Finite Group Databasebeta

← #19141626

Subgroups — #19141626

Order 5504.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#13063324C212yesmaximal
2#14582832C212yesmaximal
3#14582820C212yesmaximal
4#14582819C212yesmaximal
5#14582805C211yesmaximal, characteristic
6#14582797C211yesmaximal, characteristic
7#14582785C212yesmaximal
8#14582782C212yesmaximal
9C43×#389C211yesmaximal, characteristic
10C22×Dic86C2212yes—
11C22×Dic86C2211yescharacteristic
12#13063324—28no—
13C2×C4⋊Dic43C2212yes—
14C2×C4⋊Dic43C2211yescharacteristic
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×C4×Dic43C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C2×C4⋊C4×C43C2212yes—
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2211yescharacteristic
30C2×C42×C43C2211yescharacteristic
31#95×C43C2212yes—
32C22×C4×C43C2312yes—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2311yescharacteristic
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×Dic43C2312yes—
38C22×Dic43C2312yes—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C2×Dic86—24no—
42C2×Dic86—41no—
43C2×Dic86—41no—
44C2×Dic86—42no—
45C2×Dic86—42no—
46C2×Dic86D414yes—
47C4⋊C4×C43—24no—
48C4⋊C4×C43—41no—
49C4⋊C4×C43Q814yescomplemented
50C42×C43—41no—
51C4⋊Dic43—24no—
52C4⋊Dic43—41no—
53C4⋊Dic43—41no—
54C4⋊Dic43Q814yescomplemented
55Dic43⋊C4—24no—
56Dic43⋊C4—24no—
57Dic43⋊C4—42no—
58C4×Dic43—24no—
59C23×C43C2411yescharacteristic
60C2×C4×C43—22no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43C2×D412yes—
72C2×C4×C43C2×Q812yes—
73C2×C4×C43C2×Q814yes—
74C2×C4×C43C2×Q812yes—
75C2×Dic43—22no—
76C2×Dic43—22no—
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×Dic43C2×D414yes—
86C2×Dic43C2×Q814yes—
87Dic86—44no—
88Dic86—48no—
89C22×C43C22×D411yescharacteristic
90C22×C43C22×Q811yescharacteristic
91C22×C43C22×Q811yescharacteristic
92C22×C43H(5,𝔽2)11yescharacteristic
93C22×C43H(5,𝔽2)11yescharacteristic
94C22×C432−1+411yescharacteristic
95C22×C432−1+411yescharacteristic
96C4×C43—22no—
97C4×C43—22no—
98C4×C43—22no—
99C4×C43—24no—
100C4×C43—42no—
101Dic43—24no—
102Dic43—24no—
103Dic43—42no—
104Dic43—42no—
105#2734—431nomaximal, Sylow
106C2×C43#53411yescharacteristic
107C2×C43#54411yescharacteristic
108C2×C43#54411yescharacteristic
109C2×C43D4×Q811yescharacteristic
110C2×C43D4×Q811yescharacteristic
111C2×C43Q8211yescharacteristic
112C2×C43#56311yescharacteristic
113C2×C4⋊Q8—432no—
114#398—432no—
115#395—432no—
116#395—432no—
117#391—431no—
118#389—431no—
119#389D4311yescharacteristic
120#387—432no—
121#387—432no—
122C43#273411yescharacteristic, complemented, Sylow
123C22×Q8—431no—
124C22×Q8—432no—
125C4⋊Q8—868no—
126C2×C4⋊C4—431no—
127C2×C4⋊C4—432no—
128C2×C4⋊C4—432no—
129C2×C4⋊C4—432no—
130C2×C4⋊C4—432no—
131C2×C4⋊C4—431no—
132C2×C4⋊C4—431no—
133C2×C4⋊C4C2×D4312yes—
134C2×C4⋊C4C2×D4311yescharacteristic
135C2×C4⋊C4C2×D4311yescharacteristic
136C2×C42—432no—
137C2×C42C2×D4311yescharacteristic
138#95—432no—
139#95—432no—
140#95—432no—
141#95—432no—
142#95—432no—
143#95—432no—
144#95C2×D4312yes—
145C2×Q8—434no—
146C2×Q8—864no—
147C2×Q8—1721no—
148C2×Q8—1721no—
149C2×Q8—1722no—
150C2×Q8—1722no—
151C22×C4—432no—
152C22×C4—432no—
153C22×C4—432no—
154C22×C4—432no—
155C22×C4C22×D4312yes—
156C22×C4C22×D4311yescharacteristic
157C22×C4C22×D4312yes—
158C22×C4C22×D4311yescharacteristic
159C22×C4C22×D4311yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—434no—
163C4⋊C4—864no—
164C4⋊C4—864no—
165C4⋊C4—864no—
166C4⋊C4—1722no—
167C4⋊C4—1721no—
168C4⋊C4—1721no—
169C4⋊C4Dic8614yescomplemented
170C42—41no—
171C42—864no—
172C23C23×D4311yescharacteristic
173Q8—1724no—
174Q8—1728no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—434no—
187C2×C4—434no—
188C2×C4—862no—
189C2×C4—862no—
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×C4C2×Dic8614yes—
199C2×C4C2×Dic8612yes—
200C2×C4D4×D4312yes—
201C2×C4Q8×D4312yes—
202C22C2×D4×D4311yescharacteristic
203C22C2×Q8×D4311yescharacteristic
204C22C22×Dic8611yescharacteristic
205C22#1306337011yescharacteristic
206C22#1306337111yescharacteristic
207C22#1306337211yescharacteristic
208C22#1306337311yescharacteristic
209C4—24no—
210C4—22no—
211C4—22no—
212C4—22no—
213C4—42no—
214C4—864no—
215C4—864no—
216C4—1722no—
217C4—1722no—
218C2#1458345711yescharacteristic
219C2#1458352811yescharacteristic
220C2#1458353011yescharacteristic
221C2#1458356411yescharacteristic
222C2D4×Dic8611yescharacteristic
223C2Q8×Dic8611yescharacteristic
224C2#1458365311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#389C2
hypercenter#389D43
hypocenterC43#2734
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. C4⋊C4×C43Q8semidirect
54. C4⋊Dic43Q8semidirect
122. C43#2734semidirect
169. C4⋊C4Dic86semidirect