Finite Group Databasebeta

← #19146558

Subgroups — #19146558

Order 5504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583553C211yesmaximal, characteristic, complemented
2#14583545C211yesmaximal, characteristic, complemented
3#14583259C211yesmaximal, characteristic, complemented
4#14583230C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583190C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583128C211yesmaximal, characteristic, complemented
9#14583115C211yesmaximal, characteristic, complemented
10#14583046C211yesmaximal, characteristic, complemented
11#14583035C211yesmaximal, characteristic, complemented
12#14583012C211yesmaximal, characteristic, complemented
13#14582901C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900—21no—
18C22×D172C2211yescharacteristic
19C2×#10621873C2211yescharacteristic, complemented
20C2×D344C2211yescharacteristic
21C2×D344C2211yescharacteristic
22#13063325C2211yescharacteristic, complemented
23#13063313C2211yescharacteristic
24#13063310—21no—
25#13063309—21no—
26#13063309—21no—
27#13063305—21no—
28#13063304C2211yescharacteristic
29#13063299C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063299C2211yescharacteristic, complemented
32#13063298—21no—
33#13063293—21no—
34C4×D172C2211yescharacteristic
35C4×D172C2211yescharacteristic, complemented
36C2×C4⋊Dic43C2211yescharacteristic
37C2×C4⋊Dic43C2211yescharacteristic, complemented
38C22⋊C4×D43—21no—
39#13063257C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic, complemented
52C2×M16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic, complemented
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic, complemented
58#97×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43D411yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69#10621900—44no—
70#10621898—22no—
71#10621898—41no—
72C2×D172—21no—
73C2×D172—22no—
74C2×D172—41no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×Dic86—21no—
82C2×Dic86C2311yescharacteristic
83M16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C4⋊C4×C43D411yescharacteristic
90C22⋊C4×C43D411yescharacteristic
91C22⋊C4×C43D411yescharacteristic
92C42×C43C2311yescharacteristic
93C22⋊Dic43—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43C2311yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109D344—22no—
110D344—41no—
111#10621873—41no—
112C23×C43C2×D411yescharacteristic
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—81no—
120D4×C43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—42no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—21no—
145D172—21no—
146D172—42no—
147D172#4112yescomplemented
148C4×D43—42no—
149C4×D43—42no—
150C4×D43—81no—
151Dic86—21no—
152Dic86—21no—
153Dic86—42no—
154C8×C43—21no—
155C8×C43—21no—
156C8×C43—21no—
157C8×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43AGL(1,ℤ/8)12yes—
164C22×C43C22×D411yescharacteristic
165C2×D43—22no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—84no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43C2×#4111yescharacteristic
180C4×C43H(5,𝔽2)11yescharacteristic
181Dic43—41no—
182Dic43—41no—
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186#3306—431nomaximal, Sylow
187C2×C43—22no—
188C2×C43—41no—
189C2×C43#54611yescharacteristic
190C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C43#57711yescharacteristic
192D43—42no—
193D43—81no—
194D43—81no—
195#547—431no—
196#546—431no—
197#489—431no—
198#483—431no—
199#481—431no—
200#476—431no—
201#469—431no—
202#465—431no—
203#463—431no—
204#449—431no—
205#447—431no—
206#442—431no—
207#435D4311yescharacteristic, complemented
208#417—431no—
209C2×#102—431no—
210C43#330611yescharacteristic, complemented, Sylow
211C2×#41—431no—
212C2×#41—861no—
213C22×D4—431no—
214C2×SD16—431no—
215C2×D8—431no—
216C2×D8—431no—
217C2×M16C2×D4311yescharacteristic, complemented
218C22×C8C2×D4311yescharacteristic
219C4⋊Q8—431no—
220#124—431no—
221#123—861no—
222#123—861no—
223#123—861no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226#121—431no—
227#121—431no—
228#121—431no—
229#121—861no—
230#120—861no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4C2×D4311yescharacteristic
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C22⋊C4—861no—
237#106—431no—
238#106—431no—
239#106—431no—
240C4⋊C8C2×D4311yescharacteristic, complemented
241#103—431no—
242#103—431no—
243#103—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251C22⋊C8C2×D4311yescharacteristic
252C22⋊C8C2×D4311yescharacteristic, complemented
253#97C2×D4311yescharacteristic, complemented
254C24—861no—
255#41—862no—
256#41—1721no—
257#41—1724no—
258C2×Q8—431no—
259C2×Q8—861no—
260C2×D4—431no—
261C2×D4—431no—
262C2×D4—431no—
263C2×D4—862no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4D17211yescharacteristic
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4C22×D4311yescharacteristic
277C22×C4C22×D4311yescharacteristic
278SD16—1721no—
279D8—862no—
280D8—1721no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D4311yescharacteristic
284C2×C8C22×D4311yescharacteristic
285C2×C8C22×D4311yescharacteristic
286C2×C8C22×D4311yescharacteristic
287C4⋊C4—431no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4D17211yescharacteristic
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4D17211yescharacteristic
305C22⋊C4D17211yescharacteristic
306C42C22×D4311yescharacteristic
307C23—861no—
308C23—861no—
309C23—861no—
310C23—3441no—
311C23—1722no—
312C23—1722no—
313C23C2×D17211yescharacteristic
314C23C2×D17211yescharacteristic
315Q8—861no—
316Q8—861no—
317Q8—1722no—
318D4—22no—
319D4—432no—
320D4—861no—
321D4—861no—
322D4—861no—
323D4—861no—
324D4—861no—
325D4—3441no—
326D4—1722no—
327D4—1722no—
328D4—1722no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—3441no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4C2×D17211yescharacteristic
345C2×C4C2×D17211yescharacteristic
346C2×C4C2×D17211yescharacteristic
347C2×C4C2×D17211yescharacteristic
348C2×C4C23×D4311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—862no—
359C22—3444no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22#1306335312yes—
369C22C22×D17211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—1721no—
375C4—1721no—
376C4—1721no—
377C4—1721no—
378C4—1721no—
379C4#41×D4311yescharacteristic
380C4#1306337011yescharacteristic
381C2—22no—
382C2—41no—
383C2—3441no—
384C2—3441no—
385C2—1722no—
386C2#1458354411yescharacteristic
387C2C2×#1306335311yescharacteristic
388C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3306
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14583553C2semidirect
2. #14583545C2semidirect
3. #14583259C2semidirect
4. #14583230C2semidirect
5. #14583218C2semidirect
6. #14583190C2semidirect
7. #14583152C2semidirect
8. #14583128C2semidirect
9. #14583115C2semidirect
10. #14583046C2semidirect
11. #14583035C2semidirect
12. #14583012C2semidirect
13. #14582901C2semidirect
14. C2×#13063247C2semidirect
15. C43×#435C2semidirect
19. C2×#10621873C22semidirect
22. #13063325C22semidirect
31. #13063299C22semidirect
35. C4×D172C22semidirect
37. C2×C4⋊Dic43C22semidirect
39. #13063257C22semidirect
40. #13063257C22semidirect
41. #13063257C22semidirect
42. #13063250C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
51. #13063247C22semidirect
52. C2×M16×C43C22semidirect
55. C4⋊C8×C43C22semidirect
57. C22⋊C8×C43C22semidirect
58. #97×C43C22semidirect
147. D172#41semidirect
207. #435D43semidirect
210. C43#3306semidirect
217. C2×M16C2×D43semidirect
240. C4⋊C8C2×D43semidirect
252. C22⋊C8C2×D43semidirect
253. #97C2×D43semidirect