Finite Group Databasebeta

← #19133771

Subgroups — #19133771

Order 5504.

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

normal subgroups only

This group has 308 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#14583534C211yesmaximal, characteristic
2#14583176C211yesmaximal, characteristic, complemented
3#14583101C211yesmaximal, characteristic, complemented
4#14582643C211yesmaximal, characteristic, complemented
5#14582628C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×#486C211yesmaximal, characteristic, complemented
8C2×D4×D43—21no—
9C2×D4×D43—21no—
10C2×#10621884—21no—
11#13063296—21no—
12#13063296—21no—
13#13063293—22no—
14C4×D172C2211yescharacteristic
15C4×D172C2211yescharacteristic
16#13063258—21no—
17C4⋊(C43⋊C8)C2211yescharacteristic, complemented
18C4⋊(C43⋊C8)C2211yescharacteristic, complemented
19#13063249—21no—
20#13063245—21no—
21C4⋊Q8×C43C2211yescharacteristic, complemented
22#127×C43C2211yescharacteristic
23#102×C43—22no—
24C4×C8×C43C2211yescharacteristic, complemented
25C23×D43—22no—
26C2×Q8×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D4×C43D412yes—
30C2×C22⋊D43—22no—
31C2×C22⋊D43—22no—
32D4×D43—42no—
33D4×D43—42no—
34D4×D43—42no—
35D4×D43—42no—
36C2×D172D411yescharacteristic
37C2×D172D411yescharacteristic
38C2×C4×D43—21no—
39C2×C4×D43—21no—
40C2×C8×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43—21no—
43C42×C43C2311yescharacteristic
44C22⋊Dic43—22no—
45#10621884—42no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48C4⋊Dic43D411yescharacteristic
49C4⋊Dic43D411yescharacteristic
50C2×C43⋊C8—21no—
51C2×C43⋊C8—21no—
52C23×C43—22no—
53C22×D43—21no—
54C22×D43—21no—
55C22×D43—44no—
56C22×D43—44no—
57C22×D43—82no—
58Q8×C43—41no—
59Q8×C43—41no—
60D4×C43—42no—
61D4×C43—41no—
62D4×C43—41no—
63D4×C43—41no—
64D4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C22⋊D43—44no—
70C22⋊D43—44no—
71C2×Dic43—21no—
72C2×Dic43—21no—
73D172—21no—
74D172—21no—
75D172D812yes—
76D172SD1612yescomplemented
77C4×D43—41no—
78C4×D43—41no—
79C4×D43—41no—
80C4×D43—41no—
81C8×C43—41no—
82C43⋊C8—41no—
83C43⋊C8—41no—
84C22×C43—42no—
85C22×C43—42no—
86C22×C43—42no—
87C22×C43#12011yescharacteristic
88C2×D43—22no—
89C2×D43—22no—
90C2×D43—41no—
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—41no—
94C2×D43—88no—
95C4×C43—21no—
96C4×C43—81no—
97C4×C43C2×D811yescharacteristic
98C4×C43C2×SD1611yescharacteristic
99C4×C43AGL(1,ℤ/8)11yescharacteristic
100C4×C43AGL(1,ℤ/8)11yescharacteristic
101Dic43—41no—
102Dic43—41no—
103#1639—431nomaximal, Sylow
104C2×C43—82no—
105C2×C43#44711yescharacteristic
106C2×C43#45011yescharacteristic
107C2×C43#45511yescharacteristic
108D43—42no—
109D43—42no—
110D42—431no—
111#486D4311yescharacteristic, complemented
112#474—431no—
113#461—431no—
114#331—431no—
115D4⋊C8—431no—
116D4⋊C8—431no—
117C43#163911yescharacteristic, complemented, Sylow
118C22×D4—861no—
119C22×D4—861no—
120C2×SD16—861no—
121C4⋊Q8C2×D4311yescharacteristic, complemented
122#127C2×D4311yescharacteristic
123#121—861no—
124#121—861no—
125#120—862no—
126C4×D4—431no—
127C4×D4—431no—
128#107—861no—
129C4⋊C8—431no—
130C4⋊C8—431no—
131#103—861no—
132#102—22no—
133#102—861no—
134C4×C8C2×D4311yescharacteristic, complemented
135C24—862no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—431no—
140C2×D4—431no—
141C2×D4—862no—
142C2×D4—862no—
143C2×D4—1722no—
144C2×D4—1722no—
145C2×D4—1722no—
146C2×D4—1722no—
147C2×D4C22⋊D4312yes—
148C22×C4—861no—
149C22×C4—861no—
150SD16—1722no—
151C2×C8—21no—
152C2×C8—861no—
153C2×C8—861no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—431no—
157C4⋊C4—431no—
158C22⋊C4—862no—
159C22⋊C4—861no—
160C22⋊C4—861no—
161C42C22×D4311yescharacteristic
162C23—22no—
163C23—861no—
164C23—861no—
165C23—3442no—
166C23—1724no—
167C23—1724no—
168Q8—41no—
169Q8—41no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—432no—
176D4—432no—
177D4—861no—
178D4—861no—
179D4—1724no—
180D4—1724no—
181C2×C4—41no—
182C2×C4—861no—
183C2×C4—861no—
184C2×C4—1721no—
185C2×C4—1721no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4D4×D4311yescharacteristic
189C2×C4D4×D4311yescharacteristic
190C2×C4C2×C22⋊D4311yescharacteristic
191C8—41no—
192C8—1721no—
193C8—1721no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—862no—
198C22—862no—
199C22—3448no—
200C22—1721no—
201C22—1721no—
202C22—1721no—
203C22—1721no—
204C22#1306329311yescharacteristic
205C4—21no—
206C4—81no—
207C4—1721no—
208C4—1721no—
209C4D8×D4311yescharacteristic
210C4SD16×D4311yescharacteristic
211C4#1306334911yescharacteristic
212C4#1306335211yescharacteristic
213C2—82no—
214C2—1722no—
215C2—1722no—
216C2#1458303111yescharacteristic
217C2#1458304811yescharacteristic
218C2#1458307611yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#486C2
socleC22×C43#120
hypercenter#486D43
hypocenterC43#1639
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #14583176C2semidirect
3. #14583101C2semidirect
4. #14582643C2semidirect
5. #14582628C2semidirect
6. #14582628C2semidirect
7. C43×#486C2semidirect
17. C4⋊(C43⋊C8)C22semidirect
18. C4⋊(C43⋊C8)C22semidirect
21. C4⋊Q8×C43C22semidirect
24. C4×C8×C43C22semidirect
76. D172SD16semidirect
111. #486D43semidirect
117. C43#1639semidirect
121. C4⋊Q8C2×D43semidirect
134. C4×C8C2×D43semidirect