Finite Group Databasebeta

← #19142424

Subgroups — #19142424

Order 5504.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#14582821C212yesmaximal, complemented
3#14582816C211yesmaximal, characteristic
4#14582816C212yesmaximal
5#14582790C212yesmaximal, complemented
6#14582789C212yesmaximal, complemented
7#14582789C212yesmaximal, complemented
8#14582780C212yesmaximal, complemented
9C43×#384C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
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×Dic43C2212yes—
20C43⋊#95C2211yescharacteristic
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2211yescharacteristic
26C2×C4⋊C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2212yes—
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2212yes—
30C2×C42×C43C2211yescharacteristic
31C23×D43C2312yes—
32C22×C4×C43C2311yescharacteristic
33C22×C4×C43C2312yes—
34C22×C4×C43C2311yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2312yes—
37C22×Dic43C2312yes—
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C2×D172—41no—
41C2×D172—42no—
42C4⋊C4×C43—42no—
43C4⋊C4×C43—41no—
44C4⋊C4×C43—41no—
45C4⋊C4×C43—42no—
46C42×C43—22no—
47(C2×D43)⋊C4—24no—
48(C2×D43)⋊C4—24no—
49(C2×D43)⋊C4—24no—
50(C2×D43)⋊C4—42no—
51(C2×D43)⋊C4—42no—
52(C2×D43)⋊C4—42no—
53C4⋊Dic43—41no—
54Dic43⋊C4—24no—
55C4×Dic43—42no—
56C23×C43C2411yescharacteristic
57C22×D43—22no—
58C22×D43—22no—
59C22×D43—22no—
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—21no—
66C2×C4×C43—22no—
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—21no—
74C2×C4×C43—22no—
75C2×C4×C43#4112yes—
76C2×C4×C43#4114yes—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86D172—44no—
87C22×C43C2×#4111yescharacteristic
88C22×C43C2×#4112yes—
89C22×C43H(5,𝔽2)11yescharacteristic
90C22×C43H(5,𝔽2)12yes—
91C22×C432−1+411yescharacteristic
92C2×D43—42no—
93C2×D43—42no—
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C4×C43—22no—
100C4×C43—24no—
101C4×C43—41no—
102C4×C43—42no—
103C4×C43—41no—
104Dic43—42no—
105Dic43—42no—
106Dic43—42no—
107#2795—431nomaximal, Sylow
108C2×C43#53911yescharacteristic
109C2×C43#54212yes—
110C2×C43#55312yes—
111C2×C43#55511yescharacteristic
112C2×C43#56011yescharacteristic
113D43—82no—
114#400—431no—
115#396—432no—
116#394—431no—
117#394—432no—
118#388—432no—
119#388—432no—
120#388—432no—
121#387—432no—
122#384D4311yescharacteristic, complemented
123C43#279511yescharacteristic, complemented, Sylow
124C22×D4—431no—
125C2×C4⋊C4—432no—
126C2×C4⋊C4—431no—
127C2×C4⋊C4C2×D4312yes—
128C2×C4⋊C4C2×D4311yescharacteristic
129C2×C4⋊C4C2×D4312yes—
130C2×C4⋊C4C2×D4311yescharacteristic
131C2×C22⋊C4—432no—
132C2×C22⋊C4—432no—
133C2×C22⋊C4—432no—
134C2×C22⋊C4—432no—
135C2×C22⋊C4—432no—
136C2×C22⋊C4—432no—
137C2×C42—432no—
138C2×C42C2×D4311yescharacteristic
139#95—431no—
140#95—432no—
141#95—432no—
142#95—432no—
143#95—431no—
144#95—432no—
145C24—432no—
146C2×D4—1722no—
147C2×D4—1721no—
148C22×C4—432no—
149C22×C4—432no—
150C22×C4—432no—
151C22×C4C22×D4311yescharacteristic
152C22×C4C22×D4312yes—
153C22×C4C22×D4311yescharacteristic
154C22×C4C22×D4311yescharacteristic
155C22×C4C22×D4312yes—
156C4⋊C4—42no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—864no—
161C4⋊C4—1721no—
162C22⋊C4—864no—
163C22⋊C4—864no—
164C22⋊C4—864no—
165C22⋊C4—1722no—
166C22⋊C4—1722no—
167C22⋊C4—1722no—
168C42—22no—
169C42—1722no—
170C23—862no—
171C23—862no—
172C23—862no—
173C23—862no—
174C23—862no—
175C23—862no—
176C23—862no—
177C23C23×D4311yescharacteristic
178D4—1724no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4#1062189812yes—
200C2×C4#1062190214yes—
201C22—1722no—
202C22—1722no—
203C22—1722no—
204C22—1722no—
205C22—1722no—
206C22—1722no—
207C22—1722no—
208C22C2×#1062189811yescharacteristic
209C22C2×#1062190212yes—
210C22#1306337012yes—
211C22#1306337011yescharacteristic
212C22#1306337311yescharacteristic
213C4—24no—
214C4—22no—
215C4—41no—
216C4—42no—
217C4—41no—
218C4—1722no—
219C4—1722no—
220C4—1722no—
221C2—3442no—
222C2#1458349611yescharacteristic
223C2#1458352312yes—
224C2#1458359712yes—
225C2#1458361511yescharacteristic
226C2#1458363611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#384C2
hypercenter#384D43
hypocenterC43#2795
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #14582838C2semidirect
2. #14582821C2semidirect
5. #14582790C2semidirect
6. #14582789C2semidirect
7. #14582789C2semidirect
8. #14582780C2semidirect
9. C43×#384C2semidirect
122. #384D43semidirect
123. C43#2795semidirect