Finite Group Databasebeta

← #49132867

Subgroups — #49132867

Order 36224.

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×#22583637C211yesmaximal, characteristic, complemented
2C2×#22583634C211yesmaximal, characteristic, complemented
3#31827110C211yesmaximal, characteristic, complemented
4#31827108C211yesmaximal, characteristic, complemented
5#31826847C211yesmaximal, characteristic, complemented
6#31826714C211yesmaximal, characteristic, complemented
7#31826710C211yesmaximal, characteristic, complemented
8#31826681C211yesmaximal, characteristic, complemented
9#31826630C211yesmaximal, characteristic, complemented
10#31826624C211yesmaximal, characteristic, complemented
11#31826600C211yesmaximal, characteristic, complemented
12#31826597C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826542C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic, complemented
19C2×D4×D283C2211yescharacteristic, complemented
20#22583637—24no—
21#22583634—24no—
22C2×#17985382C2211yescharacteristic, complemented
23C2×#17985381C2211yescharacteristic, complemented
24C2×#17985380C2211yescharacteristic, complemented
25C2×#17985379C2211yescharacteristic, complemented
26C2×D2264C2211yescharacteristic
27C2×#17985377C2211yescharacteristic
28C2×#17985377C2211yescharacteristic
29C2×#17985375C2211yescharacteristic, complemented
30C2×#17985375C2211yescharacteristic, complemented
31#22583598C2211yescharacteristic, complemented
32#22583594—21no—
33#22583592—21no—
34#22583590C2211yescharacteristic, complemented
35#22583586C2211yescharacteristic, complemented
36#22583585C2211yescharacteristic
37#22583584—21no—
38#22583583—21no—
39#22583581C2211yescharacteristic
40#22583580—21no—
41#22583580—21no—
42C4×D1132C2211yescharacteristic
43C4×D1132C2211yescharacteristic, complemented
44C2×(C2×D283)⋊C4—21no—
45C22⋊C4×D283—21no—
46#22583543C2211yescharacteristic, complemented
47#22583535C2211yescharacteristic, complemented
48#22583532C2211yescharacteristic, complemented
49#22583531C2211yescharacteristic, complemented
50#22583530C2211yescharacteristic, complemented
51(C2×D283)⋊C8C2211yescharacteristic, complemented
52(C2×D283)⋊C8C2211yescharacteristic, complemented
53C4×C283⋊C8C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic, complemented
55C2×D8×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic, complemented
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283—21no—
63#17985393—22no—
64#17985393—41no—
65#17985391—22no—
66#17985391—41no—
67C2×Dic566C2311yescharacteristic
68C2×D1132—21no—
69C2×D1132—21no—
70C2×D1132D411yescharacteristic
71C2×D1132C2311yescharacteristic
72C2×D1132C2311yescharacteristic
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75C2×C22⋊D283—21no—
76C2×C22⋊D283—21no—
77D4×D283—22no—
78D4×D283—22no—
79D4×D283—41no—
80D4×D283—41no—
81C22×Dic283—21no—
82C2×C4×D283—21no—
83C2×C4×D283—21no—
84C2×C4×D283C2311yescharacteristic
85C2×C4×D283C2311yescharacteristic
86#17985382—41no—
87#17985381—22no—
88#17985380—22no—
89#17985379—22no—
90D2264—22no—
91#17985377—41no—
92#17985377D414yescomplemented
93#17985375—22no—
94#17985375—22no—
95C2×C283⋊C8C2311yescharacteristic
96C2×C283⋊C8C2311yescharacteristic
97C4⋊Dic283—21no—
98C4⋊Dic283D411yescharacteristic
99C4⋊Dic283C2311yescharacteristic
100Dic283⋊C4—21no—
101C22⋊Dic283—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4—21no—
108(C2×D283)⋊C4D411yescharacteristic
109(C2×D283)⋊C4D411yescharacteristic
110C2×Q8×C283C2311yescharacteristic
111C2×D4×C283C2311yescharacteristic
112C2×D4×C283C2311yescharacteristic
113C22×C4×C283—21no—
114SD16×C283—22no—
115D8×C283—22no—
116C2×C8×C283C2311yescharacteristic
117C2×C8×C283C2311yescharacteristic
118C4⋊C4×C283C2311yescharacteristic
119C22⋊C4×C283—21no—
120C22⋊C4×C283—21no—
121C22⋊C4×C283—21no—
122C42×C283C2311yescharacteristic
123C22×D283—21no—
124C22×D283—21no—
125C22×D283—42no—
126C22×D283—42no—
127C22×D283—42no—
128C22×D283—42no—
129C22×D283—81no—
130C22×D283—81no—
131C22×D283C2×D411yescharacteristic
132C22×D283C2×D411yescharacteristic
133Dic566—21no—
134Dic566—21no—
135D1132—21no—
136D1132—21no—
137D1132—21no—
138D1132—41no—
139D1132—42no—
140D1132—81no—
141D1132C2×D412yes—
142C22⋊D283—42no—
143C22⋊D283—42no—
144C22⋊D283—42no—
145C22⋊D283—81no—
146C2×Dic283—21no—
147C2×Dic283—21no—
148C2×Dic283—42no—
149C2×Dic283C2×D411yescharacteristic
150C2×Dic283C2×D411yescharacteristic
151C4×D283—21no—
152C4×D283—21no—
153C4×D283—21no—
154C4×D283—21no—
155C4×D283—42no—
156C4×D283—81no—
157C283⋊C8—21no—
158C283⋊C8C2×D412yes—
159C23×C283—21no—
160C23×C283—21no—
161Q8×C283—21no—
162Q8×C283—21no—
163D4×C283—21no—
164D4×C283—21no—
165D4×C283—21no—
166D4×C283C2×D412yes—
167C2×C4×C283—21no—
168C2×C4×C283—21no—
169C2×C4×C283—81no—
170C2×C4×C283C2×D411yescharacteristic
171C2×C4×C283C2×D411yescharacteristic
172C2×C4×C283C2411yescharacteristic
173C8×C283—21no—
174C8×C283—21no—
175C22×C283—22no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283—41no—
179C22×C283—41no—
180C22×C283—41no—
181C22×C283C22×D411yescharacteristic
182C2×D283—21no—
183C2×D283—21no—
184C2×D283—22no—
185C2×D283—21no—
186C2×D283—21no—
187C2×D283—21no—
188C2×D283—21no—
189C2×D283—41no—
190C2×D283—41no—
191C2×D283—41no—
192C2×D283—41no—
193C2×D283—41no—
194C2×D283—84no—
195C2×D283—84no—
196C4×C283—21no—
197C4×C283—21no—
198C4×C283—41no—
199C4×C283—41no—
200C4×C283C22×D411yescharacteristic
201C4×C283H(5,𝔽2)11yescharacteristic
202Dic283—21no—
203Dic283—21no—
204Dic283—41no—
205Dic283—41no—
206C2×C283—42no—
207C2×C283—81no—
208C2×C283D4211yescharacteristic
209C2×C283#57511yescharacteristic
210C2×C283#57611yescharacteristic
211D283—41no—
212D283—41no—
213D283—42no—
214D283—81no—
215C283#327311yescharacteristic, complemented, Sylow
216#3273—2831nomaximal, Sylow
217C2×AGL(1,ℤ/8)—2831no—
218C2×AGL(1,ℤ/8)—2831no—
219#546—2831no—
220#546—2831no—
221#495—2831no—
222#468—2831no—
223#468—2831no—
224#463—2831no—
225#463D28311yescharacteristic, complemented
226#452—2831no—
227#452—2831no—
228#447—2831no—
229#447—2831no—
230C4×D8—2831no—
231#436—2831no—
232C2×#41—2831no—
233C2×#41—2831no—
234C22×D4—2831no—
235C22×D4—2831no—
236AGL(1,ℤ/8)—5664no—
237AGL(1,ℤ/8)—5664no—
238C2×Q16—2831no—
239C2×SD16—2831no—
240C2×SD16—2831no—
241C2×SD16—2831no—
242C2×SD16C2×D28311yescharacteristic, complemented
243C2×D8—2831no—
244C2×D8—2831no—
245C2×D8—2831no—
246C2×D8C2×D28311yescharacteristic
247C2×M16—2831no—
248C2×M16—2831no—
249#124—2831no—
250#124C2×D28311yescharacteristic, complemented
251#123—5661no—
252#123—5661no—
253C22⋊Q8—2831no—
254C22⋊Q8—2831no—
255#121—2831no—
256#121—2831no—
257#121—5661no—
258#121—5661no—
259#120—5661no—
260#120—5661no—
261C4×D4—2831no—
262C4×D4—2831no—
263C4×D4C2×D28311yescharacteristic, complemented
264C2×C22⋊C4—5661no—
265C2×C22⋊C4—5661no—
266#107—2831no—
267C4⋊C8C2×D28311yescharacteristic, complemented
268#103—2831no—
269#103C2×D28311yescharacteristic, complemented
270#102—2831no—
271#102—2831no—
272#102—2831no—
273#102C2×D28311yescharacteristic, complemented
274C22⋊C8—2831no—
275C22⋊C8—2831no—
276C4×C8—2831no—
277C24—5661no—
278C24—5661no—
279#41—5662no—
280#41—5662no—
281#41—11321no—
282#41—11321no—
283C2×Q8—2831no—
284C2×Q8C22×D28311yescharacteristic
285C2×D4—2831no—
286C2×D4—2831no—
287C2×D4—2831no—
288C2×D4—5661no—
289C2×D4—5661no—
290C2×D4—5661no—
291C2×D4—5661no—
292C2×D4—5662no—
293C2×D4—5662no—
294C2×D4—5661no—
295C2×D4—5661no—
296C2×D4—11321no—
297C2×D4—11321no—
298C2×D4C22×D28311yescharacteristic
299C2×D4C22×D28311yescharacteristic
300C22×C4—21no—
301C22×C4—2831no—
302C22×C4—2831no—
303C22×C4—5661no—
304C22×C4—5661no—
305C22×C4—5661no—
306Q16—11321no—
307SD16—22no—
308SD16—5662no—
309SD16—5662no—
310SD16—5662no—
311D8—22no—
312D8—2834no—
313D8—5662no—
314D8—11321no—
315M16—5662no—
316M16—5662no—
317C2×C8—2831no—
318C2×C8—2831no—
319C2×C8C22×D28311yescharacteristic
320C2×C8C22×D28311yescharacteristic
321C4⋊C4—2831no—
322C4⋊C4—2831no—
323C4⋊C4—5661no—
324C4⋊C4—5661no—
325C4⋊C4C22×D28311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—2831no—
330C22⋊C4—2831no—
331C22⋊C4—5661no—
332C22⋊C4—5661no—
333C22⋊C4—5661no—
334C22⋊C4—5661no—
335C22⋊C4—5661no—
336C22⋊C4—5661no—
337C22⋊C4—5661no—
338C42C22×D28311yescharacteristic
339C23—21no—
340C23—21no—
341C23—2831no—
342C23—2831no—
343C23—5661no—
344C23—5661no—
345C23—11322no—
346C23—11322no—
347C23—11322no—
348C23—11322no—
349C23—22641no—
350C23—22641no—
351Q8—21no—
352Q8—21no—
353Q8—5661no—
354Q8—5661no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—2832no—
359D4—5661no—
360D4—5661no—
361D4—5661no—
362D4—11321no—
363D4—11322no—
364D4—11322no—
365D4—11322no—
366D4—11322no—
367D4—22641no—
368D4—22641no—
369D4D4×D28312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—2831no—
374C2×C4—2831no—
375C2×C4—5661no—
376C2×C4—5661no—
377C2×C4—5661no—
378C2×C4—5661no—
379C2×C4—5661no—
380C2×C4—5661no—
381C2×C4—11322no—
382C2×C4—11322no—
383C2×C4—22641no—
384C2×C4D4×D28311yescharacteristic
385C2×C4D4×D28311yescharacteristic
386C2×C4C23×D28311yescharacteristic
387C8—21no—
388C8—21no—
389C8—2832no—
390C8—5661no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—5661no—
398C22—5661no—
399C22—5661no—
400C22—5661no—
401C22—5661no—
402C22—5661no—
403C22—5662no—
404C22—11321no—
405C22—11321no—
406C22—11321no—
407C22—11321no—
408C22—11321no—
409C22—22644no—
410C22—22644no—
411C22C2×D4×D28311yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—5661no—
417C4—5661no—
418C4—11321no—
419C4—11321no—
420C4C2×D4×D28311yescharacteristic
421C4#2258365611yescharacteristic
422C2—42no—
423C2—81no—
424C2—11321no—
425C2—11321no—
426C2—11322no—
427C2—22641no—
428C2#3182709911yescharacteristic
429C2#3182726211yescharacteristic
430C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
hypercenter#463D283
hypocenterC283#3273
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. C2×#22583634C2semidirect
3. #31827110C2semidirect
4. #31827108C2semidirect
5. #31826847C2semidirect
6. #31826714C2semidirect
7. #31826710C2semidirect
8. #31826681C2semidirect
9. #31826630C2semidirect
10. #31826624C2semidirect
11. #31826600C2semidirect
12. #31826597C2semidirect
13. C4×#17985377C2semidirect
14. #31826542C2semidirect
15. #463×C283C2semidirect
18. C2×D4×D283C22semidirect
19. C2×D4×D283C22semidirect
22. C2×#17985382C22semidirect
23. C2×#17985381C22semidirect
24. C2×#17985380C22semidirect
25. C2×#17985379C22semidirect
29. C2×#17985375C22semidirect
30. C2×#17985375C22semidirect
31. #22583598C22semidirect
34. #22583590C22semidirect
35. #22583586C22semidirect
43. C4×D1132C22semidirect
46. #22583543C22semidirect
47. #22583535C22semidirect
48. #22583532C22semidirect
49. #22583531C22semidirect
50. #22583530C22semidirect
51. (C2×D283)⋊C8C22semidirect
52. (C2×D283)⋊C8C22semidirect
53. C4×C283⋊C8C22semidirect
54. C2×SD16×C283C22semidirect
56. #124×C283C22semidirect
57. C4×D4×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
92. #17985377D4semidirect
215. C283#3273semidirect
225. #463D283semidirect
242. C2×SD16C2×D283semidirect
250. #124C2×D283semidirect
263. C4×D4C2×D283semidirect
267. C4⋊C8C2×D283semidirect
269. #103C2×D283semidirect
273. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
C2×#225836342
#318271102
#318271082
#318268472
#318267142
#318267102
#318266812
#318266302
#318266242
#318266002
#318265972
C4×#179853772
#318265422
#463×C2832
#3273283