Finite Group Databasebeta

← #19136600

Subgroups — #19136600

Order 5504.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#14583638C211yesmaximal, characteristic, complemented
2#14583089C211yesmaximal, characteristic, complemented
3#14583067C211yesmaximal, characteristic, complemented
4#14582691C211yesmaximal, characteristic, complemented
5#14582688C211yesmaximal, characteristic, complemented
6#14582686C211yesmaximal, characteristic, complemented
7C43×B(4,𝔽2)C211yesmaximal, characteristic, complemented
8#13063350—21no—
9#13063321C2211yescharacteristic
10#13063318—21no—
11#13063307—21no—
12#13063306—21no—
13#13063306C2211yescharacteristic
14#13063298—21no—
15#13063297—21no—
16#13063296—21no—
17#13063294—21no—
18#13063252—21no—
19#13063242C2211yescharacteristic
20#13063240—21no—
21#13063240C2211yescharacteristic
22H(5,𝔽2)×C43C2211yescharacteristic
23#120×C43—21no—
24#120×C43C2211yescharacteristic
25#99×C43—21no—
26#99×C43C2211yescharacteristic
27C24×C43D411yescharacteristic
28#41×C43—21no—
29#41×C43—41no—
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43—21no—
33C2×D4×C43—41no—
34C2×D4×C43—41no—
35C2×D4×C43C2311yescharacteristic
36C2×C22⋊D43—21no—
37C2×C22⋊D43—21no—
38C2×C22⋊D43—21no—
39C2×C22⋊D43—21no—
40C22×Dic43D411yescharacteristic, complemented
41C2×D172D411yescharacteristic, complemented
42C2×C4×D43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43—21no—
45C22⋊C4×C43—41no—
46C22⋊C4×C43D411yescharacteristic
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43—41no—
52C22⋊Dic43D411yescharacteristic, complemented
53#10621884—41no—
54#10621882—41no—
55(C2×D43)⋊C4—21no—
56C4⋊Dic43—21no—
57Dic43⋊C4—21no—
58Dic43⋊C4—21no—
59Dic43⋊C4—41no—
60C4×Dic43D411yescharacteristic, complemented
61#10621877—21no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43—21no—
65C23×C43—41no—
66C23×C43—81no—
67C23×C43C2×D411yescharacteristic
68C23×C43C2×D411yescharacteristic
69C22×D43—21no—
70Q8×C43—21no—
71D4×C43—21no—
72D4×C43—41no—
73D4×C43—41no—
74D4×C43—41no—
75D4×C43—41no—
76D4×C43—81no—
77D4×C43—82no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—41no—
82C2×C4×C43—41no—
83C2×C4×C43C2×D411yescharacteristic
84C22⋊D43—81no—
85C22⋊D43—81no—
86C22⋊D43—81no—
87C22⋊D43—81no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93D172—41no—
94C4×D43—81no—
95C43⋊C8—41no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—42no—
103C22×C43—41no—
104C22×C43—41no—
105C22×C43—81no—
106C22×C43—81no—
107C22×C43—81no—
108C22×C43#12011yescharacteristic
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—41no—
112C4×C43—21no—
113C4×C43—41no—
114C4×C43—41no—
115C4×C43—81no—
116Dic43—41no—
117Dic43—41no—
118Dic43—41no—
119Dic43—81no—
120#2200—431nomaximal, Sylow
121C2×C43—21no—
122C2×C43—41no—
123C2×C43—41no—
124C2×C43—81no—
125C2×C43—81no—
126C2×C43B(4,𝔽2)11yescharacteristic
127D43—81no—
128#560—431no—
129#458—431no—
130B(4,𝔽2)D4311yescharacteristic, complemented
131#453—431no—
132#353—431no—
133#352—431no—
134AΣL(1,𝔽16)—431no—
135C43#220011yescharacteristic, complemented, Sylow
136H(5,𝔽2)C2×D4311yescharacteristic
137AGL(1,ℤ/8)—861no—
138#127—431no—
139#126—861no—
140#123—431no—
141#123—861no—
142#123—861no—
143#121—861no—
144#121—861no—
145#121—861no—
146#120—21no—
147#120—861no—
148#120C2×D4311yescharacteristic
149#104—861no—
150#100—431no—
151#99—21no—
152#99—431no—
153#99—861no—
154#99C2×D4311yescharacteristic
155C24C22⋊D4311yescharacteristic
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—431no—
164C2×D4—861no—
165C2×D4—861no—
166C2×D4—861no—
167C2×D4—861no—
168C2×D4C22×D4311yescharacteristic
169C22×C4—431no—
170C22×C4—861no—
171SD16—1721no—
172D8—1721no—
173M16—861no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4—1721no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—41no—
181C22⋊C4—431no—
182C22⋊C4—861no—
183C22⋊C4—861no—
184C22⋊C4—861no—
185C22⋊C4—861no—
186C22⋊C4—861no—
187C22⋊C4—1721no—
188C22⋊C4C22⋊D4311yescharacteristic
189C42—431no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—861no—
196C23D4×D4311yescharacteristic
197C23C2×C22⋊D4311yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—81no—
205D4—82no—
206D4—3441no—
207D4—3441no—
208D4—3441no—
209D4—3441no—
210D4—1721no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—861no—
217C2×C4—861no—
218C2×C4—861no—
219C2×C4—3441no—
220C2×C4—1721no—
221C2×C4—1721no—
222C2×C4D4×D4311yescharacteristic
223C8—1721no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—81no—
234C22—81no—
235C22—81no—
236C22—1721no—
237C22—1721no—
238C22—1721no—
239C22#1306329311yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—81no—
244C4—3441no—
245C4—1721no—
246C4—1721no—
247C4—1721no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—3441no—
254C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×B(4,𝔽2)C2
socleC2×C43B(4,𝔽2)
hypercenterB(4,𝔽2)D43
hypocenterC43#2200
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #14583638C2semidirect
2. #14583089C2semidirect
3. #14583067C2semidirect
4. #14582691C2semidirect
5. #14582688C2semidirect
6. #14582686C2semidirect
7. C43×B(4,𝔽2)C2semidirect
40. C22×Dic43D4semidirect
41. C2×D172D4semidirect
52. C22⋊Dic43D4semidirect
60. C4×Dic43D4semidirect
130. B(4,𝔽2)D43semidirect
135. C43#2200semidirect