Finite Group Databasebeta

← #19140713

Subgroups — #19140713

Order 5504.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13063323C211yesmaximal, characteristic
2C2×#13063315C211yesmaximal, characteristic
3#14582833C212yesmaximal
4#14582832C212yesmaximal
5#14582820C211yesmaximal, characteristic
6#14582819C211yesmaximal, characteristic
7#14582818C211yesmaximal, characteristic
8#14582768C212yesmaximal
9#14582763C212yesmaximal
10#14582744C211yesmaximal, characteristic
11C43×#395C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13#13063323—24no—
14#13063315—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C2×Dic43⋊C4C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2212yes—
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C2×Q8×C43—22no—
38C2×Q8×C43—42no—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2312yes—
49C22×Dic43C2311yescharacteristic
50C2×Dic86—22no—
51C2×Dic86—42no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—42no—
54C4⋊Dic43—22no—
55C4⋊Dic43—42no—
56Dic43⋊C4—22no—
57Dic43⋊C4—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—24no—
61Dic43⋊C4—24no—
62Dic43⋊C4—42no—
63Dic43⋊C4—42no—
64C4×Dic43D414yes—
65C4×Dic43Q818yescomplemented
66C23×C43C2411yescharacteristic
67Q8×C43—44no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—21no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2×Q814yes—
81C2×Dic43—22no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—22no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43C2×D412yes—
94C2×Dic43C2×D412yes—
95C2×Dic43C2×Q814yes—
96C2×Dic43C2×Q814yes—
97Dic86—44no—
98C22×C43C22×D411yescharacteristic
99C22×C43C22×Q812yes—
100C22×C43H(5,𝔽2)12yes—
101C22×C432−1+411yescharacteristic
102C22×C432−1+411yescharacteristic
103C4×C43—22no—
104C4×C43—24no—
105C4×C43—41no—
106C4×C43—42no—
107C4×C43—41no—
108Dic43—22no—
109Dic43—24no—
110Dic43—42no—
111Dic43—41no—
112Dic43—41no—
113Dic43C4⋊Q814yes—
114#2660—431nomaximal, Sylow
115C2×C43C2×C4⋊Q811yescharacteristic
116C2×C43#53511yescharacteristic
117C2×C43#53611yescharacteristic
118C2×C43#54412yes—
119C2×C43#54412yes—
120C2×C4⋊Q8—431no—
121C2×#125—431no—
122#398—432no—
123#398—432no—
124#395—431no—
125#395—431no—
126#395—431no—
127#395D4311yescharacteristic
128#384—432no—
129#382—432no—
130#376—431no—
131C43#266011yescharacteristic, complemented, Sylow
132C22×Q8—431no—
133C22×Q8C2×D4311yescharacteristic
134C4⋊Q8—864no—
135#125—864no—
136C2×C4⋊C4—431no—
137C2×C4⋊C4—431no—
138C2×C4⋊C4—431no—
139C2×C4⋊C4—431no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—432no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4—432no—
146C2×C4⋊C4C2×D4311yescharacteristic
147C2×C4⋊C4C2×D4312yes—
148C2×C42—431no—
149C2×C42—432no—
150#95—431no—
151#95—432no—
152#95—432no—
153#95—432no—
154#95—432no—
155#95C2×D4311yescharacteristic
156#95C2×D4312yes—
157C2×Q8—22no—
158C2×Q8—42no—
159C2×Q8—862no—
160C2×Q8—1722no—
161C22×C4—431no—
162C22×C4—432no—
163C22×C4—431no—
164C22×C4—431no—
165C22×C4—432no—
166C22×C4—431no—
167C22×C4C22×D4311yescharacteristic
168C22×C4C22×D4312yes—
169C22×C4C22×D4311yescharacteristic
170C22×C4C22×D4311yescharacteristic
171C22×C4C22×D4312yes—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—864no—
179C4⋊C4—864no—
180C4⋊C4—862no—
181C4⋊C4—1722no—
182C4⋊C4—1722no—
183C4⋊C4—1722no—
184C42—434no—
185C42—438no—
186C23C23×D4311yescharacteristic
187Q8—44no—
188Q8—1724no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—432no—
201C2×C4—434no—
202C2×C4—432no—
203C2×C4—434no—
204C2×C4—862no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—862no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—861no—
215C2×C4—861no—
216C2×C4D4×D4312yes—
217C2×C4Q8×D4314yes—
218C22C2×D4×D4311yescharacteristic
219C22C2×Q8×D4312yes—
220C22#1306337012yes—
221C22#1306337211yescharacteristic
222C22#1306337311yescharacteristic
223C4—22no—
224C4—24no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—434no—
229C4—862no—
230C4—864no—
231C4—1722no—
232C4—1721no—
233C4—1721no—
234C2C4⋊Q8×D4311yescharacteristic
235C2#1458346411yescharacteristic
236C2#1458347211yescharacteristic
237C2#1458352612yes—
238C2#1458352812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2660
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
65. C4×Dic43Q8semidirect
131. C43#2660semidirect