Finite Group Databasebeta

← #19133900

Subgroups — #19133900

Order 5504.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#14583641C211yesmaximal, characteristic
2#14583291C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14582639C211yesmaximal, characteristic, complemented
5#14582638C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic, complemented
7C43×#489C211yesmaximal, characteristic, complemented
8C2×#10621885—21no—
9C2×#10621884—21no—
10#13063314—21no—
11#13063313C2211yescharacteristic
12#13063313C2211yescharacteristic
13#13063311—21no—
14#13063311—21no—
15#13063295—21no—
16#13063295—21no—
17#13063293—21no—
18#13063248—21no—
19#13063245—21no—
20#13063236C2211yescharacteristic, complemented
21#13063236C2211yescharacteristic, complemented
22C4⋊Q8×C43C2211yescharacteristic, complemented
23#124×C43C2211yescharacteristic
24#103×C43—21no—
25#102×C43—21no—
26#97×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43D411yescharacteristic
30C2×D4×C43D411yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×D172—21no—
34C2×D172D411yescharacteristic
35C2×D172D411yescharacteristic
36C2×Dic86D411yescharacteristic
37C2×Dic86D411yescharacteristic
38C2×C8×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C22⋊C4×C43—21no—
42C22⋊C4×C43—21no—
43C42×C43C2311yescharacteristic
44C22⋊Dic43—21no—
45#10621885—42no—
46#10621884—42no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53C4×Dic43—21no—
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56C23×C43—21no—
57C22×D43—21no—
58C22×D43—21no—
59C22×D43—81no—
60C22×D43—81no—
61C22×D43—81no—
62Q8×C43—41no—
63Q8×C43—41no—
64Q8×C43—41no—
65D4×C43—41no—
66C2×C4×C43—21no—
67C2×C4×C43—41no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C22⋊D43—81no—
72C22⋊D43—81no—
73C2×Dic43—21no—
74C2×Dic43—21no—
75D172—41no—
76D172—41no—
77D172—81no—
78Dic86—41no—
79Dic86—41no—
80C8×C43—41no—
81C43⋊C8—22no—
82C43⋊C8—41no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43#12011yescharacteristic
87C2×D43—41no—
88C2×D43—41no—
89C2×D43—41no—
90C2×D43—41no—
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—84no—
94C4×C43—21no—
95C4×C43—21no—
96C4×C43—21no—
97C4×C43—41no—
98C4×C43—81no—
99Dic43—41no—
100Dic43—41no—
101#1659—431nomaximal, Sylow
102C2×C43—81no—
103C2×C43#45311yescharacteristic
104C2×C43#45511yescharacteristic
105C2×C43#45511yescharacteristic
106D43—81no—
107D43—81no—
108H(3,𝔽4)—431no—
109#497—431no—
110#489—431no—
111#489D4311yescharacteristic, complemented
112#329—431no—
113#329—431no—
114#329—431no—
115C43#165911yescharacteristic, complemented, Sylow
116C2×Q16—861no—
117C2×SD16—861no—
118C4⋊Q8C2×D4311yescharacteristic, complemented
119#124—431no—
120#124—431no—
121#124—861no—
122#124—861no—
123#124—861no—
124#124C2×D4311yescharacteristic
125#120—861no—
126#120—861no—
127#120—861no—
128#103—21no—
129#103—861no—
130#102—21no—
131#102—861no—
132#97—431no—
133#97—431no—
134#97C2×D4311yescharacteristic, complemented
135C24—861no—
136C2×Q8—21no—
137C2×Q8—431no—
138C2×Q8—431no—
139C2×Q8C22⋊D4311yescharacteristic
140C2×D4—431no—
141C2×D4—431no—
142C2×D4—861no—
143C2×D4—861no—
144C2×D4—861no—
145C2×D4C22⋊D4311yescharacteristic
146Q16—1722no—
147SD16—1722no—
148C2×C8—21no—
149C2×C8—861no—
150C2×C8—861no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—861no—
156C22⋊C4—861no—
157C22⋊C4—861no—
158C22⋊C4—861no—
159C22⋊C4—861no—
160C22⋊C4—861no—
161C22⋊C4—861no—
162C42—861no—
163C42C22×D4311yescharacteristic
164C23—21no—
165C23—861no—
166C23—861no—
167C23—3441no—
168C23—3441no—
169C23—3441no—
170Q8—41no—
171Q8—41no—
172Q8—41no—
173Q8—1721no—
174Q8—1721no—
175D4—41no—
176D4—3441no—
177D4—3441no—
178D4—3441no—
179D4—1721no—
180D4—1721no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—861no—
184C2×C4—861no—
185C2×C4D4×D4311yescharacteristic
186C2×C4D4×D4311yescharacteristic
187C2×C4C2×C22⋊D4311yescharacteristic
188C8—41no—
189C8—862no—
190C8—1721no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—3444no—
195C22—1721no—
196C22—1721no—
197C22—1721no—
198C22—1721no—
199C22—1721no—
200C22—1721no—
201C22#1306329311yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—81no—
207C4—1721no—
208C4—1721no—
209C2—81no—
210C2—3441no—
211C2—3441no—
212C2#1458306511yescharacteristic
213C2#1458307511yescharacteristic
214C2#1458307611yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#489C2
socleC22×C43#120
hypercenter#489D43
hypocenterC43#1659
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #14583291C2semidirect
3. #14583261C2semidirect
4. #14582639C2semidirect
5. #14582638C2semidirect
6. #14582638C2semidirect
7. C43×#489C2semidirect
20. #13063236C22semidirect
21. #13063236C22semidirect
22. C4⋊Q8×C43C22semidirect
26. #97×C43C22semidirect
111. #489D43semidirect
115. C43#1659semidirect
118. C4⋊Q8C2×D43semidirect
134. #97C2×D43semidirect