Finite Group Databasebeta

← #19142767

Subgroups — #19142767

Order 5504.

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

normal subgroups only

This group has 416 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#14582837C212yesmaximal, complemented
2#14582828C212yesmaximal, complemented
3#14582816C211yesmaximal, characteristic
4#14582816C212yesmaximal
5#14582812C212yesmaximal, complemented
6#14582810C212yesmaximal, complemented
7#14582804C211yesmaximal, characteristic, complemented
8#14582788C212yesmaximal, complemented
9C43×#395C211yesmaximal, characteristic, complemented
10C22×Dic86C2211yescharacteristic
11C22×D172C2211yescharacteristic
12C2×Dic43⋊C4C2212yes—
13C2×(C2×D43)⋊C4C2212yes—
14C2×(C2×D43)⋊C4C2212yes—
15C2×(C2×D43)⋊C4C2212yes—
16C2×(C2×D43)⋊C4C2212yes—
17C2×(C2×D43)⋊C4C2212yes—
18C2×(C2×D43)⋊C4C2212yes—
19C2×C4×Dic43C2211yescharacteristic
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2211yescharacteristic
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—41no—
43C2×D172—42no—
44C2×Dic86—22no—
45C2×Dic86—41no—
46C2×Dic86—41no—
47C4⋊C4×C43—41no—
48C4⋊C4×C43—42no—
49(C2×D43)⋊C4—24no—
50(C2×D43)⋊C4—42no—
51(C2×D43)⋊C4—42no—
52(C2×D43)⋊C4—42no—
53(C2×D43)⋊C4—42no—
54(C2×D43)⋊C4—42no—
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—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
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—
89Dic86—44no—
90C22×C43C2×#4111yescharacteristic
91C22×C43H(5,𝔽2)11yescharacteristic
92C22×C43H(5,𝔽2)12yes—
93C22×C43H(5,𝔽2)11yescharacteristic
94C22×C432−1+412yes—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C4×C43—22no—
103C4×C43—41no—
104C4×C43—42no—
105C4×C43—41no—
106C4×C43—42no—
107Dic43—42no—
108Dic43—42no—
109Dic43—42no—
110#2832—431nomaximal, Sylow
111C2×C43#53811yescharacteristic
112C2×C43#54212yes—
113C2×C43H(3,𝔽4)11yescharacteristic
114C2×C43#56212yes—
115C2×C43#56311yescharacteristic
116D43—82no—
117#400—432no—
118#397—432no—
119#395D4311yescharacteristic, complemented
120#394—432no—
121#394—431no—
122#393—432no—
123#393—432no—
124#391—431no—
125#388—432no—
126C43#283211yescharacteristic, complemented, Sylow
127C22×Q8—431no—
128C22×Q8C2×D4311yescharacteristic
129C22×D4—431no—
130C2×C4⋊C4—432no—
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—432no—
145#95—431no—
146#95C2×D4312yes—
147#95C2×D4311yescharacteristic
148C24—432no—
149C2×Q8—42no—
150C2×Q8—41no—
151C2×Q8—862no—
152C2×Q8—1721no—
153C2×Q8—1721no—
154C2×D4—1722no—
155C2×D4—1721no—
156C22×C4—432no—
157C22×C4—432no—
158C22×C4—432no—
159C22×C4C22×D4311yescharacteristic
160C22×C4C22×D4312yes—
161C22×C4C22×D4311yescharacteristic
162C22×C4C22×D4312yes—
163C22×C4C22×D4311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—42no—
166C4⋊C4—1722no—
167C22⋊C4—864no—
168C22⋊C4—1722no—
169C22⋊C4—1722no—
170C22⋊C4—1722no—
171C22⋊C4—1722no—
172C22⋊C4—1722no—
173C42—1721no—
174C23—862no—
175C23—862no—
176C23—862no—
177C23—862no—
178C23—862no—
179C23—862no—
180C23—862no—
181C23C23×D4311yescharacteristic
182Q8—44no—
183Q8—1724no—
184D4—1724no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—862no—
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#1062190212yes—
207C22—1722no—
208C22—1722no—
209C22—1722no—
210C22—1722no—
211C22—1722no—
212C22—1722no—
213C22—1722no—
214C22C2×#1062190211yescharacteristic
215C22#1306337012yes—
216C22#1306337011yescharacteristic
217C22#1306337111yescharacteristic
218C22#1306337312yes—
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—1722no—
225C4—1722no—
226C4—1722no—
227C2—3442no—
228C2#1458348911yescharacteristic
229C2#1458352312yes—
230C2#1458364211yescharacteristic
231C2#1458364512yes—
232C2#1458364811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2832
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #14582837C2semidirect
2. #14582828C2semidirect
5. #14582812C2semidirect
6. #14582810C2semidirect
7. #14582804C2semidirect
8. #14582788C2semidirect
9. C43×#395C2semidirect
119. #395D43semidirect
126. C43#2832semidirect