Finite Group Databasebeta

← #19143866

Subgroups — #19143866

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×#13063371C211yesmaximal, characteristic, complemented
2C2×#13063350C211yesmaximal, characteristic, complemented
3C22×D344C211yesmaximal, characteristic, complemented
4#14583468C211yesmaximal, characteristic, complemented
5#14583047C214yesmaximal, complemented
6#14583034C214yesmaximal, complemented
7#14582903C211yesmaximal, characteristic, complemented
8#14582865C211yesmaximal, characteristic, complemented
9C43×#416C211yesmaximal, characteristic, complemented
10#13063371—24no—
11#13063371—24no—
12C2×#10621902C2212yescomplemented
13C2×#10621898—21no—
14C2×#10621898C2211yescharacteristic
15C22×D172—21no—
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic, complemented
18C2×D4×D43—22no—
19C2×D4×D43C2212yescomplemented
20#13063350—24no—
21C2×#10621884C2212yescomplemented
22C2×D344—24no—
23C2×D344C2214yescomplemented
24C2×#10621882C2212yescomplemented
25C2×#10621877C2211yescharacteristic, complemented
26#13063322—21no—
27#13063313—21no—
28#13063300C2214yescomplemented
29#13063295—22no—
30#13063245C2214yescomplemented
31(C2×D43)⋊C8C2214yescomplemented
32C2×#41×C43C2211yescharacteristic
33C22×C8×C43C2211yescharacteristic, complemented
34#117×C43C2211yescharacteristic, complemented
35#103×C43C2212yescomplemented
36#102×C43C2212yescomplemented
37C23×D43—21no—
38C23×D43—22no—
39C23×D43—21no—
40#41×C43—22no—
41#41×C43D414yescomplemented
42C2×Q8×C43C2311yescharacteristic
43C2×D4×C43—21no—
44C2×D4×C43C2311yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—22no—
48C2×C22⋊D43D412yes—
49#10621902—24no—
50#10621902—24no—
51D4×D43—216no—
52D4×D43—24no—
53D4×D43—24no—
54#10621898—28no—
55#10621898—22no—
56#10621898—22no—
57C2×D172—28no—
58C2×D172—21no—
59C2×D172—22no—
60C2×D172—21no—
61C2×D172—22no—
62C2×D172—24no—
63C2×D172—22no—
64C2×D172—22no—
65C2×D172D411yescharacteristic
66C2×D172D414yescomplemented
67C2×D172C2312yes—
68C2×D172C2312yes—
69C2×C4×D43—22no—
70C2×C4×D43C2312yes—
71C2×Dic86D411yescharacteristic
72C2×C8×C43—22no—
73C2×C8×C43C2312yes—
74C4⋊C4×C43C2312yes—
75C22⋊C4×C43—21no—
76C42×C43—21no—
77#10621884—24no—
78#10621882—24no—
79(C2×D43)⋊C4—24no—
80#10621877—22no—
81C2×C43⋊C8C2312yes—
82D344—28no—
83C23×C43—21no—
84C23×C43C2×D411yescharacteristic
85C22×D43—22no—
86C22×D43—28no—
87C22×D43—24no—
88C22×D43—22no—
89C22×D43—42no—
90C22×D43—84no—
91C22×D43—82no—
92C22×D43—82no—
93C22×D43C2×D412yes—
94Q8×C43—21no—
95Q8×C43C2×D412yes—
96D4×C43—24no—
97D4×C43—21no—
98D4×C43C2×D412yes—
99C2×C4×C43—21no—
100C2×C4×C43—24no—
101C2×C4×C43—22no—
102C2×C4×C43C2×D412yes—
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2411yescharacteristic
106C22⋊D43—28no—
107C22⋊D43—24no—
108C2×Dic43C2×D412yes—
109D172—28no—
110D172—22no—
111D172—24no—
112D172—22no—
113D172—22no—
114D172—22no—
115D172—42no—
116D172—84no—
117D172C2×D414yes—
118C4×D43—28no—
119C4×D43—22no—
120C4×D43—22no—
121Dic86—22no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—22no—
125C22×C43—22no—
126C22×C43—42no—
127C22×C43#12012yes—
128C22×C43C22×D411yescharacteristic
129C2×D43—24no—
130C2×D43—22no—
131C2×D43—24no—
132C2×D43—44no—
133C2×D43—42no—
134C2×D43—44no—
135C2×D43—84no—
136C2×D43—88no—
137C2×D43—84no—
138C4×C43—22no—
139C4×C43—42no—
140C4×C43#12012yes—
141C4×C43C22×D411yescharacteristic
142C4×C43C22×D411yescharacteristic
143Dic43—22no—
144#3008—431nomaximal, Sylow
145C2×C43—22no—
146C2×C43—42no—
147C2×C43C2×#12011yescharacteristic
148C2×C43#57612yes—
149D43—42no—
150D43—44no—
151D43—82no—
152C2×H(5,𝔽2)—431no—
153C2×AGL(1,ℤ/8)—431no—
154C22×D8—431no—
155#535—431no—
156#449—434no—
157#447—434no—
158#418—431no—
159#416D4311yescharacteristic, complemented
160#408—431no—
161C43#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—864no—
163H(5,𝔽2)—864no—
164C2×#41—431no—
165C2×#41—432no—
166C2×#41—861no—
167C2×#41C2×D4311yescharacteristic
168C22×D4—432no—
169C22×D4—431no—
170C22×D4—431no—
171C22×D4—861no—
172C22×D4—862no—
173AGL(1,ℤ/8)—864no—
174C2×SD16—432no—
175C2×D8—432no—
176C2×D8—434no—
177C2×D8—864no—
178C2×M16—431no—
179C22×C8C2×D4311yescharacteristic, complemented
180#127—861no—
181#124—861no—
182#121—434no—
183#120—862no—
184#117C2×D4311yescharacteristic, complemented
185#103C2×D4312yescomplemented
186#102—434no—
187#102C2×D4312yescomplemented
188C22⋊C8—434no—
189C24—862no—
190C24—861no—
191C24—861no—
192#41—22no—
193#41—868no—
194#41—864no—
195#41—864no—
196#41—862no—
197#41—862no—
198#41D17214yescomplemented
199C2×Q8—431no—
200C2×Q8C22×D4311yescharacteristic
201C2×D4—21no—
202C2×D4—432no—
203C2×D4—434no—
204C2×D4—431no—
205C2×D4—432no—
206C2×D4—432no—
207C2×D4—862no—
208C2×D4—868no—
209C2×D4—864no—
210C2×D4—862no—
211C2×D4—864no—
212C2×D4—8616no—
213C2×D4—864no—
214C2×D4—862no—
215C2×D4—862no—
216C2×D4—861no—
217C2×D4—862no—
218C2×D4—861no—
219C2×D4C22×D4311yescharacteristic
220C22×C4—21no—
221C22×C4—432no—
222C22×C4—862no—
223C22×C4C22×D4311yescharacteristic
224SD16—864no—
225D8—868no—
226D8—864no—
227M16—862no—
228C2×C8—22no—
229C2×C8—432no—
230C2×C8C22×D4312yes—
231C4⋊C4C22×D4312yes—
232C22⋊C4—21no—
233C22⋊C4—864no—
234C42—21no—
235C23—21no—
236C23—432no—
237C23—868no—
238C23—864no—
239C23—862no—
240C23—862no—
241C23—3442no—
242C23—3442no—
243C23—3444no—
244C23—1722no—
245C23D4×D4311yescharacteristic
246Q8—21no—
247Q8—862no—
248Q8C2×D17212yes—
249D4—24no—
250D4—21no—
251D4—434no—
252D4—868no—
253D4—868no—
254D4—864no—
255D4—864no—
256D4—862no—
257D4—862no—
258D4—862no—
259D4—862no—
260D4—3444no—
261D4—1722no—
262D4C2×D17212yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—432no—
267C2×C4—868no—
268C2×C4—862no—
269C2×C4—862no—
270C2×C4C2×D17212yes—
271C2×C4D4×D4311yescharacteristic
272C2×C4D4×D4312yes—
273C2×C4C23×D4311yescharacteristic
274C8—22no—
275C8—862no—
276C22—22no—
277C22—22no—
278C22—42no—
279C22—864no—
280C22—862no—
281C22—864no—
282C22—3444no—
283C22—3444no—
284C22—3448no—
285C22—1722no—
286C22—1724no—
287C22—1724no—
288C22#1306329512yes—
289C22C2×D4×D4311yescharacteristic
290C4—22no—
291C4—42no—
292C4—862no—
293C4#1306329512yes—
294C4C2×D4×D4311yescharacteristic
295C4C22×D17211yescharacteristic
296C2—22no—
297C2—42no—
298C2—3442no—
299C2—1722no—
300C2—1724no—
301C2C2×#1306329511yescharacteristic
302C2#1458370112yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#416C2
socleC22×C43C22×D4
hypercenter#416D43
hypocenterC43#3008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. C2×#13063350C2semidirect
3. C22×D344C2semidirect
4. #14583468C2semidirect
5. #14583047C2semidirect
6. #14583034C2semidirect
7. #14582903C2semidirect
8. #14582865C2semidirect
9. C43×#416C2semidirect
12. C2×#10621902C22semidirect
17. C22×D172C22semidirect
19. C2×D4×D43C22semidirect
21. C2×#10621884C22semidirect
23. C2×D344C22semidirect
24. C2×#10621882C22semidirect
25. C2×#10621877C22semidirect
28. #13063300C22semidirect
30. #13063245C22semidirect
31. (C2×D43)⋊C8C22semidirect
33. C22×C8×C43C22semidirect
34. #117×C43C22semidirect
35. #103×C43C22semidirect
36. #102×C43C22semidirect
41. #41×C43D4semidirect
66. C2×D172D4semidirect
159. #416D43semidirect
161. C43#3008semidirect
179. C22×C8C2×D43semidirect
184. #117C2×D43semidirect
185. #103C2×D43semidirect
187. #102C2×D43semidirect
198. #41D172semidirect