Finite Group Databasebeta

← #19142296

Subgroups — #19142296

Order 5504.

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

normal subgroups only

This group has 472 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
1#14582838C211yesmaximal, characteristic, complemented
2#14582822C212yesmaximal, complemented
3#14582819C211yesmaximal, characteristic, complemented
4#14582811C212yesmaximal, complemented
5#14582783C212yesmaximal, complemented
6#14582779C212yesmaximal
7#14582771C212yesmaximal, complemented
8#14582757C212yesmaximal, complemented
9C43×#390C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C23×Dic43C2212yes—
12C2×C4⋊Dic43C2211yescharacteristic
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×C22⋊Dic43C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C22⋊Dic43C2212yes—
19C43⋊#95C2212yes—
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2211yescharacteristic
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C22×D4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2212yes—
30C2×C42×C43C2211yescharacteristic
31C24×C43C2312yes—
32C2×D4×C43—41no—
33C2×D4×C43—41no—
34C2×D4×C43Q814yescomplemented
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43—24no—
40C22×Dic43—42no—
41C22×Dic43—42no—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2312yes—
46C2×Dic86—42no—
47C2×Dic86—41no—
48C4⋊C4×C43—41no—
49C22⋊C4×C43—42no—
50C22⋊C4×C43—42no—
51C42×C43—41no—
52C22⋊Dic43—24no—
53C22⋊Dic43—42no—
54C22⋊Dic43—42no—
55C4⋊Dic43—41no—
56Dic43⋊C4—24no—
57Dic43⋊C4—42no—
58Dic43⋊C4—42no—
59C23×C43—22no—
60C23×C43—22no—
61C23×C43—22no—
62C23×C43—22no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43C2×Q814yes—
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—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43C2×Q812yes—
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×Dic43—22no—
89C2×Dic43—48no—
90C2×Dic43#4114yes—
91Dic86—44no—
92C22×C43—24no—
93C22×C43—24no—
94C22×C43—24no—
95C22×C43—42no—
96C22×C43—42no—
97C22×C43—42no—
98C22×C43—42no—
99C22×C43C22×Q811yescharacteristic
100C22×C43C2×#4112yes—
101C22×C43H(5,𝔽2)11yescharacteristic
102C22×C43H(5,𝔽2)12yes—
103C22×C43H(5,𝔽2)11yescharacteristic
104C4×C43—22no—
105C4×C43—42no—
106C4×C43—41no—
107C4×C43—41no—
108Dic43—24no—
109Dic43—42no—
110Dic43—42no—
111Dic43—42no—
112#2784—431nomaximal, Sylow
113C2×C43—44no—
114C2×C43#53812yes—
115C2×C43#54311yescharacteristic
116C2×C43#55412yes—
117C2×C43#55511yescharacteristic
118C2×C43#56011yescharacteristic
119#400—431no—
120#396—432no—
121#395—431no—
122#393—432no—
123#390D4311yescharacteristic
124#387—432no—
125#386—432no—
126#385—432no—
127#380—432no—
128C43#278411yescharacteristic, complemented, Sylow
129C22×Q8—431no—
130C22×D4C2×D4311yescharacteristic
131C23×C4—432no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—432no—
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×C42C2×D4311yescharacteristic
143#95—431no—
144#95—432no—
145#95—431no—
146#95—432no—
147#95—432no—
148#95—432no—
149#95—432no—
150C24C22×D4312yes—
151C2×Q8—1722no—
152C2×Q8—1721no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4Dic8614yescomplemented
156C22×C4—432no—
157C22×C4—432no—
158C22×C4—432no—
159C22×C4—432no—
160C22×C4—864no—
161C22×C4—1722no—
162C22×C4—1722no—
163C22×C4C22×D4311yescharacteristic
164C22×C4C22×D4312yes—
165C22×C4C22×D4311yescharacteristic
166C22×C4C22×D4311yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—864no—
169C4⋊C4—1722no—
170C4⋊C4—1722no—
171C4⋊C4—1721no—
172C22⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—864no—
175C22⋊C4—1722no—
176C22⋊C4—1722no—
177C42—41no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23C2×Dic8614yes—
185C23C23×D4311yescharacteristic
186Q8—1724no—
187D4—44no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
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—862no—
208C2×C4—862no—
209C2×C4—1728no—
210C2×C4C2×Dic8612yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22C22×Dic8611yescharacteristic
219C22#41×D4312yes—
220C22#1306337012yes—
221C22#1306337011yescharacteristic
222C22#1306337011yescharacteristic
223C4—22no—
224C4—41no—
225C4—41no—
226C4—42no—
227C4—864no—
228C4—1722no—
229C4—1722no—
230C4—1722no—
231C2—44no—
232C2#1458348112yes—
233C2#1458352511yescharacteristic
234C2#1458360812yes—
235C2#1458361111yescharacteristic
236C2#1458363611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#390C2
hypercenter#390D43
hypocenterC43#2784
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14582838C2semidirect
2. #14582822C2semidirect
3. #14582819C2semidirect
4. #14582811C2semidirect
5. #14582783C2semidirect
7. #14582771C2semidirect
8. #14582757C2semidirect
34. C2×D4×C43Q8semidirect
128. C43#2784semidirect
155. C2×D4Dic86semidirect