Finite Group Databasebeta

← #464×D227 #44409174

Subgroups — #464×D227 #44409174

Order 29056.

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×D227C211yesmaximal, characteristic, complemented
2C2×SD16×D227C211yesmaximal, characteristic
3#124×D227C211yesmaximal, characteristic
4C4×Q8×D227C211yesmaximal, characteristic, complemented
5#28409257C211yesmaximal, characteristic, complemented
6#28409256C211yesmaximal, characteristic, complemented
7#28409255C211yesmaximal, characteristic, complemented
8#28409254C211yesmaximal, characteristic, complemented
9#28409253C211yesmaximal, characteristic, complemented
10#28409252C211yesmaximal, characteristic, complemented
11#28409251C211yesmaximal, characteristic, complemented
12C4⋊C8×D227C211yesmaximal, characteristic, complemented
13#103×D227C211yesmaximal, characteristic, complemented
14#102×D227C211yesmaximal, characteristic
15#464×C227C211yesmaximal, characteristic, complemented
16C2×Q8×D227C2211yescharacteristic
17C2×Q8×D227C2211yescharacteristic
18C2×D4×D227C2211yescharacteristic
19C2×Dic908C2211yescharacteristic, complemented
20C2×#16813874C2211yescharacteristic, complemented
21C2×#16813874C2211yescharacteristic, complemented
22Q16×D227—24no—
23C2×#16813873C2211yescharacteristic
24C2×#16813872C2211yescharacteristic
25C2×#16813871C2211yescharacteristic
26SD16×D227—24no—
27C2×C8×D227C2211yescharacteristic
28C2×C8×D227C2211yescharacteristic
29#20300277C2211yescharacteristic
30#20300276C2211yescharacteristic
31#20300275C2211yescharacteristic
32#20300274—21no—
33#20300274—21no—
34Q8×Dic227C2211yescharacteristic, complemented
35C4×Dic454—21no—
36C4×Dic454C2211yescharacteristic, complemented
37#20300253—21no—
38#20300253C2211yescharacteristic, complemented
39C4⋊C4×D227—21no—
40C4⋊C4×D227C2211yescharacteristic
41C22⋊C4×D227—21no—
42C22⋊C4×D227—21no—
43C42×D227—21no—
44C42×D227C2211yescharacteristic
45C4⋊(C227⋊C8)C2211yescharacteristic, complemented
46Dic227⋊C8C2211yescharacteristic, complemented
47Dic227⋊C8C2211yescharacteristic, complemented
48#20300213C2211yescharacteristic, complemented
49#20300212C2211yescharacteristic, complemented
50#20300211C2211yescharacteristic, complemented
51#20300210C2211yescharacteristic
52#20300209C2211yescharacteristic
53#20300208C2211yescharacteristic
54C2×Q16×C227C2211yescharacteristic, complemented
55C2×SD16×C227C2211yescharacteristic
56#124×C227C2211yescharacteristic
57C4×Q8×C227C2211yescharacteristic, complemented
58C4⋊C8×C227C2211yescharacteristic, complemented
59#103×C227C2211yescharacteristic, complemented
60#102×C227C2211yescharacteristic
61C23×D227—21no—
62C2×Dic454—21no—
63C2×Dic454—21no—
64C2×Dic454C2311yescharacteristic
65C2×Dic454C2311yescharacteristic
66Q8×D227—22no—
67Q8×D227—22no—
68Q8×D227—22no—
69Q8×D227D414yes—
70C2×D908C2311yescharacteristic
71C2×C22⋊D227—21no—
72D4×D227—22no—
73D4×D227—22no—
74C2×C4×D227—21no—
75C2×C4×D227—21no—
76C2×C4×D227—21no—
77C2×C4×D227D411yescharacteristic
78C2×C4×D227D411yescharacteristic
79C2×C4×D227C2311yescharacteristic
80Dic908—22no—
81#16813874—22no—
82#16813874—22no—
83#16813873—22no—
84#16813872—22no—
85#16813871—22no—
86C2×C227⋊C8C2311yescharacteristic
87C2×C227⋊C8C2311yescharacteristic
88C8×D227—22no—
89C8×D227—22no—
90C4⋊Dic227—21no—
91C4⋊Dic227C2311yescharacteristic
92Dic227⋊C4—21no—
93Dic227⋊C4—21no—
94Dic227⋊C4—21no—
95C22⋊Dic227—21no—
96C22⋊Dic227—21no—
97(C2×D227)⋊C4—21no—
98(C2×D227)⋊C4—21no—
99(C2×D227)⋊C4—21no—
100(C2×D227)⋊C4—21no—
101C4×Dic227—21no—
102C4×Dic227—21no—
103C4×Dic227—21no—
104C4×Dic227D411yescharacteristic
105C4×Dic227D411yescharacteristic
106C4×Dic227C2311yescharacteristic
107C2×Q8×C227C2311yescharacteristic
108C2×Q8×C227C2311yescharacteristic
109C2×D4×C227C2311yescharacteristic
110Q16×C227—22no—
111SD16×C227—22no—
112C2×C8×C227C2311yescharacteristic
113C2×C8×C227C2311yescharacteristic
114C4⋊C4×C227—21no—
115C4⋊C4×C227C2311yescharacteristic
116C22⋊C4×C227—21no—
117C22⋊C4×C227—21no—
118C42×C227—21no—
119C42×C227C2311yescharacteristic
120C22×D227—21no—
121C22×D227—42no—
122C22×D227—42no—
123C22×D227—42no—
124C22×D227C2×D411yescharacteristic
125Dic454—21no—
126Dic454—24no—
127Dic454—21no—
128Dic454—21no—
129Dic454—42no—
130Dic454C2×D412yes—
131D908—21no—
132D908—21no—
133C22⋊D227—42no—
134C2×Dic227—21no—
135C2×Dic227—21no—
136C2×Dic227—21no—
137C2×Dic227C2×D411yescharacteristic
138C2×Dic227C2×D411yescharacteristic
139C2×Dic227C2×D411yescharacteristic
140C4×D227—24no—
141C4×D227—22no—
142C4×D227—22no—
143C4×D227—42no—
144C4×D227—42no—
145C4×D227C2×D412yes—
146C4×D227#4112yes—
147C227⋊C8—21no—
148C227⋊C8—21no—
149C23×C227—21no—
150Q8×C227—21no—
151Q8×C227—21no—
152Q8×C227—21no—
153Q8×C227C2×D412yes—
154D4×C227—21no—
155D4×C227—21no—
156C2×C4×C227—21no—
157C2×C4×C227—21no—
158C2×C4×C227—21no—
159C2×C4×C227C2×D411yescharacteristic
160C2×C4×C227C2×D411yescharacteristic
161C2×C4×C227C2411yescharacteristic
162C8×C227—21no—
163C8×C227—21no—
164C22×C227—41no—
165C22×C227—41no—
166C22×C227—41no—
167C22×C227C22×D411yescharacteristic
168C2×D227—41no—
169C2×D227—41no—
170C2×D227—41no—
171C2×D227—84no—
172C2×D227#12112yes—
173C2×D227#13512yes—
174C2×D227#13712yes—
175C4×C227—22no—
176C4×C227—21no—
177C4×C227—21no—
178C4×C227—41no—
179C4×C227—41no—
180C4×C227C22×D411yescharacteristic
181C4×C227C2×#4111yescharacteristic
182Dic227—22no—
183Dic227—21no—
184Dic227—21no—
185Dic227—41no—
186Dic227—41no—
187Dic227#12112yes—
188C2×C227—81no—
189C2×C227C2×#12111yescharacteristic
190C2×C227C2×#13511yescharacteristic
191C2×C227C2×#13711yescharacteristic
192D227—81no—
193D227#46414yesdirect product factor
194C227C2×#46411yescharacteristic, complemented, Sylow
195C2×#464—2271nomaximal, Sylow
196C22×Q16—2271no—
197C22×SD16—2271no—
198C2×#124—2271no—
199C2×C4×Q8—2271no—
200#464—2271no—
201#464—2271no—
202#464—2271no—
203#464—2271no—
204#464—2271no—
205#464—2271no—
206#464—2271no—
207#464D22711yescharacteristic, direct product factor
208C2×C4⋊C8—2271no—
209C2×#103—2271no—
210C2×#102—2271no—
211C22×Q8—2271no—
212C22×Q8—2271no—
213C22×D4—2271no—
214C2×Q16—4544no—
215C2×Q16—2271no—
216C2×Q16—2271no—
217C2×Q16—2271no—
218C2×Q16C2×D22711yescharacteristic, complemented
219C2×SD16—4544no—
220C2×SD16—2271no—
221C2×SD16—2271no—
222C2×SD16—2271no—
223C2×SD16C2×D22711yescharacteristic
224C22×C8—2271no—
225C22×C8—2271no—
226#124—4541no—
227#124—4541no—
228#124—2271no—
229#124—2271no—
230#124—2271no—
231#124C2×D22711yescharacteristic
232C4×Q8—4541no—
233C4×Q8—4541no—
234C4×Q8—2271no—
235C4×Q8—2271no—
236C4×Q8—2271no—
237C4×Q8C2×D22711yescharacteristic, complemented
238C2×C4⋊C4—4541no—
239C2×C4⋊C4—2271no—
240C2×C22⋊C4—4541no—
241C2×C22⋊C4—4541no—
242C2×C42—4541no—
243C2×C42—2271no—
244C4⋊C8—2271no—
245C4⋊C8—2271no—
246C4⋊C8—2271no—
247C4⋊C8C2×D22711yescharacteristic, complemented
248#103—2271no—
249#103—2271no—
250#103—2271no—
251#103C2×D22711yescharacteristic, complemented
252#102—2271no—
253#102—2271no—
254#102—2271no—
255#102C2×D22711yescharacteristic
256C24—4541no—
257C2×Q8—4541no—
258C2×Q8—4541no—
259C2×Q8—4542no—
260C2×Q8—4542no—
261C2×Q8—4542no—
262C2×Q8—2274no—
263C2×Q8—2271no—
264C2×Q8—2271no—
265C2×Q8C22×D22711yescharacteristic
266C2×Q8C22×D22711yescharacteristic
267C2×D4—4542no—
268C2×D4—4542no—
269C2×D4—4541no—
270C2×D4—2271no—
271C2×D4C22×D22711yescharacteristic
272C22×C4—4541no—
273C22×C4—4541no—
274C22×C4—4541no—
275C22×C4—2271no—
276C22×C4—2271no—
277C22×C4—2271no—
278Q16—22no—
279Q16—4542no—
280Q16—4542no—
281Q16—4542no—
282SD16—22no—
283SD16—4542no—
284SD16—4542no—
285SD16—4542no—
286C2×C8—4542no—
287C2×C8—4542no—
288C2×C8—2271no—
289C2×C8—2271no—
290C2×C8C22×D22711yescharacteristic
291C2×C8C22×D22711yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—4541no—
294C4⋊C4—4541no—
295C4⋊C4—4541no—
296C4⋊C4—4541no—
297C4⋊C4—2271no—
298C4⋊C4C22×D22711yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—4541no—
302C22⋊C4—4541no—
303C22⋊C4—4541no—
304C22⋊C4—4541no—
305C22⋊C4—4541no—
306C22⋊C4—4541no—
307C42—21no—
308C42—4541no—
309C42—4541no—
310C42—4541no—
311C42—2271no—
312C42—2271no—
313C42—2271no—
314C42C22×D22711yescharacteristic
315C23—21no—
316C23—9082no—
317C23—9082no—
318C23—9082no—
319C23—4541no—
320C23—2271no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—9082no—
325Q8—4544no—
326Q8—4541no—
327Q8—4541no—
328Q8—4541no—
329Q8—2272no—
330Q8D4×D22712yes—
331D4—21no—
332D4—21no—
333D4—9082no—
334D4—4541no—
335D4—4541no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—9082no—
340C2×C4—9082no—
341C2×C4—4544no—
342C2×C4—4542no—
343C2×C4—4542no—
344C2×C4—4541no—
345C2×C4—4541no—
346C2×C4—4541no—
347C2×C4—2271no—
348C2×C4—2271no—
349C2×C4—2271no—
350C2×C4—2272no—
351C2×C4—2272no—
352C2×C4D4×D22711yescharacteristic
353C2×C4D4×D22711yescharacteristic
354C2×C4C23×D22711yescharacteristic
355C8—21no—
356C8—21no—
357C8—4541no—
358C8—4541no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—18164no—
363C22—9081no—
364C22—9081no—
365C22—9081no—
366C22—2272no—
367C22—2272no—
368C22—2272no—
369C22C2×D4×D22711yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—9081no—
376C4—9081no—
377C4—4542no—
378C4—4541no—
379C4—4541no—
380C4—2272no—
381C4C2×D4×D22711yescharacteristic
382C4#41×D22711yescharacteristic
383C2—81no—
384C2—18161no—
385C2—2274no—
386C2#121×D22711yescharacteristic
387C2#135×D22711yescharacteristic
388C2#137×D22711yescharacteristic
subgroupG/H
centerC22C2×D4×D227
commutator, cosocleC2×C4×C227C24
FrattiniC2×C4C23×D227
Fitting#464×C227C2
socleC22×C227C22×D4
prime radicalC2×D4×D227C22
hypercenter#464D227
hypocenterC227C2×#464
LCSG ▷ C2×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D227C2semidirect
4. C4×Q8×D227C2semidirect
5. #28409257C2semidirect
6. #28409256C2semidirect
7. #28409255C2semidirect
8. #28409254C2semidirect
9. #28409253C2semidirect
10. #28409252C2semidirect
11. #28409251C2semidirect
12. C4⋊C8×D227C2semidirect
13. #103×D227C2semidirect
15. #464×C227C2semidirect
19. C2×Dic908C22semidirect
20. C2×#16813874C22semidirect
21. C2×#16813874C22semidirect
34. Q8×Dic227C22semidirect
36. C4×Dic454C22semidirect
38. #20300253C22semidirect
45. C4⋊(C227⋊C8)C22semidirect
46. Dic227⋊C8C22semidirect
47. Dic227⋊C8C22semidirect
48. #20300213C22semidirect
49. #20300212C22semidirect
50. #20300211C22semidirect
54. C2×Q16×C227C22semidirect
57. C4×Q8×C227C22semidirect
58. C4⋊C8×C227C22semidirect
59. #103×C227C22semidirect
193. D227#464direct (N × H)
194. C227C2×#464semidirect
207. #464D227direct (N × H)
218. C2×Q16C2×D227semidirect
237. C4×Q8C2×D227semidirect
247. C4⋊C8C2×D227semidirect
251. #103C2×D227semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D2272
C2×SD16×D2272
#124×D2272
C4×Q8×D2272
#284092572
#284092562
#284092552
#284092542
#284092532
#284092522
#284092512
C4⋊C8×D2272
#103×D2272
#102×D2272
#464×C2272
C2×#464227