Finite Group Databasebeta

← #19145765

Subgroups — #19145765

Order 5504.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583433C211yesmaximal, characteristic
2C2×#13063317C211yesmaximal, characteristic, complemented
3#14583301C212yesmaximal, complemented
4#14583254C212yesmaximal, complemented
5#14583235C211yesmaximal, characteristic, complemented
6#14583230C211yesmaximal, characteristic, complemented
7#14583218C211yesmaximal, characteristic
8#14583213C211yesmaximal, characteristic
9#14583207C212yesmaximal, complemented
10#14583200C212yesmaximal, complemented
11C43×#431C211yesmaximal, characteristic, complemented
12#13063319—21no—
13#13063317—21no—
14#13063317—21no—
15#13063317C2211yescharacteristic
16#13063317C2212yes—
17#13063317C2212yes—
18#13063313C2211yescharacteristic
19#13063308—21no—
20#13063304C2211yescharacteristic
21#13063299C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23C4×D172C2211yescharacteristic
24C4×C22⋊D43—21no—
25#13063282—21no—
26C2×C4⋊Dic43C2211yescharacteristic
27C2×C4⋊Dic43C2211yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30#13063259C2212yes—
31#13063259C2212yes—
32#13063257C2212yes—
33#13063257C2212yes—
34#13063250C2212yes—
35#13063250C2212yes—
36#13063247C2212yes—
37#13063247C2212yes—
38C2×C42×C43C2211yescharacteristic
39C4⋊C8×C43C2212yes—
40C22⋊C8×C43C2211yescharacteristic
41C22⋊C8×C43C2211yescharacteristic
42C4×C8×C43C2212yes—
43C22×C4×C43D411yescharacteristic
44C22×C4×C43D411yescharacteristic
45C22×C4×C43C2311yescharacteristic
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48C22×Dic43—21no—
49C2×D172C2311yescharacteristic
50C2×C4×D43—21no—
51C2×Dic86C2311yescharacteristic
52C2×C8×C43C2312yes—
53C2×C8×C43C2312yes—
54C42×C43D411yescharacteristic
55C42×C43D411yescharacteristic
56C42×C43C2311yescharacteristic
57C42×C43C2311yescharacteristic
58C22⋊Dic43—21no—
59(C2×D43)⋊C4—21no—
60(C2×D43)⋊C4—21no—
61(C2×D43)⋊C4—21no—
62(C2×D43)⋊C4—21no—
63C4⋊Dic43—21no—
64C4⋊Dic43—21no—
65C4⋊Dic43C2312yes—
66C4⋊Dic43C2312yes—
67C4⋊Dic43C2311yescharacteristic
68C4⋊Dic43C2311yescharacteristic
69Dic43⋊C4—22no—
70Dic43⋊C4—22no—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—21no—
74Dic43⋊C4—21no—
75Dic43⋊C4—21no—
76Dic43⋊C4—21no—
77C4×Dic43—21no—
78C23×C43C2×D411yescharacteristic
79C22×D43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2411yescharacteristic
89C22⋊D43—42no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—21no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97D172—22no—
98C4×D43—42no—
99Dic86—22no—
100C8×C43—22no—
101C8×C43—22no—
102C22×C43—21no—
103C22×C43—21no—
104C22×C43#13512yes—
105C22×C43C22×D411yescharacteristic
106C2×D43—41no—
107C2×D43—41no—
108C2×D43—41no—
109C4×C43—21no—
110C4×C43—21no—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—21no—
114C4×C432−1+412yes—
115Dic43—41no—
116Dic43—42no—
117Dic43—41no—
118Dic43—41no—
119Dic43—42no—
120#3232—431nomaximal, Sylow
121C2×C43—22no—
122C2×C43#53611yescharacteristic
123C2×C43C2×#13511yescharacteristic
124C2×C43#57511yescharacteristic
125D43—81no—
126#529—431no—
127C2×#125—431no—
128#499—432no—
129#488—432no—
130#484—431no—
131#483—431no—
132#481—431no—
133#480—431no—
134#479—432no—
135#478—432no—
136#431D4311yescharacteristic, complemented
137C43#323211yescharacteristic, complemented, Sylow
138#126—861no—
139#125—432no—
140#125—432no—
141#125—431no—
142#125—861no—
143#125—861no—
144#124—431no—
145#123—861no—
146C22⋊Q8—431no—
147#121—431no—
148C4×Q8—431no—
149C4×D4—431no—
150C4×D4—861no—
151#117—861no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—431no—
154C2×C4⋊C4—861no—
155C2×C4⋊C4—861no—
156C2×C42C2×D4311yescharacteristic
157#107—432no—
158#107—432no—
159#106—432no—
160#106—432no—
161C4⋊C8C2×D4312yes—
162#103—432no—
163#103—432no—
164#102—432no—
165#102—432no—
166C22⋊C8C2×D4311yescharacteristic
167C22⋊C8C2×D4311yescharacteristic
168C4×C8C2×D4312yes—
169C2×Q8—431no—
170C2×D4—431no—
171C2×D4—861no—
172C22×C4—861no—
173C22×C4—861no—
174C22×C4—861no—
175C22×C4D17211yescharacteristic
176C22×C4D17211yescharacteristic
177C22×C4C22×D4311yescharacteristic
178C2×C8C22×D4312yes—
179C2×C8C22×D4312yes—
180C4⋊C4—432no—
181C4⋊C4—432no—
182C4⋊C4—431no—
183C4⋊C4—431no—
184C4⋊C4—861no—
185C4⋊C4—861no—
186C4⋊C4—862no—
187C4⋊C4—862no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C4⋊C4—861no—
191C4⋊C4—861no—
192C4⋊C4—861no—
193C4⋊C4—861no—
194C22⋊C4—861no—
195C22⋊C4—861no—
196C22⋊C4—861no—
197C22⋊C4—861no—
198C22⋊C4—861no—
199C42—861no—
200C42D17211yescharacteristic
201C42D17211yescharacteristic
202C42C22×D4311yescharacteristic
203C42C22×D4311yescharacteristic
204C23—861no—
205C23C2×D17211yescharacteristic
206Q8—862no—
207D4—862no—
208D4—1722no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—861no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—1722no—
218C2×C4—1722no—
219C2×C4—1722no—
220C2×C4C2×D17211yescharacteristic
221C2×C4C2×D17211yescharacteristic
222C2×C4C2×D17211yescharacteristic
223C2×C4C2×D17211yescharacteristic
224C2×C4C2×D17211yescharacteristic
225C2×C4C23×D4311yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—1721no—
231C22—1721no—
232C22—1721no—
233C22#1306334712yes—
234C22C22×D17211yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—1722no—
241C4—1721no—
242C4—1721no—
243C4—1722no—
244C4—1721no—
245C4#1306337212yes—
246C2—22no—
247C2—3441no—
248C2#1458347511yescharacteristic
249C2C2×#1306334711yescharacteristic
250C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#431C2
socleC22×C43C22×D4
hypercenter#431D43
hypocenterC43#3232
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×#13063317C2semidirect
3. #14583301C2semidirect
4. #14583254C2semidirect
5. #14583235C2semidirect
6. #14583230C2semidirect
9. #14583207C2semidirect
10. #14583200C2semidirect
11. C43×#431C2semidirect
136. #431D43semidirect
137. C43#3232semidirect