Finite Group Databasebeta

← #19136582

Subgroups — #19136582

Order 5504.

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

normal subgroups only

This group has 258 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#14583577C211yesmaximal, characteristic, complemented
2#14583086C211yesmaximal, characteristic
3#14583077C211yesmaximal, characteristic, complemented
4#14582693C211yesmaximal, characteristic, complemented
5#14582689C211yesmaximal, characteristic, complemented
6#14582685C211yesmaximal, characteristic, complemented
7C43×#458C211yesmaximal, characteristic, complemented
8#13063355—21no—
9#13063318—21no—
10#13063312C2211yescharacteristic
11#13063307—21no—
12#13063303—21no—
13#13063293—21no—
14#13063293C2211yescharacteristic
15C4×C22⋊D43—21no—
16#13063283—21no—
17C22⋊C4×D43—21no—
18#13063252—21no—
19#13063242C2211yescharacteristic
20#13063240—21no—
21#13063240C2211yescharacteristic
22H(5,𝔽2)×C43C2211yescharacteristic
23#123×C43—21no—
24#123×C43C2211yescharacteristic
25#99×C43—21no—
26#99×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28#41×C43—21no—
29#41×C43—41no—
30C2×D4×C43—21no—
31C2×D4×C43—21no—
32C2×D4×C43—41no—
33C2×D4×C43C2311yescharacteristic
34C22×C4×C43D411yescharacteristic, complemented
35C2×C22⋊D43—21no—
36C2×C22⋊D43—41no—
37C2×C4×D43—21no—
38C2×C4×D43—21no—
39C2×Dic86D411yescharacteristic, complemented
40C4⋊C4×C43—21no—
41C4⋊C4×C43—41no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43—41no—
45C22⋊C4×C43D411yescharacteristic, complemented
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43D411yescharacteristic
50#10621885—41no—
51#10621883—41no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—41no—
56C4⋊Dic43—21no—
57Dic43⋊C4—21no—
58Dic43⋊C4—21no—
59C4×Dic43—21no—
60C4×Dic43D411yescharacteristic, complemented
61#10621877—21no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43C2×D411yescharacteristic
65C23×C43C2×D411yescharacteristic
66C22×D43—21no—
67C22×D43—42no—
68C22×D43—41no—
69Q8×C43—21no—
70D4×C43—21no—
71D4×C43—41no—
72D4×C43—41no—
73D4×C43—41no—
74D4×C43—41no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43C2×D411yescharacteristic
83C22⋊D43—42no—
84C22⋊D43—82no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—41no—
89C4×D43—42no—
90C4×D43—81no—
91Dic86—41no—
92C43⋊C8—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—81no—
99C22×C43—81no—
100C22×C43#12011yescharacteristic
101C2×D43—22no—
102C2×D43—41no—
103C2×D43—41no—
104C2×D43—42no—
105C2×D43—81no—
106C4×C43—21no—
107C4×C43—41no—
108C4×C43—41no—
109C4×C43—41no—
110C4×C43—81no—
111Dic43—41no—
112Dic43—41no—
113Dic43—41no—
114Dic43—81no—
115#2197—431nomaximal, Sylow
116C2×C43—21no—
117C2×C43—41no—
118C2×C43—41no—
119C2×C43—81no—
120C2×C43B(4,𝔽2)11yescharacteristic
121D43—42no—
122#551—431no—
123#458D4311yescharacteristic, complemented
124B(4,𝔽2)—431no—
125#455—431no—
126#354—431no—
127#352—431no—
128AΣL(1,𝔽16)—431no—
129C43#219711yescharacteristic, complemented, Sylow
130H(5,𝔽2)C2×D4311yescharacteristic
131#137—861no—
132#126—861no—
133#124—431no—
134#123—21no—
135#123—861no—
136#123C2×D4311yescharacteristic
137C22⋊Q8—861no—
138#120—431no—
139#120—861no—
140C4×D4—861no—
141#117—861no—
142C2×C22⋊C4—861no—
143#104—861no—
144#100—431no—
145#99—21no—
146#99—431no—
147#99—861no—
148#99C2×D4311yescharacteristic
149C24—431no—
150#41—21no—
151#41—41no—
152C2×Q8—431no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—861no—
157C2×D4—1721no—
158C2×D4C22×D4311yescharacteristic
159C22×C4—861no—
160C22×C4—861no—
161C22×C4C22⋊D4311yescharacteristic, complemented
162Q16—1721no—
163SD16—1721no—
164M16—861no—
165C4⋊C4—21no—
166C4⋊C4—41no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—41no—
173C22⋊C4—431no—
174C22⋊C4—861no—
175C22⋊C4—861no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—1721no—
181C22⋊C4C22⋊D4311yescharacteristic, complemented
182C42—431no—
183C42—861no—
184C23—21no—
185C23—21no—
186C23—861no—
187C23—1721no—
188C23—1722no—
189C23D4×D4311yescharacteristic
190C23C2×C22⋊D4311yescharacteristic
191Q8—21no—
192Q8—1721no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—3442no—
199D4—1722no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—3441no—
211C2×C4—1722no—
212C2×C4—1721no—
213C2×C4D4×D4311yescharacteristic
214C8—1721no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22—862no—
223C22—3441no—
224C22—1721no—
225C22—1722no—
226C22—1721no—
227C22#1306329311yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—81no—
233C4—3441no—
234C4—1721no—
235C4—1721no—
236C4—1721no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—81no—
241C2—1722no—
242C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#458C2
socleC2×C43B(4,𝔽2)
hypercenter#458D43
hypocenterC43#2197
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #14583577C2semidirect
3. #14583077C2semidirect
4. #14582693C2semidirect
5. #14582689C2semidirect
6. #14582685C2semidirect
7. C43×#458C2semidirect
34. C22×C4×C43D4semidirect
39. C2×Dic86D4semidirect
45. C22⋊C4×C43D4semidirect
60. C4×Dic43D4semidirect
123. #458D43semidirect
129. C43#2197semidirect
161. C22×C4C22⋊D43semidirect
181. C22⋊C4C22⋊D43semidirect