Finite Group Databasebeta

← C2×#20245702 #26374412

Subgroups — C2×#20245702 #26374412

Order 12032.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15689556C211yesmaximal, characteristic, complemented
2C2×D16×D47C211yesmaximal, characteristic, complemented
3#20245702C218yesmaximal, direct product factor
4C2×#15688960C211yesmaximal, characteristic, complemented
5C2×D1504C211yesmaximal, characteristic, complemented
6C2×#15688958C211yesmaximal, characteristic, complemented
7C2×#15688956C211yesmaximal, characteristic, complemented
8C2×C47×SD64C211yesmaximal, characteristic, complemented
9C2×#13094047—21no—
10C2×D8×D47—21no—
11#15689556—22no—
12#15689556C2214yescomplemented
13C2×#13093967—21no—
14C2×D752C2211yescharacteristic
15C2×D752C2211yescharacteristic, complemented
16C2×#13093965—21no—
17D16×D47—22no—
18D16×D47C2214yescomplemented
19C2×C16×D47C2211yescharacteristic
20#15688960C2214yescomplemented
21D1504C2214yescomplemented
22#15688958C2214yescomplemented
23#15688956C2214yescomplemented
24C2×C47⋊C32C2211yescharacteristic, complemented
25C2×Q32×C47C2211yescharacteristic, complemented
26C2×D16×C47C2211yescharacteristic
27C47×SD64C2214yescomplemented
28C2×C32×C47C2211yescharacteristic, complemented
29C2×#10625354—41no—
30C2×D4×D47—41no—
31#13094047—24no—
32#13094047—42no—
33C2×#10625336—41no—
34C2×D376—21no—
35C2×D376—21no—
36C2×#10625334—41no—
37D8×D47—24no—
38D8×D47—42no—
39C2×C8×D47D411yescharacteristic
40#13093967—24no—
41D752—21no—
42D752—21no—
43D752C2312yes—
44D752C2312yescomplemented
45#13093965—24no—
46C2×C47⋊C16D411yescharacteristic
47C16×D47D412yes—
48C16×D47C2312yes—
49C47⋊C32C2312yescomplemented
50C2×Q16×C47—21no—
51C2×D8×C47—21no—
52Q32×C47—21no—
53Q32×C47C2312yescomplemented
54D16×C47—21no—
55D16×C47C2312yes—
56C2×C16×C47C2311yescharacteristic
57C32×C47C2312yescomplemented
58C23×D47—81no—
59C2×Q8×C47—41no—
60C2×D4×C47—41no—
61C2×C22⋊D47—81no—
62#10625354—44no—
63#10625354—82no—
64D4×D47—44no—
65D4×D47—82no—
66C2×D188—41no—
67C2×D188—41no—
68C2×D188—81no—
69C2×C4×D47—81no—
70C2×C4×D47D811yescharacteristic
71Q16×C47—22no—
72Q16×C47—41no—
73D8×C47—22no—
74D8×C47—41no—
75C2×C8×C47C2×D411yescharacteristic
76#10625336—44no—
77#10625334—44no—
78C2×C47⋊C8D811yescharacteristic
79D376—22no—
80D376—22no—
81D376—41no—
82D376—41no—
83C8×D47D812yes—
84C8×D47C2×D412yes—
85C16×C47C2×D411yescharacteristic
86C16×C47C2411yescharacteristic
87C47⋊C16C2×D412yes—
88C23×C47—81no—
89C22×D47—81no—
90C22×D47—81no—
91C22×D47—84no—
92C22×D47—164no—
93C22×D47D1611yescharacteristic
94Q8×C47—42no—
95Q8×C47—81no—
96D4×C47—42no—
97D4×C47—81no—
98C2×C4×C47—81no—
99C2×C4×C47C2×D811yescharacteristic
100C22⋊D47—84no—
101C2×Dic47D1611yescharacteristic
102D188—42no—
103D188—42no—
104D188—84no—
105D188—81no—
106D188—81no—
107C4×D47—84no—
108C4×D47D1612yes—
109C4×D47C2×D812yes—
110C8×C47C2×D811yescharacteristic
111C8×C47C22×D411yescharacteristic
112C47⋊C8C2×D812yes—
113C2×#2263—471nomaximal, Sylow
114C22×C47—82no—
115C22×C47—162no—
116C22×C47C2×D1611yescharacteristic
117C2×D47—22no—
118C2×D47—82no—
119C2×D47—82no—
120C2×D47—168no—
121C2×D47—162no—
122C2×D47—162no—
123C2×D47C2×D1612yes—
124C4×C47—82no—
125C4×C47C2×D1611yescharacteristic
126C4×C47C22×D811yescharacteristic
127Dic47C2×D1612yes—
128C2×#508—471no—
129C22×D16—471no—
130#2263—478no—
131C2×SD64—471no—
132C2×SD64D4711yescharacteristic, complemented
133C2×D32—471no—
134C2×D32—471no—
135C2×M64—471no—
136C2×C47—162no—
137C2×C47#226312yescomplemented
138C2×C47C22×D1611yescharacteristic
139D47—22no—
140D47—162no—
141D47—162no—
142C2×#135—941no—
143C22×D8—941no—
144#508—474no—
145#508—942no—
146C2×Q32C2×D4711yescharacteristic, complemented
147C2×SD32—941no—
148C2×D16—474no—
149C2×D16—471no—
150C2×D16—471no—
151C2×D16—942no—
152C2×D16—941no—
153C2×D16C2×D4711yescharacteristic
154C22×C16—471no—
155SD64—474no—
156SD64C2×D4714yescomplemented
157D32—474no—
158D32—474no—
159M64—474no—
160C2×C32—471no—
161C2×C32C2×D4711yescharacteristic, complemented
162C47C2×#226311yescharacteristic, complemented, Sylow
163C2×#41—1881no—
164C22×D4—1881no—
165#135—944no—
166#135—1882no—
167C2×Q16—21no—
168C2×SD16—1881no—
169C2×D8—21no—
170C2×D8—944no—
171C2×D8—941no—
172C2×D8—941no—
173C2×D8—1882no—
174C2×D8—1881no—
175C22×C8—471no—
176Q32—21no—
177Q32C22×D4712yescomplemented
178SD32—944no—
179D16—21no—
180D16—472no—
181D16—472no—
182D16—944no—
183D16—941no—
184D16—941no—
185D16C22×D4712yes—
186C2×C16—471no—
187C2×C16—472no—
188C2×C16—472no—
189C2×C16C22×D4711yescharacteristic
190C32—472no—
191C32C22×D4712yescomplemented
192C24—3761no—
193#41—3762no—
194#41—1884no—
195C2×Q8—41no—
196C2×D4—41no—
197C2×D4—3761no—
198C2×D4—3762no—
199C2×D4—3761no—
200C2×D4—1884no—
201C2×D4—1881no—
202C2×D4—1881no—
203C22×C4—471no—
204C22×C4—3761no—
205Q16—22no—
206Q16—41no—
207SD16—1884no—
208D8—22no—
209D8—41no—
210D8—942no—
211D8—942no—
212D8—1884no—
213D8—1881no—
214D8—1881no—
215C2×C8—471no—
216C2×C8—472no—
217C2×C8—472no—
218C2×C8D4×D4711yescharacteristic
219C16—472no—
220C16D4×D4711yescharacteristic
221C16C23×D4711yescharacteristic
222C23—81no—
223C23—471no—
224C23—3764no—
225C23—3761no—
226C23—3761no—
227C23—7524no—
228Q8—42no—
229Q8—81no—
230D4—42no—
231D4—81no—
232D4—3764no—
233D4—3764no—
234D4—3761no—
235D4—3761no—
236D4—1882no—
237D4—1882no—
238C2×C4—81no—
239C2×C4—471no—
240C2×C4—472no—
241C2×C4—472no—
242C2×C4—3764no—
243C2×C4D8×D4711yescharacteristic
244C8—472no—
245C8D8×D4711yescharacteristic
246C8C2×D4×D4711yescharacteristic
247C22—82no—
248C22—162no—
249C22—472no—
250C22—942no—
251C22—3762no—
252C22—3762no—
253C22—7528no—
254C22—7522no—
255C22—7522no—
256C22D16×D4711yescharacteristic
257C4—82no—
258C4—472no—
259C4D16×D4711yescharacteristic
260C4C2×D8×D4711yescharacteristic
261C2—162no—
262C2—942no—
263C2—7522no—
264C2—7522no—
265C2#2024570212yesdirect product factor
266C2C2×D16×D4711yescharacteristic
subgroupG/H
centerC22D16×D47
commutator, cosocleC16×C47C24
FrattiniC16C23×D47
FittingC2×C47×SD64C2
socleC22×C47C2×D16
hypercenterC2×SD64D47
hypocenterC47C2×#2263
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
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×#15689556C2semidirect
2. C2×D16×D47C2semidirect
3. #20245702C2direct (N × H)
4. C2×#15688960C2semidirect
5. C2×D1504C2semidirect
6. C2×#15688958C2semidirect
7. C2×#15688956C2semidirect
8. C2×C47×SD64C2semidirect
12. #15689556C22semidirect
15. C2×D752C22semidirect
18. D16×D47C22semidirect
20. #15688960C22semidirect
21. D1504C22semidirect
22. #15688958C22semidirect
23. #15688956C22semidirect
24. C2×C47⋊C32C22semidirect
25. C2×Q32×C47C22semidirect
27. C47×SD64C22semidirect
28. C2×C32×C47C22semidirect
44. D752C23semidirect
49. C47⋊C32C23semidirect
53. Q32×C47C23semidirect
57. C32×C47C23semidirect
132. C2×SD64D47semidirect
137. C2×C47#2263semidirect
146. C2×Q32C2×D47semidirect
156. SD64C2×D47semidirect
161. C2×C32C2×D47semidirect
162. C47C2×#2263semidirect
177. Q32C22×D47semidirect
191. C32C22×D47semidirect
265. C2#20245702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895562
C2×D16×D472
#202457022
C2×#156889602
C2×D15042
C2×#156889582
C2×#156889562
C2×C47×SD642
C2×#226347