Finite Group Databasebeta

← #19133886

Subgroups — #19133886

Order 5504.

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

normal subgroups only

This group has 230 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#14583643C211yesmaximal, characteristic, complemented
2#14583286C211yesmaximal, characteristic, complemented
3#14583263C211yesmaximal, characteristic, complemented
4#14582640C211yesmaximal, characteristic, complemented
5#14582639C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic, complemented
7C43×#496C211yesmaximal, characteristic, complemented
8C2×#10621883—21no—
9C2×#10621882—21no—
10#13063317C2211yescharacteristic
11#13063313C2211yescharacteristic
12#13063309—21no—
13#13063307—21no—
14#13063302—21no—
15#13063301—21no—
16#13063298—21no—
17#13063297—21no—
18#13063246—21no—
19#13063246—21no—
20#13063236C2211yescharacteristic
21#13063236C2211yescharacteristic
22C2×SD16×C43—21no—
23C2×D8×C43—21no—
24#127×C43C2211yescharacteristic
25#124×C43C2211yescharacteristic
26#97×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C2×D4×C43—21no—
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43D411yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C2×D172D411yescharacteristic
36C2×C4×D43—21no—
37C2×Dic86D411yescharacteristic
38SD16×C43—42no—
39D8×C43—42no—
40C2×C8×C43—21no—
41C22⋊C4×C43—21no—
42C22⋊C4×C43—21no—
43C42×C43C2311yescharacteristic
44C22⋊Dic43—21no—
45#10621883—42no—
46#10621882—42no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43D411yescharacteristic
52C4⋊Dic43D411yescharacteristic
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56C2×C43⋊C8—21no—
57C2×C43⋊C8—21no—
58C23×C43—21no—
59C23×C43—41no—
60C22×D43—21no—
61Q8×C43—41no—
62D4×C43—41no—
63D4×C43—41no—
64D4×C43—41no—
65D4×C43—41no—
66D4×C43—41no—
67D4×C43—42no—
68C2×C4×C43—21no—
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C22⋊D43—81no—
73C22⋊D43—81no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—81no—
78D172—41no—
79C4×D43—81no—
80Dic86—41no—
81C8×C43—22no—
82C43⋊C8—22no—
83C43⋊C8—41no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43—41no—
87C22×C43—81no—
88C22×C43—81no—
89C22×C43—81no—
90C22×C43#12011yescharacteristic
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—41no—
94C4×C43—21no—
95C4×C43—21no—
96C4×C43—21no—
97C4×C43—41no—
98Dic43—41no—
99Dic43—41no—
100Dic43—41no—
101#1656—431nomaximal, Sylow
102C2×C43—81no—
103C2×C43—161no—
104C2×C43#45311yescharacteristic
105C2×C43#45311yescharacteristic
106C2×C43#45411yescharacteristic
107D43—81no—
108#562—431no—
109#496—431no—
110#496D4311yescharacteristic, complemented
111#490—431no—
112#330—431no—
113#329—431no—
114#329—431no—
115C43#165611yescharacteristic, complemented, Sylow
116C2×SD16—21no—
117C2×SD16—861no—
118C2×D8—21no—
119C2×D8—861no—
120#127C2×D4311yescharacteristic
121#125—431no—
122#124—431no—
123#124C2×D4311yescharacteristic
124#123—861no—
125#123—861no—
126C22⋊Q8—861no—
127C22⋊Q8—861no—
128#121—861no—
129#121—861no—
130#102—861no—
131#102—861no—
132#97—431no—
133#97—431no—
134#97C2×D4311yescharacteristic
135C2×Q8—431no—
136C2×Q8C22⋊D4311yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—431no—
141C2×D4—861no—
142C2×D4—861no—
143C2×D4C22⋊D4311yescharacteristic
144C22×C4—861no—
145C22×C4—861no—
146SD16—42no—
147SD16—1722no—
148D8—42no—
149D8—1722no—
150C2×C8—21no—
151C2×C8—861no—
152C2×C8—861no—
153C4⋊C4—431no—
154C4⋊C4—431no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C22⋊C4—861no—
165C42C22×D4311yescharacteristic
166C23—21no—
167C23—41no—
168C23—861no—
169Q8—41no—
170Q8—1721no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—3441no—
178D4—3441no—
179D4—1721no—
180C2×C4—21no—
181C2×C4—861no—
182C2×C4—861no—
183C2×C4—861no—
184C2×C4—3441no—
185C2×C4—3441no—
186C2×C4D4×D4311yescharacteristic
187C2×C4D4×D4311yescharacteristic
188C2×C4C2×C22⋊D4311yescharacteristic
189C8—22no—
190C8—862no—
191C8—1721no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—1721no—
199C22—1721no—
200C22—1721no—
201C22#1306329311yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—1721no—
207C4—1721no—
208C4—1721no—
209C2—81no—
210C2—161no—
211C2—3441no—
212C2#1458306511yescharacteristic
213C2#1458306611yescharacteristic
214C2#1458307011yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#496C2
socleC22×C43#120
hypercenter#496D43
hypocenterC43#1656
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14583643C2semidirect
2. #14583286C2semidirect
3. #14583263C2semidirect
4. #14582640C2semidirect
5. #14582639C2semidirect
6. #14582638C2semidirect
7. C43×#496C2semidirect
110. #496D43semidirect
115. C43#1656semidirect