Finite Group Databasebeta

← #19136601

Subgroups — #19136601

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#14583636C211yesmaximal, characteristic, complemented
2#14583089C211yesmaximal, characteristic, complemented
3#14583086C211yesmaximal, characteristic, complemented
4#14582692C211yesmaximal, characteristic, complemented
5#14582690C211yesmaximal, characteristic, complemented
6#14582687C211yesmaximal, characteristic, complemented
7C43×#453C211yesmaximal, characteristic, complemented
8#13063319—21no—
9#13063306—21no—
10#13063306—21no—
11#13063306C2211yescharacteristic
12#13063297—21no—
13#13063297—21no—
14#13063297—21no—
15#13063293—21no—
16#13063293—21no—
17#13063293C2211yescharacteristic
18#13063240—21no—
19#13063240—21no—
20#13063240C2211yescharacteristic
21#13063240C2211yescharacteristic
22H(5,𝔽2)×C43C2211yescharacteristic
23AGL(1,ℤ/8)×C43—21no—
24#127×C43C2211yescharacteristic
25#104×C43—21no—
26#100×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28#41×C43—21no—
29#41×C43—41no—
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43—21no—
33C2×D4×C43—21no—
34C2×D4×C43—41no—
35C2×D4×C43D411yescharacteristic, complemented
36C2×D4×C43C2311yescharacteristic
37C2×C22⋊D43—21no—
38C2×C22⋊D43—21no—
39C2×C22⋊D43—21no—
40C2×C22⋊D43—41no—
41C22×Dic43—21no—
42C22×Dic43D411yescharacteristic, complemented
43SD16×C43—41no—
44D8×C43—41no—
45M16×C43—21no—
46C42×C43D411yescharacteristic, complemented
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43—41no—
52C22⋊Dic43D411yescharacteristic
53C22⋊Dic43D411yescharacteristic, complemented
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—21no—
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—41no—
58Dic43⋊C4—21no—
59Dic43⋊C4—21no—
60Dic43⋊C4—21no—
61Dic43⋊C4—41no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43—21no—
65C23×C43C2×D411yescharacteristic
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68C22×D43—41no—
69C22×D43—81no—
70Q8×C43—21no—
71D4×C43—21no—
72D4×C43—41no—
73D4×C43—41no—
74D4×C43—41no—
75D4×C43—41no—
76D4×C43—41no—
77D4×C43—81no—
78D4×C43—81no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—41no—
83C2×C4×C43C2×D411yescharacteristic
84C22⋊D43—81no—
85C22⋊D43—81no—
86C22⋊D43—81no—
87C22⋊D43—82no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43—81no—
95C8×C43—41no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—81no—
105C22×C43—81no—
106C22×C43#12011yescharacteristic
107C2×D43—41no—
108C2×D43—41no—
109C2×D43—42no—
110C2×D43—41no—
111C2×D43—81no—
112C4×C43—21no—
113C4×C43—41no—
114C4×C43—41no—
115Dic43—41no—
116Dic43—41no—
117Dic43—41no—
118Dic43—81no—
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)—431no—
131#453D4311yescharacteristic, complemented
132#353—431no—
133#352—431no—
134AΣL(1,𝔽16)—431no—
135C43#220011yescharacteristic, complemented, Sylow
136H(5,𝔽2)C2×D4311yescharacteristic
137AGL(1,ℤ/8)—21no—
138#127C2×D4311yescharacteristic
139#126—861no—
140#123—431no—
141#123—861no—
142#123—861no—
143#121—861no—
144#121—861no—
145#121—861no—
146#120—431no—
147#120—861no—
148#120—861no—
149#104—21no—
150#100C2×D4311yescharacteristic
151#99—431no—
152#99—431no—
153#99—861no—
154#99—861no—
155C24—431no—
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—861no—
164C2×D4—861no—
165C2×D4—861no—
166C2×D4—1721no—
167C2×D4C22⋊D4311yescharacteristic, complemented
168C2×D4C22×D4311yescharacteristic
169C22×C4—431no—
170C22×C4—861no—
171SD16—41no—
172D8—41no—
173M16—21no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4—1721no—
178C22⋊C4—431no—
179C22⋊C4—431no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4—861no—
184C22⋊C4—861no—
185C22⋊C4—861no—
186C22⋊C4—861no—
187C22⋊C4—1721no—
188C22⋊C4—1721no—
189C42C22⋊D4311yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—21no—
193C23—861no—
194C23—3441no—
195C23—1721no—
196C23D4×D4311yescharacteristic
197C23D4×D4311yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—41no—
205D4—81no—
206D4—81no—
207D4—3442no—
208D4—3441no—
209D4—3441no—
210D4—3441no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—861no—
216C2×C4—861no—
217C2×C4—861no—
218C2×C4—3441no—
219C2×C4—1721no—
220C2×C4—1721no—
221C2×C4—1721no—
222C2×C4C2×C22⋊D4311yescharacteristic
223C8—41no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—3441no—
235C22—1721no—
236C22—1721no—
237C22—1722no—
238C22—1721no—
239C22#1306329311yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—3441no—
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×#453C2
socleC2×C43B(4,𝔽2)
hypercenter#453D43
hypocenterC43#2200
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14583636C2semidirect
2. #14583089C2semidirect
3. #14583086C2semidirect
4. #14582692C2semidirect
5. #14582690C2semidirect
6. #14582687C2semidirect
7. C43×#453C2semidirect
35. C2×D4×C43D4semidirect
42. C22×Dic43D4semidirect
46. C42×C43D4semidirect
53. C22⋊Dic43D4semidirect
131. #453D43semidirect
135. C43#2200semidirect
167. C2×D4C22⋊D43semidirect
189. C42C22⋊D43semidirect