Finite Group Databasebeta

← #19146414

Subgroups — #19146414

Order 5504.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic, complemented
2#14583533C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583219C211yesmaximal, characteristic, complemented
5#14583215C211yesmaximal, characteristic, complemented
6#14583188C211yesmaximal, characteristic, complemented
7#14583131C211yesmaximal, characteristic, complemented
8#14583097C211yesmaximal, characteristic, complemented
9#14583049C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11#14582984C211yesmaximal, characteristic, complemented
12C8×C22⋊D43C211yesmaximal, characteristic, complemented
13C2×#13063247C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C2×D4×D43—21no—
18C2×D4×D43C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic, complemented
21C2×C8×D43C2211yescharacteristic, complemented
22#13063324C2211yescharacteristic, complemented
23#13063321C2211yescharacteristic
24#13063315—21no—
25#13063305—21no—
26#13063302—21no—
27#13063301C2211yescharacteristic, complemented
28#13063300C2211yescharacteristic
29#13063298—21no—
30#13063295—21no—
31#13063293—21no—
32Q8×Dic43C2211yescharacteristic, complemented
33#13063287C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36C2×C4⋊Dic43C2211yescharacteristic, complemented
37C4⋊C4×D43C2211yescharacteristic, complemented
38#13063256C2211yescharacteristic, complemented
39#13063256C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063247C2211yescharacteristic
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43C2211yescharacteristic, complemented
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43—21no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69C22×Dic43—21no—
70D4×D43—22no—
71D4×D43—41no—
72D4×D43—44no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—22no—
76C2×D172—41no—
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—21no—
83SD16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊Dic43D411yescharacteristic
93#10621884—22no—
94#10621884—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4D411yescharacteristic
107C4×Dic43—21no—
108C4×Dic43C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C8×D43—41no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43C2×D411yescharacteristic
123Q8×C43—21no—
124Q8×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—42no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—42no—
136C22⋊D43—42no—
137C22⋊D43—81no—
138C22⋊D43SD1614yescomplemented
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—81no—
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145D172—21no—
146D172—21no—
147D172—21no—
148D172—42no—
149D172—42no—
150D172#4112yes—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—42no—
154C4×D43—81no—
155Dic86—81no—
156C8×C43—21no—
157C8×C43—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43C2×SD1612yes—
166C22×C43C22×D411yescharacteristic
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—22no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—84no—
176C2×D43—84no—
177C2×D43C2×SD1612yes—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43C2×#4111yescharacteristic
183C4×C43H(5,𝔽2)11yescharacteristic
184Dic43—21no—
185Dic43—21no—
186Dic43—41no—
187Dic43—41no—
188Dic43C2×SD1612yes—
189#3295—431nomaximal, Sylow
190C2×C43—22no—
191C2×C43—81no—
192C2×C43#54611yescharacteristic
193C2×C43C22×SD1611yescharacteristic
194C2×C43#57611yescharacteristic
195D43—22no—
196D43—42no—
197D43—81no—
198#554—431no—
199D42—431no—
200#486—431no—
201#481—431no—
202#481—431no—
203#476—431no—
204#465—431no—
205#465D4311yescharacteristic, complemented
206#460—431no—
207#450—431no—
208#450—431no—
209C4×SD16—431no—
210C8×D4—431no—
211C2×#102—431no—
212C2×#102—431no—
213C43#329511yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C22×D4—431no—
216C22×D4—861no—
217C2×SD16—431no—
218C2×SD16—431no—
219C2×SD16C2×D4311yescharacteristic, complemented
220C22×C8—431no—
221C22×C8C2×D4311yescharacteristic, complemented
222C4⋊Q8—431no—
223#127—431no—
224#125—861no—
225C22⋊Q8—431no—
226C22⋊Q8—861no—
227C22⋊Q8—861no—
228C22⋊Q8C2×D4311yescharacteristic, complemented
229#121—431no—
230#121—861no—
231#121C2×D4311yescharacteristic
232#120—861no—
233#120—861no—
234C4×Q8—431no—
235C4×D4—431no—
236C4×D4—431no—
237C4×D4—861no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240#106—431no—
241#106—431no—
242#106C2×D4311yescharacteristic, complemented
243C4⋊C8—431no—
244#103C2×D4311yescharacteristic, complemented
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252#102—431no—
253#102C2×D4311yescharacteristic, complemented
254C22⋊C8—431no—
255C22⋊C8—431no—
256C4×C8—431no—
257C24—861no—
258C24—861no—
259C2×Q8—861no—
260C2×Q8C22×D4311yescharacteristic
261C2×D4—21no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—862no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—862no—
271C2×D4—861no—
272C2×D4—1721no—
273C2×D4—1721no—
274C2×D4—1724no—
275C2×D4C22×D4311yescharacteristic
276C22×C4—431no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4C22×D4311yescharacteristic
281SD16—41no—
282SD16—862no—
283SD16—1721no—
284C2×C8—41no—
285C2×C8—431no—
286C2×C8—431no—
287C2×C8—1721no—
288C2×C8C22×D4311yescharacteristic
289C2×C8C22×D4311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—431no—
292C4⋊C4—431no—
293C4⋊C4—431no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4C22×D4311yescharacteristic
300C4⋊C4C22×D4311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—431no—
304C22⋊C4—431no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C42—431no—
309C42—861no—
310C23—21no—
311C23—431no—
312C23—861no—
313C23—861no—
314C23—3441no—
315C23—3441no—
316C23—1722no—
317C23—1722no—
318C23—1722no—
319C23—1722no—
320C23D4×D4311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—3441no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—434no—
328D4—432no—
329D4—861no—
330D4—861no—
331D4—861no—
332D4—3441no—
333D4—1722no—
334D4—1722no—
335D4—1722no—
336D4—1722no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—431no—
343C2×C4—431no—
344C2×C4—431no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—1722no—
352C2×C4D4×D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—21no—
355C8—21no—
356C8—861no—
357C8—861no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—432no—
364C22—861no—
365C22—861no—
366C22—862no—
367C22—3444no—
368C22—3444no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22SD16×D4312yes—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—432no—
381C4—861no—
382C4—861no—
383C4—1721no—
384C4—1721no—
385C4#41×D4311yescharacteristic
386C4#1306337011yescharacteristic
387C2—22no—
388C2—81no—
389C2—862no—
390C2—3441no—
391C2—1722no—
392C2#1458353811yescharacteristic
393C2C2×SD16×D4311yescharacteristic
394C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3295
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14583607C2semidirect
3. #14583244C2semidirect
4. #14583219C2semidirect
5. #14583215C2semidirect
6. #14583188C2semidirect
7. #14583131C2semidirect
8. #14583097C2semidirect
9. #14583049C2semidirect
10. #14583048C2semidirect
11. #14582984C2semidirect
12. C8×C22⋊D43C2semidirect
13. C2×#13063247C2semidirect
14. #102×D43C2semidirect
15. C43×#465C2semidirect
20. C2×#10621884C22semidirect
21. C2×C8×D43C22semidirect
22. #13063324C22semidirect
27. #13063301C22semidirect
32. Q8×Dic43C22semidirect
36. C2×C4⋊Dic43C22semidirect
37. C4⋊C4×D43C22semidirect
38. #13063256C22semidirect
39. #13063256C22semidirect
40. Dic43⋊C8C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
45. #13063246C22semidirect
46. #13063246C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
52. C2×SD16×C43C22semidirect
53. C22×C8×C43C22semidirect
54. C22⋊Q8×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
138. C22⋊D43SD16semidirect
205. #465D43semidirect
213. C43#3295semidirect
219. C2×SD16C2×D43semidirect
221. C22×C8C2×D43semidirect
228. C22⋊Q8C2×D43semidirect
242. #106C2×D43semidirect
244. #103C2×D43semidirect
253. #102C2×D43semidirect