Finite Group Databasebeta

← #19133582

Subgroups — #19133582

Order 5504.

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

normal subgroups only

This group has 280 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#14583457C211yesmaximal, characteristic
2#14583213C211yesmaximal, characteristic, complemented
3#14583210C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×D4×D43—21no—
9#13063310—21no—
10#13063307—21no—
11#13063299C2211yescharacteristic
12#13063297—21no—
13#13063295—21no—
14#13063293—21no—
15C2×C4⋊Dic43C2211yescharacteristic, complemented
16C2×(C2×D43)⋊C4—21no—
17C2×(C2×D43)⋊C4C2211yescharacteristic
18#13063259—21no—
19#13063258—21no—
20#13063247—21no—
21#13063246—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic, complemented
23C43⋊#95—21no—
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic, complemented
26#95×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C23×D43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43D411yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C22×Dic43—21no—
37C22×Dic43D411yescharacteristic
38D4×D43—42no—
39D4×D43—42no—
40C2×D172—21no—
41C2×D172D411yescharacteristic
42C2×C4×D43—21no—
43C2×C8×C43—21no—
44C4⋊C4×C43D411yescharacteristic
45C22⋊C4×C43—21no—
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—42no—
52C4⋊Dic43—21no—
53C4⋊Dic43—21no—
54C4⋊Dic43D411yescharacteristic
55Dic43⋊C4—21no—
56C2×C43⋊C8—21no—
57C23×C43—21no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C22×D43—21no—
61C22×D43—21no—
62C22×D43—42no—
63C22×D43—41no—
64C22×D43—41no—
65C22×D43—81no—
66C22×D43—81no—
67C22×D43D812yes—
68D4×C43—41no—
69D4×C43—41no—
70D4×C43—41no—
71C2×C4×C43—21no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C22⋊D43—42no—
79C22⋊D43—41no—
80C22⋊D43—41no—
81C22⋊D43—81no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—41no—
85C2×Dic43—41no—
86C2×Dic43—41no—
87C2×Dic43—41no—
88D172—41no—
89D172—42no—
90C4×D43—42no—
91C8×C43—41no—
92C43⋊C8—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43#12011yescharacteristic
99C22×C43C2×D811yescharacteristic
100C22×C43AGL(1,ℤ/8)11yescharacteristic
101C2×D43—22no—
102C2×D43—41no—
103C2×D43—41no—
104C2×D43—42no—
105C2×D43—41no—
106C2×D43—41no—
107C2×D43—41no—
108C2×D43—81no—
109C2×D43—84no—
110C4×C43—21no—
111C4×C43—21no—
112C4×C43—41no—
113C4×C43—81no—
114Dic43—41no—
115Dic43—41no—
116Dic43—81no—
117#1607—431nomaximal, Sylow
118C2×C43—21no—
119C2×C43—21no—
120C2×C43—81no—
121C2×C43#44711yescharacteristic
122C2×C43#45511yescharacteristic
123C2×C43#45811yescharacteristic
124D43—42no—
125D43—81no—
126#534—431no—
127#480—431no—
128#480—431no—
129#397—431no—
130#327—431no—
131#327D4311yescharacteristic, complemented
132#323—431no—
133C43#160711yescharacteristic, complemented, Sylow
134C22×D4—861no—
135#123—861no—
136#123—861no—
137#121—431no—
138#121—861no—
139#121C2×D4311yescharacteristic
140#120—861no—
141#120—861no—
142C2×C4⋊C4—431no—
143C2×C22⋊C4—431no—
144C2×C22⋊C4—861no—
145#107—861no—
146#107—861no—
147#102—861no—
148#102—861no—
149C22⋊C8—431no—
150C22⋊C8C2×D4311yescharacteristic, complemented
151#95—861no—
152#95C2×D4311yescharacteristic, complemented
153C24—431no—
154C24—861no—
155C2×D4—21no—
156C2×D4—431no—
157C2×D4—861no—
158C2×D4—861no—
159C2×D4—861no—
160C2×D4—861no—
161C2×D4—1722no—
162C2×D4—1722no—
163C2×D4D17211yescharacteristic
164C22×C4—21no—
165C22×C4—431no—
166C22×C4—861no—
167C22×C4—861no—
168C22×C4C22×D4311yescharacteristic
169C2×C8—21no—
170C2×C8—861no—
171C4⋊C4—431no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C4⋊C4D17211yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—1722no—
183C23—21no—
184C23—432no—
185C23—861no—
186C23—861no—
187C23—861no—
188C23—3441no—
189C23—3441no—
190C23—1721no—
191C23—1721no—
192C23—1722no—
193C23D4×D4311yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—3441no—
198D4—1721no—
199D4—1722no—
200D4—1722no—
201D4—1721no—
202D4—1721no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—1722no—
211C2×C4—1721no—
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—862no—
225C22—3441no—
226C22—3444no—
227C22—1722no—
228C22—1721no—
229C22—1721no—
230C22—1721no—
231C22—1721no—
232C22—1721no—
233C22#1306329511yescharacteristic
234C22D8×D4311yescharacteristic
235C22#1306335211yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—3441no—
241C4—1721no—
242C4—1721no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—3441no—
247C2—1722no—
248C2#1458303411yescharacteristic
249C2#1458307811yescharacteristic
250C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1607
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. #14583213C2semidirect
3. #14583210C2semidirect
4. #14582826C2semidirect
5. #14582632C2semidirect
6. #14582622C2semidirect
7. C43×#327C2semidirect
15. C2×C4⋊Dic43C22semidirect
22. C22⋊(C43⋊C8)C22semidirect
25. C22⋊C8×C43C22semidirect
26. #95×C43C22semidirect
131. #327D43semidirect
133. C43#1607semidirect
150. C22⋊C8C2×D43semidirect
152. #95C2×D43semidirect