Finite Group Databasebeta

← #27182949

Subgroups — #27182949

Order 12928.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265885C211yesmaximal, characteristic, complemented
2D4×C22⋊D101C211yesmaximal, characteristic
3#20265522C211yesmaximal, characteristic, complemented
4#20265496C211yesmaximal, characteristic, complemented
5#20265494C211yesmaximal, characteristic, complemented
6#20265465C211yesmaximal, characteristic, complemented
7#20265408C211yesmaximal, characteristic, complemented
8#20265403C211yesmaximal, characteristic, complemented
9#20265375C211yesmaximal, characteristic, complemented
10#20265326C211yesmaximal, characteristic, complemented
11SD16×Dic101C211yesmaximal, characteristic, complemented
12#20265240C211yesmaximal, characteristic, complemented
13C2×#15692176C211yesmaximal, characteristic, complemented
14#102×D101C211yesmaximal, characteristic, complemented
15#450×C101C211yesmaximal, characteristic, complemented
16C22×C22⋊D101—21no—
17C2×D4×D101C2211yescharacteristic
18C2×#13108061C2211yescharacteristic, complemented
19C22×#11717579C2211yescharacteristic, complemented
20C2×C8×D101C2211yescharacteristic, complemented
21#15692254C2211yescharacteristic, complemented
22#15692251C2211yescharacteristic
23#15692245—21no—
24#15692235—21no—
25#15692232—21no—
26#15692231C2211yescharacteristic, complemented
27#15692229C2211yescharacteristic
28#15692227—21no—
29#15692226C2211yescharacteristic
30#15692224—21no—
31#15692223—21no—
32Q8×Dic101C2211yescharacteristic, complemented
33D4×Dic101C2211yescharacteristic
34C4×C22⋊D101C2211yescharacteristic
35#15692215—21no—
36C2×C4⋊Dic101C2211yescharacteristic, complemented
37C4⋊C4×D101C2211yescharacteristic, complemented
38#15692187C2211yescharacteristic, complemented
39#15692187C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41#15692184C2211yescharacteristic, complemented
42#15692179C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic, complemented
44#15692177C2211yescharacteristic, complemented
45#15692176C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692176C2211yescharacteristic, complemented
48#15692176C2211yescharacteristic, complemented
49#15692175C2211yescharacteristic, complemented
50#15692167C2211yescharacteristic, complemented
51C8×Dic101C2211yescharacteristic, complemented
52C22×D4×C101C2211yescharacteristic
53C2×SD16×C101C2211yescharacteristic
54C2×SD16×C101C2211yescharacteristic, complemented
55C22⋊Q8×C101C2211yescharacteristic, complemented
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic, complemented
58C22⋊C8×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60C2×Dic202—21no—
61C2×D404C2311yescharacteristic
62C2×C22⋊D101—21no—
63C2×C22⋊D101—21no—
64C2×C22⋊D101—21no—
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67C2×C22⋊D101—44no—
68C2×C22⋊D101D411yescharacteristic
69D4×D101—22no—
70D4×D101—41no—
71C22×Dic101—21no—
72C22×Dic101—21no—
73C2×C4×D101—21no—
74C2×C4×D101C2311yescharacteristic
75#13108061—41no—
76C2×#11717579—41no—
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C8×D101—41no—
80C4⋊Dic101—21no—
81C4⋊Dic101—21no—
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84C4⋊Dic101C2311yescharacteristic
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88#13108053D411yescharacteristic
89C22⋊Dic101—21no—
90C22⋊Dic101—21no—
91C22⋊Dic101D411yescharacteristic
92#13108051—21no—
93#13108051—21no—
94#13108051D411yescharacteristic
95C4×Dic101—21no—
96C4×Dic101C2311yescharacteristic
97C24×C101—21no—
98C2×Q8×C101C2311yescharacteristic
99C2×D4×C101—22no—
100C2×D4×C101—21no—
101C2×D4×C101—41no—
102C2×D4×C101C2311yescharacteristic
103C2×D4×C101C2311yescharacteristic
104C22×C4×C101C2311yescharacteristic
105SD16×C101—22no—
106SD16×C101—41no—
107C2×C8×C101C2311yescharacteristic
108C2×C8×C101C2311yescharacteristic
109C4⋊C4×C101—21no—
110C4⋊C4×C101C2311yescharacteristic
111C22⋊C4×C101—21no—
112C23×C101—21no—
113C23×C101—21no—
114C23×C101—42no—
115C23×C101—42no—
116C23×C101—81no—
117C23×C101C2×D411yescharacteristic
118C22×D101—21no—
119C22×D101—42no—
120C22×D101—42no—
121C22×D101—81no—
122C22×D101C2×D411yescharacteristic
123Q8×C101—21no—
124Q8×C101—21no—
125D4×C101—21no—
126D4×C101—21no—
127D4×C101—21no—
128D4×C101—42no—
129D4×C101#4112yes—
130C2×C4×C101—21no—
131C2×C4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101—21no—
134C2×C4×C101C2×D411yescharacteristic
135C2×C4×C101C2411yescharacteristic
136C22⋊D101—42no—
137C22⋊D101—42no—
138C22⋊D101—42no—
139C22⋊D101—42no—
140C22⋊D101—81no—
141C22⋊D101SD1614yescomplemented
142C2×Dic101—21no—
143C2×Dic101—21no—
144C2×Dic101—21no—
145C2×Dic101—42no—
146C2×Dic101—81no—
147C2×Dic101C2×D411yescharacteristic
148C2×Dic101C2×D411yescharacteristic
149C2×Dic101C2×D411yescharacteristic
150D404—21no—
151D404—21no—
152C4×D101—21no—
153C4×D101—21no—
154C4×D101—81no—
155Dic202—81no—
156C8×C101—21no—
157C8×C101—21no—
158#11717579—21no—
159#11717579—21no—
160C22×C101—21no—
161C22×C101—21no—
162C22×C101—22no—
163C22×C101—41no—
164C22×C101—41no—
165C22×C101—41no—
166C22×C101—41no—
167C22×C101—41no—
168C22×C101—84no—
169C22×C101C2×SD1612yes—
170C22×C101C22×D411yescharacteristic
171C2×D101—21no—
172C2×D101—21no—
173C2×D101—41no—
174C2×D101—41no—
175C2×D101—41no—
176C2×D101—84no—
177C2×D101C2×SD1612yes—
178C4×C101—21no—
179C4×C101—41no—
180C4×C101—41no—
181C4×C101C2×#4111yescharacteristic
182C4×C101H(5,𝔽2)11yescharacteristic
183Dic101—21no—
184Dic101—21no—
185Dic101—41no—
186Dic101—41no—
187Dic101—41no—
188Dic101C2×SD1612yes—
189C2×C101—22no—
190C2×C101—42no—
191C2×C101—81no—
192C2×C101#54611yescharacteristic
193C2×C101C22×SD1611yescharacteristic
194C2×C101#57611yescharacteristic
195D101—22no—
196D101—81no—
197#3295—1011nomaximal, Sylow
198C101#329511yescharacteristic, complemented, Sylow
199#554—1011no—
200D42—1011no—
201#486—1011no—
202#481—1011no—
203#481—1011no—
204#476—1011no—
205#465—1011no—
206#465—1011no—
207#460—1011no—
208#450—1011no—
209#450D10111yescharacteristic, complemented
210C4×SD16—1011no—
211C8×D4—1011no—
212C2×#102—1011no—
213C2×#102—1011no—
214C22×D4—1011no—
215C22×D4—2021no—
216C22×D4C2×D10111yescharacteristic
217C2×SD16—1011no—
218C2×SD16C2×D10111yescharacteristic
219C2×SD16C2×D10111yescharacteristic, complemented
220C22×C8—1011no—
221C22×C8—1011no—
222C4⋊Q8—1011no—
223#127—1011no—
224#125—2021no—
225C22⋊Q8—1011no—
226C22⋊Q8—2021no—
227C22⋊Q8—2021no—
228C22⋊Q8C2×D10111yescharacteristic, complemented
229#121—1011no—
230#121—1011no—
231#121—2021no—
232#120—2021no—
233#120—2021no—
234C4×Q8—1011no—
235C4×D4—1011no—
236C4×D4—1011no—
237C4×D4—2021no—
238C2×C4⋊C4—1011no—
239C2×C4⋊C4—1011no—
240#106—1011no—
241#106—1011no—
242#106—1011no—
243C4⋊C8—1011no—
244#103—1011no—
245#102—1011no—
246#102—1011no—
247#102—1011no—
248#102—1011no—
249#102—1011no—
250#102—1011no—
251#102—1011no—
252#102C2×D10111yescharacteristic
253#102C2×D10111yescharacteristic, complemented
254C22⋊C8—1011no—
255C22⋊C8C2×D10111yescharacteristic, complemented
256C4×C8—1011no—
257C24—21no—
258C24—2021no—
259C2×Q8—2021no—
260C2×Q8C22×D10111yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—1011no—
265C2×D4—1011no—
266C2×D4—4044no—
267C2×D4—4041no—
268C2×D4—2021no—
269C2×D4—2021no—
270C2×D4—2021no—
271C2×D4—2021no—
272C2×D4—2021no—
273C2×D4—2022no—
274C2×D4C22×D10111yescharacteristic
275C2×D4C22×D10111yescharacteristic
276C22×C4—1011no—
277C22×C4—2021no—
278C22×C4—2021no—
279C22×C4—2021no—
280C22×C4C22×D10111yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—4041no—
284C2×C8—1011no—
285C2×C8—1011no—
286C2×C8—4041no—
287C2×C8—4041no—
288C2×C8C22×D10111yescharacteristic
289C2×C8C22×D10111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1011no—
292C4⋊C4—1011no—
293C4⋊C4—1011no—
294C4⋊C4—1011no—
295C4⋊C4—2021no—
296C4⋊C4—2021no—
297C4⋊C4—2021no—
298C4⋊C4—2021no—
299C4⋊C4—2021no—
300C4⋊C4C22×D10111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—1011no—
303C22⋊C4—1011no—
304C22⋊C4—2021no—
305C22⋊C4—2021no—
306C22⋊C4—2021no—
307C22⋊C4—2021no—
308C42—1011no—
309C42—2021no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—8081no—
316C23—1011no—
317C23—4042no—
318C23—4042no—
319C23—2021no—
320C23D4×D10111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—8081no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—8081no—
329D4—1014no—
330D4—4042no—
331D4—4042no—
332D4—4042no—
333D4—4042no—
334D4—2021no—
335D4—2021no—
336D4#1310807312yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—8081no—
342C2×C4—8081no—
343C2×C4—1011no—
344C2×C4—1011no—
345C2×C4—1011no—
346C2×C4—4042no—
347C2×C4—2021no—
348C2×C4—2021no—
349C2×C4—2021no—
350C2×C4—2021no—
351C2×C4—2021no—
352C2×C4D4×D10111yescharacteristic
353C2×C4C23×D10111yescharacteristic
354C8—21no—
355C8—21no—
356C8—2021no—
357C8—2021no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—8084no—
368C22—1012no—
369C22—4041no—
370C22—4041no—
371C22—4041no—
372C22—2021no—
373C22—2021no—
374C22SD16×D10112yes—
375C22C2×D4×D10111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—1012no—
380C4—4041no—
381C4—4041no—
382C4—4041no—
383C4—2021no—
384C4—2021no—
385C4C2×#1310807311yescharacteristic
386C4#1569230011yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—8081no—
391C2—2022no—
392C2#2026581411yescharacteristic
393C2C2×SD16×D10111yescharacteristic
394C2#2026598111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#450×C101C2
socleC22×C101C22×D4
prime radicalD4×C22⋊D101C2
hypercenter#450D101
hypocenterC101#3295
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20265885C2semidirect
3. #20265522C2semidirect
4. #20265496C2semidirect
5. #20265494C2semidirect
6. #20265465C2semidirect
7. #20265408C2semidirect
8. #20265403C2semidirect
9. #20265375C2semidirect
10. #20265326C2semidirect
11. SD16×Dic101C2semidirect
12. #20265240C2semidirect
13. C2×#15692176C2semidirect
14. #102×D101C2semidirect
15. #450×C101C2semidirect
18. C2×#13108061C22semidirect
19. C22×#11717579C22semidirect
20. C2×C8×D101C22semidirect
21. #15692254C22semidirect
26. #15692231C22semidirect
32. Q8×Dic101C22semidirect
36. C2×C4⋊Dic101C22semidirect
37. C4⋊C4×D101C22semidirect
38. #15692187C22semidirect
39. #15692187C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692179C22semidirect
43. #15692177C22semidirect
44. #15692177C22semidirect
47. #15692176C22semidirect
48. #15692176C22semidirect
49. #15692175C22semidirect
50. #15692167C22semidirect
51. C8×Dic101C22semidirect
54. C2×SD16×C101C22semidirect
55. C22⋊Q8×C101C22semidirect
57. #102×C101C22semidirect
58. C22⋊C8×C101C22semidirect
141. C22⋊D101SD16semidirect
198. C101#3295semidirect
209. #450D101semidirect
219. C2×SD16C2×D101semidirect
228. C22⋊Q8C2×D101semidirect
253. #102C2×D101semidirect
255. C22⋊C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658852
D4×C22⋊D1012
#202655222
#202654962
#202654942
#202654652
#202654082
#202654032
#202653752
#202653262
SD16×Dic1012
#202652402
C2×#156921762
#102×D1012
#450×C1012
#3295101