Finite Group Databasebeta

← #19142743

Subgroups — #19142743

Order 5504.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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#14582829C211yesmaximal, characteristic, complemented
2#14582828C212yesmaximal, complemented
3#14582825C212yesmaximal, complemented
4#14582821C212yesmaximal, complemented
5#14582817C212yesmaximal
6#14582810C212yesmaximal, complemented
7#14582800C211yesmaximal, characteristic
8#14582781C212yesmaximal, complemented
9C43×#395C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12C2×Dic43⋊C4C2212yes—
13C2×Dic43⋊C4C2212yes—
14C2×(C2×D43)⋊C4C2212yes—
15C2×(C2×D43)⋊C4C2212yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×C4×Dic43C2211yescharacteristic
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C22×Q8×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2212yes—
29#95×C43C2212yes—
30#95×C43C2211yescharacteristic
31C23×D43C2312yes—
32C2×Q8×C43—41no—
33C2×Q8×C43—42no—
34C22×C4×C43C2312yes—
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C2×D172—22no—
43C2×D172—41no—
44C2×D172—41no—
45C4⋊C4×C43—41no—
46C4⋊C4×C43—42no—
47(C2×D43)⋊C4—42no—
48(C2×D43)⋊C4—42no—
49(C2×D43)⋊C4—42no—
50(C2×D43)⋊C4—42no—
51(C2×D43)⋊C4—42no—
52(C2×D43)⋊C4—42no—
53C4⋊Dic43—41no—
54Dic43⋊C4—24no—
55Dic43⋊C4—42no—
56C4×Dic43—41no—
57C23×C43C2411yescharacteristic
58C22×D43—22no—
59C22×D43—22no—
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—22no—
65Q8×C43—44no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—22no—
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—22no—
77C2×C4×C43—22no—
78C2×C4×C43#4112yes—
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—
88D172—44no—
89C22×C43C2×#4111yescharacteristic
90C22×C43H(5,𝔽2)11yescharacteristic
91C22×C43H(5,𝔽2)12yes—
92C22×C43H(5,𝔽2)11yescharacteristic
93C22×C432−1+412yes—
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—42no—
100C2×D43—42no—
101C4×C43—22no—
102C4×C43—41no—
103C4×C43—42no—
104C4×C43—41no—
105C4×C43—42no—
106Dic43—42no—
107Dic43—42no—
108Dic43—42no—
109#2830—431nomaximal, Sylow
110C2×C43#53811yescharacteristic
111C2×C43#54212yes—
112C2×C43#56011yescharacteristic
113C2×C43#56212yes—
114C2×C43#56311yescharacteristic
115D43—82no—
116#398—431no—
117#397—432no—
118#397—432no—
119#396—432no—
120#395D4311yescharacteristic, complemented
121#394—432no—
122#393—432no—
123#390—431no—
124#387—432no—
125C43#283011yescharacteristic, complemented, Sylow
126C22×Q8C2×D4311yescharacteristic
127C22×D4—431no—
128C2×C4⋊C4—432no—
129C2×C4⋊C4—432no—
130C2×C4⋊C4—431no—
131C2×C4⋊C4C2×D4311yescharacteristic
132C2×C4⋊C4C2×D4312yes—
133C2×C22⋊C4—432no—
134C2×C22⋊C4—432no—
135C2×C22⋊C4—432no—
136C2×C22⋊C4—432no—
137C2×C22⋊C4—432no—
138C2×C22⋊C4—432no—
139C2×C42—431no—
140#95—432no—
141#95—432no—
142#95—432no—
143#95—432no—
144#95—431no—
145#95C2×D4312yes—
146#95C2×D4311yescharacteristic
147C24—432no—
148C2×Q8—42no—
149C2×Q8—41no—
150C2×D4—862no—
151C2×D4—1721no—
152C2×D4—1721no—
153C22×C4—432no—
154C22×C4—432no—
155C22×C4—432no—
156C22×C4C22×D4312yes—
157C22×C4C22×D4311yescharacteristic
158C22×C4C22×D4312yes—
159C22×C4C22×D4311yescharacteristic
160C22×C4C22×D4311yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—42no—
163C4⋊C4—864no—
164C4⋊C4—1722no—
165C4⋊C4—1721no—
166C22⋊C4—1722no—
167C22⋊C4—1722no—
168C22⋊C4—1722no—
169C22⋊C4—1722no—
170C22⋊C4—1722no—
171C22⋊C4—1722no—
172C42—1721no—
173C23—862no—
174C23—862no—
175C23—862no—
176C23—862no—
177C23—862no—
178C23—862no—
179C23—862no—
180C23C23×D4311yescharacteristic
181Q8—44no—
182D4—1724no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
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×C4#1062190212yes—
205C22—1722no—
206C22—1722no—
207C22—1722no—
208C22—1722no—
209C22—1722no—
210C22—1722no—
211C22—1722no—
212C22C2×#1062190211yescharacteristic
213C22#1306337012yes—
214C22#1306337011yescharacteristic
215C22#1306337111yescharacteristic
216C22#1306337312yes—
217C4—22no—
218C4—41no—
219C4—42no—
220C4—41no—
221C4—42no—
222C4—1722no—
223C4—1722no—
224C4—1722no—
225C2—3442no—
226C2#1458348911yescharacteristic
227C2#1458352312yes—
228C2#1458363811yescharacteristic
229C2#1458364512yes—
230C2#1458364811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2830
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #14582829C2semidirect
2. #14582828C2semidirect
3. #14582825C2semidirect
4. #14582821C2semidirect
6. #14582810C2semidirect
8. #14582781C2semidirect
9. C43×#395C2semidirect
120. #395D43semidirect
125. C43#2830semidirect