Finite Group Databasebeta

← SD16×D628 #34111833

Subgroups — SD16×D628 #34111833

Order 20096.

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×D157C212yesmaximal, complemented
2Q8×D628C211yesmaximal, characteristic, complemented
3D4×D628C211yesmaximal, characteristic
4#23757646C211yesmaximal, characteristic, complemented
5#23757503C212yesmaximal, complemented
6#23757478C211yesmaximal, characteristic, complemented
7#23757473C211yesmaximal, characteristic, complemented
8#23757425C212yesmaximal, complemented
9#23757413C212yesmaximal, complemented
10C8×D628C211yesmaximal, characteristic, complemented
11C4×SD16×C157C211yesmaximal, characteristic, complemented
12C2×Q8×D157C2212yescomplemented
13C22×D628—21no—
14C2×D4×D157C2212yes—
15C2×#14578943C2212yescomplemented
16C2×#14578943C2212yescomplemented
17C2×#14578942C2212yes—
18C2×#14578941C2212yescomplemented
19SD16×D157—28no—
20C2×C8×D157C2212yescomplemented
21#19097771—21no—
22#19097771C2211yescharacteristic, complemented
23#19097768C2211yescharacteristic
24#19097751—22no—
25#19097751C2212yescomplemented
26#19097746C2212yes—
27#19097745—21no—
28#19097741—22no—
29C4×D628—21no—
30C4×D628C2211yescharacteristic
31C4⋊#11929434C2211yescharacteristic, complemented
32#19097694C2212yescomplemented
33#19097691C2212yescomplemented
34#19097683C2212yescomplemented
35C2×SD16×C157C2211yescharacteristic
36C4×Q8×C157C2211yescharacteristic, complemented
37C4×D4×C157C2211yescharacteristic
38#106×C157C2211yescharacteristic, complemented
39#103×C157C2211yescharacteristic, complemented
40#102×C157C2211yescharacteristic
41C4×C8×C157C2211yescharacteristic, complemented
42C23×D157—22no—
43C2×Dic314—22no—
44C2×Dic314C2312yes—
45Q8×D157—24no—
46Q8×D157—42no—
47C2×D628—22no—
48C2×D628—21no—
49C2×D628—21no—
50C2×D628—44no—
51C2×D628D411yescharacteristic
52C2×D628C2312yes—
53C2×C22⋊D157—22no—
54D4×D157—24no—
55D4×D157—42no—
56C2×C4×D157—22no—
57C2×C4×D157C2312yes—
58#14578943—24no—
59#14578943—42no—
60#14578942—24no—
61#14578941—24no—
62C2×#11929434C2312yes—
63C8×D157—24no—
64C4⋊Dic157—22no—
65C4⋊Dic157—21no—
66C4⋊Dic157—21no—
67C4⋊Dic157D411yescharacteristic
68#14578931—22no—
69#14578931—22no—
70#14578931D412yes—
71C2×Q8×C157C2311yescharacteristic
72C2×D4×C157C2311yescharacteristic
73C22×C4×C157—21no—
74SD16×C157D414yescomplemented
75C2×C8×C157C2311yescharacteristic
76C2×C8×C157C2311yescharacteristic
77C4⋊C4×C157—21no—
78C4⋊C4×C157C2311yescharacteristic
79C4⋊C4×C157C2311yescharacteristic
80C22⋊C4×C157—21no—
81C42×C157—21no—
82C42×C157C2311yescharacteristic
83C22×D157—22no—
84C22×D157—44no—
85C22×D157—44no—
86C22×D157—82no—
87C22×D157C2×D412yes—
88Dic314—22no—
89Dic314—22no—
90Dic314—44no—
91D628—22no—
92D628—22no—
93D628—44no—
94D628—42no—
95D628—81no—
96D628SD1614yesdirect product factor
97C22⋊D157—44no—
98C2×Dic157—22no—
99C2×Dic157C2×D412yes—
100C4×D157—22no—
101C4×D157—22no—
102C4×D157—44no—
103#11929434—22no—
104C23×C157—21no—
105Q8×C157—21no—
106Q8×C157C2×D412yescomplemented
107D4×C157—21no—
108D4×C157C2×D412yes—
109C2×C4×C157—21no—
110C2×C4×C157—21no—
111C2×C4×C157—21no—
112C2×C4×C157—42no—
113C2×C4×C157C2×D411yescharacteristic
114C2×C4×C157C2×D411yescharacteristic
115C2×C4×C157C2411yescharacteristic
116C8×C157—21no—
117C8×C157C2×D412yescomplemented
118C22×C157—22no—
119C22×C157—41no—
120C22×C157—41no—
121C22×C157C22×D411yescharacteristic
122C2×D157—22no—
123C2×D157—22no—
124C2×D157—42no—
125C2×D157—42no—
126C2×D157—42no—
127C2×D157—88no—
128C2×D157C2×SD1614yescomplemented
129C4×C157—22no—
130C4×C157—21no—
131C4×C157—41no—
132C4×C157—41no—
133C4×C157C2×SD1612yescomplemented
134C4×C157C22×D411yescharacteristic
135C4×C157H(5,𝔽2)11yescharacteristic
136Dic157—22no—
137Dic157—42no—
138C2×C157—42no—
139C2×C157D4211yescharacteristic
140C2×C157C22×SD1611yescharacteristic
141C2×C157#57711yescharacteristic
142D157—24no—
143D157—82no—
144C157D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1571nomaximal, Sylow
146C22×SD16—1572no—
147D4×Q8—1571no—
148D42—1571no—
149#492—1571no—
150#465—1572no—
151#461—1571no—
152#460—1571no—
153#450—1572no—
154#448—1572no—
155C4×SD16D15711yescharacteristic, complemented
156C8×D4—1571no—
157C22×Q8—1572no—
158C22×D4—3141no—
159C22×D4—1572no—
160C2×SD16—3148no—
161C2×SD16—1572no—
162C2×SD16—1572no—
163C2×SD16—1572no—
164C2×SD16—1572no—
165C2×SD16C2×D15711yescharacteristic
166C22×C8—1572no—
167C4⋊Q8—3141no—
168C4⋊Q8—1571no—
169#127—1571no—
170C22⋊Q8—3142no—
171C22⋊Q8—1572no—
172#121—3141no—
173#121—1572no—
174#120—3142no—
175C4×Q8C2×D15711yescharacteristic, complemented
176C4×D4—3141no—
177C4×D4—1571no—
178C4×D4C2×D15711yescharacteristic
179#106C2×D15711yescharacteristic, complemented
180C4⋊C8—1571no—
181#103—1572no—
182#103C2×D15711yescharacteristic, complemented
183#102—1572no—
184#102C2×D15711yescharacteristic
185C22⋊C8—1572no—
186C4×C8C2×D15711yescharacteristic, complemented
187C24—3142no—
188C2×Q8—3142no—
189C2×Q8—3144no—
190C2×Q8—6282no—
191C2×Q8—1572no—
192C2×Q8C22×D15711yescharacteristic
193C2×D4—3142no—
194C2×D4—3144no—
195C2×D4—3142no—
196C2×D4—3141no—
197C2×D4—3141no—
198C2×D4—6284no—
199C2×D4—6282no—
200C2×D4—1571no—
201C2×D4—1572no—
202C2×D4C22×D15711yescharacteristic
203C22×C4—21no—
204C22×C4—3142no—
205C22×C4—1572no—
206SD16—3144no—
207SD16—3144no—
208SD16—3144no—
209SD16—6282no—
210SD16D62814yesdirect product factor
211C2×C8—3144no—
212C2×C8—1572no—
213C2×C8C22×D15711yescharacteristic
214C2×C8C22×D15711yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—3142no—
217C4⋊C4—3141no—
218C4⋊C4—3141no—
219C4⋊C4—1571no—
220C4⋊C4C22×D15711yescharacteristic
221C4⋊C4C22×D15711yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—3142no—
224C22⋊C4—3142no—
225C22⋊C4—1572no—
226C42—21no—
227C42C22×D15711yescharacteristic
228C23—21no—
229C23—3142no—
230C23—6284no—
231C23—6284no—
232C23—1572no—
233C23—12562no—
234Q8—21no—
235Q8—3142no—
236Q8—3142no—
237Q8—6284no—
238Q8C2×D62812yescomplemented
239D4—21no—
240D4—3142no—
241D4—3142no—
242D4—6284no—
243D4—6284no—
244D4—6282no—
245D4—1574no—
246D4—12561no—
247D4C2×D62812yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—3142no—
253C2×C4—3142no—
254C2×C4—3142no—
255C2×C4—6284no—
256C2×C4—1572no—
257C2×C4D4×D15711yescharacteristic
258C2×C4D4×D15711yescharacteristic
259C2×C4C23×D15711yescharacteristic
260C8—21no—
261C8—3142no—
262C8C2×D62812yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—3142no—
267C22—3142no—
268C22—6282no—
269C22—6282no—
270C22—6282no—
271C22—1574no—
272C22—12568no—
273C22C2×D4×D15711yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—3142no—
279C4—6282no—
280C4SD16×D15712yescomplemented
281C4C22×D62811yescharacteristic
282C4#1909781711yescharacteristic
283C2—42no—
284C2—3144no—
285C2—12562no—
286C2D4×D62811yescharacteristic
287C2C2×SD16×D15711yescharacteristic
288C2#2375808011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×SD16×C157C2
socleC22×C157C22×D4
prime radicalD4×D628C2
hypercenterC4×SD16D157
hypocenterC157D4×SD16
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D157C2semidirect
2. Q8×D628C2semidirect
4. #23757646C2semidirect
5. #23757503C2semidirect
6. #23757478C2semidirect
7. #23757473C2semidirect
8. #23757425C2semidirect
9. #23757413C2semidirect
10. C8×D628C2semidirect
11. C4×SD16×C157C2semidirect
12. C2×Q8×D157C22semidirect
15. C2×#14578943C22semidirect
16. C2×#14578943C22semidirect
18. C2×#14578941C22semidirect
20. C2×C8×D157C22semidirect
22. #19097771C22semidirect
25. #19097751C22semidirect
31. C4⋊#11929434C22semidirect
32. #19097694C22semidirect
33. #19097691C22semidirect
34. #19097683C22semidirect
36. C4×Q8×C157C22semidirect
38. #106×C157C22semidirect
39. #103×C157C22semidirect
41. C4×C8×C157C22semidirect
74. SD16×C157D4semidirect
96. D628SD16direct (N × H)
106. Q8×C157C2×D4semidirect
117. C8×C157C2×D4semidirect
128. C2×D157C2×SD16semidirect
133. C4×C157C2×SD16semidirect
144. C157D4×SD16semidirect
155. C4×SD16D157semidirect
175. C4×Q8C2×D157semidirect
179. #106C2×D157semidirect
182. #103C2×D157semidirect
186. C4×C8C2×D157semidirect
210. SD16D628direct (N × H)
238. Q8C2×D628semidirect
262. C8C2×D628semidirect
280. C4SD16×D157semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1572
Q8×D6282
D4×D6282
#237576462
#237575032
#237574782
#237574732
#237574252
#237574132
C8×D6282
C4×SD16×C1572
D4×SD16157