Finite Group Databasebeta

← #472×D283 #49130964

Subgroups — #472×D283 #49130964

Order 36224.

488 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1AGL(1,ℤ/8)×D283C212yesmaximal, complemented
2C2×D8×D283C211yesmaximal, characteristic, complemented
3#131×D283C211yesmaximal, characteristic, complemented
4#31826736C211yesmaximal, characteristic, complemented
5#31826735C211yesmaximal, characteristic, complemented
6#31826734C212yesmaximal, complemented
7#31826733C212yesmaximal, complemented
8#31826732C211yesmaximal, characteristic, complemented
9#108×D283C211yesmaximal, characteristic, complemented
10#100×D283C212yesmaximal, complemented
11#472×C283C211yesmaximal, characteristic, complemented
12#41×D283C2211yescharacteristic
13C2×D4×D283C2212yes—
14#22583638C2212yescomplemented
15#22583637—22no—
16#22583636C2212yescomplemented
17#22583635C2212yescomplemented
18#22583634—22no—
19SD16×D283—22no—
20C2×D2264C2211yescharacteristic, complemented
21C2×#17985377C2212yescomplemented
22D8×D283—22no—
23D8×D283—21no—
24D8×D283—21no—
25D8×D283—21no—
26D8×D283—21no—
27#22583618—21no—
28#22583618C2211yescharacteristic, complemented
29#22583617C2211yescharacteristic, complemented
30#22583616—21no—
31#22583616C2211yescharacteristic, complemented
32M16×D283—21no—
33M16×D283C2211yescharacteristic
34M16×D283C2212yes—
35C2×C8×D283—21no—
36C2×C8×D283C2211yescharacteristic
37#22583546C2211yescharacteristic, complemented
38#22583545C2212yescomplemented
39#22583527C2212yescomplemented
40#22583526C2212yescomplemented
41#22583526C2212yescomplemented
42AGL(1,ℤ/8)×C283C2212yescomplemented
43C2×D8×C283C2211yescharacteristic, complemented
44#131×C283C2211yescharacteristic, complemented
45#108×C283C2211yescharacteristic, complemented
46#100×C283C2212yescomplemented
47C23×D283—22no—
48#17985393D411yescharacteristic
49#17985392—21no—
50#17985392C2311yescharacteristic
51#17985391—21no—
52#17985391D411yescharacteristic
53Q8×D283D411yescharacteristic
54C2×D1132C2312yes—
55C2×C22⋊D283—22no—
56D4×D283—21no—
57D4×D283—22no—
58D4×D283—22no—
59D4×D283—22no—
60D4×D283—22no—
61D4×D283D411yescharacteristic
62C2×C4×D283—21no—
63C2×C4×D283C2311yescharacteristic
64#17985381—22no—
65#17985380—22no—
66#17985379—22no—
67D2264—22no—
68D2264—21no—
69D2264—21no—
70#17985377—22no—
71#17985377—22no—
72#17985377—22no—
73#17985377—22no—
74#17985376—21no—
75#17985376C2311yescharacteristic
76#17985376C2312yes—
77#17985375—21no—
78#17985375—22no—
79#17985375—21no—
80#17985375—21no—
81C2×C283⋊C8—21no—
82C2×C283⋊C8C2311yescharacteristic
83C8×D283—21no—
84C8×D283—22no—
85C8×D283—21no—
86C8×D283—21no—
87C8×D283D411yescharacteristic
88C8×D283D411yescharacteristic
89C8×D283D411yescharacteristic
90C8×D283D411yescharacteristic
91#41×C283C2311yescharacteristic
92C2×D4×C283C2312yes—
93SD16×C283—22no—
94D8×C283—22no—
95D8×C283—21no—
96D8×C283—21no—
97M16×C283—21no—
98M16×C283C2311yescharacteristic
99M16×C283C2312yes—
100C2×C8×C283—21no—
101C2×C8×C283C2311yescharacteristic
102C22×D283—21no—
103C22×D283—22no—
104C22×D283—42no—
105C22×D283—42no—
106C22×D283—84no—
107C22×D283#4111yescharacteristic
108Dic566—21no—
109Dic566C2×D411yescharacteristic
110D1132—21no—
111D1132—22no—
112D1132—22no—
113D1132C2×D411yescharacteristic
114C22⋊D283—21no—
115C22⋊D283—21no—
116C22⋊D283—21no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C2×Dic283—21no—
120C2×Dic283#4111yescharacteristic
121C4×D283—21no—
122C4×D283—21no—
123C4×D283—21no—
124C4×D283C2×D411yescharacteristic
125C4×D283C2×D411yescharacteristic
126C4×D283C2×D411yescharacteristic
127C4×D283C2×D411yescharacteristic
128C283⋊C8—21no—
129C283⋊C8—22no—
130C283⋊C8C2×D411yescharacteristic
131C283⋊C8C2×D411yescharacteristic
132C23×C283—22no—
133Q8×C283C2×D411yescharacteristic
134D4×C283—21no—
135D4×C283—22no—
136D4×C283—22no—
137D4×C283C2×D411yescharacteristic
138C2×C4×C283—21no—
139C2×C4×C283C2411yescharacteristic
140C8×C283—21no—
141C8×C283—22no—
142C8×C283C2×D411yescharacteristic
143C8×C283C2×D411yescharacteristic
144C22×C283—21no—
145C22×C283—42no—
146C22×C283—82no—
147C22×C283C2×#4111yescharacteristic
148C2×D283—22no—
149C2×D283—21no—
150C2×D283—42no—
151C2×D283—42no—
152C2×D283—84no—
153C2×D283—84no—
154C2×D283—82no—
155C2×D283#12111yescharacteristic
156C2×D283#12111yescharacteristic
157C4×C283—21no—
158C4×C283C22×D411yescharacteristic
159C4×C283C22×D411yescharacteristic
160Dic283—21no—
161Dic283#12111yescharacteristic
162Dic283#12111yescharacteristic
163C2×C283—21no—
164C2×C283—41no—
165C2×C283—82no—
166C2×C283C2×#12111yescharacteristic
167D283—21no—
168D283—41no—
169D283—82no—
170D283#47212yesdirect product factor
171C283C2×#47211yescharacteristic, complemented, Sylow
172C2×#472—2831nomaximal, Sylow
173C2×AGL(1,ℤ/8)—2832no—
174C22×D8—2831no—
175C2×#131—2831no—
176#472—2832no—
177#472—2831no—
178#472—2831no—
179#472—2831no—
180#472—2832no—
181#472D28311yescharacteristic, direct product factor
182C2×#108—2831no—
183C2×#100—2832no—
184C2×#41—2831no—
185C22×D4—2832no—
186AGL(1,ℤ/8)—2832no—
187AGL(1,ℤ/8)—2832no—
188AGL(1,ℤ/8)—2832no—
189AGL(1,ℤ/8)—5662no—
190AGL(1,ℤ/8)—5662no—
191AGL(1,ℤ/8)C2×D28312yescomplemented
192C2×SD16—5662no—
193C2×D8—2832no—
194C2×D8—2831no—
195C2×D8—5661no—
196C2×D8—5661no—
197C2×D8—5661no—
198C2×D8—5661no—
199C2×D8—5662no—
200C2×D8C2×D28311yescharacteristic, complemented
201#131—2831no—
202#131—2831no—
203#131—2831no—
204#131—5661no—
205#131—5661no—
206#131C2×D28311yescharacteristic, complemented
207C2×M16—2831no—
208C2×M16—2832no—
209C2×M16—5661no—
210C22×C8—2831no—
211C22×C8—5661no—
212#108—2832no—
213#108—2831no—
214#108C2×D28311yescharacteristic, complemented
215#100—2832no—
216#100—2832no—
217#100—2832no—
218#100C2×D28312yescomplemented
219C24—5662no—
220#41—2831no—
221#41—2831no—
222#41—2831no—
223#41—5661no—
224#41—5661no—
225#41C22×D28311yescharacteristic
226C2×Q8—2831no—
227C2×D4—2831no—
228C2×D4—2832no—
229C2×D4—5662no—
230C2×D4—5662no—
231C2×D4—5662no—
232C2×D4—5662no—
233C2×D4—5662no—
234C2×D4—5661no—
235C2×D4C22×D28312yes—
236C22×C4—2831no—
237C22×C4—5661no—
238SD16—22no—
239SD16—5662no—
240SD16—5662no—
241SD16—5662no—
242D8—22no—
243D8—21no—
244D8—21no—
245D8—5662no—
246D8—5662no—
247D8—5662no—
248D8—5662no—
249D8—5662no—
250D8—5661no—
251D8—5661no—
252M16—21no—
253M16—2831no—
254M16—2832no—
255M16—5661no—
256M16—5661no—
257M16—5662no—
258M16—5661no—
259M16—5661no—
260M16C22×D28311yescharacteristic
261M16C22×D28312yes—
262C2×C8—21no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—2831no—
266C2×C8—2831no—
267C2×C8—2831no—
268C2×C8—5661no—
269C2×C8—5661no—
270C2×C8—5662no—
271C2×C8—5661no—
272C2×C8—5661no—
273C2×C8C22×D28311yescharacteristic
274C23—22no—
275C23—2831no—
276C23—5661no—
277C23—5662no—
278C23—11322no—
279C23—11322no—
280C23—22644no—
281Q8—2831no—
282Q8—5661no—
283Q8D4×D28311yescharacteristic
284D4—21no—
285D4—22no—
286D4—22no—
287D4—2831no—
288D4—5661no—
289D4—5661no—
290D4—5661no—
291D4—5661no—
292D4—5662no—
293D4—5662no—
294D4—11322no—
295D4—11322no—
296D4D4×D28311yescharacteristic
297C2×C4—21no—
298C2×C4—2831no—
299C2×C4—2831no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4C23×D28311yescharacteristic
308C8—21no—
309C8—22no—
310C8—2831no—
311C8—2831no—
312C8—5661no—
313C8—5662no—
314C8D4×D28311yescharacteristic
315C8D4×D28311yescharacteristic
316C22—21no—
317C22—42no—
318C22—82no—
319C22—2831no—
320C22—2831no—
321C22—5662no—
322C22—5661no—
323C22—11322no—
324C22—11322no—
325C22—22642no—
326C22—22644no—
327C22—22644no—
328C22#41×D28311yescharacteristic
329C4—21no—
330C4—2831no—
331C4—2831no—
332C4—5661no—
333C4C2×D4×D28311yescharacteristic
334C4C2×D4×D28311yescharacteristic
335C2—21no—
336C2—41no—
337C2—82no—
338C2—2832no—
339C2—5661no—
340C2—11321no—
341C2—22642no—
342C2#121×D28311yescharacteristic
subgroupG/H
centerC2#121×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#472×C283C2
socleC2×C283C2×#121
hypercenter#472D283
hypocenterC283C2×#472
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. AGL(1,ℤ/8)×D283C2semidirect
2. C2×D8×D283C2semidirect
3. #131×D283C2semidirect
4. #31826736C2semidirect
5. #31826735C2semidirect
6. #31826734C2semidirect
7. #31826733C2semidirect
8. #31826732C2semidirect
9. #108×D283C2semidirect
10. #100×D283C2semidirect
11. #472×C283C2semidirect
14. #22583638C22semidirect
16. #22583636C22semidirect
17. #22583635C22semidirect
20. C2×D2264C22semidirect
21. C2×#17985377C22semidirect
28. #22583618C22semidirect
29. #22583617C22semidirect
31. #22583616C22semidirect
37. #22583546C22semidirect
38. #22583545C22semidirect
39. #22583527C22semidirect
40. #22583526C22semidirect
41. #22583526C22semidirect
42. AGL(1,ℤ/8)×C283C22semidirect
43. C2×D8×C283C22semidirect
44. #131×C283C22semidirect
45. #108×C283C22semidirect
46. #100×C283C22semidirect
170. D283#472direct (N × H)
171. C283C2×#472semidirect
181. #472D283direct (N × H)
191. AGL(1,ℤ/8)C2×D283semidirect
200. C2×D8C2×D283semidirect
206. #131C2×D283semidirect
214. #108C2×D283semidirect
218. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
AGL(1,ℤ/8)×D2832
C2×D8×D2832
#131×D2832
#318267362
#318267352
#318267342
#318267332
#318267322
#108×D2832
#100×D2832
#472×C2832
C2×#472283