Finite Group Databasebeta

← #30648969

Subgroups — #30648969

Order 16256.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22550479C211yesmaximal, characteristic, complemented
2#22550350C211yesmaximal, characteristic, complemented
3#22550200C211yesmaximal, characteristic, complemented
4#22550179C211yesmaximal, characteristic, complemented
5#22550175C211yesmaximal, characteristic, complemented
6#22550070C211yesmaximal, characteristic, complemented
7#22550070C211yesmaximal, characteristic, complemented
8#22550012C211yesmaximal, characteristic, complemented
9#22550009C211yesmaximal, characteristic, complemented
10#22549987C211yesmaximal, characteristic, complemented
11#22549985C211yesmaximal, characteristic, complemented
12#22549958C211yesmaximal, characteristic, complemented
13#22549956C211yesmaximal, characteristic, complemented
14#22549934C211yesmaximal, characteristic, complemented
15#482×C127C211yesmaximal, characteristic, complemented
16C22×D508C2211yescharacteristic
17C2×D1016C2211yescharacteristic
18C2×D1016C2211yescharacteristic
19C2×#14523233C2211yescharacteristic
20C2×#14523233C2211yescharacteristic
21#16861205C2211yescharacteristic, complemented
22#16861200C2211yescharacteristic, complemented
23#16861193—21no—
24#16861191—21no—
25#16861183C2211yescharacteristic
26#16861181—21no—
27#16861180—21no—
28C4×D508—21no—
29C4×D508—21no—
30D4×Dic127C2211yescharacteristic, complemented
31#16861171C2211yescharacteristic
32#16861171C2211yescharacteristic
33#16861171C2211yescharacteristic
34#16861171C2211yescharacteristic
35#16861171C2211yescharacteristic, complemented
36#16861168C2211yescharacteristic
37C22⋊C4×D127—21no—
38C22⋊C4×D127—21no—
39#16861142C2211yescharacteristic, complemented
40#16861140C2211yescharacteristic, complemented
41Dic127⋊C8C2211yescharacteristic, complemented
42Dic127⋊C8C2211yescharacteristic, complemented
43#16861131C2211yescharacteristic
44#16861131C2211yescharacteristic
45#16861129C2211yescharacteristic
46#16861129C2211yescharacteristic
47#16861129C2211yescharacteristic, complemented
48#16861129C2211yescharacteristic, complemented
49C22⋊(C127⋊C8)C2211yescharacteristic
50#16861119C2211yescharacteristic, complemented
51C8×Dic127C2211yescharacteristic, complemented
52#121×C127C2211yescharacteristic
53#117×C127C2211yescharacteristic
54#107×C127C2211yescharacteristic, complemented
55#106×C127C2211yescharacteristic, complemented
56#102×C127C2211yescharacteristic, complemented
57#102×C127C2211yescharacteristic, complemented
58C22⋊C8×C127C2211yescharacteristic
59C23×D127—21no—
60C2×D508—22no—
61C2×D508—22no—
62C2×D508—21no—
63C2×D508C2311yescharacteristic
64C2×D508C2311yescharacteristic
65C2×D508C2311yescharacteristic
66C2×C22⋊D127—21no—
67C2×C22⋊D127—21no—
68C2×C22⋊D127—21no—
69C22×Dic127—21no—
70C2×C4×D127—21no—
71C2×C4×D127—21no—
72C2×C4×D127—21no—
73C2×C4×D127—21no—
74C2×C4×D127—21no—
75D1016—22no—
76D1016—22no—
77#14523233—22no—
78#14523233—22no—
79C2×C127⋊C8C2311yescharacteristic
80C2×C127⋊C8C2311yescharacteristic
81C4⋊Dic127—21no—
82C4⋊Dic127D411yescharacteristic
83C4⋊Dic127D411yescharacteristic
84C4⋊Dic127C2311yescharacteristic
85Dic127⋊C4—21no—
86C22⋊Dic127—21no—
87C22⋊Dic127D411yescharacteristic
88C22⋊Dic127D411yescharacteristic
89(C2×D127)⋊C4—21no—
90(C2×D127)⋊C4—21no—
91(C2×D127)⋊C4—21no—
92(C2×D127)⋊C4—21no—
93(C2×D127)⋊C4—21no—
94(C2×D127)⋊C4—21no—
95C4×Dic127C2311yescharacteristic
96C4×Dic127C2311yescharacteristic
97C2×D4×C127—21no—
98C2×D4×C127C2311yescharacteristic
99C22×C4×C127C2311yescharacteristic
100C2×C8×C127C2311yescharacteristic
101C2×C8×C127C2311yescharacteristic
102C4⋊C4×C127C2311yescharacteristic
103C4⋊C4×C127C2311yescharacteristic
104C4⋊C4×C127C2311yescharacteristic
105C22⋊C4×C127—21no—
106C22⋊C4×C127—21no—
107C42×C127—21no—
108C22×D127—21no—
109C22×D127—21no—
110C22×D127—24no—
111C22×D127—21no—
112C22×D127—81no—
113C22×D127—81no—
114D508—24no—
115D508—21no—
116D508—21no—
117D508—21no—
118D508—21no—
119D508#4112yes—
120D508#4112yes—
121C22⋊D127—81no—
122C22⋊D127—81no—
123C22⋊D127—81no—
124C2×Dic127—21no—
125C2×Dic127—81no—
126C2×Dic127C2×D411yescharacteristic
127C2×Dic127C2×D411yescharacteristic
128C2×Dic127C2×D411yescharacteristic
129C2×Dic127C2×D411yescharacteristic
130C4×D127—81no—
131C4×D127—81no—
132C4×D127—81no—
133C4×D127—81no—
134C4×D127—81no—
135C127⋊C8—21no—
136C127⋊C8—21no—
137C23×C127—21no—
138C23×C127C2×D411yescharacteristic
139D4×C127—21no—
140D4×C127—21no—
141D4×C127—81no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127C2×D411yescharacteristic
148C2×C4×C127C2411yescharacteristic
149C8×C127—21no—
150C8×C127—21no—
151C22×C127—21no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—41no—
157C22×C127C22×D411yescharacteristic
158C2×D127—22no—
159C2×D127—22no—
160C2×D127—41no—
161C2×D127—41no—
162C2×D127—41no—
163C2×D127—41no—
164C2×D127—41no—
165C2×D127—41no—
166C2×D127—41no—
167C2×D127—84no—
168C4×C127—21no—
169C4×C127—41no—
170C4×C127—41no—
171C4×C127—41no—
172C4×C127C2×#4111yescharacteristic
173C4×C127C2×#4111yescharacteristic
174Dic127—21no—
175Dic127—21no—
176Dic127—21no—
177Dic127—21no—
178Dic127—41no—
179C2×C127—41no—
180C2×C127—81no—
181C2×C127#52511yescharacteristic
182C2×C127#57611yescharacteristic
183C2×C127#57611yescharacteristic
184D127—42no—
185D127—42no—
186D127—81no—
187#3122—1271nomaximal, Sylow
188C127#312211yescharacteristic, complemented, Sylow
189#540—1271no—
190#518—1271no—
191#482—1271no—
192#482D12711yescharacteristic, complemented
193#478—1271no—
194#478—1271no—
195#459—1271no—
196#459—1271no—
197#447—1271no—
198#447—1271no—
199#442—1271no—
200#442—1271no—
201C4×D8—1271no—
202C4×D8—1271no—
203#433—1271no—
204C22×D4—1271no—
205C2×D8—1271no—
206C2×D8—1271no—
207C2×D8—1271no—
208C2×D8—1271no—
209#127—1271no—
210#125—1271no—
211#123—2541no—
212#123—2541no—
213#121—1271no—
214#121—2541no—
215#121—2541no—
216#121C2×D12711yescharacteristic
217C4×D4—1271no—
218C4×D4—1271no—
219C4×D4—1271no—
220C4×D4—1271no—
221C4×D4—1271no—
222C4×D4—1271no—
223C4×D4—2541no—
224C4×D4—2541no—
225#117—1271no—
226#117C2×D12711yescharacteristic
227C2×C22⋊C4—2541no—
228C2×C22⋊C4—2541no—
229#107—1271no—
230#107C2×D12711yescharacteristic, complemented
231#106—1271no—
232#106C2×D12711yescharacteristic, complemented
233C4⋊C8—1271no—
234C4⋊C8—1271no—
235#102—1271no—
236#102—1271no—
237#102—1271no—
238#102—1271no—
239#102—1271no—
240#102—1271no—
241#102C2×D12711yescharacteristic, complemented
242#102C2×D12711yescharacteristic, complemented
243C22⋊C8—1271no—
244C22⋊C8C2×D12711yescharacteristic
245#97—1271no—
246C4×C8—1271no—
247C24—2541no—
248C2×D4—21no—
249C2×D4—1271no—
250C2×D4—1271no—
251C2×D4—1271no—
252C2×D4—2542no—
253C2×D4—2542no—
254C2×D4—2541no—
255C2×D4—2541no—
256C2×D4—2541no—
257C2×D4—2541no—
258C2×D4C22×D12711yescharacteristic
259C22×C4—2541no—
260C22×C4—2541no—
261C22×C4—2541no—
262C22×C4—2541no—
263C22×C4—2541no—
264C22×C4—2541no—
265C22×C4C22×D12711yescharacteristic
266D8—2542no—
267D8—2542no—
268D8—2542no—
269D8—2542no—
270C2×C8—1271no—
271C2×C8—1271no—
272C2×C8C22×D12711yescharacteristic
273C2×C8C22×D12711yescharacteristic
274C4⋊C4—1271no—
275C4⋊C4—1271no—
276C4⋊C4—1271no—
277C4⋊C4—2541no—
278C4⋊C4—2541no—
279C4⋊C4C22×D12711yescharacteristic
280C4⋊C4C22×D12711yescharacteristic
281C4⋊C4C22×D12711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1271no—
285C22⋊C4—1271no—
286C22⋊C4—2541no—
287C22⋊C4—2541no—
288C22⋊C4—2541no—
289C22⋊C4—2541no—
290C22⋊C4—2541no—
291C22⋊C4—2541no—
292C22⋊C4—2541no—
293C42—21no—
294C42—1271no—
295C42—1271no—
296C23—21no—
297C23—10161no—
298C23—10161no—
299C23—2544no—
300C23—2541no—
301C23—2541no—
302C23—2541no—
303C23D4×D12711yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—1272no—
308D4—1272no—
309D4—10161no—
310D4—10161no—
311D4—10161no—
312D4—2544no—
313D4—2541no—
314D4—2541no—
315D4—2541no—
316D4—2541no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—1271no—
323C2×C4—1271no—
324C2×C4—1271no—
325C2×C4—1271no—
326C2×C4—10161no—
327C2×C4—10161no—
328C2×C4—10161no—
329C2×C4—10161no—
330C2×C4—10161no—
331C2×C4—10161no—
332C2×C4—2541no—
333C2×C4D4×D12711yescharacteristic
334C2×C4C23×D12711yescharacteristic
335C8—21no—
336C8—21no—
337C8—2541no—
338C8—2541no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—10164no—
346C22—5081no—
347C22—5081no—
348C22—5081no—
349C22—5081no—
350C22—5081no—
351C22—5081no—
352C22—5081no—
353C22—2542no—
354C22—2542no—
355C22C2×D4×D12711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—5081no—
361C4—2541no—
362C4—2541no—
363C4—2541no—
364C4—2541no—
365C4#41×D12711yescharacteristic
366C4#41×D12711yescharacteristic
367C2—41no—
368C2—81no—
369C2—10161no—
370C2—5082no—
371C2—5082no—
372C2#2255038411yescharacteristic
373C2#2255067811yescharacteristic
374C2#2255068011yescharacteristic
subgroupG/H
centerC22C2×D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting#482×C127C2
socleC22×C127C22×D4
hypercenter#482D127
hypocenterC127#3122
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #22550479C2semidirect
2. #22550350C2semidirect
3. #22550200C2semidirect
4. #22550179C2semidirect
5. #22550175C2semidirect
6. #22550070C2semidirect
7. #22550070C2semidirect
8. #22550012C2semidirect
9. #22550009C2semidirect
10. #22549987C2semidirect
11. #22549985C2semidirect
12. #22549958C2semidirect
13. #22549956C2semidirect
14. #22549934C2semidirect
15. #482×C127C2semidirect
21. #16861205C22semidirect
22. #16861200C22semidirect
30. D4×Dic127C22semidirect
35. #16861171C22semidirect
39. #16861142C22semidirect
40. #16861140C22semidirect
41. Dic127⋊C8C22semidirect
42. Dic127⋊C8C22semidirect
47. #16861129C22semidirect
48. #16861129C22semidirect
50. #16861119C22semidirect
51. C8×Dic127C22semidirect
54. #107×C127C22semidirect
55. #106×C127C22semidirect
56. #102×C127C22semidirect
57. #102×C127C22semidirect
188. C127#3122semidirect
192. #482D127semidirect
230. #107C2×D127semidirect
232. #106C2×D127semidirect
241. #102C2×D127semidirect
242. #102C2×D127semidirect

Maximal subgroups

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

subgroupindex
#225504792
#225503502
#225502002
#225501792
#225501752
#225500702
#225500122
#225500092
#225499872
#225499852
#225499582
#225499562
#225499342
#482×C1272
#3122127