Finite Group Databasebeta

← #19139958

Subgroups — #19139958

Order 5504.

468 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13063290C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic
3#14582837C211yesmaximal, characteristic
4#14582820C211yesmaximal, characteristic
5#14582819C211yesmaximal, characteristic
6#14582803C212yesmaximal
7#14582796C212yesmaximal
8#14582782C212yesmaximal
9#14582781C212yesmaximal
10#14582763C211yesmaximal, characteristic
11C43×#400C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14#13063290—24no—
15#13063290—24no—
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×C4×Dic43C2212yes—
23C2×C4×Dic43C2211yescharacteristic
24C2×C4×Dic43C2211yescharacteristic
25C2×C4×Dic43C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C22×C4×C43C2312yes—
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×Dic43C2312yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C2×Dic86—22no—
49C2×Dic86—22no—
50C2×Dic86—24no—
51C2×Dic86—22no—
52C2×Dic86Q814yescomplemented
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C4⋊Dic43—24no—
56Dic43⋊C4—22no—
57Dic43⋊C4—24no—
58Dic43⋊C4—22no—
59Dic43⋊C4—24no—
60Dic43⋊C4—24no—
61C4×Dic43—22no—
62C4×Dic43—24no—
63C4×Dic43—22no—
64C4×Dic43D414yes—
65C23×C43C2411yescharacteristic
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—22no—
69C2×C4×C43—21no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—24no—
75C2×C4×C43—22no—
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2×Q812yes—
78C2×Dic43—21no—
79C2×Dic43—22no—
80C2×Dic43—21no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43C2×D412yes—
89C2×Dic43C2×D412yes—
90C2×Dic43C2×Q812yes—
91C2×Dic43C2×Q812yes—
92C2×Dic43#4114yes—
93C2×Dic43#4112yes—
94Dic86—28no—
95Dic86—28no—
96C22×C43C22×D411yescharacteristic
97C22×C43C22×Q811yescharacteristic
98C22×C43C2×#4111yescharacteristic
99C22×C43C2×#4112yes—
100C22×C432−1+412yes—
101C4×C43—22no—
102C4×C43—22no—
103C4×C43—41no—
104C4×C43—42no—
105C4×C43—42no—
106Dic43—22no—
107Dic43—24no—
108Dic43—22no—
109Dic43—41no—
110Dic43—42no—
111Dic43C22⋊Q814yes—
112#2581—431nomaximal, Sylow
113C2×C43C2×C22⋊Q811yescharacteristic
114C2×C43#52511yescharacteristic
115C2×C43#53611yescharacteristic
116C2×C43#55612yes—
117C2×C43#55712yes—
118C2×C4×Q8—431no—
119C2×C4×Q8—431no—
120#400—431no—
121#400D4311yescharacteristic
122#395—431no—
123#395—431no—
124#391—432no—
125#389—432no—
126#387—432no—
127#387—432no—
128#382—431no—
129C43#258111yescharacteristic, complemented, Sylow
130C22×Q8—431no—
131C22×Q8—431no—
132C4×Q8—864no—
133C4×Q8—864no—
134C2×C4⋊C4—432no—
135C2×C4⋊C4—431no—
136C2×C4⋊C4—431no—
137C2×C4⋊C4—432no—
138C2×C4⋊C4—432no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4C2×D4311yescharacteristic
141C2×C4⋊C4C2×D4311yescharacteristic
142C2×C42—431no—
143C2×C42—431no—
144C2×C42—431no—
145C2×C42—432no—
146#95—432no—
147#95—431no—
148#95—432no—
149#95—432no—
150#95—432no—
151#95—432no—
152#95C2×D4311yescharacteristic
153#95C2×D4312yes—
154#95C2×D4312yes—
155C2×Q8—434no—
156C2×Q8—862no—
157C2×Q8—862no—
158C2×Q8—864no—
159C2×Q8—862no—
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—431no—
163C22×C4—432no—
164C22×C4—432no—
165C22×C4—431no—
166C22×C4C22×D4312yes—
167C22×C4C22×D4312yes—
168C22×C4C22×D4311yescharacteristic
169C22×C4C22×D4311yescharacteristic
170C22×C4C22×D4311yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—862no—
174C4⋊C4—864no—
175C4⋊C4—864no—
176C4⋊C4—864no—
177C4⋊C4—864no—
178C4⋊C4—862no—
179C42—434no—
180C42—862no—
181C42—864no—
182C42—862no—
183C23C23×D4311yescharacteristic
184Q8—868no—
185Q8—868no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—432no—
197C2×C4—432no—
198C2×C4—432no—
199C2×C4—432no—
200C2×C4—432no—
201C2×C4—434no—
202C2×C4—861no—
203C2×C4—862no—
204C2×C4—861no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—861no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4D4×D4312yes—
213C2×C4Q8×D4312yes—
214C22C2×D4×D4311yescharacteristic
215C22C2×Q8×D4311yescharacteristic
216C22#41×D4311yescharacteristic
217C22#41×D4312yes—
218C22#1306337212yes—
219C4—22no—
220C4—22no—
221C4—42no—
222C4—41no—
223C4—42no—
224C4—434no—
225C4—862no—
226C4—864no—
227C4—862no—
228C4—1722no—
229C4—1721no—
230C2C22⋊Q8×D4311yescharacteristic
231C2#1458340711yescharacteristic
232C2#1458346911yescharacteristic
233C2#1458361612yes—
234C2#1458362612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2581
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic86Q8semidirect
129. C43#2581semidirect