Finite Group Databasebeta

← #19135646

Subgroups — #19135646

Order 5504.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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#14583697C211yesmaximal, characteristic, complemented
2#14583466C211yesmaximal, characteristic, complemented
3#14582915C211yesmaximal, characteristic, complemented
4#14582904C211yesmaximal, characteristic, complemented
5#14582873C211yesmaximal, characteristic, complemented
6#14582671C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—21no—
10#13063355—21no—
11#13063351—21no—
12#13063350—21no—
13#13063345—22no—
14C2×#10621877C2211yescharacteristic
15#13063321—21no—
16#13063312—21no—
17#13063296—22no—
18#13063294—22no—
19#13063284C2211yescharacteristic
20#13063284C2211yescharacteristic
21#13063251—22no—
22#13063246—22no—
23#13063240—22no—
24C2×#41×C43C2211yescharacteristic
25C22×D4×C43C2211yescharacteristic
26AGL(1,ℤ/8)×C43—22no—
27AGL(1,ℤ/8)×C43—22no—
28C2×SD16×C43—21no—
29C2×D8×C43—21no—
30C2×M16×C43C2211yescharacteristic
31C24×C43—21no—
32#41×C43—21no—
33#41×C43—21no—
34#41×C43—21no—
35#41×C43—21no—
36C2×Q8×C43D411yescharacteristic, complemented
37C2×D4×C43—21no—
38C2×D4×C43—21no—
39C2×D4×C43—21no—
40C2×D4×C43—21no—
41C2×D4×C43—21no—
42C2×D4×C43—21no—
43C2×D4×C43D412yes—
44C2×D4×C43D411yescharacteristic, complemented
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—24no—
48C2×C22⋊D43—21no—
49#10621898—21no—
50#10621898—21no—
51#10621898—21no—
52#10621898—21no—
53C2×D172D411yescharacteristic
54C2×C4×D43—21no—
55C2×Dic86D411yescharacteristic
56SD16×C43—24no—
57D8×C43—24no—
58M16×C43—21no—
59M16×C43D412yescomplemented
60C2×C8×C43—21no—
61C22⋊Dic43—24no—
62C22⋊Dic43—21no—
63C22⋊Dic43D412yes—
64#10621885—22no—
65#10621884—22no—
66#10621883—22no—
67#10621882—22no—
68C4⋊Dic43—21no—
69C4⋊Dic43—21no—
70C4×Dic43—21no—
71C4×Dic43—21no—
72#10621877—21no—
73#10621877—21no—
74C2×C43⋊C8D412yescomplemented
75C23×C43—22no—
76C23×C43—21no—
77C23×C43—41no—
78C23×C43—41no—
79C23×C43—82no—
80C23×C43C2×D411yescharacteristic
81C22×D43—21no—
82Q8×C43—21no—
83Q8×C43—21no—
84D4×C43—21no—
85D4×C43—21no—
86D4×C43—22no—
87D4×C43—22no—
88D4×C43—41no—
89D4×C43—41no—
90D4×C43—41no—
91D4×C43—41no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D411yescharacteristic
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43#4111yescharacteristic
101C22⋊D43—41no—
102C22⋊D43—41no—
103C22⋊D43—84no—
104C2×Dic43—22no—
105C2×Dic43—21no—
106C2×Dic43—41no—
107D172—21no—
108D172—21no—
109C4×D43—41no—
110C4×D43—41no—
111Dic86—21no—
112Dic86—21no—
113C8×C43—22no—
114C43⋊C8—22no—
115C22×C43—41no—
116C22×C43—44no—
117C22×C43—42no—
118C22×C43—41no—
119C22×C43—81no—
120C22×C43—82no—
121C22×C43—82no—
122C22×C43#12011yescharacteristic
123C22×C43#12111yescharacteristic
124C22×C43#12711yescharacteristic
125C2×D43—42no—
126C2×D43—41no—
127C4×C43—41no—
128C4×C43#12011yescharacteristic
129C4×C43#12011yescharacteristic
130C4×C43#12111yescharacteristic
131C4×C43#12111yescharacteristic
132Dic43—42no—
133Dic43—41no—
134Dic43—81no—
135#2008—431nomaximal, Sylow
136C2×C43—21no—
137C2×C43—21no—
138C2×C43—21no—
139C2×C43—82no—
140C2×C43—81no—
141C2×C43#39211yescharacteristic
142D43—81no—
143#575—431no—
144C2×AGL(1,ℤ/8)D4311yescharacteristic, complemented
145#535—431no—
146#421—431no—
147#418—431no—
148#410—431no—
149#344—431no—
150C43#200811yescharacteristic, complemented, Sylow
151C2×#41—431no—
152C2×#41C2×D4311yescharacteristic
153C22×D4C2×D4311yescharacteristic
154#137—861no—
155#137—861no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—861no—
159AGL(1,ℤ/8)—861no—
160#135—862no—
161C2×SD16—21no—
162C2×D8—21no—
163C2×M16—431no—
164C2×M16C2×D4311yescharacteristic
165#127—861no—
166#124—861no—
167#121—862no—
168#120—862no—
169#117—431no—
170#117—431no—
171#104—862no—
172#102—862no—
173#99—862no—
174C24—21no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—861no—
180#41—861no—
181#41—861no—
182#41—861no—
183C2×Q8—431no—
184C2×Q8C22⋊D4311yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—431no—
192C2×D4—864no—
193C2×D4—861no—
194C2×D4C22⋊D4312yes—
195C2×D4C22⋊D4311yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—861no—
198C22×C4C22×D4311yescharacteristic
199Q16—862no—
200SD16—24no—
201SD16—862no—
202SD16—862no—
203D8—24no—
204D8—862no—
205M16—21no—
206M16—861no—
207M16—861no—
208M16C22⋊D4312yescomplemented
209C2×C8—21no—
210C2×C8—432no—
211C4⋊C4—861no—
212C4⋊C4—861no—
213C22⋊C4—432no—
214C22⋊C4—864no—
215C22⋊C4—861no—
216C42—861no—
217C42—861no—
218C23—22no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23—82no—
223C23—861no—
224C23D4×D4311yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—861no—
228Q8—861no—
229D4—21no—
230D4—21no—
231D4—22no—
232D4—22no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—861no—
238D4—861no—
239D4—3444no—
240D4—1721no—
241D4—1721no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—862no—
246C2×C4—861no—
247C2×C4—1721no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4D4×D4311yescharacteristic
251C2×C4D4×D4311yescharacteristic
252C2×C4#1062190011yescharacteristic
253C2×C4C2×C22⋊D4311yescharacteristic
254C2×C4C2×C22⋊D4311yescharacteristic
255C2×C4C2×C22⋊D4311yescharacteristic
256C8—22no—
257C8—862no—
258C22—41no—
259C22—44no—
260C22—41no—
261C22—42no—
262C22—81no—
263C22—82no—
264C22—82no—
265C22—1722no—
266C22—1721no—
267C22#1306329311yescharacteristic
268C22#1306329711yescharacteristic
269C22#1306332111yescharacteristic
270C4—41no—
271C4—3441no—
272C4—1722no—
273C4—1721no—
274C4#1306329311yescharacteristic
275C4#1306329411yescharacteristic
276C4#1306329611yescharacteristic
277C4#1306329711yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—82no—
282C2—81no—
283C2—3441no—
284C2#1458280711yescharacteristic
subgroupG/H
centerC2#14582807
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×AGL(1,ℤ/8)×C43C2
socleC2×C43#392
hypercenterC2×AGL(1,ℤ/8)D43
hypocenterC43#2008
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. #14583466C2semidirect
3. #14582915C2semidirect
4. #14582904C2semidirect
5. #14582873C2semidirect
6. #14582671C2semidirect
7. C2×AGL(1,ℤ/8)×C43C2semidirect
36. C2×Q8×C43D4semidirect
44. C2×D4×C43D4semidirect
59. M16×C43D4semidirect
74. C2×C43⋊C8D4semidirect
144. C2×AGL(1,ℤ/8)D43semidirect
150. C43#2008semidirect
184. C2×Q8C22⋊D43semidirect
195. C2×D4C22⋊D43semidirect
208. M16C22⋊D43semidirect