Finite Group Databasebeta

← C2×D17×SD64 #17192441

Subgroups — C2×D17×SD64 #17192441

Order 4352.

502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q32×D17C211yesmaximal, characteristic, complemented
2C2×D16×D17C211yesmaximal, characteristic
3C2×#11762648C211yesmaximal, characteristic, complemented
4C2×#11762647C211yesmaximal, characteristic, complemented
5C2×#11762646C211yesmaximal, characteristic, complemented
6D17×SD64C218yesmaximal, direct product factor
7C2×C32×D17C211yesmaximal, characteristic, complemented
8C2×C17×SD64C211yesmaximal, characteristic, complemented
9C2×Q16×D17—21no—
10C2×D8×D17—21no—
11C2×Dic136C2211yescharacteristic, complemented
12C2×#10587500—21no—
13Q32×D17—22no—
14Q32×D17C2214yescomplemented
15C2×D272C2211yescharacteristic
16C2×#10587497—21no—
17D16×D17—22no—
18D16×D17C2214yes—
19C2×C16×D17C2211yescharacteristic
20#11762648C2214yescomplemented
21#11762647C2214yescomplemented
22#11762646C2214yescomplemented
23C2×#10587465C2211yescharacteristic, complemented
24C32×D17C2214yescomplemented
25C2×C17×Q32C2211yescharacteristic, complemented
26C2×C17×D16C2211yescharacteristic
27C17×SD64C2214yescomplemented
28C2×C17×C32C2211yescharacteristic, complemented
29C2×Q8×D17—41no—
30C2×D4×D17—41no—
31C2×Q16×C17—21no—
32C2×D8×C17—21no—
33C2×#63231—41no—
34C2×#63228—41no—
35Q16×D17—24no—
36Q16×D17—42no—
37D8×D17—24no—
38D8×D17—42no—
39C2×Dic68—21no—
40C2×D136—21no—
41C2×C8×D17D411yescharacteristic
42C17×Q32—21no—
43C17×Q32C2312yescomplemented
44C17×D16—21no—
45C17×D16C2312yes—
46C2×C16×C17C2311yescharacteristic
47#10587500—24no—
48#10587497—24no—
49C2×#63214D411yescharacteristic
50Dic136—21no—
51Dic136C2312yescomplemented
52D272—21no—
53D272C2312yes—
54C16×D17D412yes—
55C16×D17C2312yes—
56C17×C32C2312yescomplemented
57#10587465C2312yescomplemented
58C23×D17—81no—
59C2×Q8×C17—41no—
60C2×D4×C17—41no—
61C2×C22⋊D17—81no—
62Q8×D17—44no—
63Q8×D17—82no—
64D4×D17—44no—
65D4×D17—82no—
66C2×D68—41no—
67C2×C4×D17—81no—
68C2×C4×D17D811yescharacteristic
69C2×Dic34—41no—
70C2×Dic34—81no—
71Q16×C17—22no—
72Q16×C17—41no—
73D8×C17—22no—
74D8×C17—41no—
75C2×C8×C17C2×D411yescharacteristic
76#63231—44no—
77#63228—44no—
78C2×#3622D811yescharacteristic
79Dic68—22no—
80Dic68—41no—
81D136—22no—
82D136—41no—
83C8×D17D812yes—
84C8×D17C2×D412yes—
85C16×C17C2×D411yescharacteristic
86C16×C17C2411yescharacteristic
87#63214C2×D412yes—
88C22×SD64—171nomaximal, Sylow
89C23×C17—81no—
90C22×D17—81no—
91C22×D17—84no—
92C22×D17—164no—
93C22×D17D1611yescharacteristic
94Q8×C17—42no—
95Q8×C17—81no—
96D4×C17—42no—
97D4×C17—81no—
98C2×C4×C17—81no—
99C2×C4×C17C2×D811yescharacteristic
100C22⋊D17—84no—
101C2×Dic17—81no—
102C2×Dic17D1611yescharacteristic
103D68—42no—
104D68—81no—
105C4×D17—84no—
106C4×D17D1612yes—
107C4×D17C2×D812yes—
108Dic34—42no—
109Dic34—81no—
110Dic34—84no—
111C8×C17C2×D811yescharacteristic
112C8×C17C22×D411yescharacteristic
113#3622C2×D812yes—
114C22×Q32—171no—
115C22×D16—171no—
116C2×SD64—171no—
117C2×SD64—171no—
118C2×SD64—178no—
119C2×SD64—171no—
120C2×SD64D1711yescharacteristic, direct product factor
121C22×C32—171no—
122C22×C17—82no—
123C22×C17—162no—
124C22×C17C2×D1611yescharacteristic
125C2×D17—82no—
126C2×D17—162no—
127C2×D17—168no—
128C2×D17SD6414yesdirect product factor
129C2×D17C2×D1612yes—
130C4×C17—82no—
131C4×C17C2×D1611yescharacteristic
132C4×C17C22×D811yescharacteristic
133Dic17—82no—
134Dic17C2×D1612yes—
135C22×Q16—341no—
136C22×D8—341no—
137C2×Q32—174no—
138C2×Q32—171no—
139C2×Q32—342no—
140C2×Q32—341no—
141C2×Q32C2×D1711yescharacteristic, complemented
142C2×D16—174no—
143C2×D16—171no—
144C2×D16—342no—
145C2×D16—341no—
146C2×D16C2×D1711yescharacteristic
147C22×C16—171no—
148SD64—174no—
149SD64—174no—
150SD64—174no—
151SD64C2×D1714yesdirect product factor
152C2×C32—171no—
153C2×C32—174no—
154C2×C32C2×D1711yescharacteristic, complemented
155C2×C17—162no—
156C2×C17C2×SD6412yescomplemented
157C2×C17C22×D1611yescharacteristic
158D17—162no—
159D17C2×SD6414yesdirect product factor
160C22×Q8—681no—
161C22×D4—681no—
162C2×Q16—21no—
163C2×Q16—344no—
164C2×Q16—341no—
165C2×Q16—682no—
166C2×Q16—681no—
167C2×D8—21no—
168C2×D8—344no—
169C2×D8—341no—
170C2×D8—682no—
171C2×D8—681no—
172C22×C8—171no—
173Q32—21no—
174Q32—172no—
175Q32—344no—
176Q32—341no—
177Q32C22×D1712yescomplemented
178D16—21no—
179D16—172no—
180D16—344no—
181D16—341no—
182D16C22×D1712yes—
183C2×C16—171no—
184C2×C16—172no—
185C2×C16—172no—
186C2×C16C22×D1711yescharacteristic
187C32—172no—
188C32C22×D1712yescomplemented
189C17C22×SD6411yescharacteristic, complemented, Sylow
190C24—1361no—
191C2×Q8—41no—
192C2×Q8—684no—
193C2×Q8—681no—
194C2×Q8—1361no—
195C2×Q8—1362no—
196C2×D4—41no—
197C2×D4—684no—
198C2×D4—681no—
199C2×D4—1362no—
200C2×D4—1361no—
201C22×C4—171no—
202C22×C4—1361no—
203Q16—22no—
204Q16—41no—
205Q16—342no—
206Q16—684no—
207Q16—681no—
208D8—22no—
209D8—41no—
210D8—342no—
211D8—684no—
212D8—681no—
213C2×C8—171no—
214C2×C8—172no—
215C2×C8—172no—
216C2×C8D4×D1711yescharacteristic
217C16—172no—
218C16D4×D1711yescharacteristic
219C16C23×D1711yescharacteristic
220C23—81no—
221C23—2724no—
222C23—171no—
223C23—1364no—
224C23—1361no—
225Q8—42no—
226Q8—81no—
227Q8—682no—
228Q8—1364no—
229Q8—1361no—
230D4—42no—
231D4—81no—
232D4—682no—
233D4—1364no—
234D4—1361no—
235C2×C4—81no—
236C2×C4—171no—
237C2×C4—172no—
238C2×C4—172no—
239C2×C4—1364no—
240C2×C4—1361no—
241C2×C4D8×D1711yescharacteristic
242C8—172no—
243C8D8×D1711yescharacteristic
244C8C2×D4×D1711yescharacteristic
245C22—82no—
246C22—162no—
247C22—2728no—
248C22—2722no—
249C22—174no—
250C22—172no—
251C22—1362no—
252C22D16×D1711yescharacteristic
253C4—82no—
254C4—172no—
255C4—1362no—
256C4D16×D1711yescharacteristic
257C4C2×D8×D1711yescharacteristic
258C2—162no—
259C2—2722no—
260C2—174no—
261C2D17×SD6412yesdirect product factor
262C2C2×D16×D1711yescharacteristic
subgroupG/H
centerC22D16×D17
commutator, cosocleC16×C17C24
FrattiniC16C23×D17
FittingC2×C17×SD64C2
socleC22×C17C2×D16
prime radicalC2×D16×D17C2
hypercenterC2×SD64D17
hypocenterC17C22×SD64
LCSG ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×Q32×D17C2semidirect
3. C2×#11762648C2semidirect
4. C2×#11762647C2semidirect
5. C2×#11762646C2semidirect
6. D17×SD64C2direct (N × H)
7. C2×C32×D17C2semidirect
8. C2×C17×SD64C2semidirect
11. C2×Dic136C22semidirect
14. Q32×D17C22semidirect
20. #11762648C22semidirect
21. #11762647C22semidirect
22. #11762646C22semidirect
23. C2×#10587465C22semidirect
24. C32×D17C22semidirect
25. C2×C17×Q32C22semidirect
27. C17×SD64C22semidirect
28. C2×C17×C32C22semidirect
43. C17×Q32C23semidirect
51. Dic136C23semidirect
56. C17×C32C23semidirect
57. #10587465C23semidirect
120. C2×SD64D17direct (N × H)
128. C2×D17SD64direct (N × H)
141. C2×Q32C2×D17semidirect
151. SD64C2×D17direct (N × H)
154. C2×C32C2×D17semidirect
156. C2×C17C2×SD64semidirect
159. D17C2×SD64direct (N × H)
177. Q32C22×D17semidirect
188. C32C22×D17semidirect
189. C17C22×SD64semidirect
261. C2D17×SD64direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q32×D172
C2×D16×D172
C2×#117626482
C2×#117626472
C2×#117626462
D17×SD642
C2×C32×D172
C2×C17×SD642
C22×SD6417