Finite Group Databasebeta

← C2×SD64×D73 #33244101

Subgroups — C2×SD64×D73 #33244101

Order 18688.

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×D73C211yesmaximal, characteristic, complemented
2C2×D16×D73C211yesmaximal, characteristic
3C2×#17988426C211yesmaximal, characteristic, complemented
4C2×#17988425C211yesmaximal, characteristic, complemented
5C2×#17988424C211yesmaximal, characteristic, complemented
6SD64×D73C218yesmaximal, direct product factor
7C2×C32×D73C211yesmaximal, characteristic, complemented
8C2×SD64×C73C211yesmaximal, characteristic, complemented
9C2×Q16×D73—21no—
10C2×D8×D73—21no—
11C2×Dic584C2211yescharacteristic, complemented
12C2×#14556537—21no—
13Q32×D73—22no—
14Q32×D73C2214yescomplemented
15C2×D1168C2211yescharacteristic
16C2×#14556532—21no—
17D16×D73—22no—
18D16×D73C2214yes—
19C2×C16×D73C2211yescharacteristic
20#17988426C2214yescomplemented
21#17988425C2214yescomplemented
22#17988424C2214yescomplemented
23C2×#14556497C2211yescharacteristic, complemented
24C32×D73C2214yescomplemented
25C2×Q32×C73C2211yescharacteristic, complemented
26C2×D16×C73C2211yescharacteristic
27SD64×C73C2214yescomplemented
28C2×C32×C73C2211yescharacteristic, complemented
29C2×Q8×D73—41no—
30C2×D4×D73—41no—
31C2×Dic292—21no—
32C2×#11924018—41no—
33Q16×D73—24no—
34Q16×D73—42no—
35C2×D584—21no—
36C2×#11924013—41no—
37D8×D73—24no—
38D8×D73—42no—
39C2×C8×D73D411yescharacteristic
40Dic584—21no—
41Dic584C2312yescomplemented
42#14556537—24no—
43D1168—21no—
44D1168C2312yes—
45#14556532—24no—
46C2×#11924003D411yescharacteristic
47C16×D73D412yes—
48C16×D73C2312yes—
49#14556497C2312yescomplemented
50C2×Q16×C73—21no—
51C2×D8×C73—21no—
52Q32×C73—21no—
53Q32×C73C2312yescomplemented
54D16×C73—21no—
55D16×C73C2312yes—
56C2×C16×C73C2311yescharacteristic
57C32×C73C2312yescomplemented
58C23×D73—81no—
59C2×Dic146—41no—
60C2×Dic146—81no—
61Q8×D73—44no—
62Q8×D73—82no—
63C2×D292—41no—
64C2×C22⋊D73—81no—
65D4×D73—44no—
66D4×D73—82no—
67C2×C4×D73—81no—
68C2×C4×D73D811yescharacteristic
69Dic292—22no—
70Dic292—41no—
71#11924018—44no—
72D584—22no—
73D584—41no—
74#11924013—44no—
75C2×#10596831D811yescharacteristic
76C8×D73D812yes—
77C8×D73C2×D412yes—
78#11924003C2×D412yes—
79C2×Q8×C73—41no—
80C2×D4×C73—41no—
81Q16×C73—22no—
82Q16×C73—41no—
83D8×C73—22no—
84D8×C73—41no—
85C2×C8×C73C2×D411yescharacteristic
86C16×C73C2×D411yescharacteristic
87C16×C73C2411yescharacteristic
88C23×C73—81no—
89C22×D73—81no—
90C22×D73—84no—
91C22×D73—164no—
92C22×D73D1611yescharacteristic
93Q8×C73—42no—
94Q8×C73—81no—
95D4×C73—42no—
96D4×C73—81no—
97C2×C4×C73—81no—
98C2×C4×C73C2×D811yescharacteristic
99C22⋊D73—84no—
100C2×Dic73—81no—
101C2×Dic73D1611yescharacteristic
102D292—42no—
103D292—81no—
104C4×D73—84no—
105C4×D73D1612yes—
106C4×D73C2×D812yes—
107Dic146—42no—
108Dic146—81no—
109Dic146—84no—
110C8×C73C2×D811yescharacteristic
111C8×C73C22×D411yescharacteristic
112#10596831C2×D812yes—
113C22×C73—82no—
114C22×C73—162no—
115C22×C73C2×D1611yescharacteristic
116C2×D73—82no—
117C2×D73—162no—
118C2×D73—168no—
119C2×D73SD6414yesdirect product factor
120C2×D73C2×D1612yes—
121C4×C73—82no—
122C4×C73C2×D1611yescharacteristic
123C4×C73C22×D811yescharacteristic
124Dic73—82no—
125Dic73C2×D1612yes—
126C22×SD64—731nomaximal, Sylow
127C2×C73—162no—
128C2×C73C2×SD6412yescomplemented
129C2×C73C22×D1611yescharacteristic
130D73—162no—
131D73C2×SD6414yesdirect product factor
132C22×Q32—731no—
133C22×D16—731no—
134C2×SD64—731no—
135C2×SD64—731no—
136C2×SD64—738no—
137C2×SD64—731no—
138C2×SD64D7311yescharacteristic, direct product factor
139C22×C32—731no—
140C73C22×SD6411yescharacteristic, complemented, Sylow
141C22×Q16—1461no—
142C22×D8—1461no—
143C2×Q32—734no—
144C2×Q32—731no—
145C2×Q32—1462no—
146C2×Q32—1461no—
147C2×Q32C2×D7311yescharacteristic, complemented
148C2×D16—734no—
149C2×D16—731no—
150C2×D16—1462no—
151C2×D16—1461no—
152C2×D16C2×D7311yescharacteristic
153C22×C16—731no—
154SD64—734no—
155SD64—734no—
156SD64—734no—
157SD64C2×D7314yesdirect product factor
158C2×C32—731no—
159C2×C32—734no—
160C2×C32C2×D7311yescharacteristic, complemented
161C22×Q8—2921no—
162C22×D4—2921no—
163C2×Q16—21no—
164C2×Q16—2922no—
165C2×Q16—2921no—
166C2×Q16—1464no—
167C2×Q16—1461no—
168C2×D8—21no—
169C2×D8—2922no—
170C2×D8—2921no—
171C2×D8—1464no—
172C2×D8—1461no—
173C22×C8—731no—
174Q32—21no—
175Q32—732no—
176Q32—1464no—
177Q32—1461no—
178Q32C22×D7312yescomplemented
179D16—21no—
180D16—732no—
181D16—1464no—
182D16—1461no—
183D16C22×D7312yes—
184C2×C16—731no—
185C2×C16—732no—
186C2×C16—732no—
187C2×C16C22×D7311yescharacteristic
188C32—732no—
189C32C22×D7312yescomplemented
190C24—5841no—
191C2×Q8—41no—
192C2×Q8—2924no—
193C2×Q8—2921no—
194C2×Q8—5841no—
195C2×Q8—5842no—
196C2×D4—41no—
197C2×D4—2924no—
198C2×D4—2921no—
199C2×D4—5842no—
200C2×D4—5841no—
201C22×C4—5841no—
202C22×C4—731no—
203Q16—22no—
204Q16—41no—
205Q16—2924no—
206Q16—2921no—
207Q16—1462no—
208D8—22no—
209D8—41no—
210D8—2924no—
211D8—2921no—
212D8—1462no—
213C2×C8—731no—
214C2×C8—732no—
215C2×C8—732no—
216C2×C8D4×D7311yescharacteristic
217C16—732no—
218C16D4×D7311yescharacteristic
219C16C23×D7311yescharacteristic
220C23—81no—
221C23—5844no—
222C23—5841no—
223C23—731no—
224C23—11684no—
225Q8—42no—
226Q8—81no—
227Q8—2922no—
228Q8—5844no—
229Q8—5841no—
230D4—42no—
231D4—81no—
232D4—2922no—
233D4—5844no—
234D4—5841no—
235C2×C4—81no—
236C2×C4—5844no—
237C2×C4—5841no—
238C2×C4—731no—
239C2×C4—732no—
240C2×C4—732no—
241C2×C4D8×D7311yescharacteristic
242C8—732no—
243C8D8×D7311yescharacteristic
244C8C2×D4×D7311yescharacteristic
245C22—82no—
246C22—162no—
247C22—5842no—
248C22—734no—
249C22—732no—
250C22—11688no—
251C22—11682no—
252C22D16×D7311yescharacteristic
253C4—82no—
254C4—5842no—
255C4—732no—
256C4D16×D7311yescharacteristic
257C4C2×D8×D7311yescharacteristic
258C2—162no—
259C2—734no—
260C2—11682no—
261C2SD64×D7312yesdirect product factor
262C2C2×D16×D7311yescharacteristic
subgroupG/H
centerC22D16×D73
commutator, cosocleC16×C73C24
FrattiniC16C23×D73
FittingC2×SD64×C73C2
socleC22×C73C2×D16
prime radicalC2×D16×D73C2
hypercenterC2×SD64D73
hypocenterC73C22×SD64
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
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×D73C2semidirect
3. C2×#17988426C2semidirect
4. C2×#17988425C2semidirect
5. C2×#17988424C2semidirect
6. SD64×D73C2direct (N × H)
7. C2×C32×D73C2semidirect
8. C2×SD64×C73C2semidirect
11. C2×Dic584C22semidirect
14. Q32×D73C22semidirect
20. #17988426C22semidirect
21. #17988425C22semidirect
22. #17988424C22semidirect
23. C2×#14556497C22semidirect
24. C32×D73C22semidirect
25. C2×Q32×C73C22semidirect
27. SD64×C73C22semidirect
28. C2×C32×C73C22semidirect
41. Dic584C23semidirect
49. #14556497C23semidirect
53. Q32×C73C23semidirect
57. C32×C73C23semidirect
119. C2×D73SD64direct (N × H)
128. C2×C73C2×SD64semidirect
131. D73C2×SD64direct (N × H)
138. C2×SD64D73direct (N × H)
140. C73C22×SD64semidirect
147. C2×Q32C2×D73semidirect
157. SD64C2×D73direct (N × H)
160. C2×C32C2×D73semidirect
178. Q32C22×D73semidirect
189. C32C22×D73semidirect
261. C2SD64×D73direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q32×D732
C2×D16×D732
C2×#179884262
C2×#179884252
C2×#179884242
SD64×D732
C2×C32×D732
C2×SD64×C732
C22×SD6473