Finite Group Databasebeta

← #19133708

Subgroups — #19133708

Order 5504.

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

normal subgroups only

This group has 216 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#14583622C211yesmaximal, characteristic, complemented
2#14583246C211yesmaximal, characteristic, complemented
3#14583099C211yesmaximal, characteristic, complemented
4#14583095C211yesmaximal, characteristic
5#14582646C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10621884—21no—
9C2×D344—21no—
10#13063325C2211yescharacteristic
11#13063322C2211yescharacteristic
12#13063320—22no—
13#13063313—21no—
14#13063301—21no—
15C4×Dic86—21no—
16C4×D172C2211yescharacteristic
17#13063283—21no—
18C4⋊(C43⋊C8)C2211yescharacteristic
19#13063247—21no—
20#13063247—22no—
21#13063245—21no—
22C4×Q8×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic
24C4×C8×C43C2211yescharacteristic
25C2×Q8×C43D411yescharacteristic
26C2×D172—21no—
27C2×D172—21no—
28C2×D172—21no—
29C2×D172D411yescharacteristic
30C2×C4×D43—21no—
31C2×Dic86—21no—
32C2×C8×C43—21no—
33C2×C8×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43D411yescharacteristic
36C42×C43—21no—
37C42×C43C2311yescharacteristic
38#10621884—42no—
39(C2×D43)⋊C4—22no—
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43D411yescharacteristic
44C4⋊Dic43D412yes—
45Dic43⋊C4—22no—
46C4×Dic43—22no—
47C2×C43⋊C8—21no—
48D344—42no—
49C22×D43—21no—
50C22×D43—41no—
51Q8×C43—21no—
52Q8×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43C2×D411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×Dic43—21no—
59C2×Dic43—22no—
60D172—21no—
61D172—21no—
62D172—42no—
63D172—41no—
64D172—41no—
65D172—41no—
66D172—41no—
67C4×D43—41no—
68C4×D43—41no—
69Dic86—41no—
70Dic86—41no—
71C8×C43—41no—
72C8×C43—41no—
73C43⋊C8—41no—
74C22×C43#12011yescharacteristic
75C2×D43—41no—
76C2×D43—41no—
77C2×D43—41no—
78C2×D43—81no—
79C2×D43—81no—
80C2×D43—81no—
81C4×C43—21no—
82C4×C43—41no—
83C4×C43—41no—
84C4×C43#13511yescharacteristic
85C4×C43#13511yescharacteristic
86C4×C43AGL(1,ℤ/8)11yescharacteristic
87C4×C43AGL(1,ℤ/8)11yescharacteristic
88Dic43—42no—
89Dic43—41no—
90#1628—431nomaximal, Sylow
91C2×C43#44911yescharacteristic
92C2×C43#44911yescharacteristic
93C2×C43#45411yescharacteristic
94D43—81no—
95D43—161no—
96#556—431no—
97#486—431no—
98#460—431no—
99#459—431no—
100#332—431no—
101Q8⋊C8D4311yescharacteristic, complemented
102D4⋊C8—431no—
103C43#162811yescharacteristic, complemented, Sylow
104C2×SD16—861no—
105C2×D8—861no—
106C4⋊Q8—431no—
107#127—431no—
108#126—862no—
109#124—861no—
110C22⋊Q8—861no—
111C4×Q8—861no—
112C4×Q8C2×D4311yescharacteristic
113C4×D4—431no—
114#117—861no—
115C4⋊C8—431no—
116C4⋊C8C2×D4311yescharacteristic
117#102—861no—
118#102—862no—
119#102—861no—
120C4×C8C2×D4311yescharacteristic
121C2×Q8—861no—
122C2×Q8D17211yescharacteristic
123C2×D4—431no—
124C2×D4—861no—
125C2×D4—861no—
126C2×D4—861no—
127C22×C4—861no—
128SD16—1722no—
129D8—1722no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—861no—
133C4⋊C4—21no—
134C4⋊C4—431no—
135C4⋊C4—432no—
136C4⋊C4—862no—
137C4⋊C4—861no—
138C4⋊C4D17211yescharacteristic
139C22⋊C4—862no—
140C22⋊C4—862no—
141C22⋊C4—861no—
142C42—21no—
143C42—862no—
144C42C22×D4311yescharacteristic
145C23—861no—
146C23—1721no—
147Q8—21no—
148Q8—21no—
149Q8—1721no—
150Q8—1721no—
151D4—861no—
152D4—861no—
153D4—1722no—
154D4—1721no—
155D4—1721no—
156D4—1721no—
157D4—1721no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—861no—
161C2×C4—862no—
162C2×C4—1721no—
163C2×C4—1721no—
164C2×C4C2×D17211yescharacteristic
165C2×C4D4×D4311yescharacteristic
166C2×C4D4×D4311yescharacteristic
167C8—41no—
168C8—41no—
169C8—1721no—
170C22—3441no—
171C22—3441no—
172C22—3441no—
173C22—1721no—
174C22—1721no—
175C22—1721no—
176C22#1306329511yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—1721no—
181C4—1722no—
182C4#1306334711yescharacteristic
183C4#1306334811yescharacteristic
184C4#1306335211yescharacteristic
185C4#1306335311yescharacteristic
186C2—3441no—
187C2—6881no—
188C2#1458304611yescharacteristic
189C2#1458304711yescharacteristic
190C2#1458307311yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×Q8⋊C8C2
socleC22×C43#120
hypercenterQ8⋊C8D43
hypocenterC43#1628
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14583622C2semidirect
2. #14583246C2semidirect
3. #14583099C2semidirect
5. #14582646C2semidirect
6. #14582628C2semidirect
7. C43×Q8⋊C8C2semidirect
101. Q8⋊C8D43semidirect
103. C43#1628semidirect