Finite Group Databasebeta

← #19140085

Subgroups — #19140085

Order 5504.

440 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 129 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#14582816C212yesmaximal
3#14582800C211yesmaximal, characteristic
4#14582791C212yesmaximal, complemented
5#14582791C212yesmaximal, complemented
6#14582791C212yesmaximal, complemented
7#14582789C212yesmaximal, complemented
8C4⋊C4×Dic43C212yesmaximal, complemented
9C43×#398C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C2×C4⋊Dic43C2212yes—
12C2×C4⋊Dic43C2211yescharacteristic
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—
20C2×C4×Dic43C2212yes—
21C2×C4×Dic43C2211yescharacteristic
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C2×C4⋊C4×C43C2212yes—
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29#95×C43C2212yes—
30#95×C43C2211yescharacteristic
31C23×D43C2312yes—
32C22×C4×C43C2311yescharacteristic
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2312yes—
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×Dic43C2312yes—
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C2×D172—22no—
41C2×D172—41no—
42C2×D172—41no—
43C4⋊C4×C43—24no—
44C4⋊C4×C43—41no—
45C4⋊C4×C43—41no—
46(C2×D43)⋊C4—24no—
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—24no—
53C4⋊Dic43—41no—
54C4×Dic43—24no—
55C4×Dic43—41no—
56C4×Dic43—42no—
57C23×C43C2411yescharacteristic
58C22×D43—22no—
59C22×D43—22no—
60C22×D43—22no—
61C22×D43—22no—
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
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#4112yes—
77C2×C4×C43#4114yes—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43#4114yes—
87D172—44no—
88C22×C43C2×#4112yes—
89C22×C43C2×#4111yescharacteristic
90C22×C43C2×#4112yes—
91C22×C43H(5,𝔽2)11yescharacteristic
92C22×C43H(5,𝔽2)11yescharacteristic
93C2×D43—42no—
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—42no—
100C4×C43—24no—
101C4×C43—22no—
102C4×C43—42no—
103C4×C43—41no—
104C4×C43—41no—
105Dic43—24no—
106Dic43—42no—
107Dic43—42no—
108#2593—431nomaximal, Sylow
109C2×C43#52912yes—
110C2×C43#53811yescharacteristic
111C2×C43#55312yes—
112C2×C43#55511yescharacteristic
113C2×C43#55911yescharacteristic
114D43—82no—
115#400—431no—
116#398D4311yescharacteristic, complemented
117#394—432no—
118#390—431no—
119#388—432no—
120#388—432no—
121#388—432no—
122#388—432no—
123C4×C4⋊C4—432no—
124C43#259311yescharacteristic, complemented, Sylow
125C22×D4—431no—
126C2×C4⋊C4—432no—
127C2×C4⋊C4—431no—
128C2×C4⋊C4C2×D4312yes—
129C2×C4⋊C4C2×D4311yescharacteristic
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×C42—431no—
139C2×C42—432no—
140#95—432no—
141#95—432no—
142#95—432no—
143#95—431no—
144#95C2×D4311yescharacteristic
145#95C2×D4312yes—
146C24—432no—
147C2×D4—862no—
148C2×D4—1721no—
149C2×D4—1721no—
150C22×C4—432no—
151C22×C4—432no—
152C22×C4—432no—
153C22×C4C22×D4311yescharacteristic
154C22×C4C22×D4311yescharacteristic
155C22×C4C22×D4312yes—
156C22×C4C22×D4311yescharacteristic
157C22×C4C22×D4312yes—
158C4⋊C4—24no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—864no—
162C4⋊C4—1721no—
163C22⋊C4—864no—
164C22⋊C4—864no—
165C22⋊C4—864no—
166C22⋊C4—864no—
167C22⋊C4—1722no—
168C22⋊C4—1722no—
169C42—864no—
170C42—1721no—
171C42—1722no—
172C23—862no—
173C23—862no—
174C23—862no—
175C23—862no—
176C23—862no—
177C23—862no—
178C23—862no—
179C23C23×D4311yescharacteristic
180D4—1724no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—434no—
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#1062190012yes—
202C2×C4#1062190214yes—
203C22—1722no—
204C22—1722no—
205C22—1722no—
206C22—1722no—
207C22—1722no—
208C22—1722no—
209C22—1722no—
210C22#41×D4312yes—
211C22C2×#1062190011yescharacteristic
212C22C2×#1062190212yes—
213C22#1306337011yescharacteristic
214C22#1306337111yescharacteristic
215C4—24no—
216C4—22no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—864no—
221C4—1722no—
222C4—1722no—
223C2—3442no—
224C2#1458343512yes—
225C2#1458348611yescharacteristic
226C2#1458360212yes—
227C2#1458361511yescharacteristic
228C2#1458363311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2593
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #14582838C2semidirect
4. #14582791C2semidirect
5. #14582791C2semidirect
6. #14582791C2semidirect
7. #14582789C2semidirect
8. C4⋊C4×Dic43C2semidirect
9. C43×#398C2semidirect
116. #398D43semidirect
124. C43#2593semidirect