Finite Group Databasebeta

← #29838156

Subgroups — #29838156

Order 15616.

466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#508×D61C212yesmaximal, complemented
2#21448138C212yesmaximal, complemented
3#21448135C212yesmaximal, complemented
4#21448133C212yesmaximal, complemented
5#21448130C212yesmaximal, complemented
6#21448128C211yesmaximal, characteristic, complemented
7#21448126C212yesmaximal, complemented
8C2×#16839595C211yesmaximal, characteristic, complemented
9C61×#2262C211yesmaximal, characteristic, complemented
10#135×D61—22no—
11#16840195C2212yes—
12#16840194C2212yescomplemented
13#16840193—22no—
14#16840192—22no—
15#16840191C2212yes—
16Q32×D61C2212yescomplemented
17SD32×D61—22no—
18D16×D61C2212yescomplemented
19C2×C16×D61C2211yescharacteristic
20Dic976C2211yescharacteristic, complemented
21#16839602C2212yescomplemented
22#16839601C2212yescomplemented
23#16839600C2212yescomplemented
24#16839599C2212yescomplemented
25D1952C2211yescharacteristic, complemented
26#16839597C2212yescomplemented
27#16839595C2212yescomplemented
28#16839595C2212yescomplemented
29C2×#14519683C2211yescharacteristic, complemented
30C61×#508C2212yescomplemented
31C61×Q64C2211yescharacteristic, complemented
32C61×SD64C2212yescomplemented
33C61×D32C2211yescharacteristic, complemented
34C2×C32×C61C2211yescharacteristic, complemented
35#41×D61—42no—
36#14519800—22no—
37#14519799—22no—
38#14519798—42no—
39#14519797—42no—
40#14519796—22no—
41Q16×D61—22no—
42SD16×D61—42no—
43D8×D61—22no—
44C2×C8×D61D411yescharacteristic
45Dic488C2312yes—
46#14519723—22no—
47#14519722—22no—
48#14519721—22no—
49#14519720—22no—
50D976C2312yes—
51#14519718—22no—
52C2×#11758185D411yescharacteristic
53C16×D61D412yes—
54C16×D61C2312yes—
55#14519683C2312yes—
56#135×C61—22no—
57Q32×C61C2312yes—
58SD32×C61—22no—
59D16×C61C2312yes—
60C2×C16×C61C2311yescharacteristic
61C32×C61C2311yescharacteristic
62C32×C61C2311yescharacteristic
63#41×C61—42no—
64#11758226—42no—
65Q8×D61—42no—
66#11758224—42no—
67#11758224—82no—
68D4×D61—42no—
69D4×D61—82no—
70#11758222—42no—
71#11758222—82no—
72C2×C4×D61—82no—
73C2×C4×D61D811yescharacteristic
74Q16×C61—22no—
75SD16×C61—42no—
76D8×C61—22no—
77C2×C8×C61C2×D411yescharacteristic
78#11758202—42no—
79#11758201—42no—
80#11758200—42no—
81#11758199—42no—
82C2×#92418D811yescharacteristic
83Dic244—22no—
84D488—22no—
85#11758190—42no—
86C8×D61D812yes—
87C8×D61C2×D412yes—
88C16×C61C2×D411yescharacteristic
89C16×C61C2411yescharacteristic
90#11758185C2×D412yes—
91C22×D61—82no—
92C22×D61D1611yescharacteristic
93Q8×C61—42no—
94D4×C61—42no—
95D4×C61—82no—
96C2×C4×C61—82no—
97C2×C4×C61C2×D811yescharacteristic
98C22⋊D61—82no—
99C22⋊D61—82no—
100C22⋊D61—82no—
101C2×Dic61—82no—
102C2×Dic61D1611yescharacteristic
103D244—42no—
104D244—82no—
105C4×D61—82no—
106C4×D61—82no—
107C4×D61—82no—
108C4×D61D1612yes—
109C4×D61C2×D812yes—
110Dic122—42no—
111Dic122—82no—
112C8×C61C2×D811yescharacteristic
113C8×C61C22×D411yescharacteristic
114#92418C2×D812yes—
115#33981—611nomaximal, Sylow
116C22×C61—82no—
117C22×C61C2×D1611yescharacteristic
118C2×D61—41no—
119C2×D61—82no—
120C2×D61—164no—
121C2×D61C2×D1612yes—
122C4×C61—82no—
123C4×C61C2×D1611yescharacteristic
124C4×C61C22×D811yescharacteristic
125Dic61—82no—
126Dic61C2×D1612yes—
127C2×#508—612no—
128#2264—612no—
129#2264—612no—
130#2263—612no—
131#2263—612no—
132#2262—612no—
133#2262—611no—
134#2262D6111yescharacteristic, complemented
135C2×M64—611no—
136C2×C61—21no—
137C2×C61—162no—
138C2×C61C22×D1611yescharacteristic
139D61—22no—
140D61—162no—
141C2×#135—1222no—
142#508—612no—
143#508—612no—
144#508—612no—
145#508—1222no—
146#508—1222no—
147#508C2×D6112yescomplemented
148C2×Q32—612no—
149C2×SD32—1222no—
150C2×D16—612no—
151C22×C16—611no—
152Q64—612no—
153Q64—611no—
154Q64C2×D6111yescharacteristic, complemented
155SD64—612no—
156SD64—612no—
157SD64—612no—
158SD64C2×D6112yescomplemented
159D32—612no—
160D32—611no—
161D32C2×D6111yescharacteristic, complemented
162M64—612no—
163M64—612no—
164C2×C32—611no—
165C2×C32C2×D6111yescharacteristic, complemented
166C61#3398111yescharacteristic, complemented, Sylow
167C2×#41—2442no—
168#135—22no—
169#135—1222no—
170#135—1222no—
171#135—1222no—
172#135—2442no—
173#135—2442no—
174C2×Q16—1222no—
175C2×SD16—2442no—
176C2×D8—1222no—
177C22×C8—611no—
178Q32—612no—
179Q32—1222no—
180Q32C22×D6112yes—
181SD32—22no—
182SD32—1222no—
183SD32—1222no—
184SD32—1222no—
185D16—612no—
186D16—1222no—
187D16C22×D6112yes—
188C2×C16—611no—
189C2×C16—612no—
190C2×C16—612no—
191C2×C16C22×D6111yescharacteristic
192C32—612no—
193C32C22×D6111yescharacteristic
194C32C22×D6111yescharacteristic
195#41—42no—
196#41—4882no—
197#41—4882no—
198#41—2442no—
199#41—2442no—
200#41—2442no—
201C2×Q8—2442no—
202C2×D4—4882no—
203C2×D4—2442no—
204C22×C4—611no—
205C22×C4—4882no—
206Q16—22no—
207Q16—1222no—
208Q16—2442no—
209SD16—42no—
210SD16—2442no—
211SD16—2442no—
212SD16—2442no—
213D8—22no—
214D8—1222no—
215D8—2442no—
216C2×C8—611no—
217C2×C8—612no—
218C2×C8—612no—
219C2×C8D4×D6111yescharacteristic
220C16—612no—
221C16D4×D6111yescharacteristic
222C16C23×D6111yescharacteristic
223C23—611no—
224C23—4882no—
225Q8—42no—
226Q8—4882no—
227Q8—2442no—
228D4—42no—
229D4—82no—
230D4—4882no—
231D4—4882no—
232D4—4882no—
233D4—4882no—
234D4—2442no—
235C2×C4—82no—
236C2×C4—611no—
237C2×C4—612no—
238C2×C4—612no—
239C2×C4—4882no—
240C2×C4—4882no—
241C2×C4—4882no—
242C2×C4—4882no—
243C2×C4D8×D6111yescharacteristic
244C8—612no—
245C8D8×D6111yescharacteristic
246C8C2×D4×D6111yescharacteristic
247C22—82no—
248C22—612no—
249C22—9764no—
250C22—4882no—
251C22—2441no—
252C22D16×D6111yescharacteristic
253C4—82no—
254C4—612no—
255C4—4882no—
256C4D16×D6111yescharacteristic
257C4C2×D8×D6111yescharacteristic
258C2—21no—
259C2—162no—
260C2—1222no—
261C2—9762no—
262C2C2×D16×D6111yescharacteristic
subgroupG/H
centerC4D16×D61
commutator, cosocleC16×C61C24
FrattiniC16C23×D61
FittingC61×#2262C2
socleC2×C61C22×D16
hypercenter#2262D61
hypocenterC61#33981
LCSG ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2262

Complements

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

NH ≅ G/Ntype
1. #508×D61C2semidirect
2. #21448138C2semidirect
3. #21448135C2semidirect
4. #21448133C2semidirect
5. #21448130C2semidirect
6. #21448128C2semidirect
7. #21448126C2semidirect
8. C2×#16839595C2semidirect
9. C61×#2262C2semidirect
12. #16840194C22semidirect
16. Q32×D61C22semidirect
18. D16×D61C22semidirect
20. Dic976C22semidirect
21. #16839602C22semidirect
22. #16839601C22semidirect
23. #16839600C22semidirect
24. #16839599C22semidirect
25. D1952C22semidirect
26. #16839597C22semidirect
27. #16839595C22semidirect
28. #16839595C22semidirect
29. C2×#14519683C22semidirect
30. C61×#508C22semidirect
31. C61×Q64C22semidirect
32. C61×SD64C22semidirect
33. C61×D32C22semidirect
34. C2×C32×C61C22semidirect
134. #2262D61semidirect
147. #508C2×D61semidirect
154. Q64C2×D61semidirect
158. SD64C2×D61semidirect
161. D32C2×D61semidirect
165. C2×C32C2×D61semidirect
166. C61#33981semidirect

Maximal subgroups

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

subgroupindex
#508×D612
#214481382
#214481352
#214481332
#214481302
#214481282
#214481262
C2×#168395952
C61×#22622
#3398161