Finite Group Databasebeta

← SD16×D508 #30650427

Subgroups — SD16×D508 #30650427

Order 16256.

546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D127C212yesmaximal, complemented
2Q8×D508C211yesmaximal, characteristic, complemented
3D4×D508C211yesmaximal, characteristic
4#22550249C211yesmaximal, characteristic, complemented
5#22550106C212yesmaximal, complemented
6#22550081C211yesmaximal, characteristic, complemented
7#22550076C211yesmaximal, characteristic, complemented
8#22550028C212yesmaximal, complemented
9#22550016C212yesmaximal, complemented
10C8×D508C211yesmaximal, characteristic, complemented
11C4×SD16×C127C211yesmaximal, characteristic, complemented
12C2×Q8×D127C2212yescomplemented
13C22×D508—21no—
14C2×D4×D127C2212yes—
15C2×#14523237C2212yescomplemented
16C2×#14523237C2212yescomplemented
17C2×#14523236C2212yes—
18C2×#14523235C2212yescomplemented
19SD16×D127—28no—
20C2×C8×D127C2212yescomplemented
21#16861209—21no—
22#16861209C2211yescharacteristic, complemented
23#16861206C2211yescharacteristic
24#16861189—22no—
25#16861189C2212yescomplemented
26#16861184C2212yes—
27#16861183—21no—
28#16861179—22no—
29C4×D508—21no—
30C4×D508C2211yescharacteristic
31C4⋊(C127⋊C8)C2211yescharacteristic, complemented
32#16861132C2212yescomplemented
33#16861129C2212yescomplemented
34(C2×D127)⋊C8C2212yescomplemented
35C2×SD16×C127C2211yescharacteristic
36C4×Q8×C127C2211yescharacteristic, complemented
37C4×D4×C127C2211yescharacteristic
38#106×C127C2211yescharacteristic, complemented
39#103×C127C2211yescharacteristic, complemented
40#102×C127C2211yescharacteristic
41C4×C8×C127C2211yescharacteristic, complemented
42C23×D127—22no—
43C2×Dic254—22no—
44C2×Dic254C2312yes—
45Q8×D127—24no—
46Q8×D127—42no—
47C2×D508—22no—
48C2×D508—21no—
49C2×D508—21no—
50C2×D508—44no—
51C2×D508D411yescharacteristic
52C2×D508C2312yes—
53C2×C22⋊D127—22no—
54D4×D127—24no—
55D4×D127—42no—
56C2×C4×D127—22no—
57C2×C4×D127C2312yes—
58#14523237—24no—
59#14523237—42no—
60#14523236—24no—
61#14523235—24no—
62C2×C127⋊C8C2312yes—
63C8×D127—24no—
64C4⋊Dic127—22no—
65C4⋊Dic127—21no—
66C4⋊Dic127—21no—
67C4⋊Dic127D411yescharacteristic
68(C2×D127)⋊C4—22no—
69(C2×D127)⋊C4—22no—
70(C2×D127)⋊C4D412yes—
71C2×Q8×C127C2311yescharacteristic
72C2×D4×C127C2311yescharacteristic
73C22×C4×C127—21no—
74SD16×C127D414yescomplemented
75C2×C8×C127C2311yescharacteristic
76C2×C8×C127C2311yescharacteristic
77C4⋊C4×C127—21no—
78C4⋊C4×C127C2311yescharacteristic
79C4⋊C4×C127C2311yescharacteristic
80C22⋊C4×C127—21no—
81C42×C127—21no—
82C42×C127C2311yescharacteristic
83C22×D127—22no—
84C22×D127—44no—
85C22×D127—44no—
86C22×D127—82no—
87C22×D127C2×D412yes—
88Dic254—22no—
89Dic254—22no—
90Dic254—44no—
91D508—22no—
92D508—22no—
93D508—44no—
94D508—42no—
95D508—81no—
96D508SD1614yesdirect product factor
97C22⋊D127—44no—
98C2×Dic127—22no—
99C2×Dic127C2×D412yes—
100C4×D127—22no—
101C4×D127—22no—
102C4×D127—44no—
103C127⋊C8—22no—
104C23×C127—21no—
105Q8×C127—21no—
106Q8×C127C2×D412yescomplemented
107D4×C127—21no—
108D4×C127C2×D412yes—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—42no—
113C2×C4×C127C2×D411yescharacteristic
114C2×C4×C127C2×D411yescharacteristic
115C2×C4×C127C2411yescharacteristic
116C8×C127—21no—
117C8×C127C2×D412yescomplemented
118C22×C127—22no—
119C22×C127—41no—
120C22×C127—41no—
121C22×C127C22×D411yescharacteristic
122C2×D127—22no—
123C2×D127—22no—
124C2×D127—42no—
125C2×D127—42no—
126C2×D127—42no—
127C2×D127—88no—
128C2×D127C2×SD1614yescomplemented
129C4×C127—22no—
130C4×C127—21no—
131C4×C127—41no—
132C4×C127—41no—
133C4×C127C2×SD1612yescomplemented
134C4×C127C22×D411yescharacteristic
135C4×C127H(5,𝔽2)11yescharacteristic
136Dic127—22no—
137Dic127—42no—
138C2×C127—42no—
139C2×C127D4211yescharacteristic
140C2×C127C22×SD1611yescharacteristic
141C2×C127#57711yescharacteristic
142D127—24no—
143D127—82no—
144D4×SD16—1271nomaximal, Sylow
145C127D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1272no—
147D4×Q8—1271no—
148D42—1271no—
149#492—1271no—
150#465—1272no—
151#461—1271no—
152#460—1271no—
153#450—1272no—
154#448—1272no—
155C4×SD16D12711yescharacteristic, complemented
156C8×D4—1271no—
157C22×Q8—1272no—
158C22×D4—1272no—
159C22×D4—2541no—
160C2×SD16—1272no—
161C2×SD16—1272no—
162C2×SD16—1272no—
163C2×SD16—1272no—
164C2×SD16—2548no—
165C2×SD16C2×D12711yescharacteristic
166C22×C8—1272no—
167C4⋊Q8—1271no—
168C4⋊Q8—2541no—
169#127—1271no—
170C22⋊Q8—1272no—
171C22⋊Q8—2542no—
172#121—1272no—
173#121—2541no—
174#120—2542no—
175C4×Q8C2×D12711yescharacteristic, complemented
176C4×D4—1271no—
177C4×D4—2541no—
178C4×D4C2×D12711yescharacteristic
179#106C2×D12711yescharacteristic, complemented
180C4⋊C8—1271no—
181#103—1272no—
182#103C2×D12711yescharacteristic, complemented
183#102—1272no—
184#102C2×D12711yescharacteristic
185C22⋊C8—1272no—
186C4×C8C2×D12711yescharacteristic, complemented
187C24—2542no—
188C2×Q8—1272no—
189C2×Q8—5082no—
190C2×Q8—2542no—
191C2×Q8—2544no—
192C2×Q8C22×D12711yescharacteristic
193C2×D4—1271no—
194C2×D4—1272no—
195C2×D4—5084no—
196C2×D4—5082no—
197C2×D4—2542no—
198C2×D4—2542no—
199C2×D4—2544no—
200C2×D4—2541no—
201C2×D4—2541no—
202C2×D4C22×D12711yescharacteristic
203C22×C4—21no—
204C22×C4—1272no—
205C22×C4—2542no—
206SD16—5082no—
207SD16—2544no—
208SD16—2544no—
209SD16—2544no—
210SD16D50814yesdirect product factor
211C2×C8—1272no—
212C2×C8—2544no—
213C2×C8C22×D12711yescharacteristic
214C2×C8C22×D12711yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—1271no—
217C4⋊C4—2542no—
218C4⋊C4—2541no—
219C4⋊C4—2541no—
220C4⋊C4C22×D12711yescharacteristic
221C4⋊C4C22×D12711yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—1272no—
224C22⋊C4—2542no—
225C22⋊C4—2542no—
226C42—21no—
227C42C22×D12711yescharacteristic
228C23—21no—
229C23—1272no—
230C23—10162no—
231C23—5084no—
232C23—5084no—
233C23—2542no—
234Q8—21no—
235Q8—5084no—
236Q8—2542no—
237Q8—2542no—
238Q8C2×D50812yescomplemented
239D4—21no—
240D4—1274no—
241D4—10161no—
242D4—5084no—
243D4—5084no—
244D4—5082no—
245D4—2542no—
246D4—2542no—
247D4C2×D50812yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—1272no—
253C2×C4—5084no—
254C2×C4—2542no—
255C2×C4—2542no—
256C2×C4—2542no—
257C2×C4D4×D12711yescharacteristic
258C2×C4D4×D12711yescharacteristic
259C2×C4C23×D12711yescharacteristic
260C8—21no—
261C8—2542no—
262C8C2×D50812yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—1274no—
267C22—10168no—
268C22—5082no—
269C22—5082no—
270C22—5082no—
271C22—2542no—
272C22—2542no—
273C22C2×D4×D12711yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—5082no—
279C4—2542no—
280C4SD16×D12712yescomplemented
281C4C22×D50811yescharacteristic
282C4#1686125511yescharacteristic
283C2—42no—
284C2—10162no—
285C2—2544no—
286C2D4×D50811yescharacteristic
287C2C2×SD16×D12711yescharacteristic
288C2#2255068311yescharacteristic
subgroupG/H
centerC22C2×D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC4×SD16×C127C2
socleC22×C127C22×D4
prime radicalD4×D508C2
hypercenterC4×SD16D127
hypocenterC127D4×SD16
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D127C2semidirect
2. Q8×D508C2semidirect
4. #22550249C2semidirect
5. #22550106C2semidirect
6. #22550081C2semidirect
7. #22550076C2semidirect
8. #22550028C2semidirect
9. #22550016C2semidirect
10. C8×D508C2semidirect
11. C4×SD16×C127C2semidirect
12. C2×Q8×D127C22semidirect
15. C2×#14523237C22semidirect
16. C2×#14523237C22semidirect
18. C2×#14523235C22semidirect
20. C2×C8×D127C22semidirect
22. #16861209C22semidirect
25. #16861189C22semidirect
31. C4⋊(C127⋊C8)C22semidirect
32. #16861132C22semidirect
33. #16861129C22semidirect
34. (C2×D127)⋊C8C22semidirect
36. C4×Q8×C127C22semidirect
38. #106×C127C22semidirect
39. #103×C127C22semidirect
41. C4×C8×C127C22semidirect
74. SD16×C127D4semidirect
96. D508SD16direct (N × H)
106. Q8×C127C2×D4semidirect
117. C8×C127C2×D4semidirect
128. C2×D127C2×SD16semidirect
133. C4×C127C2×SD16semidirect
145. C127D4×SD16semidirect
155. C4×SD16D127semidirect
175. C4×Q8C2×D127semidirect
179. #106C2×D127semidirect
182. #103C2×D127semidirect
186. C4×C8C2×D127semidirect
210. SD16D508direct (N × H)
238. Q8C2×D508semidirect
262. C8C2×D508semidirect
280. C4SD16×D127semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1272
Q8×D5082
D4×D5082
#225502492
#225501062
#225500812
#225500762
#225500282
#225500162
C8×D5082
C4×SD16×C1272
D4×SD16127