Finite Group Databasebeta

← SD16×D668 #36335835

Subgroups — SD16×D668 #36335835

Order 21376.

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×D167C212yesmaximal, complemented
2Q8×D668C211yesmaximal, characteristic, complemented
3D4×D668C211yesmaximal, characteristic
4#24923642C211yesmaximal, characteristic, complemented
5#24923499C212yesmaximal, complemented
6#24923474C211yesmaximal, characteristic, complemented
7#24923469C211yesmaximal, characteristic, complemented
8#24923421C212yesmaximal, complemented
9#24923409C212yesmaximal, complemented
10C8×D668C211yesmaximal, characteristic, complemented
11C4×SD16×C167C211yesmaximal, characteristic, complemented
12C2×Q8×D167C2212yescomplemented
13C22×D668—21no—
14C2×D4×D167C2212yes—
15C2×#14581939C2212yescomplemented
16C2×#14581939C2212yescomplemented
17C2×#14581938C2212yes—
18C2×#14581937C2212yescomplemented
19SD16×D167—28no—
20C2×C8×D167C2212yescomplemented
21#19128832—21no—
22#19128832C2211yescharacteristic, complemented
23#19128829C2211yescharacteristic
24#19128812—22no—
25#19128812C2212yescomplemented
26#19128807C2212yes—
27#19128806—21no—
28#19128802—22no—
29C4×D668—21no—
30C4×D668C2211yescharacteristic
31C4⋊(C167⋊C8)C2211yescharacteristic, complemented
32#19128755C2212yescomplemented
33#19128752C2212yescomplemented
34(C2×D167)⋊C8C2212yescomplemented
35C2×SD16×C167C2211yescharacteristic
36C4×Q8×C167C2211yescharacteristic, complemented
37C4×D4×C167C2211yescharacteristic
38#106×C167C2211yescharacteristic, complemented
39#103×C167C2211yescharacteristic, complemented
40#102×C167C2211yescharacteristic
41C4×C8×C167C2211yescharacteristic, complemented
42C23×D167—22no—
43C2×Dic334—22no—
44C2×Dic334C2312yes—
45Q8×D167—24no—
46Q8×D167—42no—
47C2×D668—22no—
48C2×D668—21no—
49C2×D668—21no—
50C2×D668—44no—
51C2×D668D411yescharacteristic
52C2×D668C2312yes—
53C2×C22⋊D167—22no—
54D4×D167—24no—
55D4×D167—42no—
56C2×C4×D167—22no—
57C2×C4×D167C2312yes—
58#14581939—24no—
59#14581939—42no—
60#14581938—24no—
61#14581937—24no—
62C2×C167⋊C8C2312yes—
63C8×D167—24no—
64C4⋊Dic167—22no—
65C4⋊Dic167—21no—
66C4⋊Dic167—21no—
67C4⋊Dic167D411yescharacteristic
68(C2×D167)⋊C4—22no—
69(C2×D167)⋊C4—22no—
70(C2×D167)⋊C4D412yes—
71C2×Q8×C167C2311yescharacteristic
72C2×D4×C167C2311yescharacteristic
73C22×C4×C167—21no—
74SD16×C167D414yescomplemented
75C2×C8×C167C2311yescharacteristic
76C2×C8×C167C2311yescharacteristic
77C4⋊C4×C167—21no—
78C4⋊C4×C167C2311yescharacteristic
79C4⋊C4×C167C2311yescharacteristic
80C22⋊C4×C167—21no—
81C42×C167—21no—
82C42×C167C2311yescharacteristic
83C22×D167—22no—
84C22×D167—44no—
85C22×D167—44no—
86C22×D167—82no—
87C22×D167C2×D412yes—
88Dic334—22no—
89Dic334—22no—
90Dic334—44no—
91D668—22no—
92D668—22no—
93D668—44no—
94D668—42no—
95D668—81no—
96D668SD1614yesdirect product factor
97C22⋊D167—44no—
98C2×Dic167—22no—
99C2×Dic167C2×D412yes—
100C4×D167—22no—
101C4×D167—22no—
102C4×D167—44no—
103C167⋊C8—22no—
104C23×C167—21no—
105Q8×C167—21no—
106Q8×C167C2×D412yescomplemented
107D4×C167—21no—
108D4×C167C2×D412yes—
109C2×C4×C167—21no—
110C2×C4×C167—21no—
111C2×C4×C167—21no—
112C2×C4×C167—42no—
113C2×C4×C167C2×D411yescharacteristic
114C2×C4×C167C2×D411yescharacteristic
115C2×C4×C167C2411yescharacteristic
116C8×C167—21no—
117C8×C167C2×D412yescomplemented
118C22×C167—22no—
119C22×C167—41no—
120C22×C167—41no—
121C22×C167C22×D411yescharacteristic
122C2×D167—22no—
123C2×D167—22no—
124C2×D167—42no—
125C2×D167—42no—
126C2×D167—42no—
127C2×D167—88no—
128C2×D167C2×SD1614yescomplemented
129C4×C167—22no—
130C4×C167—21no—
131C4×C167—41no—
132C4×C167—41no—
133C4×C167C2×SD1612yescomplemented
134C4×C167C22×D411yescharacteristic
135C4×C167H(5,𝔽2)11yescharacteristic
136Dic167—22no—
137Dic167—42no—
138C2×C167—42no—
139C2×C167D4211yescharacteristic
140C2×C167C22×SD1611yescharacteristic
141C2×C167#57711yescharacteristic
142D167—24no—
143D167—82no—
144C167D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1671nomaximal, Sylow
146C22×SD16—1672no—
147D4×Q8—1671no—
148D42—1671no—
149#492—1671no—
150#465—1672no—
151#461—1671no—
152#460—1671no—
153#450—1672no—
154#448—1672no—
155C4×SD16D16711yescharacteristic, complemented
156C8×D4—1671no—
157C22×Q8—1672no—
158C22×D4—3341no—
159C22×D4—1672no—
160C2×SD16—3348no—
161C2×SD16—1672no—
162C2×SD16—1672no—
163C2×SD16—1672no—
164C2×SD16—1672no—
165C2×SD16C2×D16711yescharacteristic
166C22×C8—1672no—
167C4⋊Q8—3341no—
168C4⋊Q8—1671no—
169#127—1671no—
170C22⋊Q8—3342no—
171C22⋊Q8—1672no—
172#121—3341no—
173#121—1672no—
174#120—3342no—
175C4×Q8C2×D16711yescharacteristic, complemented
176C4×D4—3341no—
177C4×D4—1671no—
178C4×D4C2×D16711yescharacteristic
179#106C2×D16711yescharacteristic, complemented
180C4⋊C8—1671no—
181#103—1672no—
182#103C2×D16711yescharacteristic, complemented
183#102—1672no—
184#102C2×D16711yescharacteristic
185C22⋊C8—1672no—
186C4×C8C2×D16711yescharacteristic, complemented
187C24—3342no—
188C2×Q8—3342no—
189C2×Q8—3344no—
190C2×Q8—6682no—
191C2×Q8—1672no—
192C2×Q8C22×D16711yescharacteristic
193C2×D4—3342no—
194C2×D4—3344no—
195C2×D4—3342no—
196C2×D4—3341no—
197C2×D4—3341no—
198C2×D4—6684no—
199C2×D4—6682no—
200C2×D4—1671no—
201C2×D4—1672no—
202C2×D4C22×D16711yescharacteristic
203C22×C4—21no—
204C22×C4—3342no—
205C22×C4—1672no—
206SD16—3344no—
207SD16—3344no—
208SD16—3344no—
209SD16—6682no—
210SD16D66814yesdirect product factor
211C2×C8—3344no—
212C2×C8—1672no—
213C2×C8C22×D16711yescharacteristic
214C2×C8C22×D16711yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—3342no—
217C4⋊C4—3341no—
218C4⋊C4—3341no—
219C4⋊C4—1671no—
220C4⋊C4C22×D16711yescharacteristic
221C4⋊C4C22×D16711yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—3342no—
224C22⋊C4—3342no—
225C22⋊C4—1672no—
226C42—21no—
227C42C22×D16711yescharacteristic
228C23—21no—
229C23—13362no—
230C23—3342no—
231C23—6684no—
232C23—6684no—
233C23—1672no—
234Q8—21no—
235Q8—3342no—
236Q8—3342no—
237Q8—6684no—
238Q8C2×D66812yescomplemented
239D4—21no—
240D4—13361no—
241D4—3342no—
242D4—3342no—
243D4—6684no—
244D4—6684no—
245D4—6682no—
246D4—1674no—
247D4C2×D66812yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—3342no—
253C2×C4—3342no—
254C2×C4—3342no—
255C2×C4—6684no—
256C2×C4—1672no—
257C2×C4D4×D16711yescharacteristic
258C2×C4D4×D16711yescharacteristic
259C2×C4C23×D16711yescharacteristic
260C8—21no—
261C8—3342no—
262C8C2×D66812yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—13368no—
267C22—3342no—
268C22—3342no—
269C22—6682no—
270C22—6682no—
271C22—6682no—
272C22—1674no—
273C22C2×D4×D16711yescharacteristic
274C4—22no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—3342no—
279C4—6682no—
280C4SD16×D16712yescomplemented
281C4C22×D66811yescharacteristic
282C4#1912887811yescharacteristic
283C2—42no—
284C2—13362no—
285C2—3344no—
286C2D4×D66811yescharacteristic
287C2C2×SD16×D16711yescharacteristic
288C2#2492407611yescharacteristic
subgroupG/H
centerC22C2×D4×D167
commutator, cosocleC2×C4×C167C24
FrattiniC2×C4C23×D167
FittingC4×SD16×C167C2
socleC22×C167C22×D4
prime radicalD4×D668C2
hypercenterC4×SD16D167
hypocenterC167D4×SD16
LCSG ▷ C2×C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D167C2semidirect
2. Q8×D668C2semidirect
4. #24923642C2semidirect
5. #24923499C2semidirect
6. #24923474C2semidirect
7. #24923469C2semidirect
8. #24923421C2semidirect
9. #24923409C2semidirect
10. C8×D668C2semidirect
11. C4×SD16×C167C2semidirect
12. C2×Q8×D167C22semidirect
15. C2×#14581939C22semidirect
16. C2×#14581939C22semidirect
18. C2×#14581937C22semidirect
20. C2×C8×D167C22semidirect
22. #19128832C22semidirect
25. #19128812C22semidirect
31. C4⋊(C167⋊C8)C22semidirect
32. #19128755C22semidirect
33. #19128752C22semidirect
34. (C2×D167)⋊C8C22semidirect
36. C4×Q8×C167C22semidirect
38. #106×C167C22semidirect
39. #103×C167C22semidirect
41. C4×C8×C167C22semidirect
74. SD16×C167D4semidirect
96. D668SD16direct (N × H)
106. Q8×C167C2×D4semidirect
117. C8×C167C2×D4semidirect
128. C2×D167C2×SD16semidirect
133. C4×C167C2×SD16semidirect
144. C167D4×SD16semidirect
155. C4×SD16D167semidirect
175. C4×Q8C2×D167semidirect
179. #106C2×D167semidirect
182. #103C2×D167semidirect
186. C4×C8C2×D167semidirect
210. SD16D668direct (N × H)
238. Q8C2×D668semidirect
262. C8C2×D668semidirect
280. C4SD16×D167semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1672
Q8×D6682
D4×D6682
#249236422
#249234992
#249234742
#249234692
#249234212
#249234092
C8×D6682
C4×SD16×C1672
D4×SD16167