Finite Group Databasebeta

← #19135580

Subgroups — #19135580

Order 5504.

324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#13063304C211yesmaximal, characteristic
2#14582759C211yesmaximal, characteristic
3#14582665C214yesmaximal
4C4×C22⋊C4×C43C211yesmaximal, characteristic
5C22×Dic86C411yescharacteristic, complemented
6#13063304—21no—
7#13063304—21no—
8#13063304—21no—
9#13063304—21no—
10C2×C4⋊Dic43—21no—
11C2×C4⋊Dic43C411yescharacteristic, complemented
12C2×Dic43⋊C4C412yescomplemented
13C2×C22⋊Dic43C2212yes—
14C2×C22⋊Dic43C2212yes—
15C43⋊#95—21no—
16C23×C4×C43C2211yescharacteristic
17C2×C22⋊C4×C43C2212yes—
18C2×C42×C43—21no—
19#95×C43—21no—
20C24×C43C2311yescharacteristic
21C22×C4×C43—22no—
22C22×C4×C43—42no—
23C22×C4×C43C2×C411yescharacteristic
24C22×C4×C43C2×C411yescharacteristic
25C22×C4×C43D411yescharacteristic
26C22×C4×C43D411yescharacteristic
27C22×C4×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×Dic43—22no—
30C22×Dic43C2×C412yes—
31C22×Dic43C2×C412yes—
32C2×Dic86—21no—
33C2×Dic86—21no—
34C2×Dic86—42no—
35C22⋊C4×C43—22no—
36C22⋊C4×C43Q814yescomplemented
37C42×C43—42no—
38C22⋊Dic43—22no—
39C22⋊Dic43—22no—
40C22⋊Dic43—24no—
41C4⋊Dic43—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43—42no—
44Dic43⋊C4—22no—
45Dic43⋊C4—22no—
46C23×C43—41no—
47C23×C43—41no—
48C23×C43C22×C411yescharacteristic
49C23×C43C2×D411yescharacteristic
50C23×C43C2×D411yescharacteristic
51C23×C43C2×Q812yes—
52C23×C43#4112yes—
53C2×C4×C43—22no—
54C2×C4×C43—22no—
55C2×C4×C43—22no—
56C2×C4×C43—24no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—42no—
61C2×C4×C43—42no—
62C2×C4×C43C22⋊C411yescharacteristic
63C2×C4×C43C22⋊C411yescharacteristic
64C2×C4×C43C22⋊C411yescharacteristic
65C2×C4×C43C22⋊C411yescharacteristic
66C2×Dic43—22no—
67C2×Dic43—22no—
68C2×Dic43—42no—
69C2×Dic43—42no—
70C2×Dic43—42no—
71C2×Dic43—42no—
72C2×Dic43—42no—
73Dic86—42no—
74Dic86—42no—
75C22×C43—21no—
76C22×C43—21no—
77C22×C43—21no—
78C22×C43—21no—
79C22×C43—21no—
80C22×C43—21no—
81C22×C43—42no—
82C22×C43—42no—
83C22×C43C2×C22⋊C411yescharacteristic
84C22×C43C4×Q812yes—
85C22×C43C22⋊Q812yes—
86C22×C43#12411yescharacteristic
87C22×C43C4⋊Q811yescharacteristic
88C4×C43—21no—
89C4×C43—21no—
90C4×C43—21no—
91C4×C43—44no—
92C4×C43#9912yes—
93Dic43—42no—
94Dic43—42no—
95Dic43—82no—
96#1996—431nomaximal, Sylow
97C2×C43—21no—
98C2×C43—22no—
99C2×C43—22no—
100C2×C43—21no—
101C2×C43#39111yescharacteristic
102C2×C43C2×#9911yescharacteristic
103C2×C43#41011yescharacteristic
104C2×C22⋊Q8—431no—
105#380—431no—
106C4×C22⋊C4D4311yescharacteristic
107#342—434no—
108C43#199611yescharacteristic, complemented, Sylow
109C22×Q8—431no—
110C23×C4C2×D4311yescharacteristic
111C22⋊Q8—861no—
112C22⋊Q8—861no—
113C22⋊Q8—861no—
114C22⋊Q8—861no—
115C2×C4⋊C4—432no—
116C2×C4⋊C4—431no—
117C2×C4⋊C4—861no—
118C2×C22⋊C4—432no—
119C2×C22⋊C4—432no—
120C2×C22⋊C4C2×D4312yes—
121C2×C42—21no—
122#95—21no—
123#95—861no—
124C24C22×D4311yescharacteristic
125C2×Q8—861no—
126C2×Q8—861no—
127C2×Q8—1722no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—432no—
131C22×C4—432no—
132C22×C4—862no—
133C22×C4C4×D4311yescharacteristic
134C22×C4C4×D4311yescharacteristic
135C22×C4D17211yescharacteristic
136C22×C4D17211yescharacteristic
137C22×C4C22⋊D4311yescharacteristic
138C22×C4C22⋊D4311yescharacteristic
139C4⋊C4—862no—
140C4⋊C4—862no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4—1722no—
144C22⋊C4—22no—
145C22⋊C4—862no—
146C22⋊C4—862no—
147C22⋊C4—864no—
148C22⋊C4Dic8614yescomplemented
149C42—42no—
150C23—41no—
151C23—41no—
152C23C2×Dic8612yes—
153C23C2×C4×D4311yescharacteristic
154C23C2×D17211yescharacteristic
155C23#1062189812yes—
156C23C2×C22⋊D4311yescharacteristic
157Q8—1722no—
158Q8—1722no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—862no—
169C2×C4—862no—
170C2×C4—1722no—
171C2×C4—1722no—
172C2×C4—1722no—
173C2×C4—1722no—
174C2×C4—1722no—
175C2×C4(C2×D43)⋊C411yescharacteristic
176C2×C4(C2×D43)⋊C411yescharacteristic
177C2×C4(C2×D43)⋊C411yescharacteristic
178C2×C4(C2×D43)⋊C411yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×(C2×D43)⋊C411yescharacteristic
188C22C4×Dic8612yes—
189C22#1306330412yes—
190C22#1306331311yescharacteristic
191C22#1306332511yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—44no—
196C4—3442no—
197C4—1722no—
198C4—1722no—
199C4#1306323912yes—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2#1458280511yescharacteristic
205C2C2×#1306323911yescharacteristic
206C2#1458287211yescharacteristic
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC4×C22⋊C4×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC4×C22⋊C4D43
hypocenterC43#1996
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×Dic86C4semidirect
11. C2×C4⋊Dic43C4semidirect
12. C2×Dic43⋊C4C4semidirect
36. C22⋊C4×C43Q8semidirect
108. C43#1996semidirect
148. C22⋊C4Dic86semidirect