Finite Group Databasebeta

← #19145689

Subgroups — #19145689

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#14583520C211yesmaximal, characteristic, complemented
2#14583286C211yesmaximal, characteristic, complemented
3#14583281C211yesmaximal, characteristic, complemented
4#14583258C211yesmaximal, characteristic, complemented
5#14583245C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583111C211yesmaximal, characteristic, complemented
8#14583096C211yesmaximal, characteristic, complemented
9#14583091C211yesmaximal, characteristic, complemented
10#14583061C211yesmaximal, characteristic, complemented
11#14583050C211yesmaximal, characteristic, complemented
12#14583044C211yesmaximal, characteristic, complemented
13#14583033C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#535C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic, complemented
17C2×#10621883C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic, complemented
20C2×#10621884C2211yescharacteristic, complemented
21C2×#10621882C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621882C2211yescharacteristic, complemented
24#13063325C2211yescharacteristic, complemented
25#13063320—21no—
26#13063313C2211yescharacteristic, complemented
27#13063311—21no—
28#13063307—21no—
29#13063304C2211yescharacteristic
30#13063303—21no—
31#13063299C2211yescharacteristic
32C4×Dic86C2211yescharacteristic, complemented
33C4×D172C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35C4⋊(C43⋊C8)C2211yescharacteristic, complemented
36#13063249C2211yescharacteristic, complemented
37#13063249C2211yescharacteristic, complemented
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic, complemented
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic, complemented
47C4×C43⋊C8C2211yescharacteristic, complemented
48C2×#41×C43C2211yescharacteristic
49C22×D4×C43C2211yescharacteristic
50#127×C43C2211yescharacteristic
51#127×C43C2211yescharacteristic
52#124×C43C2211yescharacteristic
53#124×C43C2211yescharacteristic
54#121×C43—21no—
55#121×C43—21no—
56#120×C43—21no—
57#120×C43—21no—
58#117×C43C2211yescharacteristic
59C24×C43—21no—
60#41×C43—41no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43C2311yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C2×D4×C43C2311yescharacteristic
74C22×C4×C43—21no—
75C22×C4×C43C2311yescharacteristic
76C2×C22⋊D43—21no—
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×Dic86—21no—
80C2×Dic86C2311yescharacteristic
81C4⋊C4×C43D411yescharacteristic
82C4⋊C4×C43D411yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43C2311yescharacteristic
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92#10621885—41no—
93#10621884—41no—
94#10621883—41no—
95#10621883—41no—
96#10621883—41no—
97#10621882—41no—
98#10621882—41no—
99#10621882—41no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109C4×Dic43—21no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—42no—
118C23×C43—81no—
119C23×C43—81no—
120C23×C43C2×D411yescharacteristic
121C22×D43—21no—
122Q8×C43—21no—
123Q8×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—21no—
130D4×C43—42no—
131D4×C43—42no—
132D4×C43—81no—
133D4×C43—81no—
134D4×C43—81no—
135D4×C43—81no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—42no—
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2×D411yescharacteristic
142C2×C4×C43C2×D411yescharacteristic
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2411yescharacteristic
146C22⋊D43—81no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150D172—21no—
151D172—21no—
152C4×D43—81no—
153Dic86—21no—
154Dic86—21no—
155Dic86—81no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—84no—
173C22×C43C22×D411yescharacteristic
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—41no—
183C4×C43H(5,𝔽2)11yescharacteristic
184C4×C43H(5,𝔽2)11yescharacteristic
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#3224—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43—81no—
191C2×C43—81no—
192C2×C43—81no—
193C2×C43#53511yescharacteristic
194C2×C43#57611yescharacteristic
195C2×C43#57711yescharacteristic
196D43—81no—
197#542—431no—
198#535D4311yescharacteristic, complemented
199#496—431no—
200#495—431no—
201#489—431no—
202#486—431no—
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×#41C2×D4311yescharacteristic
214C22×D4C2×D4311yescharacteristic
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⋊Q8—431no—
224#127C2×D4311yescharacteristic
225#127C2×D4311yescharacteristic
226#126—861no—
227#124—431no—
228#124—861no—
229#124C2×D4311yescharacteristic
230#124C2×D4311yescharacteristic
231#123—861no—
232C22⋊Q8—431no—
233C22⋊Q8—861no—
234#121—21no—
235#121—21no—
236#121—431no—
237#120—21no—
238#120—21no—
239C4×Q8—431no—
240C4×D4—431no—
241#117C2×D4311yescharacteristic
242C4⋊C8—431no—
243C4⋊C8—431no—
244#103—431no—
245#103—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252C22⋊C8—431no—
253C22⋊C8—431no—
254#97—431no—
255C4×C8—431no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—431no—
260C2×Q8—861no—
261C2×Q8C22×D4311yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—431no—
271C2×D4—861no—
272C2×D4C22×D4311yescharacteristic
273C2×D4C22×D4311yescharacteristic
274C2×D4C22×D4311yescharacteristic
275C22×C4—21no—
276C22×C4—861no—
277C22×C4C22×D4311yescharacteristic
278Q16—1721no—
279SD16—1721no—
280SD16—1721no—
281SD16—1721no—
282SD16—1721no—
283D8—1721no—
284D8—1721no—
285D8—1721no—
286C2×C8—431no—
287C2×C8—431no—
288C2×C8—431no—
289C2×C8—431no—
290C4⋊C4—431no—
291C4⋊C4—431no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4C22⋊D4311yescharacteristic
296C4⋊C4C22⋊D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4C22⋊D4311yescharacteristic
307C22⋊C4C22⋊D4311yescharacteristic
308C42—861no—
309C42C22×D4311yescharacteristic
310C42C22×D4311yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—861no—
318C23C2×C22⋊D4311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—861no—
322Q8—861no—
323Q8—3441no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—861no—
337D4—861no—
338D4—3441no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—3441no—
347C2×C4C2×C22⋊D4311yescharacteristic
348C2×C4C2×C22⋊D4311yescharacteristic
349C2×C4C2×C22⋊D4311yescharacteristic
350C2×C4C2×C22⋊D4311yescharacteristic
351C2×C4C2×C22⋊D4311yescharacteristic
352C2×C4C23×D4311yescharacteristic
353C8—861no—
354C8—861no—
355C8—861no—
356C8—861no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C22×C22⋊D4311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1306337011yescharacteristic
384C4#1306337011yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—3441no—
390C2#1458346611yescharacteristic
391C2#1458370211yescharacteristic
392C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#535C2
socleC22×C43C22×D4
hypercenter#535D43
hypocenterC43#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583286C2semidirect
3. #14583281C2semidirect
4. #14583258C2semidirect
5. #14583245C2semidirect
6. #14583118C2semidirect
7. #14583111C2semidirect
8. #14583096C2semidirect
9. #14583091C2semidirect
10. #14583061C2semidirect
11. #14583050C2semidirect
12. #14583044C2semidirect
13. #14583033C2semidirect
14. #14582960C2semidirect
15. C43×#535C2semidirect
16. C2×#10621885C22semidirect
19. C2×#10621883C22semidirect
20. C2×#10621884C22semidirect
23. C2×#10621882C22semidirect
24. #13063325C22semidirect
26. #13063313C22semidirect
32. C4×Dic86C22semidirect
33. C4×D172C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. C4⋊(C43⋊C8)C22semidirect
36. #13063249C22semidirect
37. #13063249C22semidirect
42. #13063246C22semidirect
43. #13063246C22semidirect
46. #13063236C22semidirect
47. C4×C43⋊C8C22semidirect
198. #535D43semidirect
212. C43#3224semidirect