Finite Group Databasebeta

← D16×D316 #34444923

Subgroups — D16×D316 #34444923

Order 20224.

812 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 159 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×D16×D79C212yesmaximal, complemented
2D8×D316C212yesmaximal, complemented
3#23765650C211yesmaximal, characteristic, complemented
4#23765487C212yesmaximal, complemented
5#23765435C212yesmaximal, complemented
6#23765313C214yesmaximal, complemented
7C16×D316C211yesmaximal, characteristic, complemented
8C4×D16×C79C211yesmaximal, characteristic, complemented
9C2×D8×D79C2214yescomplemented
10D4×D316—22no—
11C2×D1264C2212yescomplemented
12C2×D1264C2212yescomplemented
13C2×#14579102C2214yescomplemented
14D16×D79—28no—
15C2×C16×D79C2212yescomplemented
16#19098940C2212yescomplemented
17#19098800C2214yescomplemented
18#19098758—22no—
19#19098698—24no—
20C8×D316C2211yescharacteristic
21C4⋊(C79⋊C16)C2211yescharacteristic, complemented
22#19098363C2214yescomplemented
23(C2×D79)⋊C16C2212yescomplemented
24C2×D16×C79C2211yescharacteristic
25C4×D8×C79C2212yescomplemented
26#366×C79C2211yescharacteristic, complemented
27#357×C79C2212yescomplemented
28C4×C16×C79C2211yescharacteristic, complemented
29C22×D316—42no—
30C2×D4×D79—24no—
31C2×D632—22no—
32C2×D632C2314yes—
33C2×#11929609—24no—
34D8×D79—28no—
35D8×D79—44no—
36C2×C8×D79C2312yes—
37#14579158—22no—
38#14579136—24no—
39#14579135—42no—
40#14579131—44no—
41C4×D316D411yescharacteristic
42D1264—24no—
43D1264—42no—
44#14579102—28no—
45C2×C79⋊C16C2312yes—
46C16×D79—24no—
47C4⋊(C79⋊C8)D411yescharacteristic
48#14579081—24no—
49(C2×D79)⋊C8D412yes—
50C2×D8×C79C2312yes—
51C4×D4×C79—22no—
52D16×C79D414yescomplemented
53C2×C16×C79C2311yescharacteristic
54C2×C16×C79C2311yescharacteristic
55#107×C79C2312yes—
56#102×C79—22no—
57C4×C8×C79C2311yescharacteristic
58C23×D79—44no—
59C2×D316—24no—
60C2×D316—44no—
61C2×D316—42no—
62C2×D316—42no—
63C2×D316—88no—
64C2×D316D811yescharacteristic
65C2×C22⋊D79—44no—
66D4×D79—48no—
67D4×D79—84no—
68C2×C4×D79C2×D412yes—
69D632—24no—
70D632—24no—
71D632—82no—
72#11929609—48no—
73C2×C79⋊C8C2×D412yes—
74C8×D79—22no—
75C8×D79—22no—
76C4⋊Dic79D811yescharacteristic
77(C2×D79)⋊C4—44no—
78(C2×D79)⋊C4D812yes—
79C79⋊C16—22no—
80C2×D4×C79—22no—
81C22×C4×C79—42no—
82D8×C79—22no—
83D8×C79C2×D414yescomplemented
84C2×C8×C79C2×D411yescharacteristic
85C2×C8×C79C2411yescharacteristic
86C4⋊C4×C79—22no—
87C22⋊C4×C79—42no—
88C42×C79C2×D411yescharacteristic
89C16×C79—21no—
90C16×C79C2×D412yescomplemented
91C23×C79—42no—
92C22×D79—44no—
93C22×D79—88no—
94C22×D79—88no—
95C22×D79—164no—
96C22×D79C2×D812yes—
97D4×C79—24no—
98D4×C79—42no—
99C2×C4×C79—42no—
100C2×C4×C79—84no—
101C2×C4×C79C2×D811yescharacteristic
102C2×C4×C79C2×D811yescharacteristic
103C2×C4×C79C22×D411yescharacteristic
104C22⋊D79—88no—
105C2×Dic79C2×D812yes—
106D316—44no—
107D316—44no—
108D316—88no—
109D316—84no—
110D316—162no—
111D316D1614yesdirect product factor
112C4×D79—22no—
113C4×D79—22no—
114C8×C79—21no—
115C8×C79C22×D411yescharacteristic
116C8×C79H(5,𝔽2)11yescharacteristic
117C79⋊C8—22no—
118C22×C79—44no—
119C22×C79—82no—
120C22×C79—82no—
121C22×C79C22×D811yescharacteristic
122C2×D79—22no—
123C2×D79—22no—
124C2×D79—84no—
125C2×D79—84no—
126C2×D79—84no—
127C2×D79—1616no—
128C2×D79C2×D1614yescomplemented
129C4×C79—21no—
130C4×C79—82no—
131C4×C79C2×D1612yescomplemented
132C4×C79D4211yescharacteristic
133C4×C79#57611yescharacteristic
134Dic79—22no—
135D4×D16—791nomaximal, Sylow
136C2×C79—84no—
137C2×C79D4×D811yescharacteristic
138C2×C79C22×D1611yescharacteristic
139C2×C79#341511yescharacteristic
140D79—24no—
141D79—164no—
142C22×D16—792no—
143D4×D8—792no—
144#2246—791no—
145#2215—792no—
146#2206—792no—
147#2184—794no—
148C4×D16D7911yescharacteristic, complemented
149D4×C16—791no—
150C79D4×D1611yescharacteristic, complemented, Sylow
151C22×D8—794no—
152D42—1582no—
153C2×D16—794no—
154C2×D16—792no—
155C2×D16—792no—
156C2×D16—1588no—
157C2×D16C2×D7911yescharacteristic
158C22×C16—792no—
159#493—792no—
160#466—794no—
161#459—1582no—
162#447—1584no—
163C4×D8C2×D7912yescomplemented
164C8×D4—791no—
165#366C2×D7911yescharacteristic, complemented
166C4⋊C16—791no—
167#357—794no—
168#357C2×D7912yescomplemented
169C22⋊C16—792no—
170C4×C16C2×D7911yescharacteristic, complemented
171C22×D4—3162no—
172C22×D4—1584no—
173C2×D8—3164no—
174C2×D8—794no—
175C2×D8—1584no—
176C2×D8—1588no—
177C2×D8—1582no—
178C2×D8C22×D7912yes—
179C22×C8—792no—
180#127—1582no—
181#121—3162no—
182#121—1584no—
183#120—3164no—
184C4×D4—22no—
185C4×D4—791no—
186D16—3162no—
187D16—1588no—
188D16—1584no—
189D16D31614yesdirect product factor
190C2×C16—792no—
191C2×C16—1584no—
192C2×C16C22×D7911yescharacteristic
193C2×C16C22×D7911yescharacteristic
194#107C22×D7912yes—
195C4⋊C8—791no—
196#102—22no—
197#102—1584no—
198C22⋊C8—792no—
199C4×C8C22×D7911yescharacteristic
200C24—3164no—
201C2×D4—22no—
202C2×D4—3164no—
203C2×D4—3164no—
204C2×D4—3168no—
205C2×D4—3162no—
206C2×D4—3162no—
207C2×D4—791no—
208C2×D4—6328no—
209C2×D4—6324no—
210C2×D4—1584no—
211C22×C4—42no—
212C22×C4—792no—
213D8—22no—
214D8—3168no—
215D8—6322no—
216D8—1584no—
217D8—1584no—
218D8C2×D31614yescomplemented
219C2×C8—792no—
220C2×C8—1582no—
221C2×C8—1582no—
222C2×C8D4×D7911yescharacteristic
223C2×C8C23×D7911yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—791no—
226C22⋊C4—42no—
227C22⋊C4—3164no—
228C22⋊C4—792no—
229C42D4×D7911yescharacteristic
230C16—21no—
231C16—1582no—
232C16C2×D31612yescomplemented
233C23—42no—
234C23—3164no—
235C23—792no—
236C23—6328no—
237C23—6328no—
238C23—12644no—
239D4—24no—
240D4—42no—
241D4—3164no—
242D4—3164no—
243D4—794no—
244D4—6328no—
245D4—6328no—
246D4—6324no—
247D4—12642no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—792no—
251C2×C4—1582no—
252C2×C4—1582no—
253C2×C4D8×D7911yescharacteristic
254C2×C4D8×D7911yescharacteristic
255C2×C4C2×D4×D7911yescharacteristic
256C8—21no—
257C8—1582no—
258C8C22×D31611yescharacteristic
259C8#1457920711yescharacteristic
260C22—44no—
261C22—82no—
262C22—82no—
263C22—794no—
264C22—6324no—
265C22—6324no—
266C22—6324no—
267C22—1582no—
268C22—1582no—
269C22—126416no—
270C22C2×D8×D7911yescharacteristic
271C4—21no—
272C4—82no—
273C4—1582no—
274C4D16×D7912yescomplemented
275C4D4×D31611yescharacteristic
276C4#1909936511yescharacteristic
277C2—84no—
278C2—1584no—
279C2—12644no—
280C2D8×D31611yescharacteristic
281C2C2×D16×D7911yescharacteristic
282C2#2377653811yescharacteristic
subgroupG/H
centerC22C2×D8×D79
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC4×D16×C79C2
socleC22×C79C22×D8
hypercenterC4×D16D79
hypocenterC79D4×D16
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. C2×D16×D79C2semidirect
2. D8×D316C2semidirect
3. #23765650C2semidirect
4. #23765487C2semidirect
5. #23765435C2semidirect
6. #23765313C2semidirect
7. C16×D316C2semidirect
8. C4×D16×C79C2semidirect
9. C2×D8×D79C22semidirect
11. C2×D1264C22semidirect
12. C2×D1264C22semidirect
13. C2×#14579102C22semidirect
15. C2×C16×D79C22semidirect
16. #19098940C22semidirect
17. #19098800C22semidirect
21. C4⋊(C79⋊C16)C22semidirect
22. #19098363C22semidirect
23. (C2×D79)⋊C16C22semidirect
25. C4×D8×C79C22semidirect
26. #366×C79C22semidirect
27. #357×C79C22semidirect
28. C4×C16×C79C22semidirect
52. D16×C79D4semidirect
83. D8×C79C2×D4semidirect
90. C16×C79C2×D4semidirect
111. D316D16direct (N × H)
128. C2×D79C2×D16semidirect
131. C4×C79C2×D16semidirect
148. C4×D16D79semidirect
150. C79D4×D16semidirect
163. C4×D8C2×D79semidirect
165. #366C2×D79semidirect
168. #357C2×D79semidirect
170. C4×C16C2×D79semidirect
189. D16D316direct (N × H)
218. D8C2×D316semidirect
232. C16C2×D316semidirect
274. C4D16×D79semidirect

Maximal subgroups

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

subgroupindex
C2×D16×D792
D8×D3162
#237656502
#237654872
#237654352
#237653132
C16×D3162
C4×D16×C792
D4×D1679