Finite Group Databasebeta

← #19133573

Subgroups — #19133573

Order 5504.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#14583487C211yesmaximal, characteristic
2#14583055C211yesmaximal, characteristic, complemented
3#14583038C211yesmaximal, characteristic, complemented
4#14582635C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582623C211yesmaximal, characteristic, complemented
7C43×#393C211yesmaximal, characteristic, complemented
8C2×#10621885—21no—
9C2×#10621884—21no—
10#13063318—21no—
11#13063311—21no—
12#13063307—21no—
13#13063304C2211yescharacteristic
14#13063299C2211yescharacteristic
15#13063298—21no—
16#13063294—21no—
17C4×C22⋊D43—21no—
18#13063249—21no—
19#13063249—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C22⋊(C43⋊C8)C2211yescharacteristic
22C22×Q8×C43C2211yescharacteristic
23C2×C22⋊C4×C43—21no—
24C2×C22⋊C4×C43C2211yescharacteristic
25#95×C43—21no—
26#95×C43C2211yescharacteristic
27C24×C43D411yescharacteristic
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43—42no—
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43D411yescharacteristic
34C22×C4×C43C2311yescharacteristic
35C2×C22⋊D43—21no—
36C2×C22⋊D43—21no—
37C2×C22⋊D43—21no—
38C2×D172D411yescharacteristic
39C2×C4×D43—21no—
40C2×Dic86D411yescharacteristic
41C22⋊C4×C43—21no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43—42no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47#10621885—42no—
48#10621884—42no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51C4⋊Dic43D411yescharacteristic
52C4⋊Dic43D411yescharacteristic
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55C4×Dic43—21no—
56C2×C43⋊C8—21no—
57C2×C43⋊C8—21no—
58C23×C43—21no—
59C23×C43—21no—
60C23×C43—21no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65Q8×C43—22no—
66Q8×C43—22no—
67Q8×C43—41no—
68Q8×C43—41no—
69C2×C4×C43—22no—
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C22⋊D43—41no—
81C22⋊D43—41no—
82C22⋊D43—81no—
83C22⋊D43—81no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87D172—41no—
88C4×D43—81no—
89Dic86—41no—
90C43⋊C8—41no—
91C43⋊C8—41no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—42no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—81no—
99C22×C43#12011yescharacteristic
100C22×C43#13511yescharacteristic
101C22×C43#13711yescharacteristic
102C2×D43—41no—
103C2×D43—41no—
104C2×D43—41no—
105C4×C43—21no—
106C4×C43—21no—
107C4×C43—41no—
108C4×C43—42no—
109C4×C43—81no—
110Dic43—41no—
111Dic43—41no—
112Dic43—41no—
113#1606—431nomaximal, Sylow
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—81no—
117C2×C43#45211yescharacteristic
118C2×C43#45511yescharacteristic
119C2×C43B(4,𝔽2)11yescharacteristic
120D43—81no—
121#538—431no—
122#451—431no—
123#448—431no—
124#393D4311yescharacteristic, complemented
125#328—431no—
126#327—431no—
127#323—431no—
128C43#160611yescharacteristic, complemented, Sylow
129C22×Q8C2×D4311yescharacteristic
130C2×Q16—861no—
131C2×SD16—861no—
132#126—861no—
133#124—861no—
134#123—861no—
135C22⋊Q8—431no—
136#121—431no—
137#121—861no—
138#120—861no—
139C4×D4—861no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4C2×D4311yescharacteristic
142#103—861no—
143#103—861no—
144C22⋊C8—431no—
145C22⋊C8—431no—
146#95—21no—
147#95C2×D4311yescharacteristic
148C24C22⋊D4311yescharacteristic
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—431no—
153C2×D4—431no—
154C2×D4—861no—
155C2×D4—861no—
156C2×D4—861no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—861no—
160C22×C4C22⋊D4311yescharacteristic
161C22×C4C22×D4311yescharacteristic
162Q16—1722no—
163SD16—1722no—
164C2×C8—861no—
165C2×C8—861no—
166C4⋊C4—431no—
167C4⋊C4—431no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—42no—
173C22⋊C4—861no—
174C22⋊C4—861no—
175C22⋊C4—861no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C42—861no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—861no—
185C23C2×C22⋊D4311yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—1721no—
191D4—3441no—
192D4—3441no—
193D4—1721no—
194D4—1721no—
195D4—1721no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—3441no—
209C2×C4D4×D4311yescharacteristic
210C2×C4D4×D4311yescharacteristic
211C8—1721no—
212C8—1721no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—1721no—
221C22—1721no—
222C22—1721no—
223C22#1306329311yescharacteristic
224C22#1306334511yescharacteristic
225C22#1306335611yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—81no—
231C4—1721no—
232C4—1721no—
233C4—1721no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—3441no—
238C2#1458305911yescharacteristic
239C2#1458307611yescharacteristic
240C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#393C2
socleC22×C43#120
hypercenter#393D43
hypocenterC43#1606
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #14583055C2semidirect
3. #14583038C2semidirect
4. #14582635C2semidirect
5. #14582632C2semidirect
6. #14582623C2semidirect
7. C43×#393C2semidirect
124. #393D43semidirect
128. C43#1606semidirect