristic
192C2#1458306611yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#492C2
socleC22×C43#120
hypercenter#492D43
hypocenterC43#1622
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #14583610C2semidirect
2. #14583096C2semidirect
4. #14582648C2semidirect
5. #14582631C2semidirect
6. #14582628C2semidirect
7. C43×#492C2semidirect
66. D172SD16semidirect
98. #492D43semidirect
104. C43#1622semidirect