Finite Group Databasebeta

← #473×D283 #49130970

Subgroups — #473×D283 #49130970

Order 36224.

448 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×D283C212yesmaximal
2C2×Q16×D283C211yesmaximal, characteristic, complemented
3#131×D283C211yesmaximal, characteristic
4#31826741C211yesmaximal, characteristic, complemented
5#31826740C211yesmaximal, characteristic, complemented
6#31826739C212yesmaximal, complemented
7#31826738C212yesmaximal, complemented
8#31826737C211yesmaximal, characteristic, complemented
9#108×D283C211yesmaximal, characteristic, complemented
10#101×D283C212yesmaximal, complemented
11#473×C283C211yesmaximal, characteristic, complemented
12#41×D283C2211yescharacteristic
13C2×Q8×D283C2212yes—
14#22583643C2212yes—
15#22583642—22no—
16#22583641C2212yes—
17#22583640C2212yes—
18#22583639—22no—
19C2×Dic1132C2211yescharacteristic, complemented
20C2×#17985382C2212yescomplemented
21Q16×D283—22no—
22Q16×D283—21no—
23Q16×D283—21no—
24Q16×D283—21no—
25Q16×D283—21no—
26SD16×D283—22no—
27#22583618—21no—
28#22583618C2211yescharacteristic
29#22583617C2211yescharacteristic
30#22583616—21no—
31#22583616C2211yescharacteristic
32M16×D283—21no—
33M16×D283C2211yescharacteristic
34M16×D283C2212yes—
35C2×C8×D283—21no—
36C2×C8×D283C2211yescharacteristic
37#22583546C2211yescharacteristic, complemented
38#22583545C2212yescomplemented
39#22583529C2212yescomplemented
40#22583528C2212yescomplemented
41#22583528C2212yescomplemented
42#137×C283C2212yes—
43C2×Q16×C283C2211yescharacteristic, complemented
44#131×C283C2211yescharacteristic
45#108×C283C2211yescharacteristic, complemented
46#101×C283C2212yescomplemented
47#17985393D411yescharacteristic
48#17985392—21no—
49#17985392C2311yescharacteristic
50#17985391—21no—
51#17985391D411yescharacteristic
52C2×Dic566—22no—
53C2×Dic566C2312yes—
54Q8×D283—22no—
55Q8×D283—22no—
56Q8×D283—22no—
57Q8×D283—22no—
58Q8×D283D411yescharacteristic
59D4×D283—21no—
60D4×D283D411yescharacteristic
61C2×C4×D283—21no—
62C2×C4×D283—22no—
63C2×C4×D283C2311yescharacteristic
64Dic1132—22no—
65Dic1132—21no—
66Dic1132—21no—
67#17985382—22no—
68#17985382—22no—
69#17985382—22no—
70#17985382—22no—
71#17985381—22no—
72#17985380—22no—
73#17985379—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×Q8×C283C2312yes—
93Q16×C283—22no—
94Q16×C283—21no—
95Q16×C283—21no—
96SD16×C283—22no—
97M16×C283—21no—
98M16×C283C2311yescharacteristic
99M16×C283C2312yes—
100C2×C8×C283—21no—
101C2×C8×C283C2311yescharacteristic
102C22×D283—21no—
103C22×D283#4111yescharacteristic
104Dic566—21no—
105Dic566—22no—
106Dic566—22no—
107Dic566—42no—
108Dic566—42no—
109Dic566C2×D411yescharacteristic
110D1132—21no—
111D1132C2×D411yescharacteristic
112C22⋊D283—21no—
113C22⋊D283—21no—
114C22⋊D283—21no—
115C2×Dic283—21no—
116C2×Dic283—22no—
117C2×Dic283#4111yescharacteristic
118C4×D283—21no—
119C4×D283—21no—
120C4×D283—21no—
121C4×D283—42no—
122C4×D283—42no—
123C4×D283C2×D411yescharacteristic
124C4×D283C2×D411yescharacteristic
125C4×D283C2×D411yescharacteristic
126C4×D283C2×D411yescharacteristic
127C283⋊C8—21no—
128C283⋊C8—22no—
129C283⋊C8C2×D411yescharacteristic
130C283⋊C8C2×D411yescharacteristic
131Q8×C283—22no—
132Q8×C283—22no—
133Q8×C283C2×D411yescharacteristic
134D4×C283—21no—
135D4×C283C2×D411yescharacteristic
136C2×C4×C283—21no—
137C2×C4×C283—22no—
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—22no—
141C8×C283C2×D411yescharacteristic
142C8×C283C2×D411yescharacteristic
143C22×C283—21no—
144C22×C283C2×#4111yescharacteristic
145C2×D283—22no—
146C2×D283—21no—
147C2×D283—42no—
148C2×D283#12111yescharacteristic
149C2×D283#12111yescharacteristic
150C4×C283—21no—
151C4×C283—42no—
152C4×C283C22×D411yescharacteristic
153C4×C283C22×D411yescharacteristic
154Dic283—21no—
155Dic283—42no—
156Dic283#12111yescharacteristic
157Dic283#12111yescharacteristic
158C2×C283—21no—
159C2×C283—41no—
160C2×C283C2×#12111yescharacteristic
161D283—21no—
162D283—41no—
163D283#47312yesdirect product factor
164C283C2×#47311yescharacteristic, complemented, Sylow
165C2×#473—2831nomaximal, Sylow
166C2×#137—2832no—
167C22×Q16—2831no—
168C2×#131—2831no—
169#473—2832no—
170#473—2831no—
171#473—2831no—
172#473—2831no—
173#473—2832no—
174#473D28311yescharacteristic, direct product factor
175C2×#108—2831no—
176C2×#101—2832no—
177C2×#41—2831no—
178C22×Q8—2832no—
179#137—2832no—
180#137—2832no—
181#137—2832no—
182#137—5662no—
183#137—5662no—
184#137C2×D28312yes—
185C2×Q16—2832no—
186C2×Q16—2831no—
187C2×Q16—5661no—
188C2×Q16—5661no—
189C2×Q16—5661no—
190C2×Q16—5661no—
191C2×Q16—5662no—
192C2×Q16C2×D28311yescharacteristic, complemented
193C2×SD16—5662no—
194#131—2831no—
195#131—2831no—
196#131—2831no—
197#131—5661no—
198#131—5661no—
199#131C2×D28311yescharacteristic
200C2×M16—2831no—
201C2×M16—2832no—
202C2×M16—5661no—
203C22×C8—2831no—
204C22×C8—5661no—
205#108—2832no—
206#108—2831no—
207#108C2×D28311yescharacteristic, complemented
208#101—2832no—
209#101—2832no—
210#101—2832no—
211#101C2×D28312yescomplemented
212#41—2831no—
213#41—2831no—
214#41—2831no—
215#41—5661no—
216#41—5661no—
217#41C22×D28311yescharacteristic
218C2×Q8—2831no—
219C2×Q8—2832no—
220C2×Q8—5662no—
221C2×Q8—5662no—
222C2×Q8—5662no—
223C2×Q8—5662no—
224C2×Q8—5662no—
225C2×Q8C22×D28312yes—
226C2×D4—2831no—
227C2×D4—5661no—
228C22×C4—2831no—
229C22×C4—5661no—
230C22×C4—5662no—
231Q16—22no—
232Q16—21no—
233Q16—21no—
234Q16—5662no—
235Q16—5662no—
236Q16—5662no—
237Q16—5662no—
238Q16—5662no—
239Q16—5661no—
240Q16—5661no—
241SD16—22no—
242SD16—5662no—
243SD16—5662no—
244SD16—5662no—
245M16—21no—
246M16—2831no—
247M16—2832no—
248M16—5661no—
249M16—5661no—
250M16—5662no—
251M16—5661no—
252M16—5661no—
253M16C22×D28311yescharacteristic
254M16C22×D28312yes—
255C2×C8—21no—
256C2×C8—2831no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—2831no—
261C2×C8—5661no—
262C2×C8—5661no—
263C2×C8—5662no—
264C2×C8—5661no—
265C2×C8—5661no—
266C2×C8C22×D28311yescharacteristic
267C23—2831no—
268C23—5661no—
269Q8—22no—
270Q8—22no—
271Q8—2831no—
272Q8—5661no—
273Q8—5662no—
274Q8—5662no—
275Q8—11322no—
276Q8—11322no—
277Q8D4×D28311yescharacteristic
278D4—21no—
279D4—2831no—
280D4—5661no—
281D4—5661no—
282D4—5661no—
283D4—5661no—
284D4D4×D28311yescharacteristic
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—2831no—
288C2×C4—2831no—
289C2×C4—2831no—
290C2×C4—2831no—
291C2×C4—2831no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—5661no—
295C2×C4—5661no—
296C2×C4—5662no—
297C2×C4—11322no—
298C2×C4—11322no—
299C2×C4C23×D28311yescharacteristic
300C8—21no—
301C8—22no—
302C8—2831no—
303C8—2831no—
304C8—5661no—
305C8—5662no—
306C8D4×D28311yescharacteristic
307C8D4×D28311yescharacteristic
308C22—21no—
309C22—2831no—
310C22—2831no—
311C22—5662no—
312C22—5661no—
313C22—11322no—
314C22#41×D28311yescharacteristic
315C4—21no—
316C4—42no—
317C4—2831no—
318C4—2831no—
319C4—5661no—
320C4—11322no—
321C4C2×D4×D28311yescharacteristic
322C4C2×D4×D28311yescharacteristic
323C2—21no—
324C2—41no—
325C2—2832no—
326C2—5661no—
327C2—11321no—
328C2#121×D28311yescharacteristic
subgroupG/H
centerC2#121×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#473×C283C2
socleC2×C283C2×#121
prime radical#41×D283C22
hypercenter#473D283
hypocenterC283C2×#473
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D283C2semidirect
4. #31826741C2semidirect
5. #31826740C2semidirect
6. #31826739C2semidirect
7. #31826738C2semidirect
8. #31826737C2semidirect
9. #108×D283C2semidirect
10. #101×D283C2semidirect
11. #473×C283C2semidirect
19. C2×Dic1132C22semidirect
20. C2×#17985382C22semidirect
37. #22583546C22semidirect
38. #22583545C22semidirect
39. #22583529C22semidirect
40. #22583528C22semidirect
41. #22583528C22semidirect
43. C2×Q16×C283C22semidirect
45. #108×C283C22semidirect
46. #101×C283C22semidirect
163. D283#473direct (N × H)
164. C283C2×#473semidirect
174. #473D283direct (N × H)
192. C2×Q16C2×D283semidirect
207. #108C2×D283semidirect
211. #101C2×D283semidirect

Maximal subgroups

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

subgroupindex
#137×D2832
C2×Q16×D2832
#131×D2832
#318267412
#318267402
#318267392
#318267382
#318267372
#108×D2832
#101×D2832
#473×C2832
C2×#473283