Finite Group Databasebeta

← #27183170

Subgroups — #27183170

Order 12928.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265897C211yesmaximal, characteristic, complemented
2#20265823C211yesmaximal, characteristic
3#20265537C211yesmaximal, characteristic, complemented
4#20265519C211yesmaximal, characteristic, complemented
5#20265502C211yesmaximal, characteristic, complemented
6#20265468C211yesmaximal, characteristic, complemented
7#20265435C211yesmaximal, characteristic, complemented
8#20265406C211yesmaximal, characteristic, complemented
9#20265400C211yesmaximal, characteristic, complemented
10#20265341C211yesmaximal, characteristic, complemented
11#20265330C211yesmaximal, characteristic, complemented
12#20265279C211yesmaximal, characteristic, complemented
13#20265183C211yesmaximal, characteristic, complemented
14#20265174C211yesmaximal, characteristic, complemented
15#435×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C22×D404C2211yescharacteristic
18C2×Dic404C2211yescharacteristic, complemented
19C2×#13108063C2211yescharacteristic
20C2×#13108063C2211yescharacteristic
21#15692255C2211yescharacteristic, complemented
22#15692248—21no—
23#15692248—21no—
24#15692243C2211yescharacteristic
25#15692242—21no—
26#15692240—21no—
27#15692234C2211yescharacteristic
28#15692234C2211yescharacteristic
29#15692234C2211yescharacteristic, complemented
30#15692229C2211yescharacteristic
31#15692228—21no—
32#15692223—21no—
33C4×Dic202C2211yescharacteristic, complemented
34#15692220—21no—
35C4×D404C2211yescharacteristic
36#15692214C2211yescharacteristic
37#15692214C2211yescharacteristic, complemented
38C22⋊C4×D101—21no—
39#15692189C2211yescharacteristic, complemented
40#15692187C2211yescharacteristic, complemented
41#15692187C2211yescharacteristic, complemented
42#15692180C2211yescharacteristic, complemented
43#15692180C2211yescharacteristic, complemented
44#15692180C2211yescharacteristic, complemented
45#15692180C2211yescharacteristic, complemented
46#15692177C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692177C2211yescharacteristic
50#15692177C2211yescharacteristic
51#15692177C2211yescharacteristic
52C2×M16×C101C2211yescharacteristic
53C22×C8×C101C2211yescharacteristic, complemented
54C4×D4×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic, complemented
56C22⋊C8×C101C2211yescharacteristic
57C22⋊C8×C101C2211yescharacteristic, complemented
58#97×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—41no—
62C2×Dic202—21no—
63C2×Dic202C2311yescharacteristic
64C2×Dic202C2311yescharacteristic
65C2×D404—22no—
66C2×D404—21no—
67C2×D404—41no—
68C2×D404C2311yescharacteristic
69C2×D404C2311yescharacteristic
70C2×C22⋊D101—21no—
71C2×C22⋊D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74Dic404—41no—
75#13108063—22no—
76#13108063—41no—
77C4⋊Dic101—21no—
78C4⋊Dic101C2311yescharacteristic
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101—21no—
88C22⋊Dic101—21no—
89C22⋊Dic101—21no—
90C22⋊Dic101—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C4×Dic101—21no—
98C2×D4×C101D411yescharacteristic
99C22×C4×C101C2311yescharacteristic
100C22×C4×C101C2311yescharacteristic
101M16×C101—41no—
102C2×C8×C101—41no—
103C2×C8×C101C2311yescharacteristic
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C2×C8×C101C2311yescharacteristic
107C4⋊C4×C101D411yescharacteristic
108C22⋊C4×C101D411yescharacteristic
109C22⋊C4×C101D411yescharacteristic
110C42×C101C2311yescharacteristic
111C23×C101C2×D411yescharacteristic
112C23×C101C2×D411yescharacteristic
113C22×D101—21no—
114C22×D101—21no—
115C22×D101—42no—
116C22×D101—42no—
117C22×D101—81no—
118D4×C101—41no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2411yescharacteristic
128C22⋊D101—42no—
129C22⋊D101—81no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136D404—21no—
137D404—21no—
138D404—21no—
139D404—42no—
140D404#4112yes—
141C4×D101—42no—
142C4×D101—81no—
143Dic202—21no—
144Dic202—21no—
145Dic202—21no—
146Dic202—21no—
147Dic202—42no—
148C8×C101—21no—
149C8×C101—21no—
150C8×C101—21no—
151C8×C101—21no—
152C22×C101—21no—
153C22×C101—21no—
154C22×C101—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101C22×D411yescharacteristic
159C2×D101—22no—
160C2×D101—41no—
161C2×D101—41no—
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—41no—
165C2×D101—84no—
166C4×C101—21no—
167C4×C101—21no—
168C4×C101—21no—
169C4×C101—21no—
170C4×C101C2×#4111yescharacteristic
171C4×C101H(5,𝔽2)11yescharacteristic
172Dic101—41no—
173Dic101—41no—
174Dic101—41no—
175Dic101—41no—
176Dic101—41no—
177Dic101—41no—
178C2×C101—41no—
179C2×C101—41no—
180C2×C101#54611yescharacteristic
181C2×C101#57511yescharacteristic
182C2×C101#57711yescharacteristic
183D101—42no—
184D101—81no—
185#3311—1011nomaximal, Sylow
186C101#331111yescharacteristic, complemented, Sylow
187#556—1011no—
188#546—1011no—
189#489—1011no—
190#485—1011no—
191#482—1011no—
192#476—1011no—
193#470—1011no—
194#465—1011no—
195#464—1011no—
196#452—1011no—
197#450—1011no—
198#440—1011no—
199#435D10111yescharacteristic, complemented
200#418—1011no—
201#416—1011no—
202C2×#41—1011no—
203C22×D4—1011no—
204C2×Q16—1011no—
205C2×SD16—1011no—
206C2×SD16—1011no—
207C2×M16C2×D10111yescharacteristic
208C22×C8C2×D10111yescharacteristic, complemented
209C4⋊Q8—1011no—
210#126—2021no—
211#126—2021no—
212#124—1011no—
213#124—2021no—
214#123—2021no—
215C22⋊Q8—1011no—
216C22⋊Q8—1011no—
217C22⋊Q8—1011no—
218#121—1011no—
219#121—2021no—
220#120—2021no—
221C4×Q8—1011no—
222C4×Q8—2021no—
223C4×D4—1011no—
224C4×D4C2×D10111yescharacteristic
225#117—1011no—
226#117—1011no—
227C2×C22⋊C4—2021no—
228#107—1011no—
229#106—1011no—
230#106—1011no—
231C4⋊C8C2×D10111yescharacteristic, complemented
232#103—1011no—
233#103—1011no—
234#103—1011no—
235#103—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241#102—1011no—
242C22⋊C8C2×D10111yescharacteristic
243C22⋊C8C2×D10111yescharacteristic, complemented
244#97C2×D10111yescharacteristic, complemented
245C24—2021no—
246#41—4041no—
247#41—2022no—
248C2×Q8—1011no—
249C2×Q8—1011no—
250C2×Q8—2021no—
251C2×D4—1011no—
252C2×D4—1011no—
253C2×D4—4041no—
254C2×D4—2022no—
255C2×D4—2021no—
256C2×D4—2021no—
257C2×D4—2021no—
258C2×D4D40411yescharacteristic
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4C22×D10111yescharacteristic
262C22×C4C22×D10111yescharacteristic
263Q16—4041no—
264SD16—4041no—
265SD16—2022no—
266M16—41no—
267C2×C8—41no—
268C2×C8C22×D10111yescharacteristic
269C2×C8C22×D10111yescharacteristic
270C2×C8C22×D10111yescharacteristic
271C2×C8C22×D10111yescharacteristic
272C4⋊C4—1011no—
273C4⋊C4—1011no—
274C4⋊C4—1011no—
275C4⋊C4—1011no—
276C4⋊C4—2021no—
277C4⋊C4—2021no—
278C4⋊C4—2021no—
279C4⋊C4—2021no—
280C4⋊C4—2021no—
281C4⋊C4D40411yescharacteristic
282C22⋊C4—2021no—
283C22⋊C4—2021no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4D40411yescharacteristic
292C22⋊C4D40411yescharacteristic
293C42—2021no—
294C42—2021no—
295C42—2021no—
296C42C22×D10111yescharacteristic
297C23—8081no—
298C23—4042no—
299C23—4042no—
300C23—2021no—
301C23—2021no—
302C23C2×D40411yescharacteristic
303C23C2×D40411yescharacteristic
304Q8—4042no—
305Q8—2021no—
306Q8—2021no—
307Q8—2021no—
308Q8—2021no—
309D4—41no—
310D4—8081no—
311D4—1012no—
312D4—4042no—
313D4—4042no—
314D4—2021no—
315D4—2021no—
316D4—2021no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—8081no—
322C2×C4—4042no—
323C2×C4—2021no—
324C2×C4—2021no—
325C2×C4—2021no—
326C2×C4—2021no—
327C2×C4—2021no—
328C2×C4—2021no—
329C2×C4C2×D40411yescharacteristic
330C2×C4C2×D40411yescharacteristic
331C2×C4C2×D40411yescharacteristic
332C2×C4C2×D40411yescharacteristic
333C2×C4C23×D10111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—8084no—
345C22—4041no—
346C22—4041no—
347C22—4041no—
348C22—4041no—
349C22—4041no—
350C22—2022no—
351C22C22×D40411yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—4041no—
357C4—4041no—
358C4—4041no—
359C4—4041no—
360C4—4041no—
361C4—4041no—
362C4#41×D10111yescharacteristic
363C4#1569230011yescharacteristic
364C2—41no—
365C2—41no—
366C2—8081no—
367C2—4042no—
368C2#2026582211yescharacteristic
369C2#2026597711yescharacteristic
370C2#2026598911yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#435×C101C2
socleC22×C101C22×D4
prime radical#20265823C2
hypercenter#435D101
hypocenterC101#3311
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20265897C2semidirect
3. #20265537C2semidirect
4. #20265519C2semidirect
5. #20265502C2semidirect
6. #20265468C2semidirect
7. #20265435C2semidirect
8. #20265406C2semidirect
9. #20265400C2semidirect
10. #20265341C2semidirect
11. #20265330C2semidirect
12. #20265279C2semidirect
13. #20265183C2semidirect
14. #20265174C2semidirect
15. #435×C101C2semidirect
18. C2×Dic404C22semidirect
21. #15692255C22semidirect
29. #15692234C22semidirect
33. C4×Dic202C22semidirect
37. #15692214C22semidirect
39. #15692189C22semidirect
40. #15692187C22semidirect
41. #15692187C22semidirect
42. #15692180C22semidirect
43. #15692180C22semidirect
44. #15692180C22semidirect
45. #15692180C22semidirect
53. C22×C8×C101C22semidirect
55. C4⋊C8×C101C22semidirect
57. C22⋊C8×C101C22semidirect
58. #97×C101C22semidirect
186. C101#3311semidirect
199. #435D101semidirect
208. C22×C8C2×D101semidirect
231. C4⋊C8C2×D101semidirect
243. C22⋊C8C2×D101semidirect
244. #97C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658972
#202658232
#202655372
#202655192
#202655022
#202654682
#202654352
#202654062
#202654002
#202653412
#202653302
#202652792
#202651832
#202651742
#435×C1012
#3311101