Finite Group Databasebeta

← #19133616

Subgroups — #19133616

Order 5504.

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

normal subgroups only

This group has 288 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#14583218C211yesmaximal, characteristic, complemented
3#14583215C211yesmaximal, characteristic, complemented
4#14582836C211yesmaximal, 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⋊Dic43—21no—
16C2×C4⋊Dic43C2211yescharacteristic, complemented
17C2×(C2×D43)⋊C4—21no—
18C2×(C2×D43)⋊C4C2211yescharacteristic
19#13063257—21no—
20#13063256—21no—
21#13063247—21no—
22#13063246—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic, complemented
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⋊Dic43—42no—
55C4⋊Dic43D411yescharacteristic
56Dic43⋊C4—21no—
57C2×C43⋊C8—21no—
58C23×C43—21no—
59C23×C43C2×D411yescharacteristic
60C22×D43—21no—
61C22×D43—21no—
62C22×D43—21no—
63C22×D43—42no—
64C22×D43—41no—
65C22×D43—41no—
66C22×D43—81no—
67C22×D43—81no—
68C22×D43SD1612yes—
69D4×C43—41no—
70D4×C43—41no—
71D4×C43—41no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C22⋊D43—42no—
80C22⋊D43—41no—
81C22⋊D43—41no—
82C22⋊D43—81no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—41no—
86C2×Dic43—41no—
87C2×Dic43—41no—
88C2×Dic43—41no—
89D172—41no—
90D172—42no—
91C4×D43—42no—
92C8×C43—41no—
93C43⋊C8—41no—
94C22×C43—21no—
95C22×C43—21no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43#12011yescharacteristic
100C22×C43C2×SD1611yescharacteristic
101C22×C43AGL(1,ℤ/8)11yescharacteristic
102C2×D43—22no—
103C2×D43—41no—
104C2×D43—41no—
105C2×D43—42no—
106C2×D43—41no—
107C2×D43—41no—
108C2×D43—41no—
109C2×D43—81no—
110C2×D43—84no—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—42no—
114C4×C43—41no—
115Dic43—41no—
116Dic43—41no—
117Dic43—81no—
118#1613—431nomaximal, Sylow
119C2×C43—21no—
120C2×C43—21no—
121C2×C43—81no—
122C2×C43#45011yescharacteristic
123C2×C43#45311yescharacteristic
124C2×C43#45811yescharacteristic
125D43—42no—
126D43—81no—
127#534—431no—
128#481—431no—
129#481—431no—
130#399—431no—
131#327—431no—
132#327D4311yescharacteristic, complemented
133#323—431no—
134C43#161311yescharacteristic, complemented, Sylow
135C22×D4—861no—
136#123—861no—
137#123—861no—
138#121—431no—
139#121—861no—
140#121C2×D4311yescharacteristic
141#120—861no—
142#120—861no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—861no—
145C2×C22⋊C4—431no—
146C2×C22⋊C4—861no—
147#106—861no—
148#106—861no—
149#102—861no—
150#102—861no—
151C22⋊C8—431no—
152C22⋊C8C2×D4311yescharacteristic, complemented
153#95C2×D4311yescharacteristic, complemented
154C24—431no—
155C24—861no—
156C2×D4—21no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4—861no—
160C2×D4—861no—
161C2×D4—861no—
162C2×D4—1722no—
163C2×D4—1722no—
164C2×D4D17211yescharacteristic
165C22×C4—21no—
166C22×C4—431no—
167C22×C4—861no—
168C22×C4—861no—
169C22×C4C22×D4311yescharacteristic
170C2×C8—21no—
171C2×C8—861no—
172C4⋊C4—431no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—1722no—
177C4⋊C4D17211yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—861no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4—861no—
184C22⋊C4—1722no—
185C23—21no—
186C23—432no—
187C23—861no—
188C23—861no—
189C23—861no—
190C23—3441no—
191C23—3441no—
192C23—1721no—
193C23—1721no—
194C23—1722no—
195C23D4×D4311yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—3441no—
200D4—1721no—
201D4—1722no—
202D4—1722no—
203D4—1721no—
204D4—1721no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—1722no—
213C2×C4—1721no—
214C2×C4—1721no—
215C2×C4—1721no—
216C2×C4—1721no—
217C2×C4C2×D17211yescharacteristic
218C2×C4D4×D4311yescharacteristic
219C8—41no—
220C8—1721no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—862no—
227C22—3441no—
228C22—3444no—
229C22—1722no—
230C22—1721no—
231C22—1721no—
232C22—1721no—
233C22—1721no—
234C22—1721no—
235C22#1306329511yescharacteristic
236C22SD16×D4311yescharacteristic
237C22#1306334911yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—41no—
242C4—3441no—
243C4—1721no—
244C4—1721no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—3441no—
249C2—1722no—
250C2#1458305111yescharacteristic
251C2#1458306811yescharacteristic
252C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1613
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. #14583218C2semidirect
3. #14583215C2semidirect
4. #14582836C2semidirect
5. #14582632C2semidirect
6. #14582622C2semidirect
7. C43×#327C2semidirect
16. C2×C4⋊Dic43C22semidirect
23. C22⋊(C43⋊C8)C22semidirect
25. C22⋊C8×C43C22semidirect
26. #95×C43C22semidirect
132. #327D43semidirect
134. C43#1613semidirect
152. C22⋊C8C2×D43semidirect
153. #95C2×D43semidirect