Finite Group Databasebeta

← #19136594

Subgroups — #19136594

Order 5504.

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

normal subgroups only

This group has 270 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#14583642C211yesmaximal, characteristic, complemented
2#14583086C211yesmaximal, characteristic, complemented
3#14583077C211yesmaximal, characteristic, complemented
4#14582693C211yesmaximal, characteristic, complemented
5#14582686C211yesmaximal, characteristic, complemented
6#14582685C211yesmaximal, characteristic, complemented
7C43×B(4,𝔽2)C211yesmaximal, characteristic, complemented
8#13063355—21no—
9#13063312—21no—
10#13063312C2211yescharacteristic
11#13063311—21no—
12#13063311—21no—
13#13063311—21no—
14#13063294—21no—
15#13063293—21no—
16#13063293—21no—
17#13063293C2211yescharacteristic
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, complemented
28C23×D43D411yescharacteristic, complemented
29#41×C43—21no—
30#41×C43—41no—
31C2×D4×C43—21no—
32C2×D4×C43—21no—
33C2×D4×C43—21no—
34C2×D4×C43—41no—
35C2×D4×C43—41no—
36C2×D4×C43C2311yescharacteristic
37C2×C22⋊D43—21no—
38C2×C22⋊D43—21no—
39C2×C22⋊D43—21no—
40C2×C22⋊D43—41no—
41C2×Dic86—21no—
42C2×Dic86D411yescharacteristic, complemented
43C22⋊C4×C43—21no—
44C22⋊C4×C43—21no—
45C22⋊C4×C43—41no—
46C22⋊C4×C43D411yescharacteristic, complemented
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43—21no—
52C22⋊Dic43D411yescharacteristic, complemented
53#10621885—41no—
54#10621883—41no—
55(C2×D43)⋊C4—21no—
56(C2×D43)⋊C4—21no—
57(C2×D43)⋊C4—21no—
58(C2×D43)⋊C4—41no—
59C4×Dic43—21no—
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—
70C22×D43—41no—
71C22×D43—81no—
72Q8×C43—21no—
73D4×C43—21no—
74D4×C43—41no—
75D4×C43—41no—
76D4×C43—41no—
77D4×C43—41no—
78D4×C43—81no—
79D4×C43—82no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43C2×D411yescharacteristic
86C22⋊D43—81no—
87C22⋊D43—81no—
88C22⋊D43—81no—
89C22⋊D43—82no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—21no—
93C2×Dic43—41no—
94Dic86—41no—
95Dic86—81no—
96C43⋊C8—41no—
97C22×C43—21no—
98C22×C43—21no—
99C22×C43—41no—
100C22×C43—41no—
101C22×C43—41no—
102C22×C43—41no—
103C22×C43—42no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—81no—
107C22×C43—81no—
108C22×C43—81no—
109C22×C43#12011yescharacteristic
110C2×D43—41no—
111C2×D43—41no—
112C2×D43—42no—
113C2×D43—41no—
114C2×D43—81no—
115C4×C43—21no—
116C4×C43—41no—
117C4×C43—41no—
118C4×C43—81no—
119Dic43—41no—
120Dic43—41no—
121Dic43—41no—
122Dic43—81no—
123#2199—431nomaximal, Sylow
124C2×C43—21no—
125C2×C43—41no—
126C2×C43—41no—
127C2×C43—81no—
128C2×C43—81no—
129C2×C43B(4,𝔽2)11yescharacteristic
130D43—81no—
131H(3,𝔽4)—431no—
132B(4,𝔽2)—431no—
133B(4,𝔽2)D4311yescharacteristic, complemented
134#455—431no—
135#354—431no—
136AΣL(1,𝔽16)—431no—
137AΣL(1,𝔽16)—431no—
138C43#219911yescharacteristic, complemented, Sylow
139H(5,𝔽2)C2×D4311yescharacteristic
140#137—861no—
141#124—431no—
142#124—861no—
143#124—861no—
144#124—861no—
145#124—861no—
146#120—21no—
147#120—431no—
148#120—861no—
149#120—861no—
150#120—861no—
151#120C2×D4311yescharacteristic
152#104—861no—
153#100—431no—
154#99—21no—
155#99—431no—
156#99—861no—
157#99C2×D4311yescharacteristic
158C24—431no—
159C24C22⋊D4311yescharacteristic, complemented
160#41—21no—
161#41—41no—
162C2×Q8—431no—
163C2×Q8—861no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—861no—
172C2×D4—1721no—
173C2×D4C22×D4311yescharacteristic
174Q16—1721no—
175SD16—1721no—
176M16—861no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—41no—
180C22⋊C4—431no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4—861no—
184C22⋊C4—861no—
185C22⋊C4—861no—
186C22⋊C4—861no—
187C22⋊C4—861no—
188C22⋊C4—861no—
189C22⋊C4—1721no—
190C22⋊C4C22⋊D4311yescharacteristic, complemented
191C42—431no—
192C42—861no—
193C23—21no—
194C23—21no—
195C23—21no—
196C23—41no—
197C23—81no—
198C23—861no—
199C23—3441no—
200C23—1721no—
201C23D4×D4311yescharacteristic
202C23C2×C22⋊D4311yescharacteristic
203Q8—21no—
204Q8—3441no—
205Q8—1721no—
206D4—21no—
207D4—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—81no—
212D4—82no—
213D4—3442no—
214D4—3441no—
215D4—3441no—
216D4—3441no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—861no—
223C2×C4—861no—
224C2×C4—861no—
225C2×C4—1721no—
226C2×C4D4×D4311yescharacteristic
227C8—1721no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—3441no—
241C22—1721no—
242C22—1721no—
243C22—1722no—
244C22—1721no—
245C22#1306329311yescharacteristic
246C4—21no—
247C4—41no—
248C4—41no—
249C4—81no—
250C4—3441no—
251C4—1721no—
252C4—1721no—
253C4—1721no—
254C2—21no—
255C2—41no—
256C2—41no—
257C2—81no—
258C2—81no—
259C2—3441no—
260C2#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#2199
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. #14583642C2semidirect
2. #14583086C2semidirect
3. #14583077C2semidirect
4. #14582693C2semidirect
5. #14582686C2semidirect
6. #14582685C2semidirect
7. C43×B(4,𝔽2)C2semidirect
27. C24×C43D4semidirect
28. C23×D43D4semidirect
42. C2×Dic86D4semidirect
46. C22⋊C4×C43D4semidirect
52. C22⋊Dic43D4semidirect
60. C4×Dic43D4semidirect
133. B(4,𝔽2)D43semidirect
138. C43#2199semidirect
159. C24C22⋊D43semidirect
190. C22⋊C4C22⋊D43semidirect