Finite Group Databasebeta

← #19136262

Subgroups — #19136262

Order 5504.

286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583466C211yesmaximal, characteristic
2C2×#13063240C211yesmaximal, characteristic, complemented
3#14582693C212yesmaximal, complemented
4#14582691C212yesmaximal, complemented
5C2×#99×C43C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic, complemented
7#13063321C411yescharacteristic, complemented
8#13063321C2211yescharacteristic
9#13063312C411yescharacteristic, complemented
10#13063312C2211yescharacteristic
11#13063296—21no—
12#13063296—21no—
13#13063294—21no—
14#13063294—21no—
15#13063284C411yescharacteristic, complemented
16C2×C22⋊Dic43—21no—
17#13063240—21no—
18#13063240C2212yes—
19C22×D4×C43C2211yescharacteristic
20C2×C22⋊C4×C43—21no—
21#99×C43—21no—
22#99×C43C2212yes—
23C24×C43D411yescharacteristic
24C24×C43D411yescharacteristic
25C2×D4×C43—41no—
26C2×D4×C43—41no—
27C2×D4×C43C2×C411yescharacteristic
28C2×D4×C43D411yescharacteristic
29C2×D4×C43D411yescharacteristic
30C2×D4×C43C2311yescharacteristic
31C22×C4×C43—41no—
32C22×C4×C43C2×C411yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C2×C22⋊D43—21no—
37C2×C22⋊D43—21no—
38C22×Dic43—41no—
39#10621898—41no—
40#10621898—41no—
41C2×D172C2×C411yescharacteristic, complemented
42C2×C4×D43—21no—
43C2×Dic86C2×C411yescharacteristic, complemented
44C22⋊C4×C43—22no—
45C22⋊C4×C43—41no—
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43—22no—
52C22⋊Dic43—41no—
53C4⋊Dic43—21no—
54C4×Dic43C2×C411yescharacteristic, complemented
55C4×Dic43C2×C411yescharacteristic, complemented
56C23×C43—21no—
57C23×C43—21no—
58C23×C43—21no—
59C23×C43—21no—
60C23×C43—81no—
61C23×C43—81no—
62C23×C43C22⋊C411yescharacteristic
63C23×C43C22⋊C411yescharacteristic
64C23×C43C22⋊C411yescharacteristic
65C23×C43C2×D411yescharacteristic
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68D4×C43—41no—
69D4×C43—41no—
70D4×C43—41no—
71D4×C43—41no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—42no—
75C2×C4×C43—82no—
76C2×C4×C43C22⋊C411yescharacteristic
77C2×C4×C43C22×C411yescharacteristic
78C22⋊D43—41no—
79C22⋊D43—41no—
80C22⋊D43—81no—
81C22⋊D43—81no—
82C22⋊D43—81no—
83C22⋊D43—81no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—42no—
88C2×Dic43—82no—
89D172—41no—
90C4×D43—42no—
91Dic86—41no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—21no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—42no—
102C22×C43—42no—
103C22×C43—81no—
104C22×C43—81no—
105C22×C43#9911yescharacteristic
106C22×C43#9911yescharacteristic
107C22×C43C2×C22⋊C411yescharacteristic
108C2×D43—41no—
109C2×D43—41no—
110C2×D43—41no—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—82no—
114Dic43—41no—
115Dic43—41no—
116Dic43—41no—
117Dic43—82no—
118#2127—431nomaximal, Sylow
119C2×C43—21no—
120C2×C43—21no—
121C2×C43—21no—
122C2×C43—41no—
123C2×C43—41no—
124C2×C43—41no—
125C2×C43—41no—
126C2×C43C2×#9911yescharacteristic
127D43—81no—
128#535—431no—
129C2×#99—431no—
130C2×#99D4311yescharacteristic, complemented
131#354—432no—
132#353—432no—
133C43#212711yescharacteristic, complemented, Sylow
134C2×#41—431no—
135C22×D4C2×D4311yescharacteristic
136#127—431no—
137#127—431no—
138#124—431no—
139#124—431no—
140#121—861no—
141#121—861no—
142#120—861no—
143#120—861no—
144#117—431no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—861no—
147#99—21no—
148#99—432no—
149#99—861no—
150#99C2×D4312yes—
151C24D17211yescharacteristic
152C24C22⋊D4311yescharacteristic
153#41—1721no—
154#41—1721no—
155C2×Q8—431no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—431no—
159C2×D4—861no—
160C2×D4—861no—
161C2×D4—861no—
162C2×D4—861no—
163C2×D4—861no—
164C2×D4C4×D4311yescharacteristic
165C2×D4D17211yescharacteristic
166C2×D4C22⋊D4311yescharacteristic
167C2×D4C22×D4311yescharacteristic
168C22×C4—41no—
169C22×C4—861no—
170C22×C4—1721no—
171C22×C4C4×D4311yescharacteristic
172C4⋊C4—861no—
173C22⋊C4—22no—
174C22⋊C4—41no—
175C22⋊C4—861no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—862no—
181C22⋊C4—1721no—
182C42—431no—
183C42—431no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—81no—
189C23—81no—
190C23—861no—
191C23(C2×D43)⋊C411yescharacteristic
192C23(C2×D43)⋊C411yescharacteristic
193C23(C2×D43)⋊C411yescharacteristic
194C23C2×D17211yescharacteristic
195C23C2×C22⋊D4311yescharacteristic
196Q8—1721no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—3441no—
202D4—3441no—
203D4—3441no—
204D4—3441no—
205D4—1721no—
206D4—1721no—
207D4—1721no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—861no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—3442no—
216C2×C4—1722no—
217C2×C4—1722no—
218C2×C4(C2×D43)⋊C411yescharacteristic
219C2×C4C2×C4×D4311yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—1721no—
234C22—1721no—
235C22—1721no—
236C22#1306323911yescharacteristic
237C22#1306323911yescharacteristic
238C22C2×(C2×D43)⋊C411yescharacteristic
239C4—21no—
240C4—21no—
241C4—82no—
242C4—3442no—
243C4—1721no—
244C4—1721no—
245C4—1721no—
246C2—21no—
247C2—21no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—41no—
252C2—41no—
253C2—3441no—
254C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC2×#99×C43C2
socleC2×C43C2×#99
hypercenterC2×#99D43
hypocenterC43#2127
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13063240C2semidirect
3. #14582693C2semidirect
4. #14582691C2semidirect
5. C2×#99×C43C2semidirect
6. C2×#10621898C4semidirect
7. #13063321C4semidirect
9. #13063312C4semidirect
15. #13063284C4semidirect
41. C2×D172C2×C4semidirect
43. C2×Dic86C2×C4semidirect
54. C4×Dic43C2×C4semidirect
55. C4×Dic43C2×C4semidirect
130. C2×#99D43semidirect
133. C43#2127semidirect