Finite Group Databasebeta

← #19146201

Subgroups — #19146201

Order 5504.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063352C211yesmaximal, characteristic, complemented
2C2×#13063349C211yesmaximal, characteristic, complemented
3#14583544C211yesmaximal, characteristic, complemented
4#14583542C211yesmaximal, characteristic, complemented
5#14583281C211yesmaximal, characteristic, complemented
6#14583148C211yesmaximal, characteristic, complemented
7#14583144C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic, complemented
10#14583058C211yesmaximal, characteristic, complemented
11#14583034C211yesmaximal, characteristic, complemented
12#14583031C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582976C211yesmaximal, characteristic, complemented
15C43×#463C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic, complemented
19C2×D4×D43C2211yescharacteristic, complemented
20#13063352—24no—
21#13063349—24no—
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic, complemented
24C2×#10621883C2211yescharacteristic, complemented
25C2×#10621884C2211yescharacteristic, complemented
26C2×D344C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621872C2211yescharacteristic, complemented
30C2×#10621872C2211yescharacteristic, complemented
31#13063313C2211yescharacteristic, complemented
32#13063309—21no—
33#13063307—21no—
34#13063305C2211yescharacteristic, complemented
35#13063301C2211yescharacteristic, complemented
36#13063300C2211yescharacteristic
37#13063299—21no—
38#13063298—21no—
39#13063296C2211yescharacteristic
40#13063295—21no—
41#13063295—21no—
42C4×D172C2211yescharacteristic
43C4×D172C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C4—21no—
45C22⋊C4×D43—21no—
46#13063258C2211yescharacteristic, complemented
47#13063250C2211yescharacteristic, complemented
48#13063247C2211yescharacteristic, complemented
49#13063246C2211yescharacteristic, complemented
50#13063245C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic, complemented
53C4×C43⋊C8C2211yescharacteristic, complemented
54C2×SD16×C43C2211yescharacteristic, complemented
55C2×D8×C43C2211yescharacteristic
56#124×C43C2211yescharacteristic, complemented
57C4×D4×C43C2211yescharacteristic, complemented
58C4⋊C8×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60#102×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C23×D43—21no—
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C22×Dic43—21no—
72#10621902—22no—
73#10621902—41no—
74#10621900—22no—
75#10621900—41no—
76D4×D43—22no—
77D4×D43—22no—
78D4×D43—41no—
79D4×D43—41no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172D411yescharacteristic
83C2×D172C2311yescharacteristic
84C2×D172C2311yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43C2311yescharacteristic
88C2×C4×D43C2311yescharacteristic
89C2×Dic86C2311yescharacteristic
90SD16×C43—22no—
91D8×C43—22no—
92C2×C8×C43C2311yescharacteristic
93C2×C8×C43C2311yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43—21no—
98C42×C43C2311yescharacteristic
99C22⋊Dic43—21no—
100#10621885—41no—
101#10621884—22no—
102#10621883—22no—
103#10621882—41no—
104#10621882D414yescomplemented
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4D411yescharacteristic
112(C2×D43)⋊C4D411yescharacteristic
113C4⋊Dic43—21no—
114C4⋊Dic43D411yescharacteristic
115C4⋊Dic43C2311yescharacteristic
116Dic43⋊C4—21no—
117C2×C43⋊C8C2311yescharacteristic
118C2×C43⋊C8C2311yescharacteristic
119D344—22no—
120#10621873—22no—
121#10621872—22no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43—21no—
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—81no—
132C22×D43—81no—
133C22×D43C2×D411yescharacteristic
134C22×D43C2×D411yescharacteristic
135Q8×C43—21no—
136Q8×C43—21no—
137D4×C43—21no—
138D4×C43—21no—
139D4×C43—21no—
140D4×C43C2×D412yes—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—81no—
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2411yescharacteristic
147C22⋊D43—42no—
148C22⋊D43—42no—
149C22⋊D43—42no—
150C22⋊D43—81no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—42no—
154C2×Dic43C2×D411yescharacteristic
155C2×Dic43C2×D411yescharacteristic
156D172—21no—
157D172—21no—
158D172—21no—
159D172—41no—
160D172—42no—
161D172—81no—
162D172C2×D412yes—
163C4×D43—21no—
164C4×D43—21no—
165C4×D43—21no—
166C4×D43—21no—
167C4×D43—42no—
168C4×D43—81no—
169Dic86—21no—
170Dic86—21no—
171C8×C43—21no—
172C8×C43—21no—
173C43⋊C8—21no—
174C43⋊C8C2×D412yes—
175C22×C43—22no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43C22×D411yescharacteristic
182C2×D43—22no—
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—21no—
186C2×D43—21no—
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—84no—
195C2×D43—84no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43C22×D411yescharacteristic
201C4×C43H(5,𝔽2)11yescharacteristic
202Dic43—21no—
203Dic43—21no—
204Dic43—41no—
205Dic43—41no—
206#3273—431nomaximal, Sylow
207C2×C43—42no—
208C2×C43—81no—
209C2×C43D4211yescharacteristic
210C2×C43#57511yescharacteristic
211C2×C43#57611yescharacteristic
212D43—41no—
213D43—41no—
214D43—42no—
215D43—81no—
216C2×AGL(1,ℤ/8)—431no—
217C2×AGL(1,ℤ/8)—431no—
218#546—431no—
219#546—431no—
220#495—431no—
221#468—431no—
222#468—431no—
223#463—431no—
224#463D4311yescharacteristic, complemented
225#452—431no—
226#452—431no—
227#447—431no—
228#447—431no—
229C4×D8—431no—
230#436—431no—
231C43#327311yescharacteristic, complemented, Sylow
232C2×#41—431no—
233C2×#41—431no—
234C22×D4—431no—
235C22×D4—431no—
236AGL(1,ℤ/8)—864no—
237AGL(1,ℤ/8)—864no—
238C2×Q16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16—431no—
242C2×SD16C2×D4311yescharacteristic, complemented
243C2×D8—431no—
244C2×D8—431no—
245C2×D8—431no—
246C2×D8C2×D4311yescharacteristic
247C2×M16—431no—
248C2×M16—431no—
249#124—431no—
250#124C2×D4311yescharacteristic, complemented
251#123—861no—
252#123—861no—
253C22⋊Q8—431no—
254C22⋊Q8—431no—
255#121—431no—
256#121—431no—
257#121—861no—
258#121—861no—
259#120—861no—
260#120—861no—
261C4×D4—431no—
262C4×D4—431no—
263C4×D4C2×D4311yescharacteristic, complemented
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266#107—431no—
267C4⋊C8C2×D4311yescharacteristic, complemented
268#103—431no—
269#103C2×D4311yescharacteristic, complemented
270#102—431no—
271#102—431no—
272#102—431no—
273#102C2×D4311yescharacteristic, complemented
274C22⋊C8—431no—
275C22⋊C8—431no—
276C4×C8—431no—
277C24—861no—
278C24—861no—
279#41—862no—
280#41—862no—
281#41—1721no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8C22×D4311yescharacteristic
285C2×D4—431no—
286C2×D4—431no—
287C2×D4—431no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—862no—
293C2×D4—862no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C22×C4—21no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306Q16—1721no—
307SD16—22no—
308SD16—862no—
309SD16—862no—
310SD16—862no—
311D8—22no—
312D8—434no—
313D8—862no—
314D8—1721no—
315M16—862no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8C22×D4311yescharacteristic
320C2×C8C22×D4311yescharacteristic
321C4⋊C4—431no—
322C4⋊C4—431no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4C22×D4311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—431no—
330C22⋊C4—431no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C22⋊C4—861no—
337C22⋊C4—861no—
338C42C22×D4311yescharacteristic
339C23—21no—
340C23—21no—
341C23—431no—
342C23—431no—
343C23—861no—
344C23—861no—
345C23—3441no—
346C23—3441no—
347C23—1722no—
348C23—1722no—
349C23—1722no—
350C23—1722no—
351Q8—21no—
352Q8—21no—
353Q8—861no—
354Q8—861no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—432no—
359D4—861no—
360D4—861no—
361D4—861no—
362D4—3441no—
363D4—3441no—
364D4—1721no—
365D4—1722no—
366D4—1722no—
367D4—1722no—
368D4—1722no—
369D4D4×D4312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—431no—
374C2×C4—431no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—3441no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4D4×D4311yescharacteristic
385C2×C4D4×D4311yescharacteristic
386C2×C4C23×D4311yescharacteristic
387C8—21no—
388C8—21no—
389C8—432no—
390C8—861no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—861no—
398C22—861no—
399C22—861no—
400C22—861no—
401C22—861no—
402C22—861no—
403C22—862no—
404C22—3444no—
405C22—3444no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22C2×D4×D4311yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—861no—
417C4—861no—
418C4—1721no—
419C4—1721no—
420C4C2×D4×D4311yescharacteristic
421C4#1306337111yescharacteristic
422C2—42no—
423C2—81no—
424C2—3441no—
425C2—1721no—
426C2—1721no—
427C2—1722no—
428C2#1458353311yescharacteristic
429C2#1458369611yescharacteristic
430C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#463C2
socleC22×C43C22×D4
hypercenter#463D43
hypocenterC43#3273
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#13063352C2semidirect
2. C2×#13063349C2semidirect
3. #14583544C2semidirect
4. #14583542C2semidirect
5. #14583281C2semidirect
6. #14583148C2semidirect
7. #14583144C2semidirect
8. #14583115C2semidirect
9. #14583064C2semidirect
10. #14583058C2semidirect
11. #14583034C2semidirect
12. #14583031C2semidirect
13. C4×#10621882C2semidirect
14. #14582976C2semidirect
15. C43×#463C2semidirect
18. C2×D4×D43C22semidirect
19. C2×D4×D43C22semidirect
22. C2×#10621885C22semidirect
23. C2×#10621873C22semidirect
24. C2×#10621883C22semidirect
25. C2×#10621884C22semidirect
29. C2×#10621872C22semidirect
30. C2×#10621872C22semidirect
31. #13063313C22semidirect
34. #13063305C22semidirect
35. #13063301C22semidirect
43. C4×D172C22semidirect
46. #13063258C22semidirect
47. #13063250C22semidirect
48. #13063247C22semidirect
49. #13063246C22semidirect
50. #13063245C22semidirect
51. (C2×D43)⋊C8C22semidirect
52. (C2×D43)⋊C8C22semidirect
53. C4×C43⋊C8C22semidirect
54. C2×SD16×C43C22semidirect
56. #124×C43C22semidirect
57. C4×D4×C43C22semidirect
58. C4⋊C8×C43C22semidirect
59. #103×C43C22semidirect
60. #102×C43C22semidirect
104. #10621882D4semidirect
224. #463D43semidirect
231. C43#3273semidirect
242. C2×SD16C2×D43semidirect
250. #124C2×D43semidirect
263. C4×D4C2×D43semidirect
267. C4⋊C8C2×D43semidirect
269. #103C2×D43semidirect
273. #102C2×D43semidirect