Finite Group Databasebeta

← #49132746

Subgroups — #49132746

Order 36224.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583638C211yesmaximal, characteristic, complemented
2C22×D2264C211yesmaximal, characteristic, complemented
3#31827111C211yesmaximal, characteristic, complemented
4D4×D1132C211yesmaximal, characteristic, complemented
5#31826854C211yesmaximal, characteristic, complemented
6#31826718C211yesmaximal, characteristic, complemented
7#31826694C211yesmaximal, characteristic, complemented
8#31826681C211yesmaximal, characteristic, complemented
9#31826661C211yesmaximal, characteristic, complemented
10#31826618C211yesmaximal, characteristic, complemented
11#31826612C211yesmaximal, characteristic, complemented
12#31826601C211yesmaximal, characteristic, complemented
13#31826601C211yesmaximal, characteristic, complemented
14#31826578C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic, complemented
17C22×D1132C2211yescharacteristic
18C22×D1132C2211yescharacteristic, complemented
19C22×D1132C2211yescharacteristic, complemented
20C2×D4×D283—21no—
21#22583638—24no—
22C2×#17985381C2211yescharacteristic, complemented
23C2×#17985381C2211yescharacteristic, complemented
24C2×#17985381C2211yescharacteristic, complemented
25C2×D2264—24no—
26C2×D2264C2211yescharacteristic
27C2×D2264C2211yescharacteristic
28C2×D2264C2211yescharacteristic, complemented
29C2×D2264C2211yescharacteristic, complemented
30C2×D2264C2211yescharacteristic, complemented
31C2×D2264C2211yescharacteristic, complemented
32#22583607C2211yescharacteristic, complemented
33#22583598C2211yescharacteristic, complemented
34#22583595—21no—
35#22583589C2211yescharacteristic, complemented
36#22583585—21no—
37#22583584C2211yescharacteristic
38#22583584C2211yescharacteristic, complemented
39#22583584C2211yescharacteristic, complemented
40#22583583—21no—
41#22583580—21no—
42#22583580—21no—
43#22583578—21no—
44C4×D1132C2211yescharacteristic, complemented
45C4×D1132C2211yescharacteristic, complemented
46C22⋊C4×D283—21no—
47#22583542C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52#22583532C2211yescharacteristic, complemented
53#22583532C2211yescharacteristic, complemented
54C2×M16×C283C2211yescharacteristic, complemented
55C22×C8×C283C2211yescharacteristic, complemented
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic, complemented
59C22⋊C8×C283C2211yescharacteristic, complemented
60#97×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283—21no—
63C23×D283—21no—
64#17985392—22no—
65#17985392—41no—
66C2×Dic566C2311yescharacteristic
67C2×D1132—22no—
68C2×D1132—22no—
69C2×D1132—22no—
70C2×D1132—21no—
71C2×D1132—21no—
72C2×D1132—21no—
73C2×D1132—21no—
74C2×D1132—21no—
75C2×D1132—41no—
76C2×D1132—41no—
77C2×D1132—41no—
78C2×D1132C2311yescharacteristic
79C2×D1132C2311yescharacteristic
80C2×D1132C2311yescharacteristic
81C2×D1132C2311yescharacteristic
82C2×D1132C2311yescharacteristic
83C2×C22⋊D283—21no—
84C2×C22⋊D283—21no—
85C2×C22⋊D283—21no—
86C2×C22⋊D283—21no—
87D4×D283—44no—
88C2×C4×D283—21no—
89C2×C4×D283—21no—
90C2×C4×D283—21no—
91#17985381—22no—
92#17985381—22no—
93#17985381—41no—
94D2264—22no—
95D2264—22no—
96D2264—22no—
97D2264—22no—
98D2264—41no—
99D2264D414yescomplemented
100C4⋊Dic283C2311yescharacteristic
101C4⋊Dic283C2311yescharacteristic
102Dic283⋊C4—21no—
103C22⋊Dic283—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4—21no—
108(C2×D283)⋊C4—21no—
109(C2×D283)⋊C4—21no—
110(C2×D283)⋊C4—21no—
111C2×D4×C283D411yescharacteristic
112C22×C4×C283C2311yescharacteristic
113C22×C4×C283C2311yescharacteristic
114M16×C283—22no—
115C2×C8×C283—22no—
116C2×C8×C283C2311yescharacteristic
117C2×C8×C283C2311yescharacteristic
118C2×C8×C283C2311yescharacteristic
119C2×C8×C283C2311yescharacteristic
120C4⋊C4×C283D411yescharacteristic
121C22⋊C4×C283D411yescharacteristic
122C22⋊C4×C283D411yescharacteristic
123C42×C283C2311yescharacteristic
124C22×D283—21no—
125C22×D283—21no—
126C22×D283—21no—
127C22×D283—21no—
128C22×D283—21no—
129C22×D283—42no—
130C22×D283—42no—
131C22×D283—42no—
132C22×D283—42no—
133C22×D283—42no—
134C22×D283—42no—
135C22×D283—81no—
136C22×D283—81no—
137C22×D283—81no—
138Dic566—21no—
139Dic566—21no—
140D1132—21no—
141D1132—21no—
142D1132—21no—
143D1132—21no—
144D1132—21no—
145D1132—21no—
146D1132—21no—
147D1132—21no—
148D1132—42no—
149D1132—42no—
150D1132—42no—
151D1132—42no—
152D1132—81no—
153D1132C2×D412yes—
154D1132C2×D412yescomplemented
155C22⋊D283—42no—
156C22⋊D283—42no—
157C22⋊D283—42no—
158C22⋊D283—81no—
159C2×Dic283—21no—
160C2×Dic283—21no—
161C2×Dic283—21no—
162C4×D283—42no—
163C4×D283—42no—
164C4×D283—81no—
165C23×C283C2×D411yescharacteristic
166C23×C283C2×D411yescharacteristic
167D4×C283—22no—
168C2×C4×C283—21no—
169C2×C4×C283—21no—
170C2×C4×C283—21no—
171C2×C4×C283—21no—
172C2×C4×C283C2×D411yescharacteristic
173C2×C4×C283C2×D411yescharacteristic
174C2×C4×C283C2×D411yescharacteristic
175C2×C4×C283C2×D411yescharacteristic
176C2×C4×C283C2411yescharacteristic
177C8×C283—21no—
178C8×C283—21no—
179C8×C283—21no—
180C8×C283C2×D412yescomplemented
181C22×C283—21no—
182C22×C283—21no—
183C22×C283—21no—
184C22×C283—21no—
185C22×C283—21no—
186C22×C283AGL(1,ℤ/8)12yescomplemented
187C22×C283C22×D411yescharacteristic
188C2×D283—22no—
189C2×D283—22no—
190C2×D283—41no—
191C2×D283—41no—
192C2×D283—41no—
193C2×D283—41no—
194C2×D283—41no—
195C2×D283—41no—
196C2×D283—41no—
197C2×D283—41no—
198C2×D283—41no—
199C2×D283—41no—
200C2×D283—41no—
201C2×D283—41no—
202C2×D283—41no—
203C2×D283—84no—
204C2×D283—84no—
205C2×D283—84no—
206C4×C283—21no—
207C4×C283—21no—
208C4×C283—21no—
209C4×C283—21no—
210C4×C283C22×D411yescharacteristic
211C4×C283H(5,𝔽2)11yescharacteristic
212Dic283—41no—
213Dic283—41no—
214Dic283—41no—
215C2×C283—22no—
216C2×C283—41no—
217C2×C283D4211yescharacteristic
218C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C283#57611yescharacteristic
220D283—42no—
221D283—42no—
222D283—81no—
223D283—81no—
224D283—81no—
225C283#326411yescharacteristic, complemented, Sylow
226#3264—2831nomaximal, Sylow
227C2×AGL(1,ℤ/8)—2831no—
228C22×D8—2831no—
229#546—2831no—
230D42—2831no—
231#496—2831no—
232#469—2831no—
233#465—2831no—
234#463—2831no—
235#459—2831no—
236#450—2831no—
237#449—2831no—
238#447—2831no—
239#447—2831no—
240#442—2831no—
241#435D28311yescharacteristic, complemented
242C2×#41—2831no—
243C22×D4—2831no—
244C22×D4—2831no—
245C22×D4—2831no—
246C22×D4—5661no—
247AGL(1,ℤ/8)—5664no—
248C2×SD16—2831no—
249C2×SD16—2831no—
250C2×SD16—2831no—
251C2×D8—2831no—
252C2×D8—2831no—
253C2×D8—2831no—
254C2×D8—2831no—
255C2×D8—2831no—
256C2×D8—2831no—
257C2×D8—5664no—
258C2×M16C2×D28311yescharacteristic, complemented
259C22×C8C2×D28311yescharacteristic, complemented
260#127—2831no—
261#124—2831no—
262#123—5661no—
263C22⋊Q8—2831no—
264#121—2831no—
265#121—2831no—
266#121—2831no—
267#121—5661no—
268#121—5661no—
269#120—5661no—
270#120—5661no—
271#120—5661no—
272C4×D4—2831no—
273C4×D4—2831no—
274C4×D4C2×D28311yescharacteristic
275C2×C22⋊C4—5661no—
276#106—2831no—
277C4⋊C8C2×D28311yescharacteristic, complemented
278#103—2831no—
279#102—2831no—
280#102—2831no—
281#102—2831no—
282#102—2831no—
283#102—2831no—
284C22⋊C8C2×D28311yescharacteristic, complemented
285C22⋊C8C2×D28311yescharacteristic, complemented
286#97C2×D28311yescharacteristic, complemented
287C24—5661no—
288C24—5661no—
289C24—5661no—
290#41—5662no—
291#41—11321no—
292C2×Q8—2831no—
293C2×D4—2831no—
294C2×D4—2831no—
295C2×D4—2831no—
296C2×D4—2831no—
297C2×D4—2831no—
298C2×D4—5662no—
299C2×D4—5662no—
300C2×D4—5662no—
301C2×D4—5661no—
302C2×D4—5661no—
303C2×D4—5661no—
304C2×D4—5661no—
305C2×D4—5661no—
306C2×D4—5661no—
307C2×D4—5661no—
308C2×D4—5661no—
309C2×D4—5661no—
310C2×D4—11321no—
311C2×D4—11321no—
312C2×D4—11321no—
313C2×D4—11324no—
314C2×D4D113211yescharacteristic
315C22×C4—5661no—
316C22×C4—5661no—
317C22×C4—5661no—
318C22×C4C22×D28311yescharacteristic
319C22×C4C22×D28311yescharacteristic
320SD16—5662no—
321SD16—5662no—
322SD16—11321no—
323D8—2834no—
324D8—5662no—
325D8—5662no—
326D8—5662no—
327D8—5662no—
328D8—11321no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D28311yescharacteristic
332C2×C8C22×D28311yescharacteristic
333C2×C8C22×D28311yescharacteristic
334C2×C8C22×D28311yescharacteristic
335C4⋊C4—2831no—
336C4⋊C4—2831no—
337C4⋊C4—5661no—
338C4⋊C4D113211yescharacteristic
339C22⋊C4—5661no—
340C22⋊C4—5661no—
341C22⋊C4—5661no—
342C22⋊C4—5661no—
343C22⋊C4—5661no—
344C22⋊C4—5661no—
345C22⋊C4—5661no—
346C22⋊C4—5661no—
347C22⋊C4D113211yescharacteristic
348C22⋊C4D113211yescharacteristic
349C42C22×D28311yescharacteristic
350C23—5661no—
351C23—5661no—
352C23—5661no—
353C23—5661no—
354C23—5661no—
355C23—11322no—
356C23—11322no—
357C23—11322no—
358C23—11322no—
359C23—11322no—
360C23—11322no—
361C23—22641no—
362C23—22641no—
363C23—22641no—
364C23C2×D113211yescharacteristic
365C23C2×D113211yescharacteristic
366Q8—5661no—
367Q8—5661no—
368D4—22no—
369D4—2832no—
370D4—2832no—
371D4—5661no—
372D4—5661no—
373D4—5661no—
374D4—5661no—
375D4—5661no—
376D4—5661no—
377D4—5661no—
378D4—5661no—
379D4—11322no—
380D4—11322no—
381D4—11322no—
382D4—11322no—
383D4—11322no—
384D4—11322no—
385D4—11322no—
386D4—22641no—
387D4—22641no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—5661no—
393C2×C4—5661no—
394C2×C4—5661no—
395C2×C4—11322no—
396C2×C4—11322no—
397C2×C4—22641no—
398C2×C4C2×D113211yescharacteristic
399C2×C4C2×D113211yescharacteristic
400C2×C4C2×D113211yescharacteristic
401C2×C4C2×D113211yescharacteristic
402C2×C4C23×D28311yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D28312yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—5662no—
413C22—5662no—
414C22—11321no—
415C22—11321no—
416C22—11321no—
417C22—11321no—
418C22—11321no—
419C22—11321no—
420C22—11321no—
421C22—11321no—
422C22—11321no—
423C22—11321no—
424C22—11321no—
425C22—11321no—
426C22—11321no—
427C22—22644no—
428C22—22644no—
429C22—22644no—
430C22#2258363812yescomplemented
431C22C22×D113211yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—11321no—
437C4—11321no—
438C4—11321no—
439C4C2×D4×D28311yescharacteristic
440C4#2258365611yescharacteristic
441C2—22no—
442C2—41no—
443C2—11322no—
444C2—11322no—
445C2—22641no—
446C2—22641no—
447C2—22641no—
448C2D4×D113211yescharacteristic
449C2C2×#2258363811yescharacteristic
450C2#3182727011yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
hypercenter#435D283
hypocenterC283#3264
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22583638C2semidirect
2. C22×D2264C2semidirect
3. #31827111C2semidirect
4. D4×D1132C2semidirect
5. #31826854C2semidirect
6. #31826718C2semidirect
7. #31826694C2semidirect
8. #31826681C2semidirect
9. #31826661C2semidirect
10. #31826618C2semidirect
11. #31826612C2semidirect
12. #31826601C2semidirect
13. #31826601C2semidirect
14. #31826578C2semidirect
15. #435×C283C2semidirect
16. C2×#17985392C22semidirect
18. C22×D1132C22semidirect
19. C22×D1132C22semidirect
22. C2×#17985381C22semidirect
23. C2×#17985381C22semidirect
24. C2×#17985381C22semidirect
28. C2×D2264C22semidirect
29. C2×D2264C22semidirect
30. C2×D2264C22semidirect
31. C2×D2264C22semidirect
32. #22583607C22semidirect
33. #22583598C22semidirect
35. #22583589C22semidirect
38. #22583584C22semidirect
39. #22583584C22semidirect
44. C4×D1132C22semidirect
45. C4×D1132C22semidirect
47. #22583542C22semidirect
48. #22583535C22semidirect
49. #22583532C22semidirect
50. #22583532C22semidirect
51. #22583532C22semidirect
52. #22583532C22semidirect
53. #22583532C22semidirect
54. C2×M16×C283C22semidirect
55. C22×C8×C283C22semidirect
57. C4⋊C8×C283C22semidirect
58. C22⋊C8×C283C22semidirect
59. C22⋊C8×C283C22semidirect
60. #97×C283C22semidirect
99. D2264D4semidirect
154. D1132C2×D4semidirect
180. C8×C283C2×D4semidirect
186. C22×C283AGL(1,ℤ/8)semidirect
225. C283#3264semidirect
241. #435D283semidirect
258. C2×M16C2×D283semidirect
259. C22×C8C2×D283semidirect
277. C4⋊C8C2×D283semidirect
284. C22⋊C8C2×D283semidirect
285. C22⋊C8C2×D283semidirect
286. #97C2×D283semidirect
406. C8D4×D283semidirect
430. C22#22583638semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#225836382
C22×D22642
#318271112
D4×D11322
#318268542
#318267182
#318266942
#318266812
#318266612
#318266182
#318266122
#318266012
#318265782
#435×C2832
#3264283