Finite Group Databasebeta

← #19145683

Subgroups — #19145683

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#14583468C211yesmaximal, characteristic, complemented
2#14583289C211yesmaximal, characteristic, complemented
3#14583281C211yesmaximal, characteristic, complemented
4#14583261C211yesmaximal, characteristic, complemented
5#14583247C211yesmaximal, characteristic, complemented
6#14583121C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583099C211yesmaximal, characteristic, complemented
9#14583094C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14583049C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13#14583032C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#542C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621883C2211yescharacteristic, complemented
20C2×#10621884C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×#10621884C2211yescharacteristic, complemented
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25C2×#10621882C2211yescharacteristic, complemented
26#13063322C2211yescharacteristic
27#13063322C2211yescharacteristic
28#13063313C2211yescharacteristic
29#13063313C2211yescharacteristic
30#13063300—21no—
31#13063300—21no—
32#13063295—21no—
33#13063295—21no—
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35C4⋊(C43⋊C8)C2211yescharacteristic, complemented
36#13063248C2211yescharacteristic, complemented
37#13063248C2211yescharacteristic, complemented
38#13063245C2211yescharacteristic
39#13063245C2211yescharacteristic
40#13063245C2211yescharacteristic
41#13063245C2211yescharacteristic
42#13063245C2211yescharacteristic, complemented
43#13063245C2211yescharacteristic, complemented
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic, complemented
47C4×C43⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C43C2211yescharacteristic, complemented
49#126×C43—21no—
50#124×C43—21no—
51#124×C43C2211yescharacteristic, complemented
52#123×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic, complemented
57C4×D4×C43C2211yescharacteristic, complemented
58#117×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43—21no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67#10621898—41no—
68#10621898—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×Dic86C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43D411yescharacteristic
85C4⋊C4×C43D411yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43D411yescharacteristic
94C22⋊C4×C43D411yescharacteristic
95C42×C43—21no—
96C42×C43C2311yescharacteristic
97C42×C43C2311yescharacteristic
98#10621885—41no—
99#10621884—41no—
100#10621884—41no—
101#10621884—41no—
102#10621883—41no—
103#10621882—41no—
104#10621882—41no—
105#10621882—41no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122Q8×C43—21no—
123Q8×C43—21no—
124Q8×C43—81no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—81no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—81no—
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2411yescharacteristic
140C22⋊D43—42no—
141C2×Dic43—21no—
142D172—21no—
143D172—21no—
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—42no—
149D172—81no—
150D172—81no—
151D172—81no—
152D172—81no—
153C4×D43—42no—
154Dic86—21no—
155Dic86—21no—
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×C43C22×D411yescharacteristic
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
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—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43H(5,𝔽2)11yescharacteristic
186C4×C43H(5,𝔽2)11yescharacteristic
187Dic43—41no—
188#3224—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43—81no—
191C2×C43#53511yescharacteristic
192C2×C43#57611yescharacteristic
193C2×C43#57711yescharacteristic
194D43—81no—
195D43—81no—
196D43—81no—
197#542D4311yescharacteristic, complemented
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#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#127—431no—
226#126—21no—
227#124—21no—
228#124—431no—
229#124—431no—
230#124C2×D4311yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D4311yescharacteristic
234#121—861no—
235#121—861no—
236#121C2×D4311yescharacteristic
237#120—861no—
238#120—861no—
239C4×Q8C2×D4311yescharacteristic, complemented
240C4×D4C2×D4311yescharacteristic, complemented
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—861no—
257#41—1721no—
258#41—1721no—
259C2×Q8—21no—
260C2×Q8—431no—
261C2×Q8C22×D4311yescharacteristic
262C2×D4—21no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—1721no—
273C2×D4—1721no—
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—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D4311yescharacteristic
294C4⋊C4C22⋊D4311yescharacteristic
295C4⋊C4C22×D4311yescharacteristic
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4C22⋊D4311yescharacteristic
307C22⋊C4C22⋊D4311yescharacteristic
308C42—21no—
309C42C22×D4311yescharacteristic
310C42C22×D4311yescharacteristic
311C23—21no—
312C23—861no—
313C23—861no—
314C23—861no—
315C23—3441no—
316C23—3441no—
317C23—1722no—
318C23C2×C22⋊D4311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—861no—
323Q8—861no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—861no—
328D4—861no—
329D4—861no—
330D4—861no—
331D4—861no—
332D4—861no—
333D4—3441no—
334D4—3441no—
335D4—3441no—
336D4—3441no—
337D4—1722no—
338D4—1722no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—861no—
346C2×C4—1722no—
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—3444no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C22×C22⋊D4311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—1721no—
383C4#1306337111yescharacteristic
384C4#1306337111yescharacteristic
385C2—41no—
386C2—81no—
387C2—3441no—
388C2—3441no—
389C2—3441no—
390C2#1458346311yescharacteristic
391C2#1458370211yescharacteristic
392C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#542C2
socleC22×C43C22×D4
hypercenter#542D43
hypocenterC43#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #14583468C2semidirect
2. #14583289C2semidirect
3. #14583281C2semidirect
4. #14583261C2semidirect
5. #14583247C2semidirect
6. #14583121C2semidirect
7. #14583114C2semidirect
8. #14583099C2semidirect
9. #14583094C2semidirect
10. #14583059C2semidirect
11. #14583049C2semidirect
12. #14583042C2semidirect
13. #14583032C2semidirect
14. #14582960C2semidirect
15. C43×#542C2semidirect
18. C2×#10621885C22semidirect
19. C2×#10621883C22semidirect
22. C2×#10621884C22semidirect
25. C2×#10621882C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. C4⋊(C43⋊C8)C22semidirect
36. #13063248C22semidirect
37. #13063248C22semidirect
42. #13063245C22semidirect
43. #13063245C22semidirect
46. #13063236C22semidirect
47. C4×C43⋊C8C22semidirect
48. C4⋊Q8×C43C22semidirect
51. #124×C43C22semidirect
56. C4×Q8×C43C22semidirect
57. C4×D4×C43C22semidirect
197. #542D43semidirect
212. C43#3224semidirect
223. C4⋊Q8C2×D43semidirect
230. #124C2×D43semidirect
239. C4×Q8C2×D43semidirect
240. C4×D4C2×D43semidirect