Finite Group Databasebeta

← SD16×D652 #35226233

Subgroups — SD16×D652 #35226233

Order 20864.

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×D163C212yesmaximal, complemented
2Q8×D652C211yesmaximal, characteristic, complemented
3D4×D652C211yesmaximal, characteristic
4#23782038C211yesmaximal, characteristic, complemented
5#23781895C212yesmaximal, complemented
6#23781870C211yesmaximal, characteristic, complemented
7#23781865C211yesmaximal, characteristic, complemented
8#23781817C212yesmaximal, complemented
9#23781805C212yesmaximal, complemented
10C8×D652C211yesmaximal, characteristic, complemented
11C4×SD16×C163C211yesmaximal, characteristic, complemented
12C2×Q8×D163C2212yescomplemented
13C22×D652—21no—
14C2×D4×D163C2212yes—
15C2×#14579688C2212yescomplemented
16C2×#14579688C2212yescomplemented
17C2×#14579687C2212yes—
18C2×#14579686C2212yescomplemented
19SD16×D163—28no—
20C2×C8×D163C2212yescomplemented
21#19104735—21no—
22#19104735C2211yescharacteristic, complemented
23#19104732C2211yescharacteristic
24#19104715—22no—
25#19104715C2212yescomplemented
26#19104710C2212yes—
27#19104709—21no—
28#19104705—22no—
29C4×D652—21no—
30C4×D652C2211yescharacteristic
31C4⋊(C163⋊C8)C2211yescharacteristic, complemented
32#19104658C2212yescomplemented
33#19104655C2212yescomplemented
34(C2×D163)⋊C8C2212yescomplemented
35C2×SD16×C163C2211yescharacteristic
36C4×Q8×C163C2211yescharacteristic, complemented
37C4×D4×C163C2211yescharacteristic
38#106×C163C2211yescharacteristic, complemented
39#103×C163C2211yescharacteristic, complemented
40#102×C163C2211yescharacteristic
41C4×C8×C163C2211yescharacteristic, complemented
42C23×D163—22no—
43C2×Dic326—22no—
44C2×Dic326C2312yes—
45Q8×D163—24no—
46Q8×D163—42no—
47C2×D652—22no—
48C2×D652—21no—
49C2×D652—21no—
50C2×D652—44no—
51C2×D652D411yescharacteristic
52C2×D652C2312yes—
53C2×C22⋊D163—22no—
54D4×D163—24no—
55D4×D163—42no—
56C2×C4×D163—22no—
57C2×C4×D163C2312yes—
58#14579688—24no—
59#14579688—42no—
60#14579687—24no—
61#14579686—24no—
62C2×C163⋊C8C2312yes—
63C8×D163—24no—
64C4⋊Dic163—22no—
65C4⋊Dic163—21no—
66C4⋊Dic163—21no—
67C4⋊Dic163D411yescharacteristic
68(C2×D163)⋊C4—22no—
69(C2×D163)⋊C4—22no—
70(C2×D163)⋊C4D412yes—
71C2×Q8×C163C2311yescharacteristic
72C2×D4×C163C2311yescharacteristic
73C22×C4×C163—21no—
74SD16×C163D414yescomplemented
75C2×C8×C163C2311yescharacteristic
76C2×C8×C163C2311yescharacteristic
77C4⋊C4×C163—21no—
78C4⋊C4×C163C2311yescharacteristic
79C4⋊C4×C163C2311yescharacteristic
80C22⋊C4×C163—21no—
81C42×C163—21no—
82C42×C163C2311yescharacteristic
83C22×D163—22no—
84C22×D163—44no—
85C22×D163—44no—
86C22×D163—82no—
87C22×D163C2×D412yes—
88Dic326—22no—
89Dic326—22no—
90Dic326—44no—
91D652—22no—
92D652—22no—
93D652—44no—
94D652—42no—
95D652—81no—
96D652SD1614yesdirect product factor
97C22⋊D163—44no—
98C2×Dic163—22no—
99C2×Dic163C2×D412yes—
100C4×D163—22no—
101C4×D163—22no—
102C4×D163—44no—
103C163⋊C8—22no—
104C23×C163—21no—
105Q8×C163—21no—
106Q8×C163C2×D412yescomplemented
107D4×C163—21no—
108D4×C163C2×D412yes—
109C2×C4×C163—21no—
110C2×C4×C163—21no—
111C2×C4×C163—21no—
112C2×C4×C163—42no—
113C2×C4×C163C2×D411yescharacteristic
114C2×C4×C163C2×D411yescharacteristic
115C2×C4×C163C2411yescharacteristic
116C8×C163—21no—
117C8×C163C2×D412yescomplemented
118C22×C163—22no—
119C22×C163—41no—
120C22×C163—41no—
121C22×C163C22×D411yescharacteristic
122C2×D163—22no—
123C2×D163—22no—
124C2×D163—42no—
125C2×D163—42no—
126C2×D163—42no—
127C2×D163—88no—
128C2×D163C2×SD1614yescomplemented
129C4×C163—22no—
130C4×C163—21no—
131C4×C163—41no—
132C4×C163—41no—
133C4×C163C2×SD1612yescomplemented
134C4×C163C22×D411yescharacteristic
135C4×C163H(5,𝔽2)11yescharacteristic
136Dic163—22no—
137Dic163—42no—
138C2×C163—42no—
139C2×C163D4211yescharacteristic
140C2×C163C22×SD1611yescharacteristic
141C2×C163#57711yescharacteristic
142D163—24no—
143D163—82no—
144C163D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1631nomaximal, Sylow
146C22×SD16—1632no—
147D4×Q8—1631no—
148D42—1631no—
149#492—1631no—
150#465—1632no—
151#461—1631no—
152#460—1631no—
153#450—1632no—
154#448—1632no—
155C4×SD16D16311yescharacteristic, complemented
156C8×D4—1631no—
157C22×Q8—1632no—
158C22×D4—3261no—
159C22×D4—1632no—
160C2×SD16—3268no—
161C2×SD16—1632no—
162C2×SD16—1632no—
163C2×SD16—1632no—
164C2×SD16—1632no—
165C2×SD16C2×D16311yescharacteristic
166C22×C8—1632no—
167C4⋊Q8—3261no—
168C4⋊Q8—1631no—
169#127—1631no—
170C22⋊Q8—3262no—
171C22⋊Q8—1632no—
172#121—3261no—
173#121—1632no—
174#120—3262no—
175C4×Q8C2×D16311yescharacteristic, complemented
176C4×D4—3261no—
177C4×D4—1631no—
178C4×D4C2×D16311yescharacteristic
179#106C2×D16311yescharacteristic, complemented
180C4⋊C8—1631no—
181#103—1632no—
182#103C2×D16311yescharacteristic, complemented
183#102—1632no—
184#102C2×D16311yescharacteristic
185C22⋊C8—1632no—
186C4×C8C2×D16311yescharacteristic, complemented
187C24—3262no—
188C2×Q8—3262no—
189C2×Q8—3264no—
190C2×Q8—6522no—
191C2×Q8—1632no—
192C2×Q8C22×D16311yescharacteristic
193C2×D4—3262no—
194C2×D4—3264no—
195C2×D4—3262no—
196C2×D4—3261no—
197C2×D4—3261no—
198C2×D4—6524no—
199C2×D4—6522no—
200C2×D4—1631no—
201C2×D4—1632no—
202C2×D4C22×D16311yescharacteristic
203C22×C4—21no—
204C22×C4—3262no—
205C22×C4—1632no—
206SD16—3264no—
207SD16—3264no—
208SD16—3264no—
209SD16—6522no—
210SD16D65214yesdirect product factor
211C2×C8—3264no—
212C2×C8—1632no—
213C2×C8C22×D16311yescharacteristic
214C2×C8C22×D16311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—3262no—
217C4⋊C4—3261no—
218C4⋊C4—3261no—
219C4⋊C4—1631no—
220C4⋊C4C22×D16311yescharacteristic
221C4⋊C4C22×D16311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—3262no—
224C22⋊C4—3262no—
225C22⋊C4—1632no—
226C42—21no—
227C42C22×D16311yescharacteristic
228C23—21no—
229C23—13042no—
230C23—3262no—
231C23—6524no—
232C23—6524no—
233C23—1632no—
234Q8—21no—
235Q8—3262no—
236Q8—3262no—
237Q8—6524no—
238Q8C2×D65212yescomplemented
239D4—21no—
240D4—13041no—
241D4—3262no—
242D4—3262no—
243D4—6524no—
244D4—6524no—
245D4—6522no—
246D4—1634no—
247D4C2×D65212yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—3262no—
253C2×C4—3262no—
254C2×C4—3262no—
255C2×C4—6524no—
256C2×C4—1632no—
257C2×C4D4×D16311yescharacteristic
258C2×C4D4×D16311yescharacteristic
259C2×C4C23×D16311yescharacteristic
260C8—21no—
261C8—3262no—
262C8C2×D65212yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—13048no—
267C22—3262no—
268C22—3262no—
269C22—6522no—
270C22—6522no—
271C22—6522no—
272C22—1634no—
273C22C2×D4×D16311yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—3262no—
279C4—6522no—
280C4SD16×D16312yescomplemented
281C4C22×D65211yescharacteristic
282C4#1910478111yescharacteristic
283C2—42no—
284C2—13042no—
285C2—3264no—
286C2D4×D65211yescharacteristic
287C2C2×SD16×D16311yescharacteristic
288C2#2378247211yescharacteristic
subgroupG/H
centerC22C2×D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC4×SD16×C163C2
socleC22×C163C22×D4
prime radicalD4×D652C2
hypercenterC4×SD16D163
hypocenterC163D4×SD16
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D163C2semidirect
2. Q8×D652C2semidirect
4. #23782038C2semidirect
5. #23781895C2semidirect
6. #23781870C2semidirect
7. #23781865C2semidirect
8. #23781817C2semidirect
9. #23781805C2semidirect
10. C8×D652C2semidirect
11. C4×SD16×C163C2semidirect
12. C2×Q8×D163C22semidirect
15. C2×#14579688C22semidirect
16. C2×#14579688C22semidirect
18. C2×#14579686C22semidirect
20. C2×C8×D163C22semidirect
22. #19104735C22semidirect
25. #19104715C22semidirect
31. C4⋊(C163⋊C8)C22semidirect
32. #19104658C22semidirect
33. #19104655C22semidirect
34. (C2×D163)⋊C8C22semidirect
36. C4×Q8×C163C22semidirect
38. #106×C163C22semidirect
39. #103×C163C22semidirect
41. C4×C8×C163C22semidirect
74. SD16×C163D4semidirect
96. D652SD16direct (N × H)
106. Q8×C163C2×D4semidirect
117. C8×C163C2×D4semidirect
128. C2×D163C2×SD16semidirect
133. C4×C163C2×SD16semidirect
144. C163D4×SD16semidirect
155. C4×SD16D163semidirect
175. C4×Q8C2×D163semidirect
179. #106C2×D163semidirect
182. #103C2×D163semidirect
186. C4×C8C2×D163semidirect
210. SD16D652direct (N × H)
238. Q8C2×D652semidirect
262. C8C2×D652semidirect
280. C4SD16×D163semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1632
Q8×D6522
D4×D6522
#237820382
#237818952
#237818702
#237818652
#237818172
#237818052
C8×D6522
C4×SD16×C1632
D4×SD16163