Finite Group Databasebeta

← #19145043

Subgroups — #19145043

Order 5504.

656 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13063353C211yesmaximal, characteristic, complemented
2C2×#13063351C211yesmaximal, characteristic, complemented
3C2×#13063350C211yesmaximal, characteristic, complemented
4#14583445C211yesmaximal, characteristic, complemented
5C2×#13063321C211yesmaximal, characteristic, complemented
6#14583287C212yesmaximal, complemented
7#14583285C212yesmaximal, complemented
8#14583274C212yesmaximal, complemented
9#14583270C212yesmaximal, complemented
10M16×Dic43C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C22×C22⋊D43—22no—
15#13063353—24no—
16#13063351—24no—
17#13063350—24no—
18C2×#10621873C2212yescomplemented
19C2×#10621883C2212yescomplemented
20C2×#10621884C2212yescomplemented
21C2×D344C2212yescomplemented
22C2×#10621882C2212yescomplemented
23C2×#10621882C2212yescomplemented
24C2×#10621877C2211yescharacteristic
25#13063323C2211yescharacteristic, complemented
26#13063321—22no—
27#13063321C2212yes—
28#13063321C2212yes—
29#13063321C2211yescharacteristic, complemented
30#13063314C2211yescharacteristic, complemented
31#13063312C2211yescharacteristic, complemented
32#13063297—22no—
33C4×C22⋊D43—22no—
34C2×C4×Dic43C2211yescharacteristic
35#13063235C2212yescomplemented
36C8×Dic43C2212yescomplemented
37C2×#41×C43C2211yescharacteristic
38C22×D4×C43C2211yescharacteristic
39AGL(1,ℤ/8)×C43—24no—
40C2×SD16×C43C2212yescomplemented
41C2×D8×C43C2212yescomplemented
42C2×M16×C43C2211yescharacteristic
43C24×C43—21no—
44C23×D43—21no—
45#41×C43—22no—
46#41×C43—22no—
47C2×Q8×C43C2311yescharacteristic
48C2×D4×C43—21no—
49C2×D4×C43—21no—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43C2311yescharacteristic
53C2×D4×C43C2312yes—
54C22×C4×C43—21no—
55C22×C4×C43C2311yescharacteristic
56C2×C22⋊D43—22no—
57C2×C22⋊D43—24no—
58C2×C22⋊D43—24no—
59C2×C22⋊D43—21no—
60C2×C22⋊D43—48no—
61C22×Dic43D412yes—
62#10621898—22no—
63#10621898—22no—
64C2×D172—21no—
65C2×D172—22no—
66C2×D172—22no—
67C2×D172C2311yescharacteristic
68C2×D172C2312yes—
69C2×C4×D43—21no—
70C2×Dic86C2311yescharacteristic
71SD16×C43—24no—
72D8×C43—24no—
73M16×C43D414yescomplemented
74C2×C8×C43C2312yes—
75C22⋊Dic43—22no—
76#10621884—24no—
77#10621883—24no—
78#10621882—24no—
79#10621882—24no—
80(C2×D43)⋊C4—22no—
81Dic43⋊C4—22no—
82C4×Dic43D412yes—
83C4×Dic43C2311yescharacteristic
84C4×Dic43C2311yescharacteristic
85#10621877D414yescomplemented
86C2×C43⋊C8C2312yes—
87D344—24no—
88#10621873—24no—
89C23×C43—21no—
90C23×C43—22no—
91C23×C43—44no—
92C23×C43—42no—
93C23×C43C2×D411yescharacteristic
94C22×D43—21no—
95C22×D43—22no—
96C22×D43—44no—
97C22×D43—42no—
98Q8×C43—21no—
99Q8×C43—21no—
100D4×C43—21no—
101D4×C43—22no—
102D4×C43—21no—
103D4×C43—22no—
104D4×C43—42no—
105D4×C43—42no—
106C2×C4×C43—21no—
107C2×C4×C43—42no—
108C2×C4×C43C2×D411yescharacteristic
109C2×C4×C43C2×D412yes—
110C2×C4×C43C2×D412yes—
111C2×C4×C43C2411yescharacteristic
112C22⋊D43—48no—
113C22⋊D43—42no—
114C22⋊D43—44no—
115C22⋊D43—48no—
116C2×Dic43—24no—
117C2×Dic43—21no—
118C2×Dic43C2×D412yes—
119C2×Dic43C2×D412yes—
120D172—22no—
121D172—21no—
122D172—21no—
123D172—22no—
124D172—42no—
125C4×D43—42no—
126Dic86—21no—
127Dic86—21no—
128C8×C43C2×D414yescomplemented
129C43⋊C8C2×D414yescomplemented
130C22×C43—22no—
131C22×C43—42no—
132C22×C43—41no—
133C22×C43—44no—
134C22×C43—42no—
135C22×C43—84no—
136C22×C43#12712yes—
137C22×C43C22×D411yescharacteristic
138C2×D43—42no—
139C2×D43—41no—
140C2×D43—44no—
141C2×D43—42no—
142C2×D43—84no—
143C4×C43—41no—
144C4×C43#12712yes—
145C4×C43C22×D411yescharacteristic
146C4×C43C22×D411yescharacteristic
147Dic43—22no—
148Dic43—41no—
149Dic43AGL(1,ℤ/8)14yescomplemented
150#3151—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43—81no—
153C2×C43—82no—
154C2×C43C2×#12711yescharacteristic
155C2×C43C2×AGL(1,ℤ/8)12yes—
156D43—81no—
157D43—82no—
158C2×AGL(1,ℤ/8)—431no—
159C2×AGL(1,ℤ/8)—431no—
160C2×AGL(1,ℤ/8)—431no—
161C2×AGL(1,ℤ/8)D4311yescharacteristic, complemented
162#532—431no—
163C2×#127—431no—
164#496—432no—
165#496—432no—
166#493—432no—
167#492—432no—
168C4×M16—431no—
169C43#315111yescharacteristic, complemented, Sylow
170C2×#41—431no—
171C2×#41C2×D4311yescharacteristic
172C22×D4—431no—
173C22×D4—862no—
174C22×D4C2×D4311yescharacteristic
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—864no—
177AGL(1,ℤ/8)—864no—
178AGL(1,ℤ/8)—864no—
179C2×SD16—432no—
180C2×SD16—432no—
181C2×SD16—432no—
182C2×SD16C2×D4312yescomplemented
183C2×D8—432no—
184C2×D8—432no—
185C2×D8—432no—
186C2×D8C2×D4312yescomplemented
187C2×M16—431no—
188C2×M16C2×D4311yescharacteristic
189C4⋊Q8—431no—
190#127—432no—
191#127—432no—
192#127—431no—
193#127—862no—
194#124—431no—
195#124—431no—
196#121—862no—
197C4×D4—862no—
198C2×C42—431no—
199#97—432no—
200C4×C8—432no—
201C24—21no—
202C24—861no—
203#41—22no—
204#41—22no—
205#41—862no—
206#41—862no—
207C2×Q8—431no—
208C2×Q8C22×D4311yescharacteristic
209C2×D4—21no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—22no—
213C2×D4—431no—
214C2×D4—432no—
215C2×D4—862no—
216C2×D4—864no—
217C2×D4—864no—
218C2×D4—861no—
219C2×D4—862no—
220C2×D4—861no—
221C2×D4—862no—
222C2×D4—1728no—
223C2×D4C22×D4311yescharacteristic
224C2×D4C22×D4312yes—
225C22×C4—21no—
226C22×C4—432no—
227C22×C4—861no—
228C22×C4C22×D4311yescharacteristic
229SD16—24no—
230SD16—864no—
231SD16—864no—
232SD16—864no—
233D8—24no—
234D8—864no—
235D8—864no—
236D8—864no—
237M16—434no—
238M16C22⋊D4314yescomplemented
239C2×C8—432no—
240C2×C8C22×D4312yes—
241C4⋊C4—862no—
242C22⋊C4—862no—
243C22⋊C4—862no—
244C42—432no—
245C42—431no—
246C42—431no—
247C23—21no—
248C23—22no—
249C23—44no—
250C23—42no—
251C23—861no—
252C23—862no—
253C23—1724no—
254C23—1722no—
255C23D4×D4311yescharacteristic
256Q8—21no—
257Q8—21no—
258Q8—861no—
259Q8—861no—
260D4—21no—
261D4—22no—
262D4—21no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—861no—
267D4—862no—
268D4—861no—
269D4—862no—
270D4—1728no—
271D4—1724no—
272D4—1728no—
273D4—1722no—
274D4—1722no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—432no—
278C2×C4—432no—
279C2×C4—864no—
280C2×C4—861no—
281C2×C4—1722no—
282C2×C4D4×D4311yescharacteristic
283C2×C4D4×D4312yes—
284C2×C4C2×C22⋊D4312yes—
285C2×C4C23×D4311yescharacteristic
286C8—434no—
287C8C2×C22⋊D4314yescomplemented
288C22—22no—
289C22—44no—
290C22—42no—
291C22—41no—
292C22—42no—
293C22—84no—
294C22—3444no—
295C22—1724no—
296C22—1722no—
297C22—1721no—
298C22—1722no—
299C22#1306332112yes—
300C22C2×D4×D4311yescharacteristic
301C4—41no—
302C4—434no—
303C4—862no—
304C4—1721no—
305C4#1306332112yes—
306C4C2×D4×D4311yescharacteristic
307C4C22×C22⋊D4311yescharacteristic
308C2—22no—
309C2—82no—
310C2—81no—
311C2—3442no—
312C2—3441no—
313C2C2×#1306332111yescharacteristic
314C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×AGL(1,ℤ/8)×C43C2
socleC22×C43C22×D4
hypercenterC2×AGL(1,ℤ/8)D43
hypocenterC43#3151
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13063353C2semidirect
2. C2×#13063351C2semidirect
3. C2×#13063350C2semidirect
4. #14583445C2semidirect
5. C2×#13063321C2semidirect
6. #14583287C2semidirect
7. #14583285C2semidirect
8. #14583274C2semidirect
9. #14583270C2semidirect
10. M16×Dic43C2semidirect
11. C2×AGL(1,ℤ/8)×C43C2semidirect
18. C2×#10621873C22semidirect
19. C2×#10621883C22semidirect
20. C2×#10621884C22semidirect
21. C2×D344C22semidirect
22. C2×#10621882C22semidirect
23. C2×#10621882C22semidirect
25. #13063323C22semidirect
29. #13063321C22semidirect
30. #13063314C22semidirect
31. #13063312C22semidirect
35. #13063235C22semidirect
36. C8×Dic43C22semidirect
40. C2×SD16×C43C22semidirect
41. C2×D8×C43C22semidirect
73. M16×C43D4semidirect
85. #10621877D4semidirect
128. C8×C43C2×D4semidirect
129. C43⋊C8C2×D4semidirect
149. Dic43AGL(1,ℤ/8)semidirect
161. C2×AGL(1,ℤ/8)D43semidirect
169. C43#3151semidirect
182. C2×SD16C2×D43semidirect
186. C2×D8C2×D43semidirect
238. M16C22⋊D43semidirect
287. C8C2×C22⋊D43semidirect