Finite Group Databasebeta

← #19145371

Subgroups — #19145371

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#14583409C211yesmaximal, characteristic
2C22⋊Q8×D43C211yesmaximal, characteristic, complemented
3#14583243C211yesmaximal, characteristic, complemented
4#14583239C211yesmaximal, characteristic, complemented
5#14583231C211yesmaximal, characteristic, complemented
6#14583211C211yesmaximal, characteristic, complemented
7#14583140C211yesmaximal, characteristic, complemented
8#14583138C211yesmaximal, characteristic, complemented
9#14583126C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583058C211yesmaximal, characteristic, complemented
12#14583056C211yesmaximal, characteristic, complemented
13#14583036C211yesmaximal, characteristic, complemented
14C2×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C2×Dic172C2211yescharacteristic, complemented
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C22×C43⋊C8C2211yescharacteristic
23#13063307—21no—
24#13063305C2211yescharacteristic
25#13063305C2211yescharacteristic
26#13063304C2211yescharacteristic
27#13063304C2211yescharacteristic
28#13063303—21no—
29#13063302—21no—
30#13063301C2211yescharacteristic
31#13063296C2211yescharacteristic
32#13063293—21no—
33D4×Dic43—21no—
34(C22⋊D43)⋊C4—21no—
35#13063283C2211yescharacteristic
36C4⋊C4×D43—21no—
37C4⋊C4×D43C2211yescharacteristic
38C22⋊C4×D43—21no—
39#13063259C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063248C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67C22×Dic43D411yescharacteristic
68Q8×D43—41no—
69Q8×D43—41no—
70#10621900—41no—
71#10621900—41no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—41no—
75C2×C4×D43—41no—
76C2×C4×D43D411yescharacteristic
77C2×C4×D43D411yescharacteristic
78C2×C4×D43C2311yescharacteristic
79C2×C4×D43C2311yescharacteristic
80C2×Dic86—21no—
81C2×Dic86C2311yescharacteristic
82C2×Dic86C2311yescharacteristic
83SD16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95#10621885—41no—
96#10621883—41no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101C4⋊Dic43—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
113Dic172—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—22no—
117C22×D43—22no—
118C22×D43—41no—
119C22×D43C2×D411yescharacteristic
120C22×D43C2×D411yescharacteristic
121Q8×C43—21no—
122Q8×C43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—42no—
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—
134C22⋊D43—42no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—41no—
140C2×Dic43—42no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—42no—
150C4×D43—42no—
151Dic86—21no—
152Dic86—21no—
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—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43#13712yes—
166C22×C43C22×D411yescharacteristic
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—44no—
173C2×D43#13512yes—
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43H(5,𝔽2)11yescharacteristic
179C4×C43H(5,𝔽2)11yescharacteristic
180Dic43—21no—
181Dic43—21no—
182Dic43—41no—
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186#3190—431nomaximal, Sylow
187C2×C43—22no—
188C2×C43—81no—
189C2×C43#53411yescharacteristic
190C2×C43C2×#13511yescharacteristic
191C2×C43C2×#13711yescharacteristic
192D43—22no—
193D43—41no—
194#525—431no—
195C2×C22⋊Q8—431no—
196#485—431no—
197#485—431no—
198#483—431no—
199#480—431no—
200#467—431no—
201#467—431no—
202#465—431no—
203#465D4311yescharacteristic, complemented
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×Q16—431no—
215C2×SD16—431no—
216C2×SD16C2×D4311yescharacteristic, complemented
217C22×C8—431no—
218C22×C8C2×D4311yescharacteristic
219#123—861no—
220C22⋊Q8—431no—
221C22⋊Q8—431no—
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226C22⋊Q8—861no—
227C22⋊Q8C2×D4311yescharacteristic
228#121—431no—
229#121C2×D4311yescharacteristic
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#107—431no—
239#106—431no—
240#106C2×D4311yescharacteristic, complemented
241#103—431no—
242#103—431no—
243#103—431no—
244#103—431no—
245#103—431no—
246#103C2×D4311yescharacteristic, complemented
247#102—431no—
248#102C2×D4311yescharacteristic, complemented
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—431no—
258C2×Q8—861no—
259C2×Q8—1721no—
260C2×Q8—1721no—
261C2×Q8C22×D4311yescharacteristic
262C2×D4—21no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4C22×D4311yescharacteristic
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—1721no—
278Q16—1721no—
279SD16—41no—
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—431no—
289C4⋊C4—431no—
290C4⋊C4—861no—
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—21no—
309C23—431no—
310C23—431no—
311C23—862no—
312C23—862no—
313C23—1721no—
314C23D4×D4311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—861no—
318Q8—861no—
319Q8—861no—
320Q8—861no—
321Q8—1722no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—1722no—
326D4—1722no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—861no—
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—1721no—
347C2×C4—1722no—
348C2×C4D4×D4311yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—21no—
351C8—21no—
352C8—861no—
353C8—861no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—432no—
360C22—861no—
361C22—861no—
362C22—861no—
363C22—861no—
364C22—861no—
365C22—1724no—
366C22#1306335412yes—
367C22C2×D4×D4311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—861no—
373C4—861no—
374C4—1721no—
375C4—1721no—
376C4—1721no—
377C4—1721no—
378C4#1306337011yescharacteristic
379C4#1306337111yescharacteristic
380C2—22no—
381C2—81no—
382C2—862no—
383C2—1721no—
384C2#1458345711yescharacteristic
385C2#135×D4311yescharacteristic
386C2C2×#1306335411yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3190
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D43C2semidirect
3. #14583243C2semidirect
4. #14583239C2semidirect
5. #14583231C2semidirect
6. #14583211C2semidirect
7. #14583140C2semidirect
8. #14583138C2semidirect
9. #14583126C2semidirect
10. #14583062C2semidirect
11. #14583058C2semidirect
12. #14583056C2semidirect
13. #14583036C2semidirect
14. C2×(C2×D43)⋊C8C2semidirect
15. C43×#465C2semidirect
19. C2×Dic172C22semidirect
20. C2×#10621885C22semidirect
21. C2×#10621883C22semidirect
39. #13063259C22semidirect
40. #13063258C22semidirect
41. #13063256C22semidirect
42. #13063250C22semidirect
43. #13063250C22semidirect
44. #13063249C22semidirect
45. #13063248C22semidirect
46. #13063248C22semidirect
47. #13063246C22semidirect
52. C2×SD16×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
203. #465D43semidirect
209. C43#3190semidirect
216. C2×SD16C2×D43semidirect
240. #106C2×D43semidirect
246. #103C2×D43semidirect
248. #102C2×D43semidirect