Finite Group Databasebeta

← #19145364

Subgroups — #19145364

Order 5504.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583411C211yesmaximal, characteristic, complemented
2#121×D43C211yesmaximal, characteristic, complemented
3#14583236C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583136C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583129C211yesmaximal, characteristic, complemented
9#14583127C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13#14583034C211yesmaximal, characteristic, complemented
14C22⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic, complemented
17C2×D4×D43—21no—
18C2×D4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×D344C2211yescharacteristic, complemented
23C2×#10621882C2211yescharacteristic, complemented
24C2×C8×D43C2211yescharacteristic, complemented
25C2×C8×D43C2211yescharacteristic, complemented
26#13063309—21no—
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic, complemented
29#13063300C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic, complemented
32#13063299C2211yescharacteristic
33#13063298—21no—
34#13063297—21no—
35#13063296C2211yescharacteristic
36#13063295—21no—
37C4×D172—21no—
38C4×D172—21no—
39C4⋊C4×D43C2211yescharacteristic
40C22⋊C4×D43—21no—
41#13063258C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43D411yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C22×Dic43D411yescharacteristic
69D4×D43—44no—
70D4×D43—41no—
71D4×D43—41no—
72#10621898—41no—
73#10621898—41no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43D411yescharacteristic
84C2×C4×D43D411yescharacteristic
85C2×C4×D43C2311yescharacteristic
86C2×C4×D43C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C2×C8×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C42×C43—21no—
96C22⋊Dic43—21no—
97#10621883—41no—
98#10621882—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111D344—41no—
112#10621873—41no—
113C8×D43—41no—
114C8×D43—41no—
115C23×C43—21no—
116C23×C43C2×D411yescharacteristic
117C22×D43—22no—
118C22×D43—22no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—41no—
122C22×D43—42no—
123C22×D43—42no—
124C22×D43—42no—
125C22×D43C2×D411yescharacteristic
126C22×D43C2×D411yescharacteristic
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—42no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—42no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—41no—
144C2×Dic43C2×D411yescharacteristic
145C2×Dic43C2×D411yescharacteristic
146D172—21no—
147D172—21no—
148D172—21no—
149D172—21no—
150D172—42no—
151D172—42no—
152D172—42no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—41no—
158C4×D43—41no—
159C4×D43—42no—
160C4×D43—42no—
161Dic86—21no—
162Dic86—21no—
163C8×C43—21no—
164C8×C43—21no—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43C22×D411yescharacteristic
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—44no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—84no—
186C2×D43#13512yes—
187C2×D43AGL(1,ℤ/8)12yes—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43H(5,𝔽2)11yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—21no—
195Dic43—21no—
196Dic43—41no—
197Dic43—41no—
198#3188—431nomaximal, Sylow
199C2×C43—41no—
200C2×C43—81no—
201C2×C43#53411yescharacteristic
202C2×C43C2×#13511yescharacteristic
203C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
204D43—22no—
205D43—22no—
206D43—81no—
207D43—81no—
208#525—431no—
209C2×#121—431no—
210#484—431no—
211#482—431no—
212#482D4311yescharacteristic, complemented
213#481—431no—
214#466—431no—
215#466—431no—
216#465—431no—
217#465—431no—
218#450—431no—
219#449—431no—
220#449—431no—
221#447—431no—
222C2×C22⋊C8—431no—
223C43#318811yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C22×D4—431no—
226C22×D4—861no—
227C23×C4—431no—
228C2×SD16—431no—
229C2×SD16—431no—
230C2×D8—431no—
231C2×D8—431no—
232C22×C8—431no—
233C22×C8—431no—
234#123—861no—
235C22⋊Q8—431no—
236C22⋊Q8—431no—
237#121—431no—
238#121—431no—
239#121—431no—
240#121—431no—
241#121—431no—
242#121—861no—
243#121—861no—
244#121C2×D4311yescharacteristic
245#120—861no—
246C4×D4—861no—
247C4×D4—861no—
248#117C2×D4311yescharacteristic, complemented
249C2×C4⋊C4—431no—
250C2×C22⋊C4—861no—
251#107—431no—
252#107C2×D4311yescharacteristic, complemented
253#106—431no—
254#106C2×D4311yescharacteristic, complemented
255#103—431no—
256#103—431no—
257#102—431no—
258#102—431no—
259#102—431no—
260#102—431no—
261#102C2×D4311yescharacteristic, complemented
262#102C2×D4311yescharacteristic, complemented
263C22⋊C8—431no—
264C22⋊C8—431no—
265C22⋊C8—431no—
266C22⋊C8C2×D4311yescharacteristic, complemented
267C24—431no—
268C24—861no—
269#41—1721no—
270#41—1721no—
271C2×Q8—431no—
272C2×D4—21no—
273C2×D4—431no—
274C2×D4—431no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—1721no—
283C2×D4—1721no—
284C2×D4—1724no—
285C2×D4C22×D4311yescharacteristic
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—1721no—
294C22×C4—1721no—
295C22×C4C22×D4311yescharacteristic
296SD16—1721no—
297SD16—1721no—
298D8—1721no—
299D8—1721no—
300C2×C8—431no—
301C2×C8—431no—
302C2×C8—1721no—
303C2×C8—1721no—
304C2×C8C22×D4311yescharacteristic
305C2×C8C22×D4311yescharacteristic
306C4⋊C4—431no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4C22×D4311yescharacteristic
311C4⋊C4C22×D4311yescharacteristic
312C4⋊C4C22×D4311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C42—21no—
323C23—21no—
324C23—431no—
325C23—431no—
326C23—862no—
327C23—862no—
328C23—861no—
329C23—861no—
330C23—1721no—
331C23—1722no—
332C23—1722no—
333C23—1722no—
334C23D4×D4311yescharacteristic
335Q8—861no—
336Q8—861no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—861no—
341D4—861no—
342D4—861no—
343D4—861no—
344D4—1722no—
345D4—1722no—
346D4—1722no—
347D4—1722no—
348D4—1722no—
349D4—1722no—
350D4—1722no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—431no—
357C2×C4—431no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1721no—
369C2×C4D4×D4311yescharacteristic
370C2×C4C23×D4311yescharacteristic
371C8—21no—
372C8—21no—
373C8—861no—
374C8—861no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—432no—
382C22—432no—
383C22—861no—
384C22—861no—
385C22—861no—
386C22—861no—
387C22—3444no—
388C22—1724no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C2×D4×D4311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—861no—
401C4—861no—
402C4—1721no—
403C4—1721no—
404C4#1306337111yescharacteristic
405C4#1306337111yescharacteristic
406C2—41no—
407C2—81no—
408C2—862no—
409C2—862no—
410C2—3441no—
411C2—3441no—
412C2#1458346011yescharacteristic
413C2#135×D4311yescharacteristic
414C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3188
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14583411C2semidirect
2. #121×D43C2semidirect
3. #14583236C2semidirect
4. #14583223C2semidirect
5. #14583219C2semidirect
6. #14583136C2semidirect
7. #14583134C2semidirect
8. #14583129C2semidirect
9. #14583127C2semidirect
10. #14583051C2semidirect
11. #14583046C2semidirect
12. #14583042C2semidirect
13. #14583034C2semidirect
14. C22⋊C8×D43C2semidirect
15. C43×#482C2semidirect
16. C2×#10621898C22semidirect
20. C2×#10621873C22semidirect
21. C2×#10621883C22semidirect
22. C2×D344C22semidirect
23. C2×#10621882C22semidirect
24. C2×C8×D43C22semidirect
25. C2×C8×D43C22semidirect
28. #13063305C22semidirect
31. #13063300C22semidirect
41. #13063258C22semidirect
42. #13063256C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
45. #13063247C22semidirect
46. #13063245C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
53. #117×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
58. C22⋊C8×C43C22semidirect
212. #482D43semidirect
223. C43#3188semidirect
248. #117C2×D43semidirect
252. #107C2×D43semidirect
254. #106C2×D43semidirect
261. #102C2×D43semidirect
262. #102C2×D43semidirect
266. C22⋊C8C2×D43semidirect