Finite Group Databasebeta

← #19143859

Subgroups — #19143859

Order 5504.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#13063370C211yesmaximal, characteristic, complemented
2C2×#13063351C211yesmaximal, characteristic, complemented
3#14583466C211yesmaximal, characteristic, complemented
4#14583041C214yesmaximal, complemented
5#14583031C214yesmaximal, complemented
6#14582904C211yesmaximal, characteristic, complemented
7#14582896C211yesmaximal, characteristic, complemented
8#14582865C211yesmaximal, characteristic, complemented
9C22×D8×C43C211yesmaximal, characteristic, complemented
10#13063370—24no—
11#13063370—24no—
12C2×#10621898C2211yescharacteristic
13C2×#10621898C2211yescharacteristic
14C2×#10621900—21no—
15C2×#10621900C2212yescomplemented
16C22×C22⋊D43—22no—
17C2×D4×D43—21no—
18C2×D4×D43C2212yescomplemented
19#13063351—24no—
20C2×#10621883C2212yescomplemented
21C2×#10621882C2212yescomplemented
22C2×#10621877C2211yescharacteristic, complemented
23#13063321—21no—
24#13063312—21no—
25#13063296C2214yescomplemented
26#13063294—22no—
27#13063284C2211yescharacteristic, complemented
28#13063250C2212yescomplemented
29#13063247C2212yescomplemented
30#13063246C2214yescomplemented
31(C2×D43)⋊C8C2214yescomplemented
32C22×D4×C43C2211yescharacteristic
33C22×D4×C43C2211yescharacteristic, complemented
34C2×D8×C43—24no—
35C2×D8×C43C2214yescomplemented
36C22×C8×C43C2211yescharacteristic, complemented
37C24×C43—21no—
38C24×C43—21no—
39C23×D43—22no—
40C2×D4×C43—21no—
41C2×D4×C43—22no—
42C2×D4×C43—21no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43D414yescomplemented
46C2×D4×C43C2312yes—
47C2×D4×C43C2312yes—
48C22×C4×C43C2311yescharacteristic
49C2×C22⋊D43—216no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—21no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—24no—
54C2×C22⋊D43D412yes—
55C22×Dic43—22no—
56#10621900—28no—
57#10621900—24no—
58#10621900—24no—
59D4×D43—28no—
60D4×D43—24no—
61D4×D43—24no—
62#10621898—22no—
63#10621898—22no—
64#10621898—22no—
65#10621898D414yescomplemented
66C2×D172D411yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43C2312yes—
70C2×Dic86D411yescharacteristic
71C2×Dic86C2311yescharacteristic
72D8×C43—28no—
73C2×C8×C43—22no—
74C2×C8×C43C2312yes—
75C22⋊Dic43—24no—
76C22⋊Dic43—21no—
77#10621883—24no—
78#10621882—24no—
79C4⋊Dic43C2312yes—
80C4×Dic43—21no—
81#10621877—22no—
82C2×C43⋊C8C2312yes—
83C23×C43—22no—
84C23×C43—24no—
85C23×C43—22no—
86C23×C43—42no—
87C23×C43—82no—
88C23×C43—82no—
89C23×C43C2×D411yescharacteristic
90C22×D43—21no—
91C22×D43—28no—
92C22×D43—84no—
93C22×D43C2×D412yes—
94D4×C43—24no—
95D4×C43—22no—
96D4×C43—22no—
97D4×C43—22no—
98D4×C43—42no—
99D4×C43C2×D414yes—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2×D412yes—
102C2×C4×C43C2×D412yes—
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—28no—
105C22⋊D43—28no—
106C22⋊D43—24no—
107C22⋊D43—24no—
108C22⋊D43—84no—
109C2×Dic43—28no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43C2×D412yes—
113D172—22no—
114D172—21no—
115D172C2×D412yes—
116C4×D43—24no—
117C4×D43—22no—
118C4×D43—22no—
119Dic86—22no—
120Dic86—21no—
121Dic86C2×D412yes—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—22no—
125C22×C43—24no—
126C22×C43—44no—
127C22×C43—42no—
128C22×C43—44no—
129C22×C43—84no—
130C22×C43—84no—
131C22×C43#12012yes—
132C22×C43C22×D411yescharacteristic
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—24no—
136C2×D43—42no—
137C2×D43—88no—
138C4×C43#12012yes—
139C4×C43C22×D411yescharacteristic
140C4×C43C22×D411yescharacteristic
141Dic43—22no—
142Dic43—22no—
143Dic43—42no—
144#3008—431nomaximal, Sylow
145C2×C43—22no—
146C2×C43—44no—
147C2×C43—82no—
148C2×C43C2×#12011yescharacteristic
149C2×C43#57612yes—
150D43—42no—
151D43—42no—
152C2×H(5,𝔽2)—431no—
153C2×AGL(1,ℤ/8)—431no—
154C22×D8D4311yescharacteristic, complemented
155#535—431no—
156#449—434no—
157#447—434no—
158#418—431no—
159#416—431no—
160#408—431no—
161C43#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—864no—
163H(5,𝔽2)—864no—
164C2×#41—431no—
165C2×#41—432no—
166C2×#41—431no—
167C2×#41—861no—
168C22×D4—432no—
169C22×D4—861no—
170C22×D4—862no—
171C22×D4C2×D4311yescharacteristic
172C22×D4C2×D4311yescharacteristic, complemented
173AGL(1,ℤ/8)—864no—
174C2×SD16—432no—
175C2×D8—24no—
176C2×D8—432no—
177C2×D8C2×D4314yescomplemented
178C2×M16—431no—
179C22×C8C2×D4311yescharacteristic, complemented
180#127—861no—
181#124—861no—
182#121—434no—
183#120—862no—
184#117—431no—
185#103—432no—
186#102—434no—
187#102—432no—
188C22⋊C8—434no—
189C24—21no—
190C24—21no—
191C24—862no—
192#41—434no—
193#41—864no—
194#41—868no—
195#41—864no—
196#41—862no—
197#41—862no—
198#41—862no—
199C2×Q8—431no—
200C2×Q8—431no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—432no—
207C2×D4—431no—
208C2×D4—431no—
209C2×D4—862no—
210C2×D4—864no—
211C2×D4—868no—
212C2×D4—862no—
213C2×D4—8616no—
214C2×D4—861no—
215C2×D4—864no—
216C2×D4—864no—
217C2×D4C22⋊D4314yescomplemented
218C2×D4C22×D4312yes—
219C2×D4C22×D4312yes—
220C22×C4—432no—
221C22×C4—862no—
222C22×C4—861no—
223C22×C4C22×D4311yescharacteristic
224SD16—864no—
225D8—28no—
226D8—864no—
227M16—862no—
228C2×C8—22no—
229C2×C8—432no—
230C2×C8C22×D4312yes—
231C4⋊C4—432no—
232C22⋊C4—864no—
233C22⋊C4—861no—
234C42—861no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—432no—
242C23—868no—
243C23—861no—
244C23—3444no—
245C23D4×D4311yescharacteristic
246Q8—432no—
247Q8—862no—
248Q8—861no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—432no—
255D4—868no—
256D4—868no—
257D4—864no—
258D4—864no—
259D4—862no—
260D4—861no—
261D4—3444no—
262D4C2×C22⋊D4314yes—
263C2×C4—432no—
264C2×C4—868no—
265C2×C4—861no—
266C2×C4—864no—
267C2×C4—862no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4D4×D4311yescharacteristic
271C2×C4D4×D4312yes—
272C2×C4C2×C22⋊D4312yes—
273C2×C4C23×D4311yescharacteristic
274C8—22no—
275C8—862no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—84no—
283C22—862no—
284C22—862no—
285C22—864no—
286C22—3448no—
287C22—1722no—
288C22#1306329312yes—
289C22C2×D4×D4311yescharacteristic
290C4—862no—
291C4—862no—
292C4—1722no—
293C4#1306329312yes—
294C4C2×D4×D4311yescharacteristic
295C4C22×C22⋊D4311yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—1722no—
300C2—1722no—
301C2C2×#1306329311yescharacteristic
302C2#1458370012yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC22×D8×C43C2
socleC22×C43C22×D4
hypercenterC22×D8D43
hypocenterC43#3008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13063370C2semidirect
2. C2×#13063351C2semidirect
3. #14583466C2semidirect
4. #14583041C2semidirect
5. #14583031C2semidirect
6. #14582904C2semidirect
7. #14582896C2semidirect
8. #14582865C2semidirect
9. C22×D8×C43C2semidirect
15. C2×#10621900C22semidirect
18. C2×D4×D43C22semidirect
20. C2×#10621883C22semidirect
21. C2×#10621882C22semidirect
22. C2×#10621877C22semidirect
25. #13063296C22semidirect
27. #13063284C22semidirect
28. #13063250C22semidirect
29. #13063247C22semidirect
30. #13063246C22semidirect
31. (C2×D43)⋊C8C22semidirect
33. C22×D4×C43C22semidirect
35. C2×D8×C43C22semidirect
36. C22×C8×C43C22semidirect
45. C2×D4×C43D4semidirect
65. #10621898D4semidirect
154. C22×D8D43semidirect
161. C43#3008semidirect
172. C22×D4C2×D43semidirect
177. C2×D8C2×D43semidirect
179. C22×C8C2×D43semidirect
217. C2×D4C22⋊D43semidirect