Finite Group Databasebeta

← #19133565

Subgroups — #19133565

Order 5504.

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

normal subgroups only

This group has 282 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#14583040C211yesmaximal, characteristic, complemented
3#14583037C211yesmaximal, characteristic, complemented
4#14582820C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×#10621900—21no—
9C22×Dic86C2211yescharacteristic
10C2×#10621873—21no—
11C2×#10621883—21no—
12#13063303—21no—
13#13063302—21no—
14#13063299C2211yescharacteristic
15#13063298—21no—
16#13063297—21no—
17#13063297—21no—
18C2×C4⋊Dic43—21no—
19C2×Dic43⋊C4C2211yescharacteristic
20#13063250—21no—
21#13063248—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic
23C43⋊#95—21no—
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×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×Dic86—21no—
44C2×Dic86—21no—
45C2×Dic86—42no—
46C2×C8×C43—21no—
47C4⋊C4×C43D411yescharacteristic
48C22⋊C4×C43—21no—
49C22⋊Dic43—21no—
50#10621883—42no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53C4⋊Dic43—42no—
54C4⋊Dic43D411yescharacteristic
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57Dic43⋊C4—21no—
58C2×C43⋊C8—21no—
59#10621873—42no—
60C23×C43—21no—
61C23×C43C2×D411yescharacteristic
62C22×D43—21no—
63D4×C43—41no—
64D4×C43—41no—
65D4×C43—41no—
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C22⋊D43—42no—
74C22⋊D43—41no—
75C22⋊D43—41no—
76C22⋊D43—81no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—22no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—42no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43—41no—
86C2×Dic43SD1612yescomplemented
87D172—41no—
88C4×D43—42no—
89Dic86—22no—
90Dic86—22no—
91Dic86—42no—
92Dic86—41no—
93Dic86—41no—
94C8×C43—41no—
95C43⋊C8—41no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43#12011yescharacteristic
102C22×C43C2×SD1611yescharacteristic
103C22×C43AGL(1,ℤ/8)11yescharacteristic
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—41no—
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—42no—
110C4×C43—41no—
111Dic43—22no—
112Dic43—41no—
113Dic43—42no—
114Dic43—41no—
115#1604—431nomaximal, Sylow
116C2×C43—21no—
117C2×C43—21no—
118C2×C43—81no—
119C2×C43#45011yescharacteristic
120C2×C43#45611yescharacteristic
121C2×C43B(4,𝔽2)11yescharacteristic
122D43—81no—
123#537—431no—
124#448—431no—
125#448—431no—
126#395—431no—
127#327—431no—
128#327D4311yescharacteristic, complemented
129#324—431no—
130C43#160411yescharacteristic, complemented, Sylow
131C2×#41—861no—
132C22×Q8—431no—
133C2×SD16—861no—
134C2×SD16—861no—
135C22⋊Q8—861no—
136C22⋊Q8—861no—
137#121—431no—
138#121—861no—
139#121—861no—
140#121—861no—
141#121C2×D4311yescharacteristic
142C2×C4⋊C4—431no—
143C2×C4⋊C4—861no—
144#103—861no—
145#103—861no—
146C22⋊C8—431no—
147C22⋊C8C2×D4311yescharacteristic
148#95—861no—
149#95C2×D4311yescharacteristic
150#41—1722no—
151#41—1722no—
152C2×Q8—861no—
153C2×Q8—861no—
154C2×Q8—861no—
155C2×Q8—1722no—
156C2×D4—21no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4—861no—
160C2×D4—861no—
161C2×D4D17211yescharacteristic
162C22×C4—21no—
163C22×C4—431no—
164C22×C4—431no—
165C22×C4—861no—
166C22×C4—861no—
167C22×C4—861no—
168C22×C4C22×D4311yescharacteristic
169SD16—1722no—
170SD16—1722no—
171C2×C8—21no—
172C2×C8—861no—
173C4⋊C4—431no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4—1722no—
178C4⋊C4D17211yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C23—21no—
184C23—861no—
185C23D4×D4311yescharacteristic
186Q8—862no—
187Q8—862no—
188Q8—1721no—
189Q8—1721no—
190Q8—1722no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—3441no—
195D4—1721no—
196D4—1722no—
197D4—1721no—
198D4—1721no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—432no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—862no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—1722no—
211C2×C4—1722no—
212C2×C4—1721no—
213C2×C4—1721no—
214C2×C4—1721no—
215C2×C4C2×D17211yescharacteristic
216C2×C4D4×D4311yescharacteristic
217C8—41no—
218C8—1721no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—1721no—
225C22—1721no—
226C22—1721no—
227C22#1306329511yescharacteristic
228C22SD16×D4311yescharacteristic
229C22#1306334911yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—862no—
235C4—1721no—
236C4—1722no—
237C4—1721no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—3441no—
242C2#1458305111yescharacteristic
243C2#1458308311yescharacteristic
244C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1604
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14583040C2semidirect
3. #14583037C2semidirect
4. #14582820C2semidirect
5. #14582632C2semidirect
6. #14582624C2semidirect
7. C43×#327C2semidirect
86. C2×Dic43SD16semidirect
128. #327D43semidirect
130. C43#1604semidirect