Finite Group Databasebeta

← #27183160

Subgroups — #27183160

Order 12928.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265868C211yesmaximal, characteristic, complemented
2#20265812C211yesmaximal, characteristic
3#20265541C211yesmaximal, characteristic, complemented
4#20265500C211yesmaximal, characteristic, complemented
5#20265489C211yesmaximal, characteristic, complemented
6#20265478C211yesmaximal, characteristic, complemented
7#20265420C211yesmaximal, characteristic, complemented
8#20265403C211yesmaximal, characteristic, complemented
9#20265326C211yesmaximal, characteristic, complemented
10#20265326C211yesmaximal, characteristic, complemented
11#20265275C211yesmaximal, characteristic, complemented
12#20265247C211yesmaximal, characteristic, complemented
13#20265180C211yesmaximal, characteristic, complemented
14#102×D101C211yesmaximal, characteristic, complemented
15#460×C101C211yesmaximal, characteristic, complemented
16C2×D4×D101—21no—
17C2×D4×D101C2211yescharacteristic
18C2×D4×D101C2211yescharacteristic
19C2×#13108061C2211yescharacteristic
20C2×#13108057C2211yescharacteristic, complemented
21C2×C8×D101C2211yescharacteristic, complemented
22#15692249—21no—
23#15692247C2211yescharacteristic, complemented
24#15692245—21no—
25#15692240—21no—
26#15692231C2211yescharacteristic, complemented
27#15692231C2211yescharacteristic, complemented
28#15692226—21no—
29#15692226C2211yescharacteristic
30#15692226C2211yescharacteristic
31#15692223—21no—
32#15692223—21no—
33C4×D404C2211yescharacteristic
34C4×D404C2211yescharacteristic
35#15692213C2211yescharacteristic, complemented
36#15692212—21no—
37C4⋊C4×D101C2211yescharacteristic, complemented
38#15692189C2211yescharacteristic, complemented
39#15692188C2211yescharacteristic, complemented
40#15692187C2211yescharacteristic, complemented
41#15692179C2211yescharacteristic, complemented
42#15692177C2211yescharacteristic
43#15692177C2211yescharacteristic
44#15692176C2211yescharacteristic, complemented
45#15692176C2211yescharacteristic, complemented
46#15692176C2211yescharacteristic, complemented
47#15692176C2211yescharacteristic, complemented
48#15692175C2211yescharacteristic
49#15692167C2211yescharacteristic, complemented
50#15692167C2211yescharacteristic, complemented
51#15692166C2211yescharacteristic, complemented
52C2×SD16×C101C2211yescharacteristic, complemented
53C2×SD16×C101C2211yescharacteristic, complemented
54#127×C101C2211yescharacteristic
55C4×Q8×C101C2211yescharacteristic, complemented
56C4⋊C8×C101C2211yescharacteristic, complemented
57#102×C101C2211yescharacteristic, complemented
58#102×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60C23×D101—21no—
61C2×D404D411yescharacteristic
62C2×D404C2311yescharacteristic
63C2×C22⋊D101—21no—
64C2×C22⋊D101—21no—
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67D4×D101—22no—
68D4×D101—22no—
69D4×D101—41no—
70D4×D101—41no—
71D4×D101—44no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74C2×C4×D101C2311yescharacteristic
75C2×C4×D101C2311yescharacteristic
76#13108061—22no—
77#13108057—41no—
78C2×#11717579C2311yescharacteristic
79C2×#11717579C2311yescharacteristic
80C8×D101—41no—
81C4⋊Dic101D411yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84C4⋊Dic101C2311yescharacteristic
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88#13108053—21no—
89#13108053—21no—
90C22⋊Dic101—21no—
91C22⋊Dic101—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95#13108051—21no—
96#13108051D411yescharacteristic
97#13108051D411yescharacteristic
98C4×Dic101—21no—
99C2×Q8×C101C2311yescharacteristic
100C2×D4×C101—21no—
101C2×D4×C101—21no—
102C2×D4×C101C2311yescharacteristic
103C2×D4×C101C2311yescharacteristic
104SD16×C101—41no—
105SD16×C101—41no—
106C2×C8×C101C2311yescharacteristic
107C2×C8×C101C2311yescharacteristic
108C4⋊C4×C101—21no—
109C4⋊C4×C101C2311yescharacteristic
110C42×C101—21no—
111C42×C101C2311yescharacteristic
112C23×C101—21no—
113C23×C101—21no—
114C22×D101—21no—
115C22×D101—42no—
116C22×D101—42no—
117C22×D101—42no—
118C22×D101—42no—
119C22×D101—81no—
120C22×D101—81no—
121C22×D101C2×D411yescharacteristic
122C22×D101C2×D411yescharacteristic
123Q8×C101—21no—
124Q8×C101—21no—
125D4×C101—21no—
126D4×C101—21no—
127D4×C101—21no—
128D4×C101—21no—
129D4×C101—42no—
130D4×C101—81no—
131C2×C4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101C2×D411yescharacteristic
134C2×C4×C101C2×D411yescharacteristic
135C2×C4×C101C2411yescharacteristic
136C22⋊D101—42no—
137C22⋊D101—42no—
138C22⋊D101—42no—
139C22⋊D101—42no—
140C2×Dic101—21no—
141C2×Dic101—21no—
142C2×Dic101—21no—
143C2×Dic101C2×D411yescharacteristic
144C2×Dic101C2×D411yescharacteristic
145D404—22no—
146D404—21no—
147D404#4112yes—
148C4×D101—21no—
149C4×D101—21no—
150C4×D101—21no—
151C4×D101—21no—
152C4×D101—42no—
153C4×D101—42no—
154C8×C101—21no—
155C8×C101—21no—
156#11717579—21no—
157#11717579—21no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101—41no—
164C22×C101C22×D411yescharacteristic
165C2×D101—21no—
166C2×D101—21no—
167C2×D101—21no—
168C2×D101—22no—
169C2×D101—21no—
170C2×D101—21no—
171C2×D101—41no—
172C2×D101—41no—
173C2×D101—84no—
174C2×D101—84no—
175C2×D101AGL(1,ℤ/8)12yes—
176C4×C101—21no—
177C4×C101—21no—
178C4×C101—41no—
179C4×C101—41no—
180C4×C101C2×#4111yescharacteristic
181C4×C101H(5,𝔽2)11yescharacteristic
182Dic101—21no—
183Dic101—21no—
184Dic101—41no—
185Dic101—41no—
186Dic101—41no—
187C2×C101—81no—
188C2×C101—81no—
189C2×C101#54611yescharacteristic
190C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C101#57711yescharacteristic
192D101—22no—
193D101—41no—
194D101—42no—
195#3310—1011nomaximal, Sylow
196C101#331011yescharacteristic, complemented, Sylow
197#552—1011no—
198D42—1011no—
199#490—1011no—
200#482—1011no—
201#480—1011no—
202#478—1011no—
203#468—1011no—
204#465—1011no—
205#460D10111yescharacteristic, complemented
206#450—1011no—
207#450—1011no—
208#440—1011no—
209#435—1011no—
210#418—1011no—
211C2×#102—1011no—
212C22×D4—1011no—
213C22×D4—1011no—
214C22×D4—2021no—
215C2×SD16—1011no—
216C2×SD16C2×D10111yescharacteristic, complemented
217C2×SD16C2×D10111yescharacteristic, complemented
218C2×M16—1011no—
219C22×C8—1011no—
220#127C2×D10111yescharacteristic
221#126—2021no—
222#125—1011no—
223#125—2021no—
224#123—2021no—
225C22⋊Q8—1011no—
226C22⋊Q8—1011no—
227#121—1011no—
228#121—1011no—
229#121—2021no—
230#120—2021no—
231#120—2021no—
232C4×Q8C2×D10111yescharacteristic, complemented
233C4×D4—1011no—
234C4×D4—1011no—
235#117—1011no—
236#117—2021no—
237C2×C4⋊C4—1011no—
238#107—1011no—
239#107—1011no—
240#106—1011no—
241C4⋊C8C2×D10111yescharacteristic, complemented
242#103—1011no—
243#102—1011no—
244#102—1011no—
245#102—1011no—
246#102—1011no—
247#102—1011no—
248#102—1011no—
249#102—1011no—
250#102C2×D10111yescharacteristic, complemented
251#102C2×D10111yescharacteristic, complemented
252C22⋊C8—1011no—
253C22⋊C8—1011no—
254#97—1011no—
255C24—2021no—
256C24—2021no—
257C2×Q8C22×D10111yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—1011no—
261C2×D4—1011no—
262C2×D4—4044no—
263C2×D4—4041no—
264C2×D4—4041no—
265C2×D4—2021no—
266C2×D4—2021no—
267C2×D4—2022no—
268C2×D4—2022no—
269C2×D4—2021no—
270C2×D4—2021no—
271C2×D4C22×D10111yescharacteristic
272C2×D4C22×D10111yescharacteristic
273C22×C4—1011no—
274C22×C4—1011no—
275C22×C4—2021no—
276C22×C4—2021no—
277SD16—41no—
278SD16—41no—
279SD16—2022no—
280M16—4041no—
281C2×C8—1011no—
282C2×C8—1011no—
283C2×C8—4041no—
284C2×C8C22×D10111yescharacteristic
285C2×C8C22×D10111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—1011no—
288C4⋊C4—1011no—
289C4⋊C4—1011no—
290C4⋊C4—1011no—
291C4⋊C4—2021no—
292C4⋊C4—2021no—
293C4⋊C4—2021no—
294C4⋊C4—2021no—
295C4⋊C4—2021no—
296C4⋊C4C22×D10111yescharacteristic
297C22⋊C4—1011no—
298C22⋊C4—1011no—
299C22⋊C4—2021no—
300C22⋊C4—2021no—
301C22⋊C4—2021no—
302C22⋊C4—2021no—
303C22⋊C4—2021no—
304C22⋊C4—2021no—
305C42—21no—
306C42—2021no—
307C42C22×D10111yescharacteristic
308C23—21no—
309C23—21no—
310C23—8081no—
311C23—8081no—
312C23—1011no—
313C23—1011no—
314C23—4042no—
315C23—4042no—
316C23—4042no—
317C23—4042no—
318C23—2021no—
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—1012no—
328D4—4042no—
329D4—4042no—
330D4—4042no—
331D4—4042no—
332D4—2022no—
333D4—2021no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—1011no—
337C2×C4—1011no—
338C2×C4—4042no—
339C2×C4—4042no—
340C2×C4—2021no—
341C2×C4—2021no—
342C2×C4—2021no—
343C2×C4—2021no—
344C2×C4—2021no—
345C2×C4—2021no—
346C2×C4—2021no—
347C2×C4D4×D10111yescharacteristic
348C2×C4D4×D10111yescharacteristic
349C2×C4C23×D10111yescharacteristic
350C8—21no—
351C8—21no—
352C8—2021no—
353C8—2021no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—8084no—
361C22—8084no—
362C22—1012no—
363C22—4041no—
364C22—4041no—
365C22—2021no—
366C22—2022no—
367C22—2021no—
368C22—2021no—
369C22—2021no—
370C22—2021no—
371C22C2×D4×D10111yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—4041no—
377C4—4041no—
378C4—4041no—
379C4—2021no—
380C4—2021no—
381C4#41×D10111yescharacteristic
382C4#1569230011yescharacteristic
383C2—81no—
384C2—81no—
385C2—4042no—
386C2—4041no—
387C2—2022no—
388C2#2026582411yescharacteristic
389C2AGL(1,ℤ/8)×D10111yescharacteristic
390C2#2026598311yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#460×C101C2
socleC22×C101C22×D4
prime radical#20265812C2
hypercenter#460D101
hypocenterC101#3310
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20265868C2semidirect
3. #20265541C2semidirect
4. #20265500C2semidirect
5. #20265489C2semidirect
6. #20265478C2semidirect
7. #20265420C2semidirect
8. #20265403C2semidirect
9. #20265326C2semidirect
10. #20265326C2semidirect
11. #20265275C2semidirect
12. #20265247C2semidirect
13. #20265180C2semidirect
14. #102×D101C2semidirect
15. #460×C101C2semidirect
20. C2×#13108057C22semidirect
21. C2×C8×D101C22semidirect
23. #15692247C22semidirect
26. #15692231C22semidirect
27. #15692231C22semidirect
35. #15692213C22semidirect
37. C4⋊C4×D101C22semidirect
38. #15692189C22semidirect
39. #15692188C22semidirect
40. #15692187C22semidirect
41. #15692179C22semidirect
44. #15692176C22semidirect
45. #15692176C22semidirect
46. #15692176C22semidirect
47. #15692176C22semidirect
49. #15692167C22semidirect
50. #15692167C22semidirect
51. #15692166C22semidirect
52. C2×SD16×C101C22semidirect
53. C2×SD16×C101C22semidirect
55. C4×Q8×C101C22semidirect
56. C4⋊C8×C101C22semidirect
57. #102×C101C22semidirect
58. #102×C101C22semidirect
196. C101#3310semidirect
205. #460D101semidirect
216. C2×SD16C2×D101semidirect
217. C2×SD16C2×D101semidirect
232. C4×Q8C2×D101semidirect
241. C4⋊C8C2×D101semidirect
250. #102C2×D101semidirect
251. #102C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658682
#202658122
#202655412
#202655002
#202654892
#202654782
#202654202
#202654032
#202653262
#202652752
#202652472
#202651802
#102×D1012
#460×C1012
#3310101