Finite Group Databasebeta

← #19138906

Subgroups — #19138906

Order 5504.

584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4×C22⋊D43C211yesmaximal, characteristic
2#14582837C212yesmaximal, complemented
3#14582834C212yesmaximal, complemented
4#14582795C212yesmaximal, complemented
5#14582778C212yesmaximal
6#14582772C212yesmaximal, complemented
7#14582759C211yesmaximal, characteristic, complemented
8#14582756C212yesmaximal, complemented
9C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
10C22×C22⋊D43C2211yescharacteristic
11C22×C4×D43C2211yescharacteristic
12C4×C22⋊D43—24no—
13C2×C4⋊Dic43C2212yes—
14C2×Dic43⋊C4C2211yescharacteristic
15C2×Dic43⋊C4C2214yes—
16C2×C22⋊Dic43C2211yescharacteristic
17C2×C22⋊Dic43C2212yes—
18C2×(C2×D43)⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4C2214yes—
20C2×C4×Dic43C2211yescharacteristic
21C43⋊#95C2214yes—
22C43⋊#95C2212yes—
23C43⋊#95C2214yes—
24C23×C4×C43C2211yescharacteristic
25C23×C4×C43C2212yes—
26C2×C4⋊C4×C43—24no—
27C2×C4⋊C4×C43C2212yes—
28C2×C4⋊C4×C43C2212yes—
29C24×C43C2311yescharacteristic
30C23×D43C2311yescharacteristic
31C22×C4×C43—24no—
32C22×C4×C43—24no—
33C22×C4×C43—44no—
34C22×C4×C43D414yes—
35C22×C4×C43C2314yes—
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—22no—
39C2×C22⋊D43—22no—
40C2×C22⋊D43Q814yes—
41C22×Dic43C2311yescharacteristic
42C22×Dic43C2314yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C2×C4×D43—22no—
46C2×C4×D43—24no—
47C4⋊C4×C43—24no—
48C4⋊C4×C43—24no—
49C22⋊Dic43—22no—
50C22⋊Dic43—24no—
51(C2×D43)⋊C4—22no—
52(C2×D43)⋊C4—44no—
53C4⋊Dic43—24no—
54Dic43⋊C4—22no—
55Dic43⋊C4—44no—
56C4×Dic43—22no—
57C23×C43—22no—
58C23×C43—22no—
59C23×C43C2×D412yes—
60C23×C43C2×Q812yes—
61C23×C43#4112yes—
62C23×C43C2411yescharacteristic
63C22×D43—21no—
64C22×D43—22no—
65C22×D43—21no—
66C22×D43—22no—
67C22×D43C2×Q812yes—
68C2×C4×C43—22no—
69C2×C4×C43—28no—
70C2×C4×C43—24no—
71C2×C4×C43—24no—
72C2×C4×C43—24no—
73C2×C4×C43—48no—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2×D412yes—
76C2×C4×C43#4114yes—
77C22⋊D43—28no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—24no—
83C2×Dic43—24no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—24no—
87C2×Dic43C2×Q812yes—
88C4×D43—44no—
89C22×C43—22no—
90C22×C43—22no—
91C22×C43—24no—
92C22×C43—24no—
93C22×C43C22⋊Q814yes—
94C22×C43C22×D411yescharacteristic
95C22×C43C22×Q811yescharacteristic
96C22×C43C2×#4112yes—
97C22×C43C2×#4111yescharacteristic
98C22×C43H(5,𝔽2)12yes—
99C2×D43—22no—
100C2×D43—24no—
101C2×D43—41no—
102C2×D43—41no—
103C2×D43—42no—
104C4×C43—22no—
105C4×C43—44no—
106C4×C43#12314yes—
107Dic43—22no—
108Dic43—41no—
109Dic43—41no—
110Dic43—44no—
111#2487—431nomaximal, Sylow
112C2×C43—24no—
113C2×C43C2×C22⋊Q811yescharacteristic
114C2×C43C2×#12311yescharacteristic
115C2×C43#53511yescharacteristic
116C2×C43#55312yes—
117C2×C43#55412yes—
118D43—42no—
119C2×C4×D4—431no—
120C22×C4⋊C4D4311yescharacteristic, complemented
121#400—432no—
122#399—432no—
123#389—432no—
124#386—432no—
125#385—432no—
126#380—431no—
127#380—432no—
128C43#248711yescharacteristic, complemented, Sylow
129C22×D4—431no—
130C23×C4—431no—
131C23×C4C2×D4311yescharacteristic
132C23×C4C2×D4312yes—
133C4×D4—864no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—431no—
136C2×C4⋊C4—432no—
137C2×C4⋊C4—434no—
138C2×C4⋊C4C2×D4312yes—
139C2×C4⋊C4C2×D4312yes—
140C2×C22⋊C4—431no—
141C2×C22⋊C4—432no—
142C2×C22⋊C4—431no—
143C2×C22⋊C4—434no—
144C2×C42—431no—
145#95—434no—
146#95—432no—
147#95—434no—
148C24—431no—
149C24C22×D4311yescharacteristic
150C2×D4—434no—
151C2×D4—862no—
152C2×D4—862no—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—44no—
156C22×C4—431no—
157C22×C4—431no—
158C22×C4—434no—
159C22×C4—431no—
160C22×C4—864no—
161C22×C4—862no—
162C22×C4C22⋊D4314yes—
163C22×C4C22×D4314yes—
164C22×C4C22×D4311yescharacteristic
165C22×C4C22×D4311yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—24no—
168C4⋊C4—864no—
169C4⋊C4—862no—
170C4⋊C4—1724no—
171C22⋊C4—864no—
172C22⋊C4—862no—
173C22⋊C4—862no—
174C22⋊C4—1724no—
175C42—862no—
176C23—22no—
177C23—22no—
178C23—432no—
179C23—861no—
180C23—862no—
181C23—861no—
182C23—862no—
183C23Q8×D4312yes—
184C23#1062190212yes—
185C23C2×C22⋊D4312yes—
186C23C23×D4311yescharacteristic
187D4—868no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—48no—
194C2×C4—432no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—861no—
199C2×C4—864no—
200C2×C4—862no—
201C2×C4—864no—
202C2×C4—864no—
203C2×C4—862no—
204C2×C4—1724no—
205C2×C4#1062189814yes—
206C2×C4C2×C22⋊D4312yes—
207C2×C4C2×C22⋊D4312yes—
208C22—24no—
209C22—24no—
210C22—22no—
211C22—22no—
212C22—864no—
213C22—862no—
214C22—1722no—
215C22—1721no—
216C22—1721no—
217C22#1306330114yes—
218C22C22×C22⋊D4311yescharacteristic
219C22C2×Q8×D4311yescharacteristic
220C22C2×#1062189812yes—
221C22C2×#1062190211yescharacteristic
222C22#1306337012yes—
223C4—22no—
224C4—44no—
225C4—862no—
226C4—1724no—
227C4—1721no—
228C4—1721no—
229C4#1306330814yes—
230C2—24no—
231C2—1722no—
232C2C2×#1306330111yescharacteristic
233C2C2×#1306330811yescharacteristic
234C2#1458346611yescharacteristic
235C2#1458359712yes—
236C2#1458360412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC22×C4⋊C4×C43C2
hypercenterC22×C4⋊C4D43
hypocenterC43#2487
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14582837C2semidirect
3. #14582834C2semidirect
4. #14582795C2semidirect
6. #14582772C2semidirect
7. #14582759C2semidirect
8. #14582756C2semidirect
9. C22×C4⋊C4×C43C2semidirect
120. C22×C4⋊C4D43semidirect
128. C43#2487semidirect