Finite Group Databasebeta

← #19145464

Subgroups — #19145464

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583472C211yesmaximal, characteristic, complemented
2#14583466C211yesmaximal, characteristic
3#14583241C211yesmaximal, characteristic, complemented
4#14583237C211yesmaximal, characteristic, complemented
5#14583222C211yesmaximal, characteristic, complemented
6#14583221C211yesmaximal, characteristic, complemented
7#14583144C211yesmaximal, characteristic, complemented
8#14583142C211yesmaximal, characteristic, complemented
9#14583127C211yesmaximal, characteristic, complemented
10#14583125C211yesmaximal, characteristic, complemented
11#14583050C211yesmaximal, characteristic, complemented
12#14583036C211yesmaximal, characteristic, complemented
13#14583036C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic, complemented
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621872C2211yescharacteristic, complemented
21C2×C8×D43C2211yescharacteristic, complemented
22#13063324—21no—
23#13063321—21no—
24#13063312—21no—
25#13063311—21no—
26#13063310—21no—
27#13063307—21no—
28#13063305C2211yescharacteristic, complemented
29#13063304C2211yescharacteristic
30#13063301C2211yescharacteristic, complemented
31#13063296C2211yescharacteristic
32#13063296C2211yescharacteristic
33#13063296C2211yescharacteristic
34#13063296C2211yescharacteristic
35#13063294—21no—
36#13063294—21no—
37#13063284C2211yescharacteristic
38#13063283C2211yescharacteristic, complemented
39#13063259C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063249C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72C2×C22⋊D43D411yescharacteristic
73Q8×D43—41no—
74Q8×D43—41no—
75#10621898—41no—
76#10621898—41no—
77C2×D172D411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43C2311yescharacteristic
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—21no—
82C2×Dic86D411yescharacteristic
83C2×Dic86C2311yescharacteristic
84SD16×C43—41no—
85SD16×C43—41no—
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97#10621883—41no—
98#10621883—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112#10621872—41no—
113C8×D43—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—42no—
117C23×C43—81no—
118C23×C43—81no—
119C23×C43C2×D411yescharacteristic
120C22×D43C2×D411yescharacteristic
121C22×D43C2×D411yescharacteristic
122Q8×C43—21no—
123Q8×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—42no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—41no—
136C22⋊D43—41no—
137C22⋊D43—81no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C22⋊D43—81no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147D172—41no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—42no—
153Dic86—21no—
154Dic86—21no—
155Dic86—41no—
156Dic86—42no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—84no—
171C22×C43C22×D411yescharacteristic
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—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—41no—
186Dic43—41no—
187Dic43—41no—
188Dic43—41no—
189#3200—431nomaximal, Sylow
190C2×C43—41no—
191C2×C43—81no—
192C2×C43—81no—
193C2×C43#53411yescharacteristic
194C2×C43#57711yescharacteristic
195C2×C43#57711yescharacteristic
196D43—41no—
197D43—41no—
198#536—431no—
199#535—431no—
200#485—431no—
201#485—431no—
202#482—431no—
203#482—431no—
204#468—431no—
205#468—431no—
206#465—431no—
207#465—431no—
208#450—431no—
209#450D4311yescharacteristic, complemented
210#448—431no—
211#448—431no—
212#408—431no—
213C43#320011yescharacteristic, complemented, Sylow
214C2×#41—431no—
215C22×Q8—431no—
216C22×D4C2×D4311yescharacteristic
217C2×SD16—431no—
218C2×SD16—431no—
219C2×SD16C2×D4311yescharacteristic
220C2×SD16C2×D4311yescharacteristic
221C2×M16—431no—
222C22×C8—431no—
223C4⋊Q8—861no—
224#127—861no—
225#124—861no—
226#124—861no—
227#123—861no—
228#123—861no—
229C22⋊Q8—431no—
230C22⋊Q8—431no—
231C22⋊Q8—431no—
232C22⋊Q8C2×D4311yescharacteristic
233#121—431no—
234#121—431no—
235#121—431no—
236#121—431no—
237#120—861no—
238#120—861no—
239#117—431no—
240#117—431no—
241#107—431no—
242#107—431no—
243#106—431no—
244#106—431no—
245#103—431no—
246#103—431no—
247#103—431no—
248#103—431no—
249#102—431no—
250#102—431no—
251#102C2×D4311yescharacteristic
252#102C2×D4311yescharacteristic
253C22⋊C8—431no—
254C22⋊C8—431no—
255C22⋊C8—431no—
256C22⋊C8C2×D4311yescharacteristic
257C24—21no—
258#41—1721no—
259#41—1721no—
260C2×Q8—431no—
261C2×Q8—431no—
262C2×Q8—861no—
263C2×Q8—1721no—
264C2×Q8—1721no—
265C2×Q8C22×D4311yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—431no—
270C2×D4—431no—
271C2×D4—431no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4C22×D4311yescharacteristic
277C2×D4C22×D4311yescharacteristic
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—861no—
281C22×C4C22×D4311yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—1721no—
285SD16—1721no—
286M16—1721no—
287C2×C8—431no—
288C2×C8—431no—
289C2×C8—1721no—
290C2×C8C22×D4311yescharacteristic
291C2×C8C22×D4311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—431no—
294C4⋊C4—431no—
295C4⋊C4—431no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4C22×D4311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C42—861no—
311C42—861no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—431no—
318C23—431no—
319C23D4×D4311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—861no—
323Q8—861no—
324Q8—1721no—
325Q8—1722no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—3441no—
332D4—3441no—
333D4—3441no—
334D4—3441no—
335D4—1721no—
336D4—1721no—
337D4—1721no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—431no—
343C2×C4—431no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—1722no—
353C2×C4D4×D4311yescharacteristic
354C2×C4C23×D4311yescharacteristic
355C8—21no—
356C8—21no—
357C8—861no—
358C8—861no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—861no—
370C22—861no—
371C22—861no—
372C22—861no—
373C22—861no—
374C22—861no—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—861no—
380C4—861no—
381C4—1721no—
382C4—1721no—
383C4—1721no—
384C4—1721no—
385C4#1306337011yescharacteristic
386C4#1306337011yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—1721no—
391C2—1721no—
392C2#1458345911yescharacteristic
393C2#1458370511yescharacteristic
394C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3200
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583472C2semidirect
3. #14583241C2semidirect
4. #14583237C2semidirect
5. #14583222C2semidirect
6. #14583221C2semidirect
7. #14583144C2semidirect
8. #14583142C2semidirect
9. #14583127C2semidirect
10. #14583125C2semidirect
11. #14583050C2semidirect
12. #14583036C2semidirect
13. #14583036C2semidirect
14. #14582864C2semidirect
15. C43×#450C2semidirect
17. C2×Q8×D43C22semidirect
20. C2×#10621872C22semidirect
21. C2×C8×D43C22semidirect
28. #13063305C22semidirect
30. #13063301C22semidirect
38. #13063283C22semidirect
39. #13063259C22semidirect
40. #13063258C22semidirect
41. #13063257C22semidirect
42. #13063256C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
45. #13063249C22semidirect
46. #13063249C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
209. #450D43semidirect
213. C43#3200semidirect