Finite Group Databasebeta

← #19142274

Subgroups — #19142274

Order 5504.

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

normal subgroups only

This group has 448 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#14582841C212yesmaximal, complemented
2#14582826C212yesmaximal, complemented
3#14582816C211yesmaximal, characteristic
4#14582791C212yesmaximal, complemented
5#14582777C212yesmaximal
6#14582773C212yesmaximal, complemented
7#14582770C212yesmaximal, complemented
8#14582764C211yesmaximal, characteristic, complemented
9C43×#400C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C22×C4×D43C2212yes—
12C2×C4⋊Dic43C2212yes—
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊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⋊#95C2211yescharacteristic
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C2×C4⋊C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28#95×C43C2212yes—
29#95×C43C2211yescharacteristic
30#95×C43C2212yes—
31C23×D43C2312yes—
32C22×C4×C43C2312yes—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2312yes—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×Dic43C2312yes—
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C2×D172—24no—
41C2×D172—41no—
42C2×C4×D43—42no—
43C2×C4×D43—42no—
44C2×C4×D43—42no—
45C4⋊C4×C43—41no—
46C4⋊C4×C43—41no—
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—
52C4⋊Dic43—42no—
53C4⋊Dic43—41no—
54Dic43⋊C4—42no—
55C4×Dic43—22no—
56C23×C43C2411yescharacteristic
57C22×D43—22no—
58C22×D43—22no—
59C22×D43—22no—
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43#4114yes—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43#4112yes—
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—
87C4×D43—48no—
88C22×C43C2×#4112yes—
89C22×C43C2×#4111yescharacteristic
90C22×C43H(5,𝔽2)11yescharacteristic
91C22×C43H(5,𝔽2)12yes—
92C22×C432−1+411yescharacteristic
93C2×D43—24no—
94C2×D43—24no—
95C2×D43—24no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—42no—
100C4×C43—22no—
101C4×C43—42no—
102C4×C43—41no—
103C4×C43—41no—
104C4×C43—42no—
105Dic43—42no—
106Dic43—42no—
107Dic43—42no—
108#2782—431nomaximal, Sylow
109C2×C43#53912yes—
110C2×C43#53911yescharacteristic
111C2×C43#55111yescharacteristic
112C2×C43#55312yes—
113C2×C43H(3,𝔽4)11yescharacteristic
114D43—44no—
115#400—432no—
116#400D4311yescharacteristic, complemented
117#397—432no—
118#394—431no—
119#388—432no—
120#386—432no—
121#385—432no—
122#385—432no—
123#382—431no—
124C43#278211yescharacteristic, complemented, Sylow
125C22×D4—431no—
126C23×C4—432no—
127C2×C4⋊C4—432no—
128C2×C4⋊C4—431no—
129C2×C4⋊C4—432no—
130C2×C4⋊C4C2×D4311yescharacteristic
131C2×C4⋊C4C2×D4311yescharacteristic
132C2×C22⋊C4—432no—
133C2×C22⋊C4—432no—
134C2×C22⋊C4—432no—
135C2×C22⋊C4—432no—
136C2×C22⋊C4—432no—
137C2×C42—431no—
138#95—432no—
139#95—432no—
140#95—432no—
141#95—432no—
142#95—431no—
143#95C2×D4312yes—
144#95C2×D4312yes—
145#95C2×D4311yescharacteristic
146C24—432no—
147C2×D4—864no—
148C2×D4—1721no—
149C22×C4—432no—
150C22×C4—432no—
151C22×C4—432no—
152C22×C4—1722no—
153C22×C4—1722no—
154C22×C4—1722no—
155C22×C4C22×D4311yescharacteristic
156C22×C4C22×D4311yescharacteristic
157C22×C4C22×D4312yes—
158C22×C4C22×D4312yes—
159C22×C4C22×D4311yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—1722no—
163C4⋊C4—1721no—
164C4⋊C4—1722no—
165C22⋊C4—864no—
166C22⋊C4—864no—
167C22⋊C4—864no—
168C22⋊C4—1722no—
169C22⋊C4—1722no—
170C42—862no—
171C23—434no—
172C23—862no—
173C23—862no—
174C23—862no—
175C23—862no—
176C23—862no—
177C23—862no—
178C23C23×D4311yescharacteristic
179D4—1724no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—1728no—
202C2×C4#1062190212yes—
203C22—864no—
204C22—864no—
205C22—864no—
206C22—1722no—
207C22—1722no—
208C22—1722no—
209C22—1722no—
210C22#41×D4312yes—
211C22C2×#1062190211yescharacteristic
212C22#1306337011yescharacteristic
213C22#1306337112yes—
214C22#1306337211yescharacteristic
215C4—22no—
216C4—41no—
217C4—41no—
218C4—42no—
219C4—42no—
220C4—1722no—
221C4—1722no—
222C4—1722no—
223C2—1724no—
224C2#1458349012yes—
225C2#1458349811yescharacteristic
226C2#1458357711yescharacteristic
227C2#1458360212yes—
228C2#1458364111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2782
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #14582841C2semidirect
2. #14582826C2semidirect
4. #14582791C2semidirect
6. #14582773C2semidirect
7. #14582770C2semidirect
8. #14582764C2semidirect
9. C43×#400C2semidirect
116. #400D43semidirect
124. C43#2782semidirect