Finite Group Databasebeta

← #19133630

Subgroups — #19133630

Order 5504.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#14583476C211yesmaximal, characteristic
2#14583217C211yesmaximal, characteristic, complemented
3#14582837C211yesmaximal, characteristic, complemented
4#14582634C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#481C211yesmaximal, characteristic, complemented
8C2×#10621900—21no—
9#13063303—21no—
10#13063302—21no—
11#13063299C2211yescharacteristic
12#13063298—21no—
13#13063297—21no—
14#13063297—21no—
15C2×Dic43⋊C4C2211yescharacteristic
16#13063256—21no—
17#13063245—21no—
18C22⋊(C43⋊C8)C2211yescharacteristic
19C43⋊#95—21no—
20C43⋊#95—21no—
21C43⋊#95C2211yescharacteristic
22#121×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24#106×C43—21no—
25#102×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C2×D4×C43—21no—
28C2×D4×C43D411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37C22×Dic43D411yescharacteristic
38#10621900—42no—
39#10621900—42no—
40C2×D172D411yescharacteristic
41C2×C4×D43—21no—
42C2×Dic86—21no—
43C2×C8×C43—21no—
44C4⋊C4×C43—21no—
45C4⋊C4×C43—21no—
46C4⋊C4×C43D411yescharacteristic
47C22⋊C4×C43—21no—
48C22⋊Dic43—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51C4⋊Dic43D411yescharacteristic
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55C2×C43⋊C8—21no—
56C23×C43—21no—
57C23×C43C2×D411yescharacteristic
58C22×D43—21no—
59D4×C43—41no—
60D4×C43—41no—
61D4×C43—41no—
62C2×C4×C43—21no—
63C2×C4×C43—41no—
64C2×C4×C43—42no—
65C2×C4×C43—41no—
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C22⋊D43—42no—
69C22⋊D43—41no—
70C22⋊D43—41no—
71C22⋊D43—81no—
72C2×Dic43—21no—
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—42no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43SD1612yes—
82D172—41no—
83C4×D43—42no—
84Dic86—42no—
85C8×C43—41no—
86C43⋊C8—41no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43#12011yescharacteristic
93C22×C43C2×SD1611yescharacteristic
94C22×C43AGL(1,ℤ/8)11yescharacteristic
95C2×D43—41no—
96C2×D43—41no—
97C2×D43—41no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—41no—
101C4×C43—81no—
102Dic43—22no—
103Dic43—41no—
104Dic43—41no—
105Dic43—81no—
106#1616—431nomaximal, Sylow
107C2×C43—21no—
108C2×C43—21no—
109C2×C43—81no—
110C2×C43#45011yescharacteristic
111C2×C43#45411yescharacteristic
112C2×C43#45811yescharacteristic
113D43—81no—
114#537—431no—
115#481—431no—
116#481D4311yescharacteristic, complemented
117#400—431no—
118#327—431no—
119#327—431no—
120#324—431no—
121C43#161611yescharacteristic, complemented, Sylow
122C2×#41—861no—
123C22⋊Q8—861no—
124C22⋊Q8—861no—
125#121—431no—
126#121—861no—
127#121—861no—
128#121—861no—
129#121C2×D4311yescharacteristic
130C2×C4⋊C4—431no—
131C2×C4⋊C4C2×D4311yescharacteristic
132#106—21no—
133#106—861no—
134#102—21no—
135#102—861no—
136C22⋊C8—431no—
137C22⋊C8C2×D4311yescharacteristic
138#95—431no—
139#95—861no—
140#95—861no—
141#41—1722no—
142#41—1722no—
143C2×Q8—861no—
144C2×D4—21no—
145C2×D4—431no—
146C2×D4—861no—
147C2×D4—861no—
148C2×D4—861no—
149C2×D4C22⋊D4311yescharacteristic
150C22×C4—21no—
151C22×C4—431no—
152C22×C4—431no—
153C22×C4—861no—
154C22×C4—861no—
155C22×C4—861no—
156C22×C4C22×D4311yescharacteristic
157C2×C8—21no—
158C2×C8—861no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—431no—
162C4⋊C4—861no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4C22⋊D4311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C23—21no—
171C23—861no—
172C23D4×D4311yescharacteristic
173Q8—1722no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—3441no—
178D4—1721no—
179D4—1722no—
180D4—1721no—
181D4—1721no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—432no—
187C2×C4—861no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—1722no—
192C2×C4—1722no—
193C2×C4—1721no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4—1721no—
197C2×C4D4×D4311yescharacteristic
198C2×C4C2×C22⋊D4311yescharacteristic
199C8—41no—
200C8—1721no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—1721no—
207C22—1721no—
208C22—1721no—
209C22#1306329311yescharacteristic
210C22SD16×D4311yescharacteristic
211C22#1306335211yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—862no—
217C4—3441no—
218C4—1721no—
219C4—1721no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—3441no—
224C2#1458304811yescharacteristic
225C2#1458307011yescharacteristic
226C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#481C2
socleC22×C43#120
hypercenter#481D43
hypocenterC43#1616
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #14583217C2semidirect
3. #14582837C2semidirect
4. #14582634C2semidirect
5. #14582633C2semidirect
6. #14582624C2semidirect
7. C43×#481C2semidirect
116. #481D43semidirect
121. C43#1616semidirect