Finite Group Databasebeta

← #19142022

Subgroups — #19142022

Order 5504.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#14582839C212yesmaximal, complemented
2#14582832C212yesmaximal, complemented
3#14582811C211yesmaximal, characteristic
4#14582803C212yesmaximal, complemented
5#14582792C212yesmaximal
6#14582771C212yesmaximal
7#14582766C212yesmaximal, complemented
8#14582760C211yesmaximal, characteristic
9C43×#397C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C23×Dic43C2211yescharacteristic
12C2×C4⋊Dic43C2212yes—
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×C22⋊Dic43C2212yes—
16C2×C22⋊Dic43C2211yescharacteristic
17C2×C4×Dic43C2212yes—
18C43⋊#95C2212yes—
19C43⋊#95C2212yes—
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2211yescharacteristic
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C2×C4⋊C4×C43C2211yescharacteristic
27C2×C22⋊C4×C43C2212yes—
28C2×C22⋊C4×C43C2211yescharacteristic
29#95×C43C2212yes—
30#95×C43C2211yescharacteristic
31C24×C43C2311yescharacteristic
32C22×C4×C43C2312yes—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2311yescharacteristic
35C22×C4×C43C2312yes—
36C22×Dic43—22no—
37C22×Dic43—41no—
38C22×Dic43—41no—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C2×Dic86—24no—
44C2×Dic86—41no—
45C4⋊C4×C43—41no—
46C22⋊C4×C43—24no—
47C22⋊C4×C43—41no—
48C22⋊Dic43—24no—
49C22⋊Dic43—41no—
50C4⋊Dic43—42no—
51Dic43⋊C4—42no—
52Dic43⋊C4—42no—
53C4×Dic43—24no—
54C23×C43—22no—
55C23×C43—21no—
56C23×C43—21no—
57C23×C43—22no—
58C23×C43#4112yes—
59C23×C43C2411yescharacteristic
60C2×C4×C43—22no—
61C2×C4×C43—22no—
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×Dic43—22no—
71C2×Dic43—22no—
72C2×Dic43—22no—
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—44no—
82C2×Dic43#4114yes—
83Dic86—44no—
84C22×C43—22no—
85C22×C43—24no—
86C22×C43—42no—
87C22×C43—41no—
88C22×C43—41no—
89C22×C43C2×#4112yes—
90C22×C43C2×#4111yescharacteristic
91C22×C43H(5,𝔽2)11yescharacteristic
92C22×C43H(5,𝔽2)11yescharacteristic
93C22×C432−1+412yes—
94C4×C43—42no—
95C4×C43—41no—
96C4×C43—42no—
97C4×C43—41no—
98Dic43—24no—
99Dic43—42no—
100Dic43—42no—
101Dic43—42no—
102#2764—431nomaximal, Sylow
103C2×C43—42no—
104C2×C43#53811yescharacteristic
105C2×C43#54212yes—
106C2×C43#55111yescharacteristic
107C2×C43#55212yes—
108C2×C43#56311yescharacteristic
109#400—432no—
110#398—432no—
111#397D4311yescharacteristic
112#393—431no—
113#391—432no—
114#388—432no—
115#385—432no—
116#383—432no—
117#381—431no—
118C43#276411yescharacteristic, complemented, Sylow
119C22×Q8—431no—
120C23×C4—431no—
121C2×C4⋊C4—432no—
122C2×C4⋊C4—432no—
123C2×C4⋊C4—432no—
124C2×C4⋊C4C2×D4311yescharacteristic
125C2×C22⋊C4—432no—
126C2×C22⋊C4—431no—
127C2×C22⋊C4C2×D4312yes—
128C2×C22⋊C4C2×D4311yescharacteristic
129C2×C42—432no—
130#95—432no—
131#95—432no—
132#95—432no—
133#95—432no—
134#95—432no—
135#95—432no—
136#95—432no—
137#95—431no—
138#95C2×D4311yescharacteristic
139#95C2×D4312yes—
140C24C22×D4311yescharacteristic
141C2×Q8—864no—
142C2×Q8—1721no—
143C22×C4—432no—
144C22×C4—432no—
145C22×C4—432no—
146C22×C4—432no—
147C22×C4—862no—
148C22×C4—1721no—
149C22×C4—1721no—
150C22×C4C22×D4311yescharacteristic
151C22×C4C22×D4312yes—
152C22×C4C22×D4311yescharacteristic
153C22×C4C22×D4312yes—
154C4⋊C4—41no—
155C4⋊C4—1722no—
156C4⋊C4—1722no—
157C4⋊C4—1722no—
158C22⋊C4—24no—
159C22⋊C4—41no—
160C22⋊C4—864no—
161C22⋊C4—1721no—
162C42—864no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23—22no—
167C23#1062190012yes—
168C23C23×D4311yescharacteristic
169Q8—1724no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—434no—
181C2×C4—862no—
182C2×C4—862no—
183C2×C4—862no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—1724no—
193C22—24no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—42no—
198C22#41×D4312yes—
199C22C2×#1062190011yescharacteristic
200C22#1306337011yescharacteristic
201C22#1306337111yescharacteristic
202C22#1306337212yes—
203C4—41no—
204C4—42no—
205C4—41no—
206C4—42no—
207C4—864no—
208C4—1722no—
209C4—1722no—
210C4—1722no—
211C2—42no—
212C2#1458348611yescharacteristic
213C2#1458351512yes—
214C2#1458357911yescharacteristic
215C2#1458358612yes—
216C2#1458365211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2764
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #14582839C2semidirect
2. #14582832C2semidirect
4. #14582803C2semidirect
7. #14582766C2semidirect
118. C43#2764semidirect