Finite Group Databasebeta

← #19140911

Subgroups — #19140911

Order 5504.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063324C212yesmaximal, complemented
2C2×#13063302C212yesmaximal
3#14582830C212yesmaximal, complemented
4#14582819C212yesmaximal, complemented
5#14582811C211yesmaximal, characteristic
6#14582787C212yesmaximal
7#14582784C212yesmaximal, complemented
8#14582771C211yesmaximal, characteristic
9C43×#399C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C22×Dic86C2212yes—
12C23×Dic43C2211yescharacteristic
13#13063324—28no—
14#13063302—28no—
15C2×C4⋊Dic43C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2211yescharacteristic
22C2×C4×Dic43C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2211yescharacteristic
28C2×C4⋊C4×C43C2212yes—
29C2×C4⋊C4×C43C2211yescharacteristic
30C2×C22⋊C4×C43C2212yes—
31C2×C22⋊C4×C43C2211yescharacteristic
32#95×C43C2211yescharacteristic
33C24×C43C2311yescharacteristic
34C22×C4×C43C2311yescharacteristic
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2312yes—
38C22×Dic43—24no—
39C22×Dic43—41no—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C2×Dic86—24no—
45C2×Dic86—24no—
46C2×Dic86—24no—
47C2×Dic86—41no—
48C2×Dic86—42no—
49C4⋊C4×C43—24no—
50C4⋊C4×C43—41no—
51C22⋊C4×C43—24no—
52C22⋊C4×C43—41no—
53C22⋊Dic43—24no—
54C22⋊Dic43Q814yescomplemented
55C4⋊Dic43D418yes—
56Dic43⋊C4—24no—
57Dic43⋊C4—24no—
58Dic43⋊C4—24no—
59Dic43⋊C4—24no—
60C4×Dic43—24no—
61C23×C43—22no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43—22no—
65C23×C43C2×Q812yes—
66C23×C43C2411yescharacteristic
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43C2×D414yes—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—44no—
87C2×Dic43C2×D414yes—
88C2×Dic43C2×D414yes—
89C2×Dic43C2×Q814yes—
90Dic86—44no—
91Dic86—48no—
92C22×C43—22no—
93C22×C43—24no—
94C22×C43—42no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43C22×D412yes—
98C22×C43C22×Q811yescharacteristic
99C22×C43H(5,𝔽2)11yescharacteristic
100C22×C432−1+411yescharacteristic
101C22×C432−1+412yes—
102C4×C43—24no—
103C4×C43—42no—
104C4×C43—41no—
105C4×C43—41no—
106Dic43—24no—
107Dic43—24no—
108Dic43—24no—
109Dic43—42no—
110#2677—431nomaximal, Sylow
111C2×C43—42no—
112C2×C43#53612yes—
113C2×C43#54411yescharacteristic
114C2×C43D4211yescharacteristic
115C2×C43D4×Q812yes—
116C2×C43#56311yescharacteristic
117C2×C4⋊Q8—432no—
118C2×C22⋊Q8—432no—
119#399D4311yescharacteristic
120#398—432no—
121#395—432no—
122#393—431no—
123#388—432no—
124#387—432no—
125#385—431no—
126C43#267711yescharacteristic, complemented, Sylow
127C22×Q8—432no—
128C22×Q8—431no—
129C23×C4—431no—
130C4⋊Q8—868no—
131C22⋊Q8—868no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—432no—
135C2×C4⋊C4—432no—
136C2×C4⋊C4—432no—
137C2×C4⋊C4C2×D4312yes—
138C2×C4⋊C4C2×D4311yescharacteristic
139C2×C22⋊C4—431no—
140C2×C22⋊C4—432no—
141C2×C22⋊C4C2×D4312yes—
142C2×C22⋊C4C2×D4311yescharacteristic
143C2×C42—432no—
144#95—432no—
145#95—432no—
146#95—432no—
147#95—432no—
148#95—431no—
149#95C2×D4311yescharacteristic
150C24C22×D4311yescharacteristic
151C2×Q8—864no—
152C2×Q8—864no—
153C2×Q8—864no—
154C2×Q8—1721no—
155C2×Q8—1722no—
156C22×C4—432no—
157C22×C4—432no—
158C22×C4—432no—
159C22×C4—432no—
160C22×C4—864no—
161C22×C4—1721no—
162C22×C4C22×D4311yescharacteristic
163C22×C4C22×D4312yes—
164C22×C4C22×D4311yescharacteristic
165C22×C4C22×D4312yes—
166C4⋊C4—24no—
167C4⋊C4—41no—
168C4⋊C4—438no—
169C4⋊C4—864no—
170C4⋊C4—864no—
171C4⋊C4—864no—
172C4⋊C4—864no—
173C22⋊C4—24no—
174C22⋊C4—41no—
175C22⋊C4—434no—
176C22⋊C4—864no—
177C42—864no—
178C23—22no—
179C23—21no—
180C23—22no—
181C23—21no—
182C23Q8×D4312yes—
183C23C23×D4311yescharacteristic
184Q8—1728no—
185Q8—1724no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—434no—
196C2×C4—434no—
197C2×C4—434no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—1724no—
208C2×C4D4×D4314yes—
209C22—24no—
210C22—22no—
211C22—41no—
212C22—42no—
213C22—41no—
214C22C2×D4×D4312yes—
215C22C2×Q8×D4311yescharacteristic
216C22#1306337011yescharacteristic
217C22#1306337212yes—
218C22#1306337211yescharacteristic
219C4—24no—
220C4—41no—
221C4—42no—
222C4—41no—
223C4—864no—
224C4—864no—
225C4—864no—
226C4—1722no—
227C2—42no—
228C2#1458347112yes—
229C2#1458352811yescharacteristic
230C2#1458353411yescharacteristic
231C2#1458356212yes—
232C2#1458365211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43#2677
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
3. #14582830C2semidirect
4. #14582819C2semidirect
7. #14582784C2semidirect
54. C22⋊Dic43Q8semidirect
126. C43#2677semidirect