Finite Group Databasebeta

← #19136235

Subgroups — #19136235

Order 5504.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583407C211yesmaximal, characteristic
2#14582880C211yesmaximal, characteristic, complemented
3#14582871C211yesmaximal, characteristic, complemented
4#14582689C211yesmaximal, characteristic, complemented
5#14582687C211yesmaximal, characteristic, complemented
6#14582685C211yesmaximal, characteristic, complemented
7C43×#352C211yesmaximal, characteristic, complemented
8C2×#10621900C2211yescharacteristic
9C22×C4×D43C411yescharacteristic, complemented
10M16×D43—21no—
11#13063308C411yescharacteristic, complemented
12#13063303—21no—
13#13063298—21no—
14#13063295C411yescharacteristic, complemented
15#13063293C2211yescharacteristic
16#13063287—21no—
17(C22⋊D43)⋊C4—21no—
18#13063281—21no—
19#13063281C411yescharacteristic, complemented
20#13063243—21no—
21#13063242C2211yescharacteristic
22#13063240C2211yescharacteristic
23#13063239—21no—
24#123×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C23×D43C2×C411yescharacteristic
28C2×D4×C43C2311yescharacteristic
29C22×C4×C43C2×C411yescharacteristic
30C2×C22⋊D43—21no—
31C2×C22⋊D43C2×C411yescharacteristic
32C2×C22⋊D43D411yescharacteristic
33C22×Dic43C2×C411yescharacteristic
34C22×Dic43D411yescharacteristic
35#10621900—41no—
36#10621900—41no—
37C2×D172—21no—
38C2×C4×D43—21no—
39C2×C4×D43—21no—
40C2×C4×D43—41no—
41C2×C4×D43—41no—
42C2×C4×D43D411yescharacteristic
43C2×Dic86D411yescharacteristic
44M16×C43—21no—
45C4⋊C4×C43—21no—
46C22⋊C4×C43—21no—
47C22⋊C4×C43—21no—
48C22⋊C4×C43C2×C411yescharacteristic
49C22⋊Dic43—21no—
50C22⋊Dic43C2×C411yescharacteristic
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—41no—
57C4×Dic43—21no—
58C4×Dic43—41no—
59#10621877—21no—
60#10621872—41no—
61C8×D43—41no—
62C23×C43C22×C411yescharacteristic
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65C22×D43—42no—
66C22×D43—41no—
67C22×D43C22⋊C411yescharacteristic
68D4×C43—41no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43C2×D411yescharacteristic
74C22⋊D43—41no—
75C22⋊D43—41no—
76C22⋊D43—42no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—41no—
83C2×Dic43C22⋊C411yescharacteristic
84C2×Dic43C22⋊C411yescharacteristic
85C2×Dic43C22⋊C411yescharacteristic
86D172—42no—
87C4×D43—21no—
88C4×D43—21no—
89C4×D43—42no—
90C4×D43—41no—
91C4×D43—41no—
92Dic86—41no—
93C8×C43—41no—
94C43⋊C8—41no—
95C22×C43—21no—
96C22×C43—21no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43C2×C22⋊C411yescharacteristic
100C2×D43—22no—
101C2×D43—21no—
102C2×D43—41no—
103C2×D43—42no—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—42no—
107C4×C43—21no—
108C4×C43—41no—
109C4×C43—41no—
110C4×C43—81no—
111Dic43—21no—
112Dic43—21no—
113Dic43—41no—
114Dic43—81no—
115Dic43#9911yescharacteristic
116Dic43#9911yescharacteristic
117#2120—431nomaximal, Sylow
118C2×C43—21no—
119C2×C43—41no—
120C2×C43—41no—
121C2×C43C2×#9911yescharacteristic
122D43—41no—
123D43—42no—
124#525—431no—
125#413—431no—
126#410—431no—
127#352—431no—
128#352D4311yescharacteristic, complemented
129AΣL(1,𝔽16)—431no—
130AΣL(1,𝔽16)—431no—
131C43#212011yescharacteristic, complemented, Sylow
132C2×#41—431no—
133C23×C4—431no—
134C2×M16—861no—
135#123—431no—
136#123C2×D4311yescharacteristic
137C22⋊Q8—861no—
138#121—861no—
139#120—431no—
140#120—431no—
141C4×D4—861no—
142C4×D4—861no—
143#117—431no—
144#117—861no—
145#101—861no—
146#100—431no—
147#100C2×D4311yescharacteristic
148#99—431no—
149#99—861no—
150#99C2×D4311yescharacteristic
151C24—431no—
152#41—1721no—
153#41—1721no—
154C2×Q8—431no—
155C2×D4—431no—
156C2×D4—431no—
157C2×D4—861no—
158C2×D4—861no—
159C2×D4C22×D4311yescharacteristic
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—431no—
163C22×C4—861no—
164C22×C4—861no—
165C22×C4—1721no—
166C22×C4—1721no—
167C22×C4C4×D4311yescharacteristic
168M16—21no—
169M16—861no—
170M16—1721no—
171C2×C8—1721no—
172C4⋊C4—21no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C4⋊C4—1721no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—431no—
179C22⋊C4—861no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4C4×D4311yescharacteristic
184C42—861no—
185C42—1721no—
186C23—431no—
187C23—861no—
188C23—1721no—
189C23—1722no—
190C23C2×C4×D4311yescharacteristic
191C23D4×D4311yescharacteristic
192Q8—1721no—
193D4—41no—
194D4—1722no—
195D4—1721no—
196D4—1721no—
197D4—1722no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—431no—
203C2×C4—431no—
204C2×C4—431no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—1721no—
213C2×C4—1721no—
214C2×C4—1722no—
215C2×C4—1721no—
216C2×C4D4×D4311yescharacteristic
217C8—41no—
218C8—1721no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—862no—
224C22—861no—
225C22—1721no—
226C22—1721no—
227C22—1722no—
228C22—1722no—
229C22—1721no—
230C22C22⋊C4×D4311yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—431no—
236C4—431no—
237C4—861no—
238C4—861no—
239C4—3441no—
240C4—1721no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—1722no—
245C2—1721no—
246C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#352C2
socleC2×C43C2×#99
hypercenter#352D43
hypocenterC43#2120
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #14582880C2semidirect
3. #14582871C2semidirect
4. #14582689C2semidirect
5. #14582687C2semidirect
6. #14582685C2semidirect
7. C43×#352C2semidirect
9. C22×C4×D43C4semidirect
11. #13063308C4semidirect
14. #13063295C4semidirect
19. #13063281C4semidirect
128. #352D43semidirect
131. C43#2120semidirect