Finite Group Databasebeta

← #19142783

Subgroups — #19142783

Order 5504.

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

normal subgroups only

This group has 380 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#14582841C212yesmaximal, complemented
2#14582840C212yesmaximal, complemented
3#14582837C212yesmaximal, complemented
4#14582827C212yesmaximal
5#14582824C211yesmaximal, characteristic
6#14582819C212yesmaximal, complemented
7#14582811C211yesmaximal, characteristic
8#14582772C212yesmaximal
9C43×#385C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12C2×Dic43⋊C4C2212yes—
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×C22⋊Dic43C2212yes—
16C2×C22⋊Dic43C2212yes—
17C43⋊#95C2211yescharacteristic
18C43⋊#95C2212yes—
19C43⋊#95C2212yes—
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2211yescharacteristic
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C23×C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2212yes—
28C2×C22⋊C4×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2211yescharacteristic
30#95×C43C2212yes—
31C24×C43C2311yescharacteristic
32C22×C4×C43—42no—
33C22×C4×C43—41no—
34C22×C4×C43C2311yescharacteristic
35C22×C4×C43C2312yes—
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C2×Dic86—41no—
43C2×Dic86—42no—
44C4⋊C4×C43—42no—
45C22⋊C4×C43—22no—
46C22⋊C4×C43—41no—
47C22⋊Dic43—24no—
48C22⋊Dic43—42no—
49C4⋊Dic43—41no—
50Dic43⋊C4—42no—
51Dic43⋊C4—42no—
52Dic43⋊C4—42no—
53C23×C43—22no—
54C23×C43—21no—
55C23×C43—22no—
56C23×C43—21no—
57C23×C43#4112yes—
58C23×C43C2411yescharacteristic
59C2×C4×C43—22no—
60C2×C4×C43—22no—
61C2×C4×C43—22no—
62C2×C4×C43—22no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—44no—
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—22no—
82Dic86—44no—
83C22×C43—24no—
84C22×C43—22no—
85C22×C43—41no—
86C22×C43—42no—
87C22×C43—41no—
88C22×C43C2×#4111yescharacteristic
89C22×C43H(5,𝔽2)12yes—
90C22×C43H(5,𝔽2)11yescharacteristic
91C22×C432−1+412yes—
92C22×C432−1+411yescharacteristic
93C4×C43—42no—
94C4×C43—41no—
95C4×C43—42no—
96C4×C43—41no—
97Dic43—42no—
98Dic43—42no—
99Dic43—42no—
100Dic43—42no—
101#2835—431nomaximal, Sylow
102C2×C43—42no—
103C2×C43#53912yes—
104C2×C43#53911yescharacteristic
105C2×C43H(3,𝔽4)11yescharacteristic
106C2×C43#56312yes—
107C2×C43#56311yescharacteristic
108#400—432no—
109#400—432no—
110#400—432no—
111#397—431no—
112#397—432no—
113#395—432no—
114#393—431no—
115#385—432no—
116#385D4311yescharacteristic
117C43#283511yescharacteristic, complemented, Sylow
118C22×Q8—431no—
119C23×C4C2×D4311yescharacteristic
120C2×C4⋊C4—432no—
121C2×C4⋊C4—432no—
122C2×C4⋊C4—432no—
123C2×C4⋊C4—431no—
124C2×C4⋊C4C2×D4312yes—
125C2×C22⋊C4—432no—
126C2×C22⋊C4—432no—
127C2×C22⋊C4C2×D4311yescharacteristic
128C2×C22⋊C4C2×D4311yescharacteristic
129#95—432no—
130#95—432no—
131#95—431no—
132#95—432no—
133#95—432no—
134#95—432no—
135#95—432no—
136#95—432no—
137#95—431no—
138#95C2×D4312yes—
139C24C22×D4311yescharacteristic
140C2×Q8—1721no—
141C2×Q8—1722no—
142C22×C4—42no—
143C22×C4—41no—
144C22×C4—432no—
145C22×C4—432no—
146C22×C4—432no—
147C22×C4—432no—
148C22×C4C22×D4311yescharacteristic
149C22×C4C22×D4312yes—
150C22×C4C22×D4311yescharacteristic
151C22×C4C22×D4312yes—
152C4⋊C4—42no—
153C4⋊C4—1722no—
154C4⋊C4—1722no—
155C4⋊C4—1722no—
156C4⋊C4—1721no—
157C22⋊C4—22no—
158C22⋊C4—41no—
159C22⋊C4—864no—
160C22⋊C4—1722no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23#1062189812yes—
166C23C23×D4311yescharacteristic
167Q8—1724no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—862no—
180C2×C4—862no—
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—
191C22—24no—
192C22—22no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22C2×#1062189811yescharacteristic
197C22#1306337012yes—
198C22#1306337011yescharacteristic
199C22#1306337212yes—
200C22#1306337311yescharacteristic
201C4—42no—
202C4—41no—
203C4—41no—
204C4—42no—
205C4—1722no—
206C4—1722no—
207C4—1722no—
208C4—1722no—
209C2—42no—
210C2#1458349112yes—
211C2#1458349611yescharacteristic
212C2#1458364211yescharacteristic
213C2#1458365012yes—
214C2#1458365211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2835
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #14582841C2semidirect
2. #14582840C2semidirect
3. #14582837C2semidirect
6. #14582819C2semidirect
117. C43#2835semidirect