Finite Group Databasebeta

← #19145686

Subgroups — #19145686

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#14583514C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic, complemented
3#14583287C211yesmaximal, characteristic, complemented
4#14583282C211yesmaximal, characteristic, complemented
5#14583257C211yesmaximal, characteristic, complemented
6#14583244C211yesmaximal, characteristic, complemented
7#14583122C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583096C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583051C211yesmaximal, characteristic, complemented
12#14583041C211yesmaximal, characteristic, complemented
13#14583031C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621883C2211yescharacteristic, complemented
22C2×#10621883C2211yescharacteristic, complemented
23C2×#10621882C2211yescharacteristic
24#13063324C2211yescharacteristic, complemented
25#13063321C2211yescharacteristic
26#13063318—21no—
27#13063313C2211yescharacteristic
28#13063312C2211yescharacteristic
29#13063312C2211yescharacteristic, complemented
30#13063311—21no—
31#13063308—21no—
32#13063305C2211yescharacteristic
33#13063304—21no—
34#13063297—21no—
35#13063297—21no—
36#13063296C2211yescharacteristic
37#13063293—21no—
38#13063293—21no—
39C4×Dic86C2211yescharacteristic, complemented
40#13063282C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×D8×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic, complemented
54#127×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C22×Dic43—21no—
72#10621900—41no—
73#10621900—41no—
74D4×D43—41no—
75D4×D43—41no—
76C2×D172C2311yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79C2×Dic86C2311yescharacteristic
80C2×Dic86C2311yescharacteristic
81D8×C43—41no—
82D8×C43—41no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93#10621883—41no—
94#10621883—41no—
95#10621883—41no—
96#10621882—41no—
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—
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4D411yescharacteristic
107Dic43⋊C4D411yescharacteristic
108C4×Dic43—21no—
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112Dic172—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C22×D43—21no—
118C22×D43—42no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43C2×D411yescharacteristic
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—81no—
129D4×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—81no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—42no—
136C22⋊D43—42no—
137C22⋊D43—81no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—42no—
144C2×Dic43C2×D411yescharacteristic
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147D172—21no—
148D172—21no—
149C4×D43—21no—
150C4×D43—21no—
151Dic86—21no—
152Dic86—21no—
153Dic86—21no—
154Dic86—21no—
155Dic86—81no—
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×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43C22×D411yescharacteristic
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—84no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43H(5,𝔽2)11yescharacteristic
181C4×C43H(5,𝔽2)11yescharacteristic
182Dic43—21no—
183Dic43—21no—
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#3224—431nomaximal, Sylow
189C2×C43—81no—
190C2×C43—81no—
191C2×C43—81no—
192C2×C43#53511yescharacteristic
193C2×C43#57611yescharacteristic
194C2×C43#57711yescharacteristic
195D43—41no—
196D43—81no—
197#542—431no—
198#535—431no—
199#496—431no—
200#495—431no—
201#489—431no—
202#486—431no—
203#464—431no—
204#463—431no—
205#460—431no—
206#459D4311yescharacteristic, complemented
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×D8C2×D4311yescharacteristic
222C2×D8C2×D4311yescharacteristic, complemented
223C4⋊Q8—431no—
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×D4C2×D4311yescharacteristic, complemented
241#117—431no—
242C4⋊C8—431no—
243C4⋊C8C2×D4311yescharacteristic, complemented
244#103—431no—
245#103—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102C2×D4311yescharacteristic
251#102C2×D4311yescharacteristic, complemented
252C22⋊C8—431no—
253C22⋊C8—431no—
254#97—431no—
255C4×C8—431no—
256C24—861no—
257#41—1721no—
258#41—1721no—
259C2×Q8—431no—
260C2×Q8—431no—
261C2×Q8—861no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—431no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4C22×D4311yescharacteristic
273C2×D4C22×D4311yescharacteristic
274C2×D4C22×D4311yescharacteristic
275C22×C4—21no—
276C22×C4—431no—
277C22×C4—861no—
278Q16—1721no—
279SD16—1721no—
280SD16—1721no—
281SD16—1721no—
282SD16—1721no—
283D8—41no—
284D8—41no—
285D8—1721no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8C22×D4311yescharacteristic
289C2×C8C22×D4311yescharacteristic
290C4⋊C4—431no—
291C4⋊C4—431no—
292C4⋊C4—431no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—431no—
299C22⋊C4—431no—
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—21no—
314C23—431no—
315C23—861no—
316C23—3441no—
317C23—3441no—
318C23—1722no—
319Q8—861no—
320Q8—861no—
321Q8—861no—
322Q8—861no—
323Q8—3441no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—861no—
333D4—861no—
334D4—3441no—
335D4—3441no—
336D4—3441no—
337D4—1722no—
338D4—1722no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—431no—
342C2×C4—431no—
343C2×C4—431no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
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—41no—
364C22—41no—
365C22—41no—
366C22—861no—
367C22—861no—
368C22—861no—
369C22—3444no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C2×D4×D4311yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—861no—
378C4—861no—
379C4—861no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1306337011yescharacteristic
384C4#1306337111yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—3441no—
389C2—1721no—
390C2#1458346511yescharacteristic
391C2#1458370011yescharacteristic
392C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14583514C2semidirect
2. #14583462C2semidirect
3. #14583287C2semidirect
4. #14583282C2semidirect
5. #14583257C2semidirect
6. #14583244C2semidirect
7. #14583122C2semidirect
8. #14583114C2semidirect
9. #14583096C2semidirect
10. #14583062C2semidirect
11. #14583051C2semidirect
12. #14583041C2semidirect
13. #14583031C2semidirect
14. #14582959C2semidirect
15. C43×#459C2semidirect
18. C2×Dic172C22semidirect
21. C2×#10621883C22semidirect
22. C2×#10621883C22semidirect
24. #13063324C22semidirect
29. #13063312C22semidirect
39. C4×Dic86C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
46. #13063246C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
53. C2×D8×C43C22semidirect
55. C4×D4×C43C22semidirect
56. C4⋊C8×C43C22semidirect
58. #102×C43C22semidirect
206. #459D43semidirect
212. C43#3224semidirect
222. C2×D8C2×D43semidirect
240. C4×D4C2×D43semidirect
243. C4⋊C8C2×D43semidirect
251. #102C2×D43semidirect