Finite Group Databasebeta

← #19140266

Subgroups — #19140266

Order 5504.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13063281C212yesmaximal, complemented
2#14582829C211yesmaximal, characteristic, complemented
3#14582822C212yesmaximal, complemented
4#14582792C212yesmaximal, complemented
5#14582781C212yesmaximal, complemented
6#14582779C212yesmaximal
7#14582771C212yesmaximal, complemented
8#14582764C211yesmaximal, characteristic, complemented
9C43×#394C211yesmaximal, characteristic
10C23×Dic43C2212yes—
11#13063281—28no—
12C2×C4⋊Dic43C2211yescharacteristic
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C4×Dic43C2212yes—
21C2×C4×Dic43C2211yescharacteristic
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C22×D4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2212yes—
31#95×C43C2211yescharacteristic
32C24×C43C2312yes—
33C2×D4×C43—24no—
34C2×D4×C43—41no—
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43—24no—
40C22×Dic43—24no—
41C22×Dic43—24no—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C4⋊C4×C43—41no—
47C22⋊C4×C43—24no—
48C22⋊C4×C43—24no—
49C22⋊Dic43—24no—
50C22⋊Dic43—24no—
51C22⋊Dic43—42no—
52C4⋊Dic43—41no—
53C4⋊Dic43—41no—
54Dic43⋊C4—24no—
55Dic43⋊C4—24no—
56Dic43⋊C4—24no—
57C4×Dic43—24no—
58C4×Dic43D414yescomplemented
59C23×C43—22no—
60C23×C43—22no—
61C23×C43—22no—
62C23×C43—22no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43#4114yes—
66C23×C43C2411yescharacteristic
67D4×C43—44no—
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—22no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43C2×D412yes—
78C2×Dic43—216no—
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×Dic43—22no—
89C2×Dic43C2×D414yes—
90C2×Dic43#4114yes—
91C22×C43—24no—
92C22×C43—24no—
93C22×C43—24no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43—42no—
97C22×C43—42no—
98C22×C43C22×D411yescharacteristic
99C22×C43C2×#4112yes—
100C22×C43C2×#4112yes—
101C22×C43H(5,𝔽2)11yescharacteristic
102C22×C432−1+411yescharacteristic
103C4×C43—22no—
104C4×C43—42no—
105C4×C43—41no—
106C4×C43—41no—
107Dic43—24no—
108Dic43—24no—
109Dic43—42no—
110Dic43—42no—
111#2609—431nomaximal, Sylow
112C2×C43—44no—
113C2×C43#52512yes—
114C2×C43#53711yescharacteristic
115C2×C43#55111yescharacteristic
116C2×C43#55212yes—
117C2×C43#55511yescharacteristic
118C2×#117—432no—
119#398—431no—
120#396—432no—
121#394D4311yescharacteristic
122#388—432no—
123#387—432no—
124#386—432no—
125#385—432no—
126#382—431no—
127C43#260911yescharacteristic, complemented, Sylow
128C22×D4C2×D4311yescharacteristic
129C23×C4—432no—
130#117—868no—
131C2×C4⋊C4—432no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—431no—
135C2×C4⋊C4—431no—
136C2×C4⋊C4C2×D4311yescharacteristic
137C2×C22⋊C4—432no—
138C2×C22⋊C4—432no—
139C2×C22⋊C4—432no—
140C2×C22⋊C4C2×D4312yes—
141C2×C22⋊C4C2×D4312yes—
142C2×C42—431no—
143C2×C42—432no—
144#95—432no—
145#95—432no—
146#95—431no—
147#95—432no—
148#95—432no—
149#95C2×D4311yescharacteristic
150C24C22×D4312yes—
151C2×D4—24no—
152C2×D4—41no—
153C22×C4—432no—
154C22×C4—432no—
155C22×C4—432no—
156C22×C4—432no—
157C22×C4—864no—
158C22×C4—864no—
159C22×C4—864no—
160C22×C4C22×D4311yescharacteristic
161C22×C4C22×D4311yescharacteristic
162C22×C4C22×D4312yes—
163C22×C4C22×D4311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—864no—
166C4⋊C4—864no—
167C4⋊C4—864no—
168C4⋊C4—1721no—
169C4⋊C4—1721no—
170C22⋊C4—24no—
171C22⋊C4—24no—
172C22⋊C4—864no—
173C22⋊C4—864no—
174C22⋊C4—1722no—
175C42—434no—
176C42—864no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23#1062190014yes—
184C23C23×D4311yescharacteristic
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—434no—
196C2×C4—434no—
197C2×C4—8616no—
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—862no—
208C2×C4D4×D4312yes—
209C22—24no—
210C22—24no—
211C22—24no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22C2×D4×D4311yescharacteristic
217C22#41×D4312yes—
218C22C2×#1062190012yes—
219C22#1306337011yescharacteristic
220C22#1306337211yescharacteristic
221C4—22no—
222C4—41no—
223C4—41no—
224C4—42no—
225C4—864no—
226C4—864no—
227C4—1722no—
228C4—1722no—
229C2—44no—
230C2#1458340912yes—
231C2#1458347611yescharacteristic
232C2#1458358011yescharacteristic
233C2#1458358612yes—
234C2#1458361111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2609
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063281C2semidirect
2. #14582829C2semidirect
3. #14582822C2semidirect
4. #14582792C2semidirect
5. #14582781C2semidirect
7. #14582771C2semidirect
8. #14582764C2semidirect
58. C4×Dic43D4semidirect
127. C43#2609semidirect