Finite Group Databasebeta

← #19145795

Subgroups — #19145795

Order 5504.

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

normal subgroups only

This group has 366 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#14583308C212yesmaximal, complemented
4#14583264C212yesmaximal, complemented
5#14583224C214yesmaximal, complemented
6#14583190C212yesmaximal, complemented
7#14583180C212yesmaximal, complemented
8C43×#432C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10#13063325C2211yescharacteristic
11#13063325C2211yescharacteristic
12#13063325C2211yescharacteristic
13#13063322C2211yescharacteristic
14#13063317C2212yes—
15#13063313—21no—
16#13063304—21no—
17#13063304—21no—
18#13063299—21no—
19#13063299C2212yes—
20C4×Dic86—21no—
21C4×Dic86—21no—
22C4×D172—21no—
23C4×D172C2212yes—
24#13063284C2212yes—
25#13063259C2214yes—
26#13063257C2214yes—
27#13063247C2214yes—
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×Dic86—21no—
44C2×Dic86—21no—
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⋊Dic43C2312yes—
57C4⋊Dic43C2312yes—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61C4×Dic43—22no—
62C23×C43C2×D411yescharacteristic
63C22×D43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—41no—
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2411yescharacteristic
73C22⋊D43—44no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77D172—24no—
78D172—42no—
79D172—42no—
80C4×D43—44no—
81Dic86—42no—
82Dic86—42no—
83Dic86—42no—
84C8×C43—24no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43C22×D411yescharacteristic
89C2×D43—42no—
90C2×D43—42no—
91C2×D43—42no—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—21no—
96C4×C43AGL(1,ℤ/8)12yes—
97C4×C432−1+412yes—
98Dic43—42no—
99Dic43—42no—
100Dic43—42no—
101#3235—431nomaximal, Sylow
102C2×C43—41no—
103C2×C43#53611yescharacteristic
104C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C43#57511yescharacteristic
106D43—82no—
107#533—431no—
108#532—431no—
109#501—432no—
110#490—432no—
111#482—434no—
112#476—432no—
113#474—432no—
114#432D4311yescharacteristic, complemented
115C43#323511yescharacteristic, complemented, Sylow
116C2×#41—861no—
117C4⋊Q8—431no—
118C4⋊Q8—431no—
119C4⋊Q8—431no—
120#127—431no—
121#125—432no—
122#124—861no—
123C22⋊Q8—861no—
124C22⋊Q8—861no—
125#121—432no—
126#121—861no—
127C4×Q8—861no—
128C4×Q8—861no—
129C4×D4—432no—
130C4×D4—861no—
131#117—432no—
132C2×C42C2×D4311yescharacteristic
133#107—434no—
134#106—434no—
135C4⋊C8C2×D4312yes—
136#102—434no—
137#102—434no—
138C22⋊C8C2×D4312yes—
139#97C2×D4312yes—
140#41—1724no—
141C2×Q8—861no—
142C2×Q8—861no—
143C2×Q8—861no—
144C2×D4—432no—
145C2×D4—862no—
146C2×D4—861no—
147C2×D4—861no—
148C22×C4—862no—
149C22×C4D17211yescharacteristic
150C22×C4D17211yescharacteristic
151C22×C4C22×D4311yescharacteristic
152C2×C8C22×D4314yes—
153C4⋊C4—432no—
154C4⋊C4—432no—
155C4⋊C4—432no—
156C4⋊C4—861no—
157C4⋊C4—862no—
158C4⋊C4—862no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C22⋊C4—862no—
162C22⋊C4—862no—
163C22⋊C4—862no—
164C42—862no—
165C42D17211yescharacteristic
166C42D17211yescharacteristic
167C42C22×D4311yescharacteristic
168C42C22×D4311yescharacteristic
169C23—862no—
170C23C2×D17211yescharacteristic
171Q8—1722no—
172Q8—1722no—
173Q8—1722no—
174D4—864no—
175D4—1722no—
176D4—1722no—
177D4—1724no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—862no—
182C2×C4—862no—
183C2×C4—862no—
184C2×C4—1724no—
185C2×C4C2×D17211yescharacteristic
186C2×C4C2×D17211yescharacteristic
187C2×C4C2×D17211yescharacteristic
188C2×C4C2×D17211yescharacteristic
189C2×C4C2×D17211yescharacteristic
190C2×C4C23×D4311yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—1722no—
196C22—1722no—
197C22—1722no—
198C22C22×D17211yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—1722no—
204C4—1722no—
205C4—1722no—
206C4#1306335312yes—
207C4#1306337212yes—
208C2—41no—
209C2—3442no—
210C2#1458347511yescharacteristic
211C2C2×#1306335311yescharacteristic
212C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3235
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. #14583308C2semidirect
4. #14583264C2semidirect
5. #14583224C2semidirect
6. #14583190C2semidirect
7. #14583180C2semidirect
8. C43×#432C2semidirect
114. #432D43semidirect
115. C43#3235semidirect