Finite Group Databasebeta

← #19133153

Subgroups — #19133153

Order 5504.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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#14583444C211yesmaximal, characteristic
2#14582949C211yesmaximal, characteristic, complemented
3#14582763C211yesmaximal, characteristic, complemented
4#14582634C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic, complemented
6#14582632C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×#10621900—21no—
9#13063324C411yescharacteristic, complemented
10#13063321C411yescharacteristic, complemented
11#13063311—21no—
12#13063299C2211yescharacteristic
13#13063297—21no—
14D4×Dic43C411yescharacteristic, complemented
15#13063287C411yescharacteristic, complemented
16(C22⋊D43)⋊C4—21no—
17C2×Dic43⋊C4—21no—
18C2×C4×Dic43C2211yescharacteristic
19Dic43⋊C8—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C8×Dic43—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×D4×C43—21no—
28C2×D4×C43C2×C411yescharacteristic
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×D172C2×C411yescharacteristic
41C2×C4×D43—21no—
42C2×Dic86—21no—
43C2×C8×C43—21no—
44C4⋊C4×C43C2×C411yescharacteristic
45C22⋊C4×C43—21no—
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43C2×C411yescharacteristic
50Dic43⋊C4—21no—
51Dic43⋊C4—42no—
52C4×Dic43C2×C411yescharacteristic
53C4×Dic43C2×C411yescharacteristic
54C4×Dic43D411yescharacteristic
55C4×Dic43D411yescharacteristic
56C2×C43⋊C8—21no—
57C23×C43—21no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60D4×C43—41no—
61D4×C43—41no—
62D4×C43—41no—
63C2×C4×C43—21no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43C22×C411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C22⋊D43—42no—
71C22⋊D43—41no—
72C22⋊D43—41no—
73C22⋊D43—42no—
74C2×Dic43—21no—
75C2×Dic43—41no—
76C2×Dic43—42no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43C22⋊C411yescharacteristic
81C2×Dic43C22⋊C411yescharacteristic
82C2×Dic43C22⋊C411yescharacteristic
83C2×Dic43C22⋊C411yescharacteristic
84C2×Dic43D812yes—
85C2×Dic43SD1612yes—
86D172—41no—
87C4×D43—42no—
88Dic86—42no—
89C8×C43—41no—
90C43⋊C8—41no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—41no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43C2×C22⋊C411yescharacteristic
97C22×C43C2×D811yescharacteristic
98C22×C43C2×SD1611yescharacteristic
99C2×D43—41no—
100C2×D43—41no—
101C2×D43—41no—
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—81no—
106Dic43—21no—
107Dic43—21no—
108Dic43—41no—
109Dic43—81no—
110Dic43#10212yes—
111Dic43#10212yes—
112#1517—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—81no—
116C2×C43#41011yescharacteristic
117C2×C43C2×#10211yescharacteristic
118C2×C43#42111yescharacteristic
119D43—81no—
120#532—431no—
121#431—431no—
122#382—431no—
123#327—431no—
124#327—431no—
125#327—431no—
126#327D4311yescharacteristic, complemented
127C43#151711yescharacteristic, complemented, Sylow
128C2×#41—861no—
129C4⋊Q8—431no—
130#127—431no—
131#124—861no—
132#121—431no—
133#121—861no—
134#121C2×D4311yescharacteristic
135C4×D4—431no—
136C4×D4—431no—
137C4×D4—861no—
138C2×C4⋊C4—861no—
139C2×C42—431no—
140C4⋊C8—861no—
141C22⋊C8—431no—
142C22⋊C8C2×D4311yescharacteristic
143C4×C8—861no—
144#95—431no—
145#95—861no—
146#95C2×D4311yescharacteristic
147#41—1722no—
148#41—1722no—
149C2×Q8—861no—
150C2×D4—21no—
151C2×D4—431no—
152C2×D4—861no—
153C2×D4—861no—
154C2×D4—861no—
155C2×D4C4×D4311yescharacteristic
156C22×C4—21no—
157C22×C4—431no—
158C22×C4—431no—
159C22×C4—861no—
160C22×C4—861no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163C2×C8—21no—
164C2×C8—861no—
165C4⋊C4—431no—
166C4⋊C4—861no—
167C4⋊C4—1722no—
168C4⋊C4C4×D4311yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C42—431no—
174C42—431no—
175C42—431no—
176C42—431no—
177C23—21no—
178C23—861no—
179C23D4×D4311yescharacteristic
180Q8—1722no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—1721no—
185D4—1722no—
186D4—1722no—
187D4—1721no—
188D4—1721no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—431no—
195C2×C4—431no—
196C2×C4—432no—
197C2×C4—432no—
198C2×C4—431no—
199C2×C4—431no—
200C2×C4—861no—
201C2×C4—1722no—
202C2×C4—1722no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4—1721no—
207C2×C4C2×C4×D4311yescharacteristic
208C2×C4D4×D4311yescharacteristic
209C8—41no—
210C8—1721no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—1721no—
217C22—1721no—
218C22—1721no—
219C22C22⋊C4×D4311yescharacteristic
220C22D8×D4311yescharacteristic
221C22SD16×D4311yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—432no—
227C4—432no—
228C4—861no—
229C4—861no—
230C4—3441no—
231C4—1721no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—3441no—
236C2#1458287111yescharacteristic
237C2#102×D4311yescharacteristic
238C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43C2×C22⋊C4
hypercenter#327D43
hypocenterC43#1517
LCSG ▷ C2×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. #14582949C2semidirect
3. #14582763C2semidirect
4. #14582634C2semidirect
5. #14582633C2semidirect
6. #14582632C2semidirect
7. C43×#327C2semidirect
9. #13063324C4semidirect
10. #13063321C4semidirect
14. D4×Dic43C4semidirect
15. #13063287C4semidirect
126. #327D43semidirect
127. C43#1517semidirect