Finite Group Databasebeta

← #19142559

Subgroups — #19142559

Order 5504.

392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 149 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#14582832C212yesmaximal
2#14582831C212yesmaximal
3#14582820C212yesmaximal
4#14582806C212yesmaximal
5#14582805C211yesmaximal, characteristic
6#14582797C211yesmaximal, characteristic
7#14582796C212yesmaximal
8#14582782C212yesmaximal
9C43×#391C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12C2×C4⋊Dic43C2211yescharacteristic
13C2×C4⋊Dic43C2212yes—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×C4×Dic43C2212yes—
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C22×Q8×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C42×C43C2211yescharacteristic
29#95×C43C2212yes—
30#95×C43C2212yes—
31C2×Q8×C43—41no—
32C2×Q8×C43—41no—
33C2×Q8×C43Q814yescomplemented
34C22×C4×C43C2312yes—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C2×Dic86—22no—
44C2×Dic86—41no—
45C2×Dic86—41no—
46C4⋊C4×C43—41no—
47C42×C43—41no—
48C4⋊Dic43—41no—
49C4⋊Dic43—42no—
50C4⋊Dic43—41no—
51C4⋊Dic43—42no—
52C4⋊Dic43Q814yescomplemented
53Dic43⋊C4—24no—
54Dic43⋊C4—42no—
55Dic43⋊C4—42no—
56C4×Dic43—42no—
57C23×C43C2411yescharacteristic
58Q8×C43—44no—
59C2×C4×C43—22no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—22no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43C2×Q814yes—
71C2×C4×C43C2×Q812yes—
72C2×C4×C43C2×Q812yes—
73C2×C4×C43#4112yes—
74C2×Dic43—22no—
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×Q814yes—
86Dic86—44no—
87C22×C43C22×Q811yescharacteristic
88C22×C43C22×Q811yescharacteristic
89C22×C43C2×#4111yescharacteristic
90C22×C43H(5,𝔽2)11yescharacteristic
91C22×C43H(5,𝔽2)11yescharacteristic
92C22×C43H(5,𝔽2)11yescharacteristic
93C22×C432−1+411yescharacteristic
94C4×C43—22no—
95C4×C43—24no—
96C4×C43—22no—
97C4×C43—22no—
98C4×C43—42no—
99Dic43—24no—
100Dic43—42no—
101Dic43—42no—
102Dic43—42no—
103#2806—431nomaximal, Sylow
104C2×C43#53811yescharacteristic
105C2×C43#54311yescharacteristic
106C2×C43#54411yescharacteristic
107C2×C43#55411yescharacteristic
108C2×C43#55711yescharacteristic
109C2×C43Q8211yescharacteristic
110C2×C43#56211yescharacteristic
111#398—432no—
112#398—432no—
113#395—432no—
114#391—432no—
115#391—431no—
116#391D4311yescharacteristic
117#389—431no—
118#389—432no—
119#387—432no—
120C43#280611yescharacteristic, complemented, Sylow
121C22×Q8—431no—
122C22×Q8C2×D4311yescharacteristic
123C2×C4⋊C4—431no—
124C2×C4⋊C4—432no—
125C2×C4⋊C4—432no—
126C2×C4⋊C4—432no—
127C2×C4⋊C4—431no—
128C2×C4⋊C4—431no—
129C2×C4⋊C4—432no—
130C2×C4⋊C4—432no—
131C2×C4⋊C4C2×D4311yescharacteristic
132C2×C42—432no—
133C2×C42C2×D4311yescharacteristic
134#95—432no—
135#95—432no—
136#95—432no—
137#95—432no—
138#95—432no—
139#95—432no—
140#95C2×D4312yes—
141#95C2×D4312yes—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—862no—
145C2×Q8—1721no—
146C2×Q8—1721no—
147C2×Q8Dic8614yescomplemented
148C22×C4—432no—
149C22×C4—432no—
150C22×C4—432no—
151C22×C4—432no—
152C22×C4C22×D4312yes—
153C22×C4C22×D4311yescharacteristic
154C22×C4C22×D4312yes—
155C22×C4C22×D4311yescharacteristic
156C22×C4C22×D4311yescharacteristic
157C4⋊C4—41no—
158C4⋊C4—434no—
159C4⋊C4—864no—
160C4⋊C4—1722no—
161C4⋊C4—1722no—
162C4⋊C4—1721no—
163C4⋊C4—1722no—
164C4⋊C4—1721no—
165C4⋊C4—1722no—
166C42—41no—
167C42—1722no—
168C23C23×D4311yescharacteristic
169Q8—44no—
170Q8—1724no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—434no—
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—862no—
193C2×C4—862no—
194C2×C4C2×Dic8612yes—
195C2×C4C2×Dic8614yes—
196C2×C4Q8×D4312yes—
197C2×C4#1062190212yes—
198C22C2×Q8×D4311yescharacteristic
199C22C22×Dic8611yescharacteristic
200C22C2×#1062190211yescharacteristic
201C22#1306337011yescharacteristic
202C22#1306337011yescharacteristic
203C22#1306337111yescharacteristic
204C22#1306337211yescharacteristic
205C4—22no—
206C4—22no—
207C4—24no—
208C4—22no—
209C4—42no—
210C4—864no—
211C4—1722no—
212C4—1722no—
213C4—1722no—
214C2#1458348911yescharacteristic
215C2#1458352511yescharacteristic
216C2#1458352811yescharacteristic
217C2#1458361011yescharacteristic
218C2#1458362811yescharacteristic
219C2Q8×Dic8611yescharacteristic
220C2#1458364311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#391C2
hypercenter#391D43
hypocenterC43#2806
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
33. C2×Q8×C43Q8semidirect
52. C4⋊Dic43Q8semidirect
120. C43#2806semidirect
147. C2×Q8Dic86semidirect