Finite Group Databasebeta

← #19146200

Subgroups — #19146200

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×#13063349C211yesmaximal, characteristic, complemented
2#14583543C211yesmaximal, characteristic, complemented
3#14583537C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583145C211yesmaximal, characteristic, complemented
6#14583142C211yesmaximal, characteristic, complemented
7#14583116C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583058C211yesmaximal, characteristic, complemented
11#14583033C211yesmaximal, characteristic, complemented
12#14583031C211yesmaximal, characteristic, complemented
13D8×Dic43C211yesmaximal, characteristic, complemented
14#14582975C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic, complemented
18#13063349—24no—
19C2×#10621885C2211yescharacteristic, complemented
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×#10621882C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621872C2211yescharacteristic, complemented
25#13063314C2211yescharacteristic, complemented
26#13063312C2211yescharacteristic, complemented
27#13063308—21no—
28#13063306—21no—
29#13063304C2211yescharacteristic, complemented
30#13063301C2211yescharacteristic, complemented
31#13063299C2211yescharacteristic
32#13063297—21no—
33#13063297—21no—
34#13063296C2211yescharacteristic
35#13063294—21no—
36#13063293—21no—
37D4×Dic43C2211yescharacteristic, complemented
38D4×Dic43C2211yescharacteristic, complemented
39C4×C22⋊D43C2211yescharacteristic
40C2×C22⋊Dic43—21no—
41C2×(C2×D43)⋊C4—21no—
42#13063259C2211yescharacteristic, complemented
43Dic43⋊C8C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic, complemented
48#13063246C2211yescharacteristic, complemented
49#13063246C2211yescharacteristic, complemented
50C22⋊(C43⋊C8)C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C8×Dic43C2211yescharacteristic, complemented
53C2×#41×C43C2211yescharacteristic
54C22×D4×C43C2211yescharacteristic, complemented
55AGL(1,ℤ/8)×C43—24no—
56C2×SD16×C43C2211yescharacteristic, complemented
57C2×SD16×C43C2211yescharacteristic, complemented
58C2×D8×C43C2211yescharacteristic
59C2×D8×C43C2211yescharacteristic
60C2×M16×C43C2211yescharacteristic, complemented
61C24×C43—21no—
62C23×D43—21no—
63#41×C43—22no—
64#41×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C2×D4×C43C2311yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79C2×C22⋊D43D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83#10621900—22no—
84#10621900—41no—
85D4×D43—22no—
86D4×D43—41no—
87C2×D172C2311yescharacteristic
88C2×C4×D43C2311yescharacteristic
89C2×Dic86C2311yescharacteristic
90SD16×C43—22no—
91SD16×C43—22no—
92D8×C43—22no—
93D8×C43D414yescomplemented
94M16×C43—22no—
95C2×C8×C43C2311yescharacteristic
96C2×C8×C43C2311yescharacteristic
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101C22⋊Dic43—21no—
102C22⋊Dic43—21no—
103C22⋊Dic43D411yescharacteristic
104#10621885—41no—
105#10621883—22no—
106#10621882—22no—
107#10621882—41no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4D411yescharacteristic
113C4⋊Dic43C2311yescharacteristic
114C4⋊Dic43C2311yescharacteristic
115Dic43⋊C4—21no—
116Dic43⋊C4—21no—
117Dic43⋊C4D411yescharacteristic
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121#10621873—22no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—81no—
129C23×C43C2×D411yescharacteristic
130C22×D43—21no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—81no—
134C22×D43C2×D411yescharacteristic
135Q8×C43—21no—
136Q8×C43—21no—
137D4×C43—21no—
138D4×C43—21no—
139D4×C43—21no—
140D4×C43—21no—
141D4×C43—42no—
142D4×C43—42no—
143D4×C43C2×D412yes—
144D4×C43C2×D412yes—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—42no—
149C2×C4×C43C2×D411yescharacteristic
150C2×C4×C43C2411yescharacteristic
151C22⋊D43—41no—
152C22⋊D43—42no—
153C22⋊D43—42no—
154C22⋊D43—81no—
155C22⋊D43—81no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—42no—
160C2×Dic43—81no—
161C2×Dic43—81no—
162C2×Dic43C2×D411yescharacteristic
163C2×Dic43C2×D411yescharacteristic
164C2×Dic43C2×D411yescharacteristic
165D172—21no—
166D172—21no—
167C4×D43—21no—
168C4×D43—21no—
169Dic86—21no—
170Dic86—21no—
171C8×C43—21no—
172C8×C43C2×D412yes—
173C43⋊C8—21no—
174C43⋊C8—21no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—84no—
188C22×C43C22×D411yescharacteristic
189C2×D43—21no—
190C2×D43—21no—
191C2×D43—21no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—84no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43C22×D411yescharacteristic
199C4×C43H(5,𝔽2)11yescharacteristic
200Dic43—21no—
201Dic43—21no—
202Dic43—21no—
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206#3273—431nomaximal, Sylow
207C2×C43—42no—
208C2×C43—41no—
209C2×C43—42no—
210C2×C43—81no—
211C2×C43D4211yescharacteristic
212C2×C43#57511yescharacteristic
213C2×C43#57611yescharacteristic
214D43—41no—
215D43—81no—
216C2×AGL(1,ℤ/8)—431no—
217C2×AGL(1,ℤ/8)D4311yescharacteristic, complemented
218#546—431no—
219#546—431no—
220#495—431no—
221#468—431no—
222#468—431no—
223#463—431no—
224#463—431no—
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×#41C2×D4311yescharacteristic
234C22×D4—431no—
235C22×D4C2×D4311yescharacteristic, complemented
236AGL(1,ℤ/8)—24no—
237AGL(1,ℤ/8)—864no—
238C2×Q16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16C2×D4311yescharacteristic, complemented
242C2×SD16C2×D4311yescharacteristic, complemented
243C2×D8—431no—
244C2×D8—431no—
245C2×D8C2×D4311yescharacteristic
246C2×D8C2×D4311yescharacteristic
247C2×M16—431no—
248C2×M16C2×D4311yescharacteristic, complemented
249#124—431no—
250#124—431no—
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×D4—431no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266#107—431no—
267C4⋊C8—431no—
268#103—431no—
269#103—431no—
270#102—431no—
271#102—431no—
272#102—431no—
273#102—431no—
274C22⋊C8—431no—
275C22⋊C8—431no—
276C4×C8—431no—
277C24—21no—
278C24—861no—
279#41—22no—
280#41—41no—
281#41—862no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8C22×D4311yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—431no—
290C2×D4—431no—
291C2×D4—861no—
292C2×D4—862no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—1721no—
297C2×D4C22×D4311yescharacteristic
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C22×C4—21no—
301C22×C4—431no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4C22×D4311yescharacteristic
306Q16—1721no—
307SD16—22no—
308SD16—22no—
309SD16—862no—
310SD16—862no—
311D8—22no—
312D8—862no—
313D8—1721no—
314D8C22⋊D4314yescomplemented
315M16—22no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8C22×D4311yescharacteristic
320C2×C8C22×D4311yescharacteristic
321C4⋊C4—431no—
322C4⋊C4—431no—
323C4⋊C4—431no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C22⋊C4—431no—
327C22⋊C4—431no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C22⋊C4—861no—
337C22⋊C4—861no—
338C42—431no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—431no—
346C23—861no—
347C23—3441no—
348C23—1722no—
349C23—1722no—
350C23D4×D4311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—861no—
354Q8—861no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—42no—
360D4—42no—
361D4—861no—
362D4—861no—
363D4—3441no—
364D4—3441no—
365D4—1721no—
366D4—1722no—
367D4—1722no—
368D4C2×C22⋊D4312yes—
369D4C2×C22⋊D4312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—431no—
375C2×C4—431no—
376C2×C4—431no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—3441no—
383C2×C4—3441no—
384C2×C4—1722no—
385C2×C4D4×D4311yescharacteristic
386C2×C4C23×D4311yescharacteristic
387C8—21no—
388C8—861no—
389C8—861no—
390C8C2×C22⋊D4312yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—861no—
405C22—861no—
406C22—861no—
407C22—3444no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22C2×D4×D4311yescharacteristic
412C4—21no—
413C4—41no—
414C4—861no—
415C4—861no—
416C4—861no—
417C4—1721no—
418C4—1721no—
419C4—1721no—
420C4C22×C22⋊D4311yescharacteristic
421C4#1306337011yescharacteristic
422C2—41no—
423C2—42no—
424C2—42no—
425C2—81no—
426C2—3441no—
427C2—1721no—
428C2D4×C22⋊D4311yescharacteristic
429C2#1458369511yescharacteristic
430C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×AGL(1,ℤ/8)×C43C2
socleC22×C43C22×D4
hypercenterC2×AGL(1,ℤ/8)D43
hypocenterC43#3273
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. #14583543C2semidirect
3. #14583537C2semidirect
4. #14583280C2semidirect
5. #14583145C2semidirect
6. #14583142C2semidirect
7. #14583116C2semidirect
8. #14583112C2semidirect
9. #14583061C2semidirect
10. #14583058C2semidirect
11. #14583033C2semidirect
12. #14583031C2semidirect
13. D8×Dic43C2semidirect
14. #14582975C2semidirect
15. C2×AGL(1,ℤ/8)×C43C2semidirect
17. C2×D4×D43C22semidirect
19. C2×#10621885C22semidirect
20. C2×#10621873C22semidirect
21. C2×#10621883C22semidirect
24. C2×#10621872C22semidirect
25. #13063314C22semidirect
26. #13063312C22semidirect
29. #13063304C22semidirect
30. #13063301C22semidirect
37. D4×Dic43C22semidirect
38. D4×Dic43C22semidirect
42. #13063259C22semidirect
43. Dic43⋊C8C22semidirect
44. #13063250C22semidirect
45. #13063249C22semidirect
46. #13063247C22semidirect
47. #13063246C22semidirect
48. #13063246C22semidirect
49. #13063246C22semidirect
50. C22⋊(C43⋊C8)C22semidirect
51. (C2×D43)⋊C8C22semidirect
52. C8×Dic43C22semidirect
54. C22×D4×C43C22semidirect
56. C2×SD16×C43C22semidirect
57. C2×SD16×C43C22semidirect
60. C2×M16×C43C22semidirect
93. D8×C43D4semidirect
217. C2×AGL(1,ℤ/8)D43semidirect
231. C43#3273semidirect
235. C22×D4C2×D43semidirect
241. C2×SD16C2×D43semidirect
242. C2×SD16C2×D43semidirect
248. C2×M16C2×D43semidirect
314. D8C22⋊D43semidirect