Finite Group Databasebeta

← #27181275

Subgroups — #27181275

Order 12928.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265712C211yesmaximal, characteristic, complemented
2C4×D4×D101C211yesmaximal, characteristic, complemented
3#20265509C211yesmaximal, characteristic, complemented
4#20265492C211yesmaximal, characteristic, complemented
5#20265474C211yesmaximal, characteristic, complemented
6#20265393C211yesmaximal, characteristic, complemented
7#20265392C211yesmaximal, characteristic, complemented
8#20265329C211yesmaximal, characteristic, complemented
9#20265312C211yesmaximal, characteristic
10#20265288C211yesmaximal, characteristic, complemented
11#20265286C211yesmaximal, characteristic, complemented
12#20265276C211yesmaximal, characteristic, complemented
13#20265274C211yesmaximal, characteristic, complemented
14#20265233C211yesmaximal, characteristic, complemented
15#478×C101C211yesmaximal, characteristic, complemented
16C2×D4×D101C2211yescharacteristic
17C22×C4×D101—21no—
18C2×#13108063C2211yescharacteristic
19C2×#13108062C2211yescharacteristic
20C2×D808C2211yescharacteristic
21C2×#13108059C2211yescharacteristic
22#15692250—21no—
23#15692243C2211yescharacteristic, complemented
24#15692240—21no—
25#15692235C2211yescharacteristic
26#15692230C2211yescharacteristic
27#15692220C2211yescharacteristic, complemented
28C4×D404C2211yescharacteristic
29D4×Dic101C2211yescharacteristic
30#15692217—21no—
31#15692217C2211yescharacteristic
32#15692217C2211yescharacteristic, complemented
33C4×C22⋊D101—21no—
34#15692215—21no—
35#15692213—21no—
36C4⋊C4×D101C2211yescharacteristic
37C22⋊C4×D101—21no—
38C42×D101C2211yescharacteristic
39#15692188C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41C4⋊#11717579C2211yescharacteristic, complemented
42#15692180C2211yescharacteristic, complemented
43#15692178C2211yescharacteristic, complemented
44#15692177C2211yescharacteristic, complemented
45#15692175C2211yescharacteristic
46#15692175C2211yescharacteristic
47#15692175C2211yescharacteristic, complemented
48#15692167C2211yescharacteristic
49#15692167C2211yescharacteristic
50#15692165C2211yescharacteristic, complemented
51#15692165C2211yescharacteristic, complemented
52#125×C101C2211yescharacteristic, complemented
53C4×D4×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56C4⋊C8×C101C2211yescharacteristic, complemented
57#102×C101C2211yescharacteristic
58#102×C101C2211yescharacteristic
59C23×D101—21no—
60C2×Dic202C2311yescharacteristic
61C2×D404—21no—
62C2×D404C2311yescharacteristic
63C2×D404C2311yescharacteristic
64C2×C22⋊D101—21no—
65D4×D101—22no—
66D4×D101—22no—
67C22×Dic101—21no—
68C2×C4×D101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—44no—
73C2×C4×D101D411yescharacteristic
74C2×C4×D101D411yescharacteristic
75C2×C4×D101C2311yescharacteristic
76#13108063—22no—
77#13108062—22no—
78D808—22no—
79#13108059—22no—
80C2×#11717579C2311yescharacteristic
81C2×#11717579C2311yescharacteristic
82C4⋊Dic101—21no—
83C4⋊Dic101C2311yescharacteristic
84#13108053—21no—
85#13108053—21no—
86C22⋊Dic101—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94C4×Dic101—21no—
95C4×Dic101D411yescharacteristic
96C4×Dic101D411yescharacteristic
97C4×Dic101C2311yescharacteristic
98C2×D4×C101C2311yescharacteristic
99C22×C4×C101—21no—
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101—21no—
103C4⋊C4×C101—21no—
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C42×C101C2311yescharacteristic
109C23×C101—21no—
110C22×D101—24no—
111C22×D101—21no—
112C22×D101—21no—
113C22×D101—42no—
114C22×D101—42no—
115C22×D101C2×D411yescharacteristic
116D4×C101—21no—
117D4×C101#4112yes—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—42no—
122C2×C4×C101C2×D411yescharacteristic
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2411yescharacteristic
125C22⋊D101—24no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—42no—
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131C2×Dic101C2×D411yescharacteristic
132D404—21no—
133D404—21no—
134D404—21no—
135D404—42no—
136D404#4112yes—
137C4×D101—22no—
138C4×D101—21no—
139C4×D101—21no—
140C4×D101—41no—
141C4×D101—42no—
142C4×D101—42no—
143C4×D101—42no—
144C4×D101—42no—
145Dic202—21no—
146Dic202—21no—
147C8×C101—21no—
148C8×C101—21no—
149#11717579—21no—
150#11717579—21no—
151C22×C101—22no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101C22×D411yescharacteristic
155C2×D101—21no—
156C2×D101—21no—
157C2×D101—22no—
158C2×D101—48no—
159C2×D101—41no—
160C2×D101—41no—
161C2×D101—41no—
162C2×D101—41no—
163C2×D101—41no—
164C2×D101AGL(1,ℤ/8)12yes—
165C4×C101—21no—
166C4×C101—21no—
167C4×C101—41no—
168C4×C101—41no—
169C4×C101—41no—
170C4×C101C2×#4111yescharacteristic
171C4×C101C2×#4111yescharacteristic
172Dic101—21no—
173Dic101—21no—
174Dic101—21no—
175Dic101—41no—
176Dic101—41no—
177C2×C101—42no—
178C2×C101#52511yescharacteristic
179C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C101#57511yescharacteristic
181D101—22no—
182D101—42no—
183D101—81no—
184#3114—1011nomaximal, Sylow
185C101#311411yescharacteristic, complemented, Sylow
186#529—1011no—
187C2×C4×D4—1011no—
188#483—1011no—
189#480—1011no—
190#478—1011no—
191#478D10111yescharacteristic, complemented
192#463—1011no—
193#463—1011no—
194#450—1011no—
195#447—1011no—
196#442—1011no—
197#442—1011no—
198#440—1011no—
199#440—1011no—
200#432—1011no—
201C22×D4—1011no—
202C23×C4—2021no—
203C2×SD16—1011no—
204C2×SD16—1011no—
205C2×D8—1011no—
206C2×D8—1011no—
207#126—2021no—
208#125C2×D10111yescharacteristic, complemented
209#124—1011no—
210#123—2021no—
211C22⋊Q8—1011no—
212#121—1011no—
213C4×Q8—1011no—
214C4×D4—1011no—
215C4×D4—1011no—
216C4×D4—1011no—
217C4×D4—1011no—
218C4×D4—2021no—
219C4×D4—2021no—
220C4×D4—2021no—
221C4×D4C2×D10111yescharacteristic
222#117—2021no—
223C2×C4⋊C4—1011no—
224C2×C22⋊C4—2021no—
225C2×C42—1011no—
226#107—1011no—
227#107C2×D10111yescharacteristic, complemented
228#106—1011no—
229#106C2×D10111yescharacteristic, complemented
230C4⋊C8—1011no—
231C4⋊C8C2×D10111yescharacteristic, complemented
232#103—1011no—
233#103—1011no—
234#102—1011no—
235#102—1011no—
236#102—1011no—
237#102—1011no—
238#102C2×D10111yescharacteristic
239#102C2×D10111yescharacteristic
240C22⋊C8—1011no—
241C22⋊C8—1011no—
242#97—1011no—
243#97—1011no—
244C24—2021no—
245C2×Q8—1011no—
246C2×D4—1011no—
247C2×D4—1011no—
248C2×D4—2021no—
249C2×D4—2021no—
250C2×D4—2022no—
251C2×D4—2022no—
252C2×D4C22×D10111yescharacteristic
253C22×C4—21no—
254C22×C4—1011no—
255C22×C4—1011no—
256C22×C4—1011no—
257C22×C4—4044no—
258C22×C4—2021no—
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4—2021no—
262C22×C4—2021no—
263SD16—2022no—
264SD16—2022no—
265D8—2022no—
266D8—2022no—
267C2×C8—1011no—
268C2×C8—1011no—
269C2×C8C22×D10111yescharacteristic
270C2×C8C22×D10111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—1011no—
274C4⋊C4—2021no—
275C4⋊C4—2021no—
276C4⋊C4—2021no—
277C4⋊C4C22×D10111yescharacteristic
278C4⋊C4C22×D10111yescharacteristic
279C4⋊C4C22×D10111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2021no—
282C22⋊C4—2021no—
283C22⋊C4—2021no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C42—1011no—
290C42—1011no—
291C42—1011no—
292C42—2021no—
293C42C22×D10111yescharacteristic
294C23—21no—
295C23—1011no—
296C23—4042no—
297C23—4042no—
298C23—2024no—
299C23—2021no—
300C23—2021no—
301Q8—2021no—
302Q8—2021no—
303D4—21no—
304D4—1012no—
305D4—4042no—
306D4—2024no—
307D4—2021no—
308D4—2021no—
309D4—2021no—
310D4#1310807512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—1011no—
316C2×C4—1011no—
317C2×C4—1011no—
318C2×C4—4042no—
319C2×C4—4041no—
320C2×C4—4042no—
321C2×C4—4042no—
322C2×C4—4042no—
323C2×C4—4042no—
324C2×C4—2022no—
325C2×C4—2021no—
326C2×C4—2021no—
327C2×C4—2021no—
328C2×C4—2021no—
329C2×C4D4×D10111yescharacteristic
330C2×C4D4×D10111yescharacteristic
331C2×C4C23×D10111yescharacteristic
332C8—21no—
333C8—21no—
334C8—2021no—
335C8—2021no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—1012no—
340C22—4048no—
341C22—4041no—
342C22—4041no—
343C22—4041no—
344C22—4041no—
345C22—4041no—
346C22—2022no—
347C22—2021no—
348C22—2021no—
349C22C2×D4×D10111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—4041no—
356C4—4041no—
357C4—2021no—
358C4—2021no—
359C4—2021no—
360C4#41×D10111yescharacteristic
361C4C2×#1310807511yescharacteristic
362C2—42no—
363C2—8081no—
364C2—4042no—
365C2—2022no—
366C2#2026569011yescharacteristic
367C2AGL(1,ℤ/8)×D10111yescharacteristic
368C2#2026597411yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#478×C101C2
socleC22×C101C22×D4
prime radical#20265312C2
hypercenter#478D101
hypocenterC101#3114
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20265712C2semidirect
2. C4×D4×D101C2semidirect
3. #20265509C2semidirect
4. #20265492C2semidirect
5. #20265474C2semidirect
6. #20265393C2semidirect
7. #20265392C2semidirect
8. #20265329C2semidirect
10. #20265288C2semidirect
11. #20265286C2semidirect
12. #20265276C2semidirect
13. #20265274C2semidirect
14. #20265233C2semidirect
15. #478×C101C2semidirect
23. #15692243C22semidirect
27. #15692220C22semidirect
32. #15692217C22semidirect
39. #15692188C22semidirect
40. #15692186C22semidirect
41. C4⋊#11717579C22semidirect
42. #15692180C22semidirect
43. #15692178C22semidirect
44. #15692177C22semidirect
47. #15692175C22semidirect
50. #15692165C22semidirect
51. #15692165C22semidirect
52. #125×C101C22semidirect
54. #107×C101C22semidirect
55. #106×C101C22semidirect
56. C4⋊C8×C101C22semidirect
185. C101#3114semidirect
191. #478D101semidirect
208. #125C2×D101semidirect
227. #107C2×D101semidirect
229. #106C2×D101semidirect
231. C4⋊C8C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202657122
C4×D4×D1012
#202655092
#202654922
#202654742
#202653932
#202653922
#202653292
#202653122
#202652882
#202652862
#202652762
#202652742
#202652332
#478×C1012
#3114101