Finite Group Databasebeta

← SD16×D428 #28348158

Subgroups — SD16×D428 #28348158

Order 13696.

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×D107C212yesmaximal, complemented
2Q8×D428C211yesmaximal, characteristic, complemented
3D4×D428C211yesmaximal, characteristic
4#20293000C211yesmaximal, characteristic, complemented
5#20292857C212yesmaximal, complemented
6#20292832C211yesmaximal, characteristic, complemented
7#20292827C211yesmaximal, characteristic, complemented
8#20292779C212yesmaximal, complemented
9#20292767C212yesmaximal, complemented
10C8×D428C211yesmaximal, characteristic, complemented
11C4×SD16×C107C211yesmaximal, characteristic, complemented
12C2×Q8×D107C2212yescomplemented
13C22×D428—21no—
14C2×D4×D107C2212yes—
15C2×#13133807C2212yescomplemented
16C2×#13133807C2212yescomplemented
17C2×#13133806C2212yes—
18C2×#13133805C2212yescomplemented
19SD16×D107—28no—
20C2×C8×D107C2212yescomplemented
21#16812109—21no—
22#16812109C2211yescharacteristic, complemented
23#16812106C2211yescharacteristic
24#16812089—22no—
25#16812089C2212yescomplemented
26#16812084C2212yes—
27#16812083—21no—
28#16812079—22no—
29C4×D428—21no—
30C4×D428C2211yescharacteristic
31C4⋊(C107⋊C8)C2211yescharacteristic, complemented
32#16812032C2212yescomplemented
33#16812029C2212yescomplemented
34(C2×D107)⋊C8C2212yescomplemented
35C2×SD16×C107C2211yescharacteristic
36C4×Q8×C107C2211yescharacteristic, complemented
37C4×D4×C107C2211yescharacteristic
38#106×C107C2211yescharacteristic, complemented
39#103×C107C2211yescharacteristic, complemented
40#102×C107C2211yescharacteristic
41C4×C8×C107C2211yescharacteristic, complemented
42C23×D107—22no—
43C2×Dic214—22no—
44C2×Dic214C2312yes—
45Q8×D107—24no—
46Q8×D107—42no—
47C2×D428—22no—
48C2×D428—21no—
49C2×D428—21no—
50C2×D428—44no—
51C2×D428D411yescharacteristic
52C2×D428C2312yes—
53C2×C22⋊D107—22no—
54D4×D107—24no—
55D4×D107—42no—
56C2×C4×D107—22no—
57C2×C4×D107C2312yes—
58#13133807—24no—
59#13133807—42no—
60#13133806—24no—
61#13133805—24no—
62C2×C107⋊C8C2312yes—
63C8×D107—24no—
64C4⋊Dic107—21no—
65C4⋊Dic107—21no—
66C4⋊Dic107—22no—
67C4⋊Dic107D411yescharacteristic
68(C2×D107)⋊C4—22no—
69(C2×D107)⋊C4—22no—
70(C2×D107)⋊C4D412yes—
71C2×Q8×C107C2311yescharacteristic
72C2×D4×C107C2311yescharacteristic
73C22×C4×C107—21no—
74SD16×C107D414yescomplemented
75C2×C8×C107C2311yescharacteristic
76C2×C8×C107C2311yescharacteristic
77C4⋊C4×C107—21no—
78C4⋊C4×C107C2311yescharacteristic
79C4⋊C4×C107C2311yescharacteristic
80C22⋊C4×C107—21no—
81C42×C107—21no—
82C42×C107C2311yescharacteristic
83C23×C107—21no—
84C22×D107—22no—
85C22×D107—44no—
86C22×D107—44no—
87C22×D107—82no—
88C22×D107C2×D412yes—
89Q8×C107—21no—
90Q8×C107C2×D412yescomplemented
91D4×C107—21no—
92D4×C107C2×D412yes—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—21no—
96C2×C4×C107—42no—
97C2×C4×C107C2×D411yescharacteristic
98C2×C4×C107C2×D411yescharacteristic
99C2×C4×C107C2411yescharacteristic
100C22⋊D107—44no—
101C2×Dic107—22no—
102C2×Dic107C2×D412yes—
103D428—22no—
104D428—22no—
105D428—44no—
106D428—42no—
107D428—81no—
108D428SD1614yesdirect product factor
109C4×D107—22no—
110C4×D107—22no—
111C4×D107—44no—
112Dic214—22no—
113Dic214—22no—
114Dic214—44no—
115C8×C107—21no—
116C8×C107C2×D412yescomplemented
117C107⋊C8—22no—
118C22×C107—22no—
119C22×C107—41no—
120C22×C107—41no—
121C22×C107C22×D411yescharacteristic
122C2×D107—22no—
123C2×D107—22no—
124C2×D107—42no—
125C2×D107—42no—
126C2×D107—42no—
127C2×D107—88no—
128C2×D107C2×SD1614yescomplemented
129C4×C107—22no—
130C4×C107—21no—
131C4×C107—41no—
132C4×C107—41no—
133C4×C107C2×SD1612yescomplemented
134C4×C107C22×D411yescharacteristic
135C4×C107H(5,𝔽2)11yescharacteristic
136Dic107—22no—
137Dic107—42no—
138C2×C107—42no—
139C2×C107D4211yescharacteristic
140C2×C107C22×SD1611yescharacteristic
141C2×C107#57711yescharacteristic
142D107—24no—
143D107—82no—
144D4×SD16—1071nomaximal, Sylow
145C107D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1072no—
147D4×Q8—1071no—
148D42—1071no—
149#492—1071no—
150#465—1072no—
151#461—1071no—
152#460—1071no—
153#450—1072no—
154#448—1072no—
155C4×SD16D10711yescharacteristic, complemented
156C8×D4—1071no—
157C22×Q8—1072no—
158C22×D4—1072no—
159C22×D4—2141no—
160C2×SD16—1072no—
161C2×SD16—1072no—
162C2×SD16—1072no—
163C2×SD16—1072no—
164C2×SD16—2148no—
165C2×SD16C2×D10711yescharacteristic
166C22×C8—1072no—
167C4⋊Q8—1071no—
168C4⋊Q8—2141no—
169#127—1071no—
170C22⋊Q8—1072no—
171C22⋊Q8—2142no—
172#121—1072no—
173#121—2141no—
174#120—2142no—
175C4×Q8C2×D10711yescharacteristic, complemented
176C4×D4—1071no—
177C4×D4—2141no—
178C4×D4C2×D10711yescharacteristic
179#106C2×D10711yescharacteristic, complemented
180C4⋊C8—1071no—
181#103—1072no—
182#103C2×D10711yescharacteristic, complemented
183#102—1072no—
184#102C2×D10711yescharacteristic
185C22⋊C8—1072no—
186C4×C8C2×D10711yescharacteristic, complemented
187C24—2142no—
188C2×Q8—1072no—
189C2×Q8—4282no—
190C2×Q8—2142no—
191C2×Q8—2144no—
192C2×Q8C22×D10711yescharacteristic
193C2×D4—1071no—
194C2×D4—1072no—
195C2×D4—4284no—
196C2×D4—4282no—
197C2×D4—2142no—
198C2×D4—2142no—
199C2×D4—2144no—
200C2×D4—2141no—
201C2×D4—2141no—
202C2×D4C22×D10711yescharacteristic
203C22×C4—21no—
204C22×C4—1072no—
205C22×C4—2142no—
206SD16—4282no—
207SD16—2144no—
208SD16—2144no—
209SD16—2144no—
210SD16D42814yesdirect product factor
211C2×C8—1072no—
212C2×C8—2144no—
213C2×C8C22×D10711yescharacteristic
214C2×C8C22×D10711yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—1071no—
217C4⋊C4—2142no—
218C4⋊C4—2141no—
219C4⋊C4—2141no—
220C4⋊C4C22×D10711yescharacteristic
221C4⋊C4C22×D10711yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—1072no—
224C22⋊C4—2142no—
225C22⋊C4—2142no—
226C42—21no—
227C42C22×D10711yescharacteristic
228C23—21no—
229C23—8562no—
230C23—1072no—
231C23—4284no—
232C23—4284no—
233C23—2142no—
234Q8—21no—
235Q8—4284no—
236Q8—2142no—
237Q8—2142no—
238Q8C2×D42812yescomplemented
239D4—21no—
240D4—8561no—
241D4—1074no—
242D4—4284no—
243D4—4284no—
244D4—4282no—
245D4—2142no—
246D4—2142no—
247D4C2×D42812yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—1072no—
253C2×C4—4284no—
254C2×C4—2142no—
255C2×C4—2142no—
256C2×C4—2142no—
257C2×C4D4×D10711yescharacteristic
258C2×C4D4×D10711yescharacteristic
259C2×C4C23×D10711yescharacteristic
260C8—21no—
261C8—2142no—
262C8C2×D42812yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—8568no—
267C22—1074no—
268C22—4282no—
269C22—4282no—
270C22—4282no—
271C22—2142no—
272C22—2142no—
273C22C2×D4×D10711yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—4282no—
279C4—2142no—
280C4SD16×D10712yescomplemented
281C4C22×D42811yescharacteristic
282C4#1681215511yescharacteristic
283C2—42no—
284C2—8562no—
285C2—2144no—
286C2D4×D42811yescharacteristic
287C2C2×SD16×D10711yescharacteristic
288C2#2029343411yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×SD16×C107C2
socleC22×C107C22×D4
prime radicalD4×D428C2
hypercenterC4×SD16D107
hypocenterC107D4×SD16
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D107C2semidirect
2. Q8×D428C2semidirect
4. #20293000C2semidirect
5. #20292857C2semidirect
6. #20292832C2semidirect
7. #20292827C2semidirect
8. #20292779C2semidirect
9. #20292767C2semidirect
10. C8×D428C2semidirect
11. C4×SD16×C107C2semidirect
12. C2×Q8×D107C22semidirect
15. C2×#13133807C22semidirect
16. C2×#13133807C22semidirect
18. C2×#13133805C22semidirect
20. C2×C8×D107C22semidirect
22. #16812109C22semidirect
25. #16812089C22semidirect
31. C4⋊(C107⋊C8)C22semidirect
32. #16812032C22semidirect
33. #16812029C22semidirect
34. (C2×D107)⋊C8C22semidirect
36. C4×Q8×C107C22semidirect
38. #106×C107C22semidirect
39. #103×C107C22semidirect
41. C4×C8×C107C22semidirect
74. SD16×C107D4semidirect
90. Q8×C107C2×D4semidirect
108. D428SD16direct (N × H)
116. C8×C107C2×D4semidirect
128. C2×D107C2×SD16semidirect
133. C4×C107C2×SD16semidirect
145. C107D4×SD16semidirect
155. C4×SD16D107semidirect
175. C4×Q8C2×D107semidirect
179. #106C2×D107semidirect
182. #103C2×D107semidirect
186. C4×C8C2×D107semidirect
210. SD16D428direct (N × H)
238. Q8C2×D428semidirect
262. C8C2×D428semidirect
280. C4SD16×D107semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1072
Q8×D4282
D4×D4282
#202930002
#202928572
#202928322
#202928272
#202927792
#202927672
C8×D4282
C4×SD16×C1072
D4×SD16107