Finite Group Databasebeta

← #19133538

Subgroups — #19133538

Order 5504.

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

normal subgroups only

This group has 320 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#14583486C211yesmaximal, characteristic, complemented
2#14583050C211yesmaximal, characteristic, complemented
3#14582807C211yesmaximal, characteristic, complemented
4#14582637C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#447C211yesmaximal, characteristic, complemented
8C22×C22⋊D43—21no—
9C2×#10621883—21no—
10#13063320—21no—
11#13063311—21no—
12#13063309—21no—
13#13063304C2211yescharacteristic
14#13063297—21no—
15#13063293—21no—
16D4×Dic43—21no—
17C2×C22⋊Dic43—21no—
18C2×(C2×D43)⋊C4C2211yescharacteristic
19#13063246—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C43⋊#95C2211yescharacteristic
22C22×D4×C43C2211yescharacteristic
23C2×D8×C43—21no—
24#121×C43C2211yescharacteristic
25#102×C43—21no—
26C22⋊C8×C43C2211yescharacteristic
27C24×C43—21no—
28C23×D43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43—42no—
33C2×D4×C43D411yescharacteristic, complemented
34C22×C4×C43C2311yescharacteristic
35C2×C22⋊D43—21no—
36C2×C22⋊D43—21no—
37C2×C22⋊D43—42no—
38C2×C22⋊D43—42no—
39C2×C22⋊D43—42no—
40C22×Dic43—21no—
41C22×Dic43—21no—
42C22×Dic43D411yescharacteristic
43C2×Dic86D411yescharacteristic, complemented
44D8×C43—42no—
45C2×C8×C43—21no—
46C4⋊C4×C43D411yescharacteristic, complemented
47C22⋊C4×C43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—42no—
51#10621883—42no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—21no—
56C4⋊Dic43—21no—
57C4⋊Dic43D411yescharacteristic, complemented
58Dic43⋊C4—21no—
59C4×Dic43—21no—
60C2×C43⋊C8—21no—
61C23×C43—22no—
62C23×C43—21no—
63C23×C43—41no—
64C23×C43—41no—
65C23×C43—41no—
66C23×C43—41no—
67C23×C43—41no—
68C23×C43—41no—
69C23×C43C2×D411yescharacteristic
70C22×D43—21no—
71C22×D43—21no—
72C22×D43—21no—
73C22×D43—41no—
74C22×D43—41no—
75D4×C43—22no—
76D4×C43—22no—
77D4×C43—41no—
78D4×C43—41no—
79D4×C43—41no—
80D4×C43—41no—
81D4×C43—41no—
82C2×C4×C43—21no—
83C2×C4×C43—41no—
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C22⋊D43—48no—
87C22⋊D43—81no—
88C22⋊D43—81no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—41no—
94C2×Dic43—41no—
95C2×Dic43—41no—
96C2×Dic43—81no—
97Dic86—41no—
98C8×C43—41no—
99C43⋊C8—41no—
100C22×C43—21no—
101C22×C43—21no—
102C22×C43—42no—
103C22×C43—42no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—42no—
107C22×C43—41no—
108C22×C43—81no—
109C22×C43—81no—
110C22×C43—81no—
111C22×C43—81no—
112C22×C43#12011yescharacteristic
113C22×C43#13511yescharacteristic
114C22×C43AGL(1,ℤ/8)11yescharacteristic
115C2×D43—42no—
116C2×D43—41no—
117C2×D43—41no—
118C2×D43—41no—
119C2×D43—81no—
120C4×C43—21no—
121C4×C43—21no—
122C4×C43—41no—
123Dic43—42no—
124Dic43—41no—
125Dic43—41no—
126Dic43—41no—
127#1600—431nomaximal, Sylow
128C2×C43—21no—
129C2×C43—21no—
130C2×C43—81no—
131C2×C43—82no—
132C2×C43#44911yescharacteristic
133C2×C43#45311yescharacteristic
134C2×C43B(4,𝔽2)11yescharacteristic
135D43—81no—
136#538—431no—
137#450—431no—
138#447D4311yescharacteristic, complemented
139#392—431no—
140#328—431no—
141#327—431no—
142#323—431no—
143C43#160011yescharacteristic, complemented, Sylow
144C22×D4—861no—
145C22×D4C2×D4311yescharacteristic
146C2×SD16—861no—
147C2×D8—21no—
148#126—861no—
149#124—861no—
150#123—861no—
151C22⋊Q8—431no—
152#121—861no—
153#121C2×D4311yescharacteristic
154#120—861no—
155C4×D4—861no—
156C2×C22⋊C4—431no—
157C2×C22⋊C4—861no—
158#102—21no—
159#102—861no—
160C22⋊C8—431no—
161C22⋊C8C2×D4311yescharacteristic
162#95—431no—
163C24—21no—
164C24—431no—
165C2×Q8—431no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—42no—
170C2×D4—861no—
171C2×D4—861no—
172C2×D4—1722no—
173C2×D4—1722no—
174C2×D4—1722no—
175C2×D4C22⋊D4311yescharacteristic, complemented
176C22×C4—431no—
177C22×C4—861no—
178C22×C4—861no—
179C22×C4C22×D4311yescharacteristic
180SD16—1722no—
181D8—42no—
182C2×C8—21no—
183C2×C8—861no—
184C4⋊C4—431no—
185C4⋊C4—861no—
186C4⋊C4—861no—
187C4⋊C4C22⋊D4311yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—861no—
190C22⋊C4—861no—
191C22⋊C4—861no—
192C22⋊C4—861no—
193C22⋊C4—861no—
194C22⋊C4—861no—
195C22⋊C4—1722no—
196C42—861no—
197C23—22no—
198C23—21no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—41no—
205C23—861no—
206C23—861no—
207C23—861no—
208C23—1721no—
209C23—1721no—
210C23D4×D4311yescharacteristic
211Q8—1721no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—3441no—
220D4—3441no—
221D4—1728no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—862no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—3441no—
229C2×C4—1721no—
230C2×C4—1721no—
231C2×C4—1721no—
232C2×C4D4×D4311yescharacteristic
233C2×C4C2×C22⋊D4311yescharacteristic
234C8—41no—
235C8—1721no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—3441no—
249C22—1722no—
250C22—1721no—
251C22—1721no—
252C22—1721no—
253C22#1306329311yescharacteristic
254C22#1306334411yescharacteristic
255C22#1306334911yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—1722no—
260C4—1721no—
261C4—1721no—
262C4—1721no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2—81no—
267C2—3441no—
268C2#1458304111yescharacteristic
269C2#1458306511yescharacteristic
270C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#447C2
socleC22×C43#120
hypercenter#447D43
hypocenterC43#1600
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14583486C2semidirect
2. #14583050C2semidirect
3. #14582807C2semidirect
4. #14582637C2semidirect
5. #14582633C2semidirect
6. #14582622C2semidirect
7. C43×#447C2semidirect
33. C2×D4×C43D4semidirect
43. C2×Dic86D4semidirect
46. C4⋊C4×C43D4semidirect
57. C4⋊Dic43D4semidirect
138. #447D43semidirect
143. C43#1600semidirect
175. C2×D4C22⋊D43semidirect
187. C4⋊C4C22⋊D43semidirect