Finite Group Databasebeta

← #30650738

Subgroups — #30650738

Order 16256.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22550572C211yesmaximal, characteristic, complemented
2#22550547C211yesmaximal, characteristic, complemented
3#22550241C211yesmaximal, characteristic, complemented
4#22550201C211yesmaximal, characteristic, complemented
5#22550190C211yesmaximal, characteristic, complemented
6#22550184C211yesmaximal, characteristic, complemented
7#22550129C211yesmaximal, characteristic, complemented
8#22550112C211yesmaximal, characteristic, complemented
9#22550072C211yesmaximal, characteristic, complemented
10#22550023C211yesmaximal, characteristic, complemented
11#22550023C211yesmaximal, characteristic, complemented
12#22549978C211yesmaximal, characteristic, complemented
13#22549878C211yesmaximal, characteristic, complemented
14#22549873C211yesmaximal, characteristic, complemented
15#435×C127C211yesmaximal, characteristic, complemented
16C2×#14523248C2211yescharacteristic
17C2×#14523248C2211yescharacteristic
18C2×#14523237C2211yescharacteristic
19C2×D1016C2211yescharacteristic
20C2×D1016C2211yescharacteristic
21#16861206C2211yescharacteristic
22#16861205—21no—
23#16861204—21no—
24#16861201C2211yescharacteristic
25#16861191—21no—
26#16861183C2211yescharacteristic
27#16861183C2211yescharacteristic
28#16861183C2211yescharacteristic
29#16861183C2211yescharacteristic
30#16861182—21no—
31#16861182—21no—
32#16861181—21no—
33C4×Dic254C2211yescharacteristic
34C4×D508C2211yescharacteristic
35#16861171—21no—
36(C22⋊D127)⋊C4—21no—
37#16861168C2211yescharacteristic
38C2×C4⋊Dic127C2211yescharacteristic
39#16861143C2211yescharacteristic
40#16861143C2211yescharacteristic
41#16861141C2211yescharacteristic
42#16861134C2211yescharacteristic
43#16861134C2211yescharacteristic
44#16861134C2211yescharacteristic
45#16861131C2211yescharacteristic
46#16861131C2211yescharacteristic
47#16861131C2211yescharacteristic
48#16861131C2211yescharacteristic
49#16861131C2211yescharacteristic
50#16861131C2211yescharacteristic
51#16861131C2211yescharacteristic
52C2×M16×C127C2211yescharacteristic
53C22×C8×C127C2211yescharacteristic
54C4×D4×C127C2211yescharacteristic
55C4⋊C8×C127C2211yescharacteristic
56C22⋊C8×C127C2211yescharacteristic
57C22⋊C8×C127C2211yescharacteristic
58#97×C127C2211yescharacteristic
59#14523248—22no—
60#14523248—22no—
61#14523248—41no—
62#14523248—41no—
63C2×Dic254C2311yescharacteristic
64C2×D508—21no—
65C2×D508—21no—
66C2×D508C2311yescharacteristic
67C2×D508C2311yescharacteristic
68C2×D508C2311yescharacteristic
69C2×C22⋊D127—21no—
70C2×C22⋊D127—21no—
71C2×C22⋊D127—21no—
72C2×C22⋊D127—21no—
73C2×C22⋊D127—21no—
74C2×C22⋊D127—21no—
75C22×Dic127—21no—
76C2×C4×D127—21no—
77C2×C4×D127—21no—
78C2×C4×D127—21no—
79#14523237—22no—
80D1016—41no—
81D1016—41no—
82C4⋊Dic127—21no—
83C4⋊Dic127C2311yescharacteristic
84C4⋊Dic127C2311yescharacteristic
85C4⋊Dic127C2311yescharacteristic
86C4⋊Dic127C2311yescharacteristic
87Dic127⋊C4—21no—
88Dic127⋊C4—21no—
89Dic127⋊C4—21no—
90C22⋊Dic127—21no—
91(C2×D127)⋊C4—21no—
92(C2×D127)⋊C4—21no—
93(C2×D127)⋊C4—21no—
94(C2×D127)⋊C4—21no—
95(C2×D127)⋊C4—21no—
96C4×Dic127—21no—
97C4×Dic127—21no—
98C2×D4×C127D411yescharacteristic
99C22×C4×C127C2311yescharacteristic
100C22×C4×C127C2311yescharacteristic
101M16×C127—41no—
102C2×C8×C127—41no—
103C2×C8×C127C2311yescharacteristic
104C2×C8×C127C2311yescharacteristic
105C2×C8×C127C2311yescharacteristic
106C2×C8×C127C2311yescharacteristic
107C4⋊C4×C127D411yescharacteristic
108C22⋊C4×C127D411yescharacteristic
109C22⋊C4×C127D411yescharacteristic
110C42×C127C2311yescharacteristic
111C22×D127—21no—
112C22×D127—21no—
113C22×D127—21no—
114Dic254—21no—
115Dic254#4112yes—
116D508—21no—
117D508—21no—
118D508—21no—
119D508—21no—
120D508—21no—
121D508—21no—
122D508—42no—
123D508—81no—
124C22⋊D127—42no—
125C22⋊D127—42no—
126C22⋊D127—42no—
127C22⋊D127—81no—
128C22⋊D127—81no—
129C22⋊D127—81no—
130C2×Dic127—21no—
131C2×Dic127—21no—
132C2×Dic127—21no—
133C2×Dic127—21no—
134C2×Dic127—21no—
135C2×Dic127—81no—
136C4×D127—42no—
137C4×D127—42no—
138C4×D127—81no—
139C23×C127C2×D411yescharacteristic
140C23×C127C2×D411yescharacteristic
141D4×C127—41no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127C2×D411yescharacteristic
147C2×C4×C127C2×D411yescharacteristic
148C2×C4×C127C2×D411yescharacteristic
149C2×C4×C127C2×D411yescharacteristic
150C2×C4×C127C2411yescharacteristic
151C8×C127—21no—
152C8×C127—21no—
153C8×C127—21no—
154C8×C127—21no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127C22×D411yescharacteristic
162C2×D127—41no—
163C2×D127—41no—
164C2×D127—41no—
165C2×D127—41no—
166C2×D127—41no—
167C2×D127—41no—
168C2×D127—41no—
169C2×D127—41no—
170C2×D127—41no—
171C4×C127—21no—
172C4×C127—21no—
173C4×C127—21no—
174C4×C127—21no—
175C4×C127C2×#4111yescharacteristic
176C4×C127H(5,𝔽2)11yescharacteristic
177Dic127—22no—
178Dic127—41no—
179Dic127—41no—
180Dic127—41no—
181Dic127—41no—
182C2×C127—41no—
183C2×C127—41no—
184C2×C127#54611yescharacteristic
185C2×C127#57511yescharacteristic
186C2×C127#57611yescharacteristic
187D127—81no—
188D127—81no—
189D127—81no—
190#3309—1271nomaximal, Sylow
191C127#330911yescharacteristic, complemented, Sylow
192#553—1271no—
193#550—1271no—
194#490—1271no—
195#482—1271no—
196#480—1271no—
197#479—1271no—
198#469—1271no—
199#466—1271no—
200#459—1271no—
201#449—1271no—
202#449—1271no—
203#440—1271no—
204#435D12711yescharacteristic, complemented
205#417—1271no—
206#416—1271no—
207C2×#41—1271no—
208C2×#41—1271no—
209C2×SD16—1271no—
210C2×D8—1271no—
211C2×D8—1271no—
212C2×M16C2×D12711yescharacteristic
213C22×C8C2×D12711yescharacteristic
214#127—1271no—
215#127—2541no—
216#126—2541no—
217#125—1271no—
218#123—2541no—
219#121—1271no—
220#121—1271no—
221#121—1271no—
222#121—1271no—
223#121—2541no—
224#121—2541no—
225#121—2541no—
226C4×Q8—1271no—
227C4×D4—1271no—
228C4×D4—2541no—
229C4×D4—2541no—
230C4×D4C2×D12711yescharacteristic
231#117—1271no—
232C2×C4⋊C4—1271no—
233#107—1271no—
234#107—1271no—
235#106—1271no—
236C4⋊C8C2×D12711yescharacteristic
237#103—1271no—
238#103—1271no—
239#103—1271no—
240#102—1271no—
241#102—1271no—
242#102—1271no—
243#102—1271no—
244#102—1271no—
245#102—1271no—
246#102—1271no—
247C22⋊C8C2×D12711yescharacteristic
248C22⋊C8C2×D12711yescharacteristic
249#97C2×D12711yescharacteristic
250#41—5081no—
251#41—5081no—
252#41—2542no—
253#41—2542no—
254C2×Q8—1271no—
255C2×D4—1271no—
256C2×D4—1271no—
257C2×D4—1271no—
258C2×D4—2541no—
259C2×D4—2541no—
260C2×D4—2541no—
261C2×D4—2541no—
262C2×D4—2541no—
263C2×D4—2541no—
264C2×D4—2541no—
265C2×D4—2541no—
266C2×D4D50811yescharacteristic
267C22×C4—2541no—
268C22×C4—2541no—
269C22×C4—2541no—
270C22×C4—2541no—
271C22×C4C22×D12711yescharacteristic
272C22×C4C22×D12711yescharacteristic
273SD16—2542no—
274D8—5081no—
275D8—5081no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D12711yescharacteristic
279C2×C8C22×D12711yescharacteristic
280C2×C8C22×D12711yescharacteristic
281C2×C8C22×D12711yescharacteristic
282C4⋊C4—1271no—
283C4⋊C4—1271no—
284C4⋊C4—1271no—
285C4⋊C4—1271no—
286C4⋊C4—2541no—
287C4⋊C4—2541no—
288C4⋊C4—2541no—
289C4⋊C4—2541no—
290C4⋊C4D50811yescharacteristic
291C22⋊C4—2541no—
292C22⋊C4—2541no—
293C22⋊C4—2541no—
294C22⋊C4—2541no—
295C22⋊C4—2541no—
296C22⋊C4—2541no—
297C22⋊C4D50811yescharacteristic
298C22⋊C4D50811yescharacteristic
299C42—2541no—
300C42—2541no—
301C42C22×D12711yescharacteristic
302C23—2541no—
303C23—2541no—
304C23—2541no—
305C23C2×D50811yescharacteristic
306C23C2×D50811yescharacteristic
307Q8—1272no—
308Q8—2541no—
309D4—41no—
310D4—10161no—
311D4—10161no—
312D4—10161no—
313D4—10161no—
314D4—5082no—
315D4—5082no—
316D4—5082no—
317D4—5082no—
318D4—2541no—
319D4—2541no—
320D4—2541no—
321D4—2541no—
322D4—2541no—
323D4—2541no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—10161no—
329C2×C4—10161no—
330C2×C4—5082no—
331C2×C4—5082no—
332C2×C4—2541no—
333C2×C4—2541no—
334C2×C4—2541no—
335C2×C4—2541no—
336C2×C4—2541no—
337C2×C4C2×D50811yescharacteristic
338C2×C4C2×D50811yescharacteristic
339C2×C4C2×D50811yescharacteristic
340C2×C4C2×D50811yescharacteristic
341C2×C4C23×D12711yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—5081no—
353C22—5081no—
354C22—5081no—
355C22—5081no—
356C22—5081no—
357C22—5081no—
358C22—5081no—
359C22—5081no—
360C22—5081no—
361C22C22×D50811yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—5081no—
367C4—5081no—
368C4—5081no—
369C4—5081no—
370C4—2542no—
371C4#41×D12711yescharacteristic
372C4#1686125411yescharacteristic
373C2—41no—
374C2—41no—
375C2—10161no—
376C2—10161no—
377C2—10161no—
378C2#2255052111yescharacteristic
379C2#2255067611yescharacteristic
380C2#2255068111yescharacteristic
subgroupG/H
centerC22C22×D508
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting#435×C127C2
socleC22×C127C22×D4
hypercenter#435D127
hypocenterC127#3309
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #22550572C2semidirect
2. #22550547C2semidirect
3. #22550241C2semidirect
4. #22550201C2semidirect
5. #22550190C2semidirect
6. #22550184C2semidirect
7. #22550129C2semidirect
8. #22550112C2semidirect
9. #22550072C2semidirect
10. #22550023C2semidirect
11. #22550023C2semidirect
12. #22549978C2semidirect
13. #22549878C2semidirect
14. #22549873C2semidirect
15. #435×C127C2semidirect
191. C127#3309semidirect
204. #435D127semidirect

Maximal subgroups

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

subgroupindex
#225505722
#225505472
#225502412
#225502012
#225501902
#225501842
#225501292
#225501122
#225500722
#225500232
#225499782
#225498782
#225498732
#435×C1272
#3309127