Finite Group Databasebeta

← #49132749

Subgroups — #49132749

Order 36224.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C211yesmaximal, characteristic, complemented
2C22×#17985379C211yesmaximal, characteristic, complemented
3#31827126C211yesmaximal, characteristic, complemented
4#31827099C211yesmaximal, characteristic, complemented
5#31826851C211yesmaximal, characteristic, complemented
6#31826714C211yesmaximal, characteristic, complemented
7#31826699C211yesmaximal, characteristic, complemented
8#31826683C211yesmaximal, characteristic, complemented
9#31826663C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11#31826613C211yesmaximal, characteristic, complemented
12#31826601C211yesmaximal, characteristic, complemented
13#31826568C211yesmaximal, characteristic, complemented
14#31826533C211yesmaximal, characteristic, complemented
15#448×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic, complemented
17C22×D1132C2211yescharacteristic
18C2×D4×D283—21no—
19C2×D4×D283C2211yescharacteristic
20#22583637—24no—
21C2×#17985379—24no—
22C2×#17985379C2211yescharacteristic
23C2×#17985379C2211yescharacteristic
24C2×#17985379C2211yescharacteristic, complemented
25C2×#17985379C2211yescharacteristic, complemented
26C2×D2264C2211yescharacteristic
27C2×D2264C2211yescharacteristic, complemented
28C2×#17985377C2211yescharacteristic, complemented
29C2×#17985375C2211yescharacteristic, complemented
30C22×C283⋊C8C2211yescharacteristic, complemented
31#22583606C2211yescharacteristic
32#22583599—21no—
33#22583599C2211yescharacteristic, complemented
34#22583586—21no—
35#22583586C2211yescharacteristic, complemented
36#22583585C2211yescharacteristic
37#22583584—21no—
38#22583584C2211yescharacteristic, complemented
39#22583583—21no—
40#22583580—21no—
41#22583578—21no—
42Q8×Dic283C2211yescharacteristic, complemented
43#22583572C2211yescharacteristic
44C4×C22⋊D283—21no—
45C4×C22⋊D283C2211yescharacteristic
46#22583543C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic, complemented
50#22583531C2211yescharacteristic, complemented
51#22583530C2211yescharacteristic, complemented
52(C2×D283)⋊C8C2211yescharacteristic, complemented
53#22583520C2211yescharacteristic, complemented
54C22×Q8×C283C2211yescharacteristic, complemented
55C2×SD16×C283C2211yescharacteristic, complemented
56C2×SD16×C283C2211yescharacteristic, complemented
57#121×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60C22⋊C8×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283—21no—
63#17985393—22no—
64#17985393—41no—
65C2×D1132—22no—
66C2×D1132—21no—
67C2×D1132—21no—
68C2×D1132—21no—
69C2×D1132—41no—
70C2×D1132C2311yescharacteristic
71C2×D1132C2311yescharacteristic
72C2×D1132C2311yescharacteristic
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75C2×C22⋊D283—21no—
76C2×C22⋊D283—21no—
77C2×C22⋊D283D411yescharacteristic
78D4×D283—22no—
79D4×D283—41no—
80D4×D283—44no—
81C2×C4×D283—21no—
82C2×C4×D283—21no—
83C2×C4×D283C2311yescharacteristic
84#17985379—22no—
85#17985379—22no—
86#17985379—22no—
87#17985379D414yescomplemented
88D2264—22no—
89D2264—41no—
90#17985377—22no—
91#17985375—22no—
92C2×C283⋊C8—22no—
93C2×C283⋊C8C2311yescharacteristic
94C2×C283⋊C8C2311yescharacteristic
95C4⋊Dic283—21no—
96C4⋊Dic283C2311yescharacteristic
97Dic283⋊C4—21no—
98Dic283⋊C4D411yescharacteristic
99C22⋊Dic283D411yescharacteristic
100(C2×D283)⋊C4—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4D411yescharacteristic
107C4×Dic283—21no—
108C4×Dic283C2311yescharacteristic
109C2×Q8×C283—21no—
110C2×Q8×C283—22no—
111C2×Q8×C283—41no—
112C2×Q8×C283C2311yescharacteristic
113C2×Q8×C283C2311yescharacteristic
114C2×D4×C283—21no—
115C2×D4×C283C2311yescharacteristic
116C22×C4×C283—21no—
117C22×C4×C283C2311yescharacteristic
118SD16×C283—22no—
119SD16×C283—41no—
120C2×C8×C283C2311yescharacteristic
121C2×C8×C283C2311yescharacteristic
122C4⋊C4×C283C2311yescharacteristic
123C22⋊C4×C283—21no—
124C22×D283—21no—
125C22×D283—21no—
126C22×D283—21no—
127C22×D283—42no—
128C22×D283—42no—
129C22×D283—42no—
130C22×D283—42no—
131C22×D283—81no—
132C22×D283—81no—
133C22×D283C2×D411yescharacteristic
134D1132—21no—
135D1132—21no—
136D1132—21no—
137D1132—21no—
138D1132—21no—
139D1132—42no—
140D1132—42no—
141D1132—42no—
142D1132C2×D412yes—
143C22⋊D283—22no—
144C22⋊D283—42no—
145C22⋊D283—42no—
146C22⋊D283—42no—
147C22⋊D283—81no—
148C2×Dic283—21no—
149C2×Dic283C2×D411yescharacteristic
150C2×Dic283C2×D411yescharacteristic
151C2×Dic283C2×D411yescharacteristic
152C4×D283—21no—
153C4×D283—21no—
154C4×D283—42no—
155C4×D283—42no—
156C283⋊C8—21no—
157C283⋊C8C2×D412yescomplemented
158C23×C283—21no—
159C23×C283C2×D411yescharacteristic
160Q8×C283—21no—
161Q8×C283—21no—
162Q8×C283—21no—
163Q8×C283—42no—
164Q8×C283C2×D412yescomplemented
165D4×C283—21no—
166D4×C283—21no—
167D4×C283—42no—
168C2×C4×C283—21no—
169C2×C4×C283—21no—
170C2×C4×C283—21no—
171C2×C4×C283—21no—
172C2×C4×C283—21no—
173C2×C4×C283—42no—
174C2×C4×C283C2×D411yescharacteristic
175C2×C4×C283C2411yescharacteristic
176C8×C283—21no—
177C8×C283—21no—
178C22×C283—21no—
179C22×C283—21no—
180C22×C283—41no—
181C22×C283—41no—
182C22×C283—41no—
183C22×C283AGL(1,ℤ/8)12yescomplemented
184C22×C283C22×D411yescharacteristic
185C2×D283—21no—
186C2×D283—22no—
187C2×D283—21no—
188C2×D283—21no—
189C2×D283—41no—
190C2×D283—41no—
191C2×D283—41no—
192C2×D283—41no—
193C2×D283—41no—
194C2×D283—41no—
195C2×D283—41no—
196C2×D283—41no—
197C2×D283—84no—
198C2×D283—84no—
199C4×C283—21no—
200C4×C283—22no—
201C4×C283—41no—
202C4×C283—41no—
203C4×C283C22×D411yescharacteristic
204C4×C283H(5,𝔽2)11yescharacteristic
205Dic283—21no—
206Dic283—21no—
207Dic283—21no—
208Dic283—41no—
209C2×C283—22no—
210C2×C283—81no—
211C2×C283D4211yescharacteristic
212C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C283#57711yescharacteristic
214D283—41no—
215D283—42no—
216D283—81no—
217D283—81no—
218C283#326511yescharacteristic, complemented, Sylow
219#3265—2831nomaximal, Sylow
220C2×AGL(1,ℤ/8)—2831no—
221C22×SD16—2831no—
222#548—2831no—
223D42—2831no—
224#496—2831no—
225#468—2831no—
226#466—2831no—
227#463—2831no—
228#460—2831no—
229#450—2831no—
230#449—2831no—
231#448D28311yescharacteristic, complemented
232#447—2831no—
233#440—2831no—
234#435—2831no—
235C2×#41—2831no—
236C22×Q8C2×D28311yescharacteristic, complemented
237C22×D4—2831no—
238C22×D4—2831no—
239C22×D4—5661no—
240AGL(1,ℤ/8)—5664no—
241C2×SD16—2831no—
242C2×SD16—2831no—
243C2×SD16—2831no—
244C2×SD16—2831no—
245C2×SD16—5664no—
246C2×SD16C2×D28311yescharacteristic, complemented
247C2×SD16C2×D28311yescharacteristic, complemented
248C2×D8—2831no—
249C2×D8—2831no—
250C2×D8—2831no—
251C2×M16—2831no—
252C22×C8—2831no—
253#127—2831no—
254#124—2831no—
255#124—5661no—
256C22⋊Q8—2831no—
257C22⋊Q8—5661no—
258#121—2831no—
259#121—2831no—
260#121—5661no—
261#121—5661no—
262#121C2×D28311yescharacteristic
263#120—5661no—
264#120—5661no—
265C4×Q8—2831no—
266C4×D4—2831no—
267C4×D4—2831no—
268C4×D4—5661no—
269#107—2831no—
270C4⋊C8—2831no—
271#103C2×D28311yescharacteristic, complemented
272#103C2×D28311yescharacteristic, complemented
273#102—2831no—
274#102—2831no—
275#102—2831no—
276#102—2831no—
277C22⋊C8—2831no—
278C22⋊C8C2×D28311yescharacteristic, complemented
279#97—2831no—
280C24—5661no—
281C24—5661no—
282#41—5662no—
283#41—11321no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D28311yescharacteristic
288C2×Q8C22×D28311yescharacteristic
289C2×D4—21no—
290C2×D4—2831no—
291C2×D4—2831no—
292C2×D4—2831no—
293C2×D4—2831no—
294C2×D4—5662no—
295C2×D4—5661no—
296C2×D4—5661no—
297C2×D4—5661no—
298C2×D4—5661no—
299C2×D4—5661no—
300C2×D4—5662no—
301C2×D4—5661no—
302C2×D4—5661no—
303C2×D4—11321no—
304C2×D4—11321no—
305C2×D4—11324no—
306C2×D4C22×D28311yescharacteristic
307C22×C4—21no—
308C22×C4—2831no—
309C22×C4—5661no—
310C22×C4—5661no—
311C22×C4C22×D28311yescharacteristic
312SD16—22no—
313SD16—41no—
314SD16—2834no—
315SD16—5662no—
316SD16—5662no—
317SD16—5662no—
318D8—5662no—
319D8—5662no—
320D8—11321no—
321M16—5662no—
322C2×C8—2831no—
323C2×C8—2831no—
324C2×C8—5662no—
325C2×C8C22×D28311yescharacteristic
326C2×C8C22×D28311yescharacteristic
327C4⋊C4—2831no—
328C4⋊C4—2831no—
329C4⋊C4—5661no—
330C4⋊C4—5661no—
331C4⋊C4C22×D28311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—2831no—
334C22⋊C4—2831no—
335C22⋊C4—5661no—
336C22⋊C4—5661no—
337C22⋊C4—5661no—
338C22⋊C4—5661no—
339C22⋊C4—5661no—
340C22⋊C4—5661no—
341C42—2831no—
342C42—5661no—
343C23—21no—
344C23—2831no—
345C23—5661no—
346C23—5661no—
347C23—5661no—
348C23—11322no—
349C23—11322no—
350C23—11322no—
351C23—11322no—
352C23—22641no—
353C23—22641no—
354C23D4×D28311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D28312yescomplemented
360D4—21no—
361D4—21no—
362D4—42no—
363D4—2832no—
364D4—5662no—
365D4—5661no—
366D4—5661no—
367D4—5661no—
368D4—5661no—
369D4—5661no—
370D4—11322no—
371D4—11322no—
372D4—11322no—
373D4—11322no—
374D4—11322no—
375D4—11322no—
376D4—22641no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—2831no—
384C2×C4—2831no—
385C2×C4—2831no—
386C2×C4—5661no—
387C2×C4—5661no—
388C2×C4—5661no—
389C2×C4—11322no—
390C2×C4—11322no—
391C2×C4D4×D28311yescharacteristic
392C2×C4C23×D28311yescharacteristic
393C8—21no—
394C8—21no—
395C8—2832no—
396C8—5661no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—5661no—
403C22—5661no—
404C22—5661no—
405C22—5662no—
406C22—11321no—
407C22—11321no—
408C22—11321no—
409C22—11321no—
410C22—11321no—
411C22—11321no—
412C22—11321no—
413C22—11321no—
414C22—22644no—
415C22—22644no—
416C22#2258363712yescomplemented
417C22C2×D4×D28311yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—41no—
422C4—5661no—
423C4—5661no—
424C4—5661no—
425C4—11321no—
426C4C2×D4×D28311yescharacteristic
427C4#2258365511yescharacteristic
428C2—22no—
429C2—81no—
430C2—11321no—
431C2—11322no—
432C2—22641no—
433C2—22641no—
434C2#3182709711yescharacteristic
435C2C2×#2258363711yescharacteristic
436C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#448×C283C2
socleC22×C283C22×D4
hypercenter#448D283
hypocenterC283#3265
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. C22×#17985379C2semidirect
3. #31827126C2semidirect
4. #31827099C2semidirect
5. #31826851C2semidirect
6. #31826714C2semidirect
7. #31826699C2semidirect
8. #31826683C2semidirect
9. #31826663C2semidirect
10. #31826614C2semidirect
11. #31826613C2semidirect
12. #31826601C2semidirect
13. #31826568C2semidirect
14. #31826533C2semidirect
15. #448×C283C2semidirect
16. C2×#17985393C22semidirect
24. C2×#17985379C22semidirect
25. C2×#17985379C22semidirect
27. C2×D2264C22semidirect
28. C2×#17985377C22semidirect
29. C2×#17985375C22semidirect
30. C22×C283⋊C8C22semidirect
33. #22583599C22semidirect
35. #22583586C22semidirect
38. #22583584C22semidirect
42. Q8×Dic283C22semidirect
46. #22583543C22semidirect
47. Dic283⋊C8C22semidirect
49. #22583532C22semidirect
50. #22583531C22semidirect
51. #22583530C22semidirect
52. (C2×D283)⋊C8C22semidirect
53. #22583520C22semidirect
54. C22×Q8×C283C22semidirect
55. C2×SD16×C283C22semidirect
56. C2×SD16×C283C22semidirect
58. #103×C283C22semidirect
59. #103×C283C22semidirect
60. C22⋊C8×C283C22semidirect
87. #17985379D4semidirect
157. C283⋊C8C2×D4semidirect
164. Q8×C283C2×D4semidirect
183. C22×C283AGL(1,ℤ/8)semidirect
218. C283#3265semidirect
231. #448D283semidirect
236. C22×Q8C2×D283semidirect
246. C2×SD16C2×D283semidirect
247. C2×SD16C2×D283semidirect
271. #103C2×D283semidirect
272. #103C2×D283semidirect
278. C22⋊C8C2×D283semidirect
359. Q8D4×D283semidirect
416. C22#22583637semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
C22×#179853792
#318271262
#318270992
#318268512
#318267142
#318266992
#318266832
#318266632
#318266142
#318266132
#318266012
#318265682
#318265332
#448×C2832
#3265283