Finite Group Databasebeta

← #19145608

Subgroups — #19145608

Order 5504.

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

normal subgroups only

This group has 390 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#14583456C211yesmaximal, characteristic, complemented
2#14583449C211yesmaximal, characteristic
3#14583293C212yesmaximal, complemented
4#14583259C212yesmaximal, complemented
5#14583110C212yesmaximal, complemented
6#14583100C212yesmaximal, complemented
7#14583063C214yesmaximal, complemented
8C43×#432C211yesmaximal, characteristic, complemented
9C2×#10621898C2212yes—
10C2×Dic172C2214yes—
11C2×#10621873C2214yes—
12#13063325C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063325C2211yescharacteristic
15#13063322C2211yescharacteristic
16#13063317—21no—
17#13063313C2212yes—
18#13063304—21no—
19#13063304C2212yes—
20#13063299—21no—
21#13063299—21no—
22C4×Dic86—21no—
23C4×Dic86C2212yes—
24C4×D172—21no—
25C4×D172—21no—
26#13063284—21no—
27#13063250C2214yes—
28#13063247C2214yes—
29C2×C42×C43C2211yescharacteristic
30C4⋊C8×C43C2212yes—
31C22⋊C8×C43C2212yes—
32#97×C43C2212yes—
33C22×C4×C43D411yescharacteristic
34C22×C4×C43D411yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—22no—
37#10621898—44no—
38C2×D172—21no—
39C2×D172—21no—
40C2×D172C2312yes—
41C2×C4×D43—22no—
42C2×Dic86—21no—
43C2×Dic86C2312yes—
44C2×Dic86C2312yes—
45C2×C8×C43C2314yes—
46C42×C43D411yescharacteristic
47C42×C43D411yescharacteristic
48C42×C43C2311yescharacteristic
49C42×C43C2311yescharacteristic
50C22⋊Dic43—22no—
51(C2×D43)⋊C4—22no—
52(C2×D43)⋊C4—22no—
53C4⋊Dic43—21no—
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56C4⋊Dic43—21no—
57C4⋊Dic43—21no—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61C4×Dic43—22no—
62Dic172—44no—
63#10621873—44no—
64C23×C43C2×D411yescharacteristic
65C22×D43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—41no—
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2411yescharacteristic
75C22⋊D43—44no—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79D172—24no—
80D172—42no—
81D172—42no—
82C4×D43—44no—
83Dic86—22no—
84Dic86—22no—
85Dic86—24no—
86Dic86—42no—
87C8×C43—24no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43C22×D411yescharacteristic
92C2×D43—42no—
93C2×D43—42no—
94C2×D43—42no—
95C4×C43—21no—
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43#13712yes—
100C4×C43H(5,𝔽2)12yes—
101Dic43—42no—
102Dic43—42no—
103Dic43—42no—
104#3216—431nomaximal, Sylow
105C2×C43—41no—
106C2×C43#53511yescharacteristic
107C2×C43C2×#13711yescharacteristic
108C2×C43#57511yescharacteristic
109D43—82no—
110#533—431no—
111#532—431no—
112#497—432no—
113#489—432no—
114#462—432no—
115#460—432no—
116#452—434no—
117#432D4311yescharacteristic, complemented
118C43#321611yescharacteristic, complemented, Sylow
119C2×#41—432no—
120C2×Q16—434no—
121C2×SD16—434no—
122C4⋊Q8—431no—
123C4⋊Q8—431no—
124C4⋊Q8—431no—
125#127—431no—
126#125—861no—
127#124—432no—
128C22⋊Q8—432no—
129C22⋊Q8—861no—
130#121—861no—
131#121—861no—
132C4×Q8—432no—
133C4×Q8—861no—
134C4×D4—861no—
135C4×D4—861no—
136#117—861no—
137C2×C42C2×D4311yescharacteristic
138C4⋊C8C2×D4312yes—
139#103—434no—
140#102—434no—
141C22⋊C8C2×D4312yes—
142#97C2×D4312yes—
143#41—1724no—
144C2×Q8—432no—
145C2×Q8—432no—
146C2×Q8—861no—
147C2×D4—432no—
148C2×D4—862no—
149C2×D4—861no—
150C2×D4—861no—
151C22×C4—862no—
152C22×C4D17211yescharacteristic
153C22×C4D17211yescharacteristic
154C22×C4C22×D4311yescharacteristic
155Q16—1724no—
156SD16—1724no—
157C2×C8C22×D4314yes—
158C4⋊C4—432no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4—861no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C4⋊C4—861no—
166C22⋊C4—862no—
167C22⋊C4—862no—
168C22⋊C4—862no—
169C42—862no—
170C42D17211yescharacteristic
171C42D17211yescharacteristic
172C42C22×D4311yescharacteristic
173C42C22×D4311yescharacteristic
174C23—862no—
175C23C2×D17211yescharacteristic
176Q8—862no—
177Q8—862no—
178Q8—864no—
179Q8—1722no—
180D4—864no—
181D4—1722no—
182D4—1724no—
183D4—1722no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—1724no—
191C2×C4C2×D17211yescharacteristic
192C2×C4C2×D17211yescharacteristic
193C2×C4C2×D17211yescharacteristic
194C2×C4C2×D17211yescharacteristic
195C2×C4C2×D17211yescharacteristic
196C2×C4C23×D4311yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—1722no—
202C22—1722no—
203C22—1722no—
204C22C22×D17211yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—1722no—
210C4—1722no—
211C4—1722no—
212C4#1306335812yes—
213C4#1306337112yes—
214C2—41no—
215C2—3442no—
216C2#1458346811yescharacteristic
217C2C2×#1306335811yescharacteristic
218C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3216
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #14583456C2semidirect
3. #14583293C2semidirect
4. #14583259C2semidirect
5. #14583110C2semidirect
6. #14583100C2semidirect
7. #14583063C2semidirect
8. C43×#432C2semidirect
117. #432D43semidirect
118. C43#3216semidirect