Finite Group Databasebeta

← #19145692

Subgroups — #19145692

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583523C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic, complemented
3#14583286C211yesmaximal, characteristic, complemented
4#14583283C211yesmaximal, characteristic, complemented
5#14583261C211yesmaximal, characteristic, complemented
6#14583120C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583098C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583051C211yesmaximal, characteristic, complemented
12#14583045C211yesmaximal, characteristic, complemented
13#14583034C211yesmaximal, characteristic, complemented
14#14582958C211yesmaximal, characteristic, complemented
15C43×#486C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic
22C2×#10621883C2211yescharacteristic, complemented
23C2×D344C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25C2×#10621882C2211yescharacteristic, complemented
26#13063321C2211yescharacteristic
27#13063320—21no—
28#13063314—21no—
29#13063313C2211yescharacteristic
30#13063313C2211yescharacteristic, complemented
31#13063312C2211yescharacteristic
32#13063310—21no—
33#13063305C2211yescharacteristic
34#13063301—21no—
35#13063300C2211yescharacteristic
36#13063297—21no—
37#13063297—21no—
38#13063293—21no—
39#13063293—21no—
40#13063290C2211yescharacteristic, complemented
41#13063287C2211yescharacteristic, complemented
42#13063282C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic, complemented
44Dic43⋊C8C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063248C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic, complemented
52C4⋊Q8×C43C2211yescharacteristic, complemented
53#127×C43C2211yescharacteristic
54#102×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43—21no—
70#10621900—41no—
71#10621900—41no—
72D4×D43—41no—
73D4×D43—41no—
74C2×D172—21no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86C2311yescharacteristic
80C2×Dic86C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621883—41no—
90#10621883—41no—
91#10621882—41no—
92#10621882—41no—
93(C2×D43)⋊C4—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)⋊C4D411yescharacteristic
101(C2×D43)⋊C4D411yescharacteristic
102C4⋊Dic43—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110Dic172—41no—
111D344—41no—
112#10621873—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—42no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43C2×D411yescharacteristic
122Q8×C43—81no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—81no—
128D4×C43—81no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—42no—
136C22⋊D43—81no—
137C22⋊D43—81no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—42no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—81no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—81no—
152Dic86—21no—
153Dic86—21no—
154Dic86—21no—
155Dic86—21no—
156C8×C43—21no—
157C8×C43—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43C22×D411yescharacteristic
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—84no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43H(5,𝔽2)11yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—21no—
184Dic43—21no—
185Dic43—21no—
186Dic43—41no—
187Dic43—41no—
188#3224—431nomaximal, Sylow
189C2×C43—81no—
190C2×C43—81no—
191C2×C43#53511yescharacteristic
192C2×C43#57611yescharacteristic
193C2×C43#57711yescharacteristic
194D43—41no—
195D43—81no—
196D43—81no—
197#542—431no—
198#535—431no—
199#496—431no—
200#495—431no—
201#489—431no—
202#486D4311yescharacteristic, complemented
203#464—431no—
204#463—431no—
205#460—431no—
206#459—431no—
207#452—431no—
208#450—431no—
209#449—431no—
210#447—431no—
211#433—431no—
212C43#322411yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C22×D4—431no—
215C2×Q16—431no—
216C2×SD16—431no—
217C2×SD16—431no—
218C2×SD16—431no—
219C2×SD16—431no—
220C2×D8—431no—
221C2×D8—431no—
222C2×D8—431no—
223C4⋊Q8C2×D4311yescharacteristic, complemented
224#127—431no—
225#127C2×D4311yescharacteristic
226#126—861no—
227#124—431no—
228#124—431no—
229#124—431no—
230#124—861no—
231#123—861no—
232C22⋊Q8—431no—
233C22⋊Q8—861no—
234#121—431no—
235#121—861no—
236#121—861no—
237#120—861no—
238#120—861no—
239C4×Q8—431no—
240C4×D4—431no—
241#117—431no—
242C4⋊C8—431no—
243C4⋊C8—431no—
244#103—431no—
245#103—431no—
246#102—431no—
247#102—431no—
248#102C2×D4311yescharacteristic
249#102C2×D4311yescharacteristic
250#102C2×D4311yescharacteristic, complemented
251#102C2×D4311yescharacteristic, complemented
252C22⋊C8—431no—
253C22⋊C8—431no—
254#97—431no—
255C4×C8C2×D4311yescharacteristic, complemented
256C24—861no—
257#41—1721no—
258#41—1721no—
259C2×Q8—21no—
260C2×Q8—431no—
261C2×Q8—431no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—1721no—
272C2×D4—1721no—
273C2×D4C22×D4311yescharacteristic
274C2×D4C22×D4311yescharacteristic
275C22×C4—431no—
276C22×C4—861no—
277C22×C4—861no—
278Q16—1721no—
279SD16—1721no—
280SD16—1721no—
281SD16—1721no—
282SD16—1721no—
283D8—1721no—
284D8—1721no—
285D8—1721no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8C22×D4311yescharacteristic
289C2×C8C22×D4311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—431no—
292C4⋊C4—431no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4C22×D4311yescharacteristic
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—431no—
298C22⋊C4—431no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C42—431no—
309C42—861no—
310C42C22×D4311yescharacteristic
311C23—21no—
312C23—21no—
313C23—431no—
314C23—861no—
315C23—861no—
316C23—3441no—
317C23—3441no—
318C23—1722no—
319Q8—81no—
320Q8—861no—
321Q8—861no—
322Q8—861no—
323Q8—861no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—81no—
330D4—861no—
331D4—861no—
332D4—861no—
333D4—861no—
334D4—3441no—
335D4—3441no—
336D4—3441no—
337D4—1722no—
338D4—1722no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—431no—
342C2×C4—431no—
343C2×C4—431no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—3441no—
349C2×C4—1722no—
350C2×C4D4×D4311yescharacteristic
351C2×C4D4×D4311yescharacteristic
352C2×C4C23×D4311yescharacteristic
353C8—21no—
354C8—21no—
355C8—861no—
356C8—861no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—861no—
364C22—861no—
365C22—861no—
366C22—3444no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C2×D4×D4311yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—861no—
379C4—861no—
380C4—861no—
381C4—1721no—
382C4—1721no—
383C4#1306337111yescharacteristic
384C4#1306337111yescharacteristic
385C2—81no—
386C2—81no—
387C2—3441no—
388C2—3441no—
389C2—1721no—
390C2#1458346711yescharacteristic
391C2#1458370011yescharacteristic
392C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14583523C2semidirect
2. #14583462C2semidirect
3. #14583286C2semidirect
4. #14583283C2semidirect
5. #14583261C2semidirect
6. #14583120C2semidirect
7. #14583113C2semidirect
8. #14583098C2semidirect
9. #14583093C2semidirect
10. #14583062C2semidirect
11. #14583051C2semidirect
12. #14583045C2semidirect
13. #14583034C2semidirect
14. #14582958C2semidirect
15. C43×#486C2semidirect
18. C2×Dic172C22semidirect
20. C2×#10621873C22semidirect
22. C2×#10621883C22semidirect
25. C2×#10621882C22semidirect
30. #13063313C22semidirect
40. #13063290C22semidirect
41. #13063287C22semidirect
43. Dic43⋊C8C22semidirect
44. Dic43⋊C8C22semidirect
45. #13063248C22semidirect
46. #13063248C22semidirect
51. #13063236C22semidirect
52. C4⋊Q8×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
58. C4×C8×C43C22semidirect
202. #486D43semidirect
212. C43#3224semidirect
223. C4⋊Q8C2×D43semidirect
250. #102C2×D43semidirect
251. #102C2×D43semidirect
255. C4×C8C2×D43semidirect