Finite Group Databasebeta

← #19145377

Subgroups — #19145377

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583412C211yesmaximal, characteristic
2C22⋊Q8×D43C211yesmaximal, characteristic, complemented
3#14583242C211yesmaximal, characteristic, complemented
4#14583238C211yesmaximal, characteristic, complemented
5#14583228C211yesmaximal, characteristic, complemented
6#14583214C211yesmaximal, characteristic, complemented
7#14583138C211yesmaximal, characteristic, complemented
8#14583130C211yesmaximal, characteristic, complemented
9#14583128C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583060C211yesmaximal, characteristic, complemented
12#14583053C211yesmaximal, characteristic, complemented
13#14583039C211yesmaximal, characteristic, complemented
14C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#467C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C2×#10621885C2211yescharacteristic, complemented
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621884C2211yescharacteristic, complemented
22C22×C43⋊C8C2211yescharacteristic
23#13063310—21no—
24#13063305C2211yescharacteristic
25#13063304C2211yescharacteristic
26#13063303—21no—
27#13063302—21no—
28#13063301C2211yescharacteristic
29#13063301C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063299C2211yescharacteristic
32#13063295—21no—
33#13063287—21no—
34(C22⋊D43)⋊C4—21no—
35#13063283C2211yescharacteristic
36C4⋊C4×D43—21no—
37C4⋊C4×D43C2211yescharacteristic
38C22⋊C4×D43—21no—
39#13063258C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C2×Q16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#103×C43C2211yescharacteristic, complemented
59C23×D43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C22×Dic43D411yescharacteristic
65#10621902—41no—
66#10621902—41no—
67Q8×D43—41no—
68Q8×D43—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—41no—
76C2×C4×D43—41no—
77C2×C4×D43D411yescharacteristic
78C2×C4×D43D411yescharacteristic
79C2×C4×D43C2311yescharacteristic
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—21no—
82C2×Dic86C2311yescharacteristic
83Q16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊Dic43—21no—
94#10621885—41no—
95#10621884—41no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109C4×Dic43—21no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113#10621873—41no—
114C23×C43C2×D411yescharacteristic
115C22×D43—22no—
116C22×D43—22no—
117C22×D43—21no—
118C22×D43—41no—
119C22×D43C2×D411yescharacteristic
120C22×D43C2×D411yescharacteristic
121Q8×C43—21no—
122Q8×C43—21no—
123Q8×C43—21no—
124Q8×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—41no—
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142D172—42no—
143D172—42no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—41no—
149C4×D43—41no—
150C4×D43—42no—
151C4×D43—42no—
152C4×D43—42no—
153Dic86—21no—
154Dic86—21no—
155Dic86—42no—
156C8×C43—21no—
157C8×C43—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#13712yes—
163C22×C43C22×D411yescharacteristic
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—44no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43#13512yes—
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43H(5,𝔽2)11yescharacteristic
180C4×C43H(5,𝔽2)11yescharacteristic
181Dic43—21no—
182Dic43—21no—
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186#3190—431nomaximal, Sylow
187C2×C43—22no—
188C2×C43#53411yescharacteristic
189C2×C43C2×#13511yescharacteristic
190C2×C43C2×#13711yescharacteristic
191D43—22no—
192D43—41no—
193D43—81no—
194#525—431no—
195C2×C22⋊Q8—431no—
196#485—431no—
197#485—431no—
198#483—431no—
199#480—431no—
200#467—431no—
201#467D4311yescharacteristic, complemented
202#465—431no—
203#465—431no—
204#452—431no—
205#452—431no—
206#451—431no—
207#448—431no—
208C2×C22⋊C8—431no—
209C43#319011yescharacteristic, complemented, Sylow
210C2×#41—431no—
211C22×Q8—431no—
212C23×C4—431no—
213C2×Q16—431no—
214C2×Q16C2×D4311yescharacteristic, complemented
215C2×SD16—431no—
216C2×SD16—431no—
217C22×C8—431no—
218C22×C8C2×D4311yescharacteristic
219#123—861no—
220C22⋊Q8—431no—
221C22⋊Q8—431no—
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—861no—
225C22⋊Q8—861no—
226C22⋊Q8C2×D4311yescharacteristic
227C22⋊Q8C2×D4311yescharacteristic
228#121—431no—
229#121—431no—
230#120—861no—
231C4×D4—861no—
232C4×D4—861no—
233#117—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—861no—
236C2×C22⋊C4—861no—
237#107—431no—
238#107C2×D4311yescharacteristic, complemented
239#106—431no—
240#106—431no—
241#103—431no—
242#103—431no—
243#103—431no—
244#103—431no—
245#103C2×D4311yescharacteristic, complemented
246#103C2×D4311yescharacteristic, complemented
247#102—431no—
248#102—431no—
249C22⋊C8—431no—
250C22⋊C8—431no—
251C22⋊C8—431no—
252C22⋊C8—431no—
253C24—431no—
254#41—1721no—
255#41—1721no—
256C2×Q8—431no—
257C2×Q8—861no—
258C2×Q8—1721no—
259C2×Q8—1721no—
260C2×Q8C22×D4311yescharacteristic
261C2×Q8C22×D4311yescharacteristic
262C2×D4—431no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—1721no—
275C22×C4—1721no—
276C22×C4C22×D4311yescharacteristic
277Q16—41no—
278Q16—1721no—
279SD16—1721no—
280SD16—1721no—
281C2×C8—41no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8—1721no—
285C2×C8C22×D4311yescharacteristic
286C2×C8C22×D4311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4C22×D4311yescharacteristic
297C4⋊C4C22×D4311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C42—861no—
308C23—431no—
309C23—431no—
310C23—862no—
311C23—862no—
312C23—861no—
313C23—1721no—
314C23D4×D4311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—861no—
320Q8—861no—
321Q8—1722no—
322D4—861no—
323D4—861no—
324D4—1722no—
325D4—1722no—
326D4—1722no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4D4×D4311yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—21no—
351C8—21no—
352C8—861no—
353C8—861no—
354C22—21no—
355C22—21no—
356C22—432no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22—861no—
362C22—1724no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22#1306335712yes—
367C22C2×D4×D4311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—861no—
374C4—861no—
375C4—1721no—
376C4—1721no—
377C4—1721no—
378C4#1306337011yescharacteristic
379C4#1306337111yescharacteristic
380C2—22no—
381C2—862no—
382C2—3441no—
383C2—1721no—
384C2#1458345711yescharacteristic
385C2#135×D4311yescharacteristic
386C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#467C2
socleC22×C43C22×D4
hypercenter#467D43
hypocenterC43#3190
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D43C2semidirect
3. #14583242C2semidirect
4. #14583238C2semidirect
5. #14583228C2semidirect
6. #14583214C2semidirect
7. #14583138C2semidirect
8. #14583130C2semidirect
9. #14583128C2semidirect
10. #14583064C2semidirect
11. #14583060C2semidirect
12. #14583053C2semidirect
13. #14583039C2semidirect
14. C2×(C2×D43)⋊C8C2semidirect
15. C43×#467C2semidirect
19. C2×#10621885C22semidirect
20. C2×#10621873C22semidirect
21. C2×#10621884C22semidirect
39. #13063258C22semidirect
40. #13063257C22semidirect
41. #13063256C22semidirect
42. #13063250C22semidirect
43. #13063249C22semidirect
44. #13063249C22semidirect
45. #13063248C22semidirect
46. #13063247C22semidirect
47. #13063245C22semidirect
52. C2×Q16×C43C22semidirect
56. #107×C43C22semidirect
57. #103×C43C22semidirect
58. #103×C43C22semidirect
201. #467D43semidirect
209. C43#3190semidirect
214. C2×Q16C2×D43semidirect
238. #107C2×D43semidirect
245. #103C2×D43semidirect
246. #103C2×D43semidirect