Finite Group Databasebeta

← #19137351

Subgroups — #19137351

Order 5504.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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#14582803C212yesmaximal, complemented
3#14582793C212yesmaximal
4#14582787C212yesmaximal
5#14582784C212yesmaximal, complemented
6#14582783C212yesmaximal, complemented
7#14582762C211yesmaximal, characteristic
8C4×Dic43⋊C4C212yesmaximal, complemented
9C4×C22⋊C4×C43C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11#13063304C418yescomplemented
12C2×C4⋊Dic43C2211yescharacteristic
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×C22⋊Dic43C2211yescharacteristic
17C2×C22⋊Dic43C2211yescharacteristic
18C2×C22⋊Dic43C2212yes—
19C2×C4×Dic43C2212yes—
20C2×C4×Dic43C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C23×C4×C43C2211yescharacteristic
28C2×C22⋊C4×C43C2212yes—
29C2×C42×C43C2211yescharacteristic
30C2×C42×C43C2211yescharacteristic
31#95×C43C2212yes—
32C24×C43C2311yescharacteristic
33C22×C4×C43—41no—
34C22×C4×C43—41no—
35C22×C4×C43C2×C414yes—
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C2×Dic86—41no—
45C2×Dic86—41no—
46C2×Dic86C2×C414yes—
47C22⋊C4×C43—24no—
48C42×C43—41no—
49C42×C43—41no—
50C22⋊Dic43—41no—
51C22⋊Dic43—41no—
52C22⋊Dic43C2×C418yes—
53C4⋊Dic43C2×C414yes—
54Dic43⋊C4—24no—
55Dic43⋊C4—42no—
56Dic43⋊C4C2×C418yes—
57C4×Dic43—24no—
58C4×Dic43—42no—
59C23×C43—22no—
60C23×C43—21no—
61C23×C43—21no—
62C23×C43—22no—
63C23×C43C22×C412yes—
64C23×C43C2411yescharacteristic
65C2×C4×C43—22no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—44no—
75C2×C4×C43C22×C412yes—
76C2×C4×C43C22×C412yes—
77C2×C4×C43#4114yes—
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—22no—
87C2×Dic43—22no—
88C2×Dic43C22×C414yes—
89C2×Dic43C22×C414yes—
90Dic86—44no—
91C22×C43—22no—
92C22×C43—22no—
93C22×C43—22no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43C23×C411yescharacteristic
97C22×C43C2×#4112yes—
98C22×C43H(5,𝔽2)11yescharacteristic
99C22×C43H(5,𝔽2)11yescharacteristic
100C22×C432−1+412yes—
101C4×C43—22no—
102C4×C43—22no—
103C4×C43—24no—
104C4×C43—42no—
105Dic43—24no—
106Dic43—24no—
107Dic43—42no—
108Dic43—42no—
109#2332—431nomaximal, Sylow
110C2×C43—42no—
111C2×C43C4×#4111yescharacteristic
112C2×C43#51811yescharacteristic
113C2×C43#51911yescharacteristic
114C2×C43#53912yes—
115C2×C43#54212yes—
116C2×C22⋊Q8—431no—
117#391—432no—
118#388—432no—
119#388—432no—
120#387—432no—
121#387—432no—
122#381—431no—
123C4×C4⋊C4—432no—
124C4×C22⋊C4D4311yescharacteristic
125C43#233211yescharacteristic, complemented, Sylow
126C22×Q8—431no—
127C23×C4C2×D4311yescharacteristic
128C22⋊Q8—438no—
129C2×C4⋊C4—432no—
130C2×C4⋊C4—431no—
131C2×C4⋊C4—432no—
132C2×C4⋊C4—432no—
133C2×C22⋊C4—432no—
134C2×C22⋊C4—431no—
135C2×C22⋊C4—431no—
136C2×C22⋊C4C2×D4312yes—
137C2×C42—432no—
138C2×C42—432no—
139C2×C42C2×D4311yescharacteristic
140C2×C42C2×D4311yescharacteristic
141#95—432no—
142#95—432no—
143#95—432no—
144#95—432no—
145#95—432no—
146#95—432no—
147#95C2×D4312yes—
148C24C22×D4311yescharacteristic
149C2×Q8—434no—
150C2×Q8—1721no—
151C2×Q8—1721no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—432no—
155C22×C4—432no—
156C22×C4—432no—
157C22×C4—432no—
158C22×C4C4×D4314yes—
159C22×C4C22×D4312yes—
160C22×C4C22×D4311yescharacteristic
161C22×C4C22×D4311yescharacteristic
162C22×C4C22×D4312yes—
163C4⋊C4—438no—
164C4⋊C4—434no—
165C4⋊C4—864no—
166C4⋊C4—1722no—
167C22⋊C4—24no—
168C22⋊C4—438no—
169C22⋊C4—1721no—
170C22⋊C4—1721no—
171C42—41no—
172C42—41no—
173C42—864no—
174C42—1722no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D4312yes—
180C23C23×D4311yescharacteristic
181Q8—1724no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—434no—
193C2×C4—434no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4C2×C4×D4312yes—
205C2×C4C2×C4×D4312yes—
206C2×C4#1062189814yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D4311yescharacteristic
213C22C2×#1062189812yes—
214C22#1306337011yescharacteristic
215C22#1306337011yescharacteristic
216C22#1306337212yes—
217C4—22no—
218C4—22no—
219C4—24no—
220C4—42no—
221C4—864no—
222C4—864no—
223C4—1722no—
224C4—1722no—
225C2—42no—
226C2C4×#1062189811yescharacteristic
227C2#1458337211yescharacteristic
228C2#1458337611yescharacteristic
229C2#1458349112yes—
230C2#1458351412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC4×C22⋊C4×C43C2
socleC23×C43C24
hypercenterC4×C22⋊C4D43
hypocenterC43#2332
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14582803C2semidirect
5. #14582784C2semidirect
6. #14582783C2semidirect
8. C4×Dic43⋊C4C2semidirect
11. #13063304C4semidirect
125. C43#2332semidirect