Finite Group Databasebeta

← SD16×D356 #26031949

Subgroups — SD16×D356 #26031949

Order 11392.

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×D89C212yesmaximal, complemented
2Q8×D356C211yesmaximal, characteristic, complemented
3D4×D356C211yesmaximal, characteristic
4#19151971C211yesmaximal, characteristic, complemented
5#19151828C212yesmaximal, complemented
6#19151803C211yesmaximal, characteristic, complemented
7#19151798C211yesmaximal, characteristic, complemented
8#19151750C212yesmaximal, complemented
9#19151738C212yesmaximal, complemented
10C8×D356C211yesmaximal, characteristic, complemented
11C4×SD16×C89C211yesmaximal, characteristic, complemented
12C2×Q8×D89C2212yescomplemented
13C22×D356—21no—
14C2×D4×D89C2212yes—
15C2×#13083563C2212yescomplemented
16C2×#13083563C2212yescomplemented
17C2×#13083562C2212yes—
18C2×#13083561C2212yescomplemented
19SD16×D89—28no—
20C2×C8×D89C2212yescomplemented
21#15668012—21no—
22#15668012C2211yescharacteristic, complemented
23#15668009C2211yescharacteristic
24#15667992—22no—
25#15667992C2212yescomplemented
26#15667987C2212yes—
27#15667986—21no—
28#15667982—22no—
29C4×D356—21no—
30C4×D356C2211yescharacteristic
31C4⋊#10623494C2211yescharacteristic, complemented
32#15667935C2212yescomplemented
33#15667932C2212yescomplemented
34#15667924C2212yescomplemented
35C2×SD16×C89C2211yescharacteristic
36C4×Q8×C89C2211yescharacteristic, complemented
37C4×D4×C89C2211yescharacteristic
38#106×C89C2211yescharacteristic, complemented
39#103×C89C2211yescharacteristic, complemented
40#102×C89C2211yescharacteristic
41C4×C8×C89C2211yescharacteristic, complemented
42C23×D89—22no—
43C2×Dic178—22no—
44C2×Dic178C2312yes—
45Q8×D89—24no—
46Q8×D89—42no—
47C2×D356—22no—
48C2×D356—21no—
49C2×D356—21no—
50C2×D356—44no—
51C2×D356D411yescharacteristic
52C2×D356C2312yes—
53C2×C22⋊D89—22no—
54D4×D89—24no—
55D4×D89—42no—
56C2×C4×D89—22no—
57C2×C4×D89C2312yes—
58#13083563—24no—
59#13083563—42no—
60#13083562—24no—
61#13083561—24no—
62C2×#10623494C2312yes—
63C8×D89—24no—
64C4⋊Dic89—21no—
65C4⋊Dic89—21no—
66C4⋊Dic89—22no—
67C4⋊Dic89D411yescharacteristic
68#13083551—22no—
69#13083551—22no—
70#13083551D412yes—
71C2×Q8×C89C2311yescharacteristic
72C2×D4×C89C2311yescharacteristic
73C22×C4×C89—21no—
74SD16×C89D414yescomplemented
75C2×C8×C89C2311yescharacteristic
76C2×C8×C89C2311yescharacteristic
77C4⋊C4×C89—21no—
78C4⋊C4×C89C2311yescharacteristic
79C4⋊C4×C89C2311yescharacteristic
80C22⋊C4×C89—21no—
81C42×C89—21no—
82C42×C89C2311yescharacteristic
83C23×C89—21no—
84C22×D89—22no—
85C22×D89—44no—
86C22×D89—44no—
87C22×D89—82no—
88C22×D89C2×D412yes—
89Q8×C89—21no—
90Q8×C89C2×D412yescomplemented
91D4×C89—21no—
92D4×C89C2×D412yes—
93C2×C4×C89—21no—
94C2×C4×C89—21no—
95C2×C4×C89—21no—
96C2×C4×C89—42no—
97C2×C4×C89C2×D411yescharacteristic
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2411yescharacteristic
100C22⋊D89—44no—
101C2×Dic89—22no—
102C2×Dic89C2×D412yes—
103D356—22no—
104D356—22no—
105D356—44no—
106D356—42no—
107D356—81no—
108D356SD1614yesdirect product factor
109C4×D89—22no—
110C4×D89—22no—
111C4×D89—44no—
112Dic178—22no—
113Dic178—22no—
114Dic178—44no—
115C8×C89—21no—
116C8×C89C2×D412yescomplemented
117#10623494—22no—
118C22×C89—22no—
119C22×C89—41no—
120C22×C89—41no—
121C22×C89C22×D411yescharacteristic
122C2×D89—22no—
123C2×D89—22no—
124C2×D89—42no—
125C2×D89—42no—
126C2×D89—42no—
127C2×D89—88no—
128C2×D89C2×SD1614yescomplemented
129C4×C89—22no—
130C4×C89—21no—
131C4×C89—41no—
132C4×C89—41no—
133C4×C89C2×SD1612yescomplemented
134C4×C89C22×D411yescharacteristic
135C4×C89H(5,𝔽2)11yescharacteristic
136Dic89—22no—
137Dic89—42no—
138C2×C89—42no—
139C2×C89D4211yescharacteristic
140C2×C89C22×SD1611yescharacteristic
141C2×C89#57711yescharacteristic
142D89—24no—
143D89—82no—
144D4×SD16—891nomaximal, Sylow
145C89D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—892no—
147D4×Q8—891no—
148D42—891no—
149#492—891no—
150#465—892no—
151#461—891no—
152#460—891no—
153#450—892no—
154#448—892no—
155C4×SD16D8911yescharacteristic, complemented
156C8×D4—891no—
157C22×Q8—892no—
158C22×D4—892no—
159C22×D4—1781no—
160C2×SD16—892no—
161C2×SD16—892no—
162C2×SD16—892no—
163C2×SD16—892no—
164C2×SD16—1788no—
165C2×SD16C2×D8911yescharacteristic
166C22×C8—892no—
167C4⋊Q8—891no—
168C4⋊Q8—1781no—
169#127—891no—
170C22⋊Q8—892no—
171C22⋊Q8—1782no—
172#121—892no—
173#121—1781no—
174#120—1782no—
175C4×Q8C2×D8911yescharacteristic, complemented
176C4×D4—891no—
177C4×D4—1781no—
178C4×D4C2×D8911yescharacteristic
179#106C2×D8911yescharacteristic, complemented
180C4⋊C8—891no—
181#103—892no—
182#103C2×D8911yescharacteristic, complemented
183#102—892no—
184#102C2×D8911yescharacteristic
185C22⋊C8—892no—
186C4×C8C2×D8911yescharacteristic, complemented
187C24—1782no—
188C2×Q8—892no—
189C2×Q8—3562no—
190C2×Q8—1782no—
191C2×Q8—1784no—
192C2×Q8C22×D8911yescharacteristic
193C2×D4—891no—
194C2×D4—892no—
195C2×D4—3564no—
196C2×D4—3562no—
197C2×D4—1782no—
198C2×D4—1782no—
199C2×D4—1784no—
200C2×D4—1781no—
201C2×D4—1781no—
202C2×D4C22×D8911yescharacteristic
203C22×C4—21no—
204C22×C4—892no—
205C22×C4—1782no—
206SD16—3562no—
207SD16—1784no—
208SD16—1784no—
209SD16—1784no—
210SD16D35614yesdirect product factor
211C2×C8—892no—
212C2×C8—1784no—
213C2×C8C22×D8911yescharacteristic
214C2×C8C22×D8911yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—891no—
217C4⋊C4—1782no—
218C4⋊C4—1781no—
219C4⋊C4—1781no—
220C4⋊C4C22×D8911yescharacteristic
221C4⋊C4C22×D8911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—892no—
224C22⋊C4—1782no—
225C22⋊C4—1782no—
226C42—21no—
227C42C22×D8911yescharacteristic
228C23—21no—
229C23—892no—
230C23—3564no—
231C23—3564no—
232C23—1782no—
233C23—7122no—
234Q8—21no—
235Q8—3564no—
236Q8—1782no—
237Q8—1782no—
238Q8C2×D35612yescomplemented
239D4—21no—
240D4—894no—
241D4—3564no—
242D4—3564no—
243D4—3562no—
244D4—1782no—
245D4—1782no—
246D4—7121no—
247D4C2×D35612yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—892no—
253C2×C4—3564no—
254C2×C4—1782no—
255C2×C4—1782no—
256C2×C4—1782no—
257C2×C4D4×D8911yescharacteristic
258C2×C4D4×D8911yescharacteristic
259C2×C4C23×D8911yescharacteristic
260C8—21no—
261C8—1782no—
262C8C2×D35612yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—894no—
267C22—3562no—
268C22—3562no—
269C22—3562no—
270C22—1782no—
271C22—1782no—
272C22—7128no—
273C22C2×D4×D8911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—3562no—
279C4—1782no—
280C4SD16×D8912yescomplemented
281C4C22×D35611yescharacteristic
282C4#1566805811yescharacteristic
283C2—42no—
284C2—1784no—
285C2—7122no—
286C2D4×D35611yescharacteristic
287C2C2×SD16×D8911yescharacteristic
288C2#1915240511yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC4×SD16×C89C2
socleC22×C89C22×D4
prime radicalD4×D356C2
hypercenterC4×SD16D89
hypocenterC89D4×SD16
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D89C2semidirect
2. Q8×D356C2semidirect
4. #19151971C2semidirect
5. #19151828C2semidirect
6. #19151803C2semidirect
7. #19151798C2semidirect
8. #19151750C2semidirect
9. #19151738C2semidirect
10. C8×D356C2semidirect
11. C4×SD16×C89C2semidirect
12. C2×Q8×D89C22semidirect
15. C2×#13083563C22semidirect
16. C2×#13083563C22semidirect
18. C2×#13083561C22semidirect
20. C2×C8×D89C22semidirect
22. #15668012C22semidirect
25. #15667992C22semidirect
31. C4⋊#10623494C22semidirect
32. #15667935C22semidirect
33. #15667932C22semidirect
34. #15667924C22semidirect
36. C4×Q8×C89C22semidirect
38. #106×C89C22semidirect
39. #103×C89C22semidirect
41. C4×C8×C89C22semidirect
74. SD16×C89D4semidirect
90. Q8×C89C2×D4semidirect
108. D356SD16direct (N × H)
116. C8×C89C2×D4semidirect
128. C2×D89C2×SD16semidirect
133. C4×C89C2×SD16semidirect
145. C89D4×SD16semidirect
155. C4×SD16D89semidirect
175. C4×Q8C2×D89semidirect
179. #106C2×D89semidirect
182. #103C2×D89semidirect
186. C4×C8C2×D89semidirect
210. SD16D356direct (N × H)
238. Q8C2×D356semidirect
262. C8C2×D356semidirect
280. C4SD16×D89semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D892
Q8×D3562
D4×D3562
#191519712
#191518282
#191518032
#191517982
#191517502
#191517382
C8×D3562
C4×SD16×C892
D4×SD1689