Finite Group Databasebeta

← #464×D283 #49130701

Subgroups — #464×D283 #49130701

Order 36224.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D283C211yesmaximal, characteristic, complemented
2C2×SD16×D283C211yesmaximal, characteristic
3#124×D283C211yesmaximal, characteristic
4C4×Q8×D283C211yesmaximal, characteristic, complemented
5#31826690C211yesmaximal, characteristic, complemented
6#31826689C211yesmaximal, characteristic, complemented
7#31826688C211yesmaximal, characteristic, complemented
8#31826687C211yesmaximal, characteristic, complemented
9#31826686C211yesmaximal, characteristic, complemented
10#31826685C211yesmaximal, characteristic, complemented
11#31826684C211yesmaximal, characteristic, complemented
12C4⋊C8×D283C211yesmaximal, characteristic, complemented
13#103×D283C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic
15#464×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic, complemented
20C2×#17985382C2211yescharacteristic, complemented
21C2×#17985382C2211yescharacteristic, complemented
22Q16×D283—24no—
23C2×#17985381C2211yescharacteristic
24C2×#17985380C2211yescharacteristic
25C2×#17985379C2211yescharacteristic
26SD16×D283—24no—
27C2×C8×D283C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583599C2211yescharacteristic
30#22583598C2211yescharacteristic
31#22583597C2211yescharacteristic
32#22583596—21no—
33#22583596—21no—
34Q8×Dic283C2211yescharacteristic, complemented
35C4×Dic566—21no—
36C4×Dic566C2211yescharacteristic, complemented
37#22583575—21no—
38#22583575C2211yescharacteristic, complemented
39C4⋊C4×D283—21no—
40C4⋊C4×D283C2211yescharacteristic
41C22⋊C4×D283—21no—
42C22⋊C4×D283—21no—
43C42×D283—21no—
44C42×D283C2211yescharacteristic
45C4⋊(C283⋊C8)C2211yescharacteristic, complemented
46Dic283⋊C8C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583534C2211yescharacteristic, complemented
50#22583533C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic
52#22583531C2211yescharacteristic
53#22583530C2211yescharacteristic
54C2×Q16×C283C2211yescharacteristic, complemented
55C2×SD16×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic
57C4×Q8×C283C2211yescharacteristic, complemented
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic
61C23×D283—21no—
62C2×Dic566—21no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66Q8×D283—22no—
67Q8×D283—22no—
68Q8×D283—22no—
69Q8×D283D414yes—
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72D4×D283—22no—
73D4×D283—22no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76C2×C4×D283—21no—
77C2×C4×D283D411yescharacteristic
78C2×C4×D283D411yescharacteristic
79C2×C4×D283C2311yescharacteristic
80Dic1132—22no—
81#17985382—22no—
82#17985382—22no—
83#17985381—22no—
84#17985380—22no—
85#17985379—22no—
86C2×C283⋊C8C2311yescharacteristic
87C2×C283⋊C8C2311yescharacteristic
88C8×D283—22no—
89C8×D283—22no—
90C4⋊Dic283—21no—
91C4⋊Dic283C2311yescharacteristic
92Dic283⋊C4—21no—
93Dic283⋊C4—21no—
94Dic283⋊C4—21no—
95C22⋊Dic283—21no—
96C22⋊Dic283—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4—21no—
101C4×Dic283—21no—
102C4×Dic283—21no—
103C4×Dic283—21no—
104C4×Dic283D411yescharacteristic
105C4×Dic283D411yescharacteristic
106C4×Dic283C2311yescharacteristic
107C2×Q8×C283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110Q16×C283—22no—
111SD16×C283—22no—
112C2×C8×C283C2311yescharacteristic
113C2×C8×C283C2311yescharacteristic
114C4⋊C4×C283—21no—
115C4⋊C4×C283C2311yescharacteristic
116C22⋊C4×C283—21no—
117C22⋊C4×C283—21no—
118C42×C283—21no—
119C42×C283C2311yescharacteristic
120C22×D283—21no—
121C22×D283—42no—
122C22×D283—42no—
123C22×D283—42no—
124C22×D283C2×D411yescharacteristic
125Dic566—21no—
126Dic566—24no—
127Dic566—21no—
128Dic566—21no—
129Dic566—42no—
130Dic566C2×D412yes—
131D1132—21no—
132D1132—21no—
133C22⋊D283—42no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283C2×D411yescharacteristic
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C4×D283—24no—
141C4×D283—22no—
142C4×D283—22no—
143C4×D283—42no—
144C4×D283—42no—
145C4×D283C2×D412yes—
146C4×D283#4112yes—
147C283⋊C8—21no—
148C283⋊C8—21no—
149C23×C283—21no—
150Q8×C283—21no—
151Q8×C283—21no—
152Q8×C283—21no—
153Q8×C283C2×D412yes—
154D4×C283—21no—
155D4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283C2×D411yescharacteristic
160C2×C4×C283C2×D411yescharacteristic
161C2×C4×C283C2411yescharacteristic
162C8×C283—21no—
163C8×C283—21no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—41no—
167C22×C283C22×D411yescharacteristic
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C2×D283—84no—
172C2×D283#12112yes—
173C2×D283#13512yes—
174C2×D283#13712yes—
175C4×C283—22no—
176C4×C283—21no—
177C4×C283—21no—
178C4×C283—41no—
179C4×C283—41no—
180C4×C283C22×D411yescharacteristic
181C4×C283C2×#4111yescharacteristic
182Dic283—22no—
183Dic283—21no—
184Dic283—21no—
185Dic283—41no—
186Dic283—41no—
187Dic283#12112yes—
188C2×C283—81no—
189C2×C283C2×#12111yescharacteristic
190C2×C283C2×#13511yescharacteristic
191C2×C283C2×#13711yescharacteristic
192D283—81no—
193D283#46414yesdirect product factor
194C283C2×#46411yescharacteristic, complemented, Sylow
195C2×#464—2831nomaximal, Sylow
196C22×Q16—2831no—
197C22×SD16—2831no—
198C2×#124—2831no—
199C2×C4×Q8—2831no—
200#464—2831no—
201#464—2831no—
202#464—2831no—
203#464—2831no—
204#464—2831no—
205#464—2831no—
206#464—2831no—
207#464D28311yescharacteristic, direct product factor
208C2×C4⋊C8—2831no—
209C2×#103—2831no—
210C2×#102—2831no—
211C22×Q8—2831no—
212C22×Q8—2831no—
213C22×D4—2831no—
214C2×Q16—2831no—
215C2×Q16—2831no—
216C2×Q16—2831no—
217C2×Q16—5664no—
218C2×Q16C2×D28311yescharacteristic, complemented
219C2×SD16—2831no—
220C2×SD16—2831no—
221C2×SD16—2831no—
222C2×SD16—5664no—
223C2×SD16C2×D28311yescharacteristic
224C22×C8—2831no—
225C22×C8—2831no—
226#124—2831no—
227#124—2831no—
228#124—2831no—
229#124—5661no—
230#124—5661no—
231#124C2×D28311yescharacteristic
232C4×Q8—2831no—
233C4×Q8—2831no—
234C4×Q8—2831no—
235C4×Q8—5661no—
236C4×Q8—5661no—
237C4×Q8C2×D28311yescharacteristic, complemented
238C2×C4⋊C4—2831no—
239C2×C4⋊C4—5661no—
240C2×C22⋊C4—5661no—
241C2×C22⋊C4—5661no—
242C2×C42—2831no—
243C2×C42—5661no—
244C4⋊C8—2831no—
245C4⋊C8—2831no—
246C4⋊C8—2831no—
247C4⋊C8C2×D28311yescharacteristic, complemented
248#103—2831no—
249#103—2831no—
250#103—2831no—
251#103C2×D28311yescharacteristic, complemented
252#102—2831no—
253#102—2831no—
254#102—2831no—
255#102C2×D28311yescharacteristic
256C24—5661no—
257C2×Q8—2834no—
258C2×Q8—2831no—
259C2×Q8—2831no—
260C2×Q8—5661no—
261C2×Q8—5661no—
262C2×Q8—5662no—
263C2×Q8—5662no—
264C2×Q8—5662no—
265C2×Q8C22×D28311yescharacteristic
266C2×Q8C22×D28311yescharacteristic
267C2×D4—2831no—
268C2×D4—5662no—
269C2×D4—5662no—
270C2×D4—5661no—
271C2×D4C22×D28311yescharacteristic
272C22×C4—2831no—
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—5661no—
276C22×C4—5661no—
277C22×C4—5661no—
278Q16—22no—
279Q16—5662no—
280Q16—5662no—
281Q16—5662no—
282SD16—22no—
283SD16—5662no—
284SD16—5662no—
285SD16—5662no—
286C2×C8—2831no—
287C2×C8—2831no—
288C2×C8—5662no—
289C2×C8—5662no—
290C2×C8C22×D28311yescharacteristic
291C2×C8C22×D28311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—2831no—
294C4⋊C4—5661no—
295C4⋊C4—5661no—
296C4⋊C4—5661no—
297C4⋊C4—5661no—
298C4⋊C4C22×D28311yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4—5661no—
305C22⋊C4—5661no—
306C22⋊C4—5661no—
307C42—21no—
308C42—2831no—
309C42—2831no—
310C42—2831no—
311C42—5661no—
312C42—5661no—
313C42—5661no—
314C42C22×D28311yescharacteristic
315C23—21no—
316C23—2831no—
317C23—5661no—
318C23—11322no—
319C23—11322no—
320C23—11322no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—2832no—
325Q8—5664no—
326Q8—5661no—
327Q8—5661no—
328Q8—5661no—
329Q8—11322no—
330Q8D4×D28312yes—
331D4—21no—
332D4—21no—
333D4—5661no—
334D4—5661no—
335D4—11322no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2831no—
340C2×C4—2832no—
341C2×C4—2832no—
342C2×C4—2831no—
343C2×C4—2831no—
344C2×C4—5662no—
345C2×C4—5662no—
346C2×C4—5664no—
347C2×C4—5661no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—11322no—
351C2×C4—11322no—
352C2×C4D4×D28311yescharacteristic
353C2×C4D4×D28311yescharacteristic
354C2×C4C23×D28311yescharacteristic
355C8—21no—
356C8—21no—
357C8—5661no—
358C8—5661no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—2832no—
363C22—2832no—
364C22—2832no—
365C22—11321no—
366C22—11321no—
367C22—11321no—
368C22—22644no—
369C22C2×D4×D28311yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—2832no—
376C4—5662no—
377C4—5661no—
378C4—5661no—
379C4—11321no—
380C4—11321no—
381C4C2×D4×D28311yescharacteristic
382C4#41×D28311yescharacteristic
383C2—81no—
384C2—2834no—
385C2—22641no—
386C2#121×D28311yescharacteristic
387C2#135×D28311yescharacteristic
388C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#464×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
hypercenter#464D283
hypocenterC283C2×#464
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D283C2semidirect
4. C4×Q8×D283C2semidirect
5. #31826690C2semidirect
6. #31826689C2semidirect
7. #31826688C2semidirect
8. #31826687C2semidirect
9. #31826686C2semidirect
10. #31826685C2semidirect
11. #31826684C2semidirect
12. C4⋊C8×D283C2semidirect
13. #103×D283C2semidirect
15. #464×C283C2semidirect
19. C2×Dic1132C22semidirect
20. C2×#17985382C22semidirect
21. C2×#17985382C22semidirect
34. Q8×Dic283C22semidirect
36. C4×Dic566C22semidirect
38. #22583575C22semidirect
45. C4⋊(C283⋊C8)C22semidirect
46. Dic283⋊C8C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583535C22semidirect
49. #22583534C22semidirect
50. #22583533C22semidirect
54. C2×Q16×C283C22semidirect
57. C4×Q8×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
193. D283#464direct (N × H)
194. C283C2×#464semidirect
207. #464D283direct (N × H)
218. C2×Q16C2×D283semidirect
237. C4×Q8C2×D283semidirect
247. C4⋊C8C2×D283semidirect
251. #103C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D2832
C2×SD16×D2832
#124×D2832
C4×Q8×D2832
#318266902
#318266892
#318266882
#318266872
#318266862
#318266852
#318266842
C4⋊C8×D2832
#103×D2832
#102×D2832
#464×C2832
C2×#464283