Finite Group Databasebeta

← #19139977

Subgroups — #19139977

Order 5504.

468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13063315C211yesmaximal, characteristic
2C2×Q8×Dic43C211yesmaximal, characteristic
3#14582831C211yesmaximal, characteristic
4#14582829C211yesmaximal, characteristic
5#14582818C211yesmaximal, characteristic
6#14582798C212yesmaximal
7#14582796C212yesmaximal
8#14582796C212yesmaximal
9#14582794C212yesmaximal
10#14582750C211yesmaximal, characteristic
11C43×#395C211yesmaximal, characteristic
12#13063315—24no—
13Q8×Dic43—24no—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2212yes—
24C2×Dic43⋊C4C2212yes—
25C2×C4×Dic43C2212yes—
26C2×C4×Dic43C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C4⋊C4×C43C2211yescharacteristic
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C2×Q8×C43—22no—
38C2×Q8×C43—24no—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2312yes—
43C22×C4×C43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2312yes—
49C22×Dic43C2311yescharacteristic
50C4⋊C4×C43—22no—
51C4⋊C4×C43—24no—
52C4⋊Dic43—22no—
53C4⋊Dic43—24no—
54C4⋊Dic43—22no—
55C4⋊Dic43—42no—
56Dic43⋊C4—22no—
57Dic43⋊C4—24no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4—42no—
62Dic43⋊C4Q818yescomplemented
63C4×Dic43—24no—
64C4×Dic43—42no—
65C4×Dic43D414yes—
66C23×C43C2411yescharacteristic
67Q8×C43—28no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43C2×D412yes—
79C2×C4×C43C2×Q814yes—
80C2×C4×C43#4114yes—
81C2×Dic43—22no—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—21no—
93C2×Dic43C2×D412yes—
94C2×Dic43C2×D412yes—
95C2×Dic43C2×Q814yes—
96C2×Dic43C2×Q814yes—
97C22×C43C22×D411yescharacteristic
98C22×C43C22×Q812yes—
99C22×C43C2×#4112yes—
100C22×C43H(5,𝔽2)11yescharacteristic
101C22×C432−1+411yescharacteristic
102C4×C43—22no—
103C4×C43—24no—
104C4×C43—24no—
105C4×C43—41no—
106C4×C43—41no—
107Dic43—22no—
108Dic43—24no—
109Dic43—41no—
110Dic43—42no—
111Dic43—41no—
112Dic43C4⋊Q814yes—
113#2584—431nomaximal, Sylow
114C2×C43#52511yescharacteristic
115C2×C43C2×C4⋊Q811yescharacteristic
116C2×C43#53711yescharacteristic
117C2×C43#55412yes—
118C2×C43#55712yes—
119C2×#125—431no—
120C2×C4×Q8—431no—
121#398—431no—
122#398—431no—
123#395—431no—
124#395D4311yescharacteristic
125#389—432no—
126#389—432no—
127#389—432no—
128#389—432no—
129C4×C4⋊C4—431no—
130C43#258411yescharacteristic, complemented, Sylow
131C22×Q8C2×D4311yescharacteristic
132#125—864no—
133C4×Q8—864no—
134C2×C4⋊C4—432no—
135C2×C4⋊C4—432no—
136C2×C4⋊C4—431no—
137C2×C4⋊C4—431no—
138C2×C4⋊C4—431no—
139C2×C4⋊C4—431no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—432no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4C2×D4311yescharacteristic
146C2×C4⋊C4C2×D4312yes—
147C2×C42—431no—
148C2×C42—432no—
149C2×C42—432no—
150#95—431no—
151#95—432no—
152#95—432no—
153#95—432no—
154#95C2×D4311yescharacteristic
155#95C2×D4312yes—
156C2×Q8—22no—
157C2×Q8—24no—
158C22×C4—431no—
159C22×C4—432no—
160C22×C4—431no—
161C22×C4—432no—
162C22×C4—431no—
163C22×C4—431no—
164C22×C4C22×D4311yescharacteristic
165C22×C4C22×D4311yescharacteristic
166C22×C4C22×D4311yescharacteristic
167C22×C4C22×D4312yes—
168C22×C4C22×D4312yes—
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—438no—
172C4⋊C4—864no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—864no—
180C4⋊C4—1722no—
181C4⋊C4—1722no—
182C42—434no—
183C42—864no—
184C42—1722no—
185C23C23×D4311yescharacteristic
186Q8—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—432no—
198C2×C4—434no—
199C2×C4—432no—
200C2×C4—434no—
201C2×C4—862no—
202C2×C4—861no—
203C2×C4—862no—
204C2×C4—861no—
205C2×C4—862no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—861no—
211C2×C4—862no—
212C2×C4—861no—
213C2×C4D4×D4312yes—
214C2×C4#1062190014yes—
215C2×C4Q8×D4314yes—
216C22C2×D4×D4311yescharacteristic
217C22C2×Q8×D4312yes—
218C22C2×#1062190012yes—
219C22#1306337111yescharacteristic
220C22#1306337311yescharacteristic
221C4—24no—
222C4—22no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—434no—
227C4—864no—
228C4—862no—
229C4—1721no—
230C4—1722no—
231C4—1721no—
232C2#1458340511yescharacteristic
233C2C4⋊Q8×D4311yescharacteristic
234C2#1458347911yescharacteristic
235C2#1458360712yes—
236C2#1458362412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2584
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
62. Dic43⋊C4Q8semidirect
130. C43#2584semidirect