Finite Group Databasebeta

← D47×#1705 #26203913

Subgroups — D47×#1705 #26203913

Order 12032.

994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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#498×D47C213yesmaximal, complemented
2#492×D47C213yesmaximal
3#20242976C213yesmaximal, complemented
4#20242975C211yesmaximal, characteristic, complemented
5#20242974C213yesmaximal, complemented
6C82×D47C211yesmaximal, characteristic, complemented
7C47×#1705C211yesmaximal, characteristic, complemented
8C2×SD16×D47—26no—
9C4⋊Q8×D47C2213yes—
10#127×D47C2211yescharacteristic
11#15689521C2213yescomplemented
12#15689520—26no—
13#15689519C2216yescomplemented
14#15689497C2213yes—
15#15689496C2213yes—
16#15689495C2213yes—
17#15689494—26no—
18#106×D47—26no—
19C4×C8×D47C2213yes—
20C8×C47⋊C8C2213yescomplemented
21C47×#498C2213yescomplemented
22C47×#492C2213yes—
23C82×C47C2211yescharacteristic, complemented
24C2×Q8×D47—23no—
25C2×D4×D47—23no—
26C2×#10625325—26no—
27C2×#10625335—26no—
28C2×#10625336—26no—
29SD16×D47—424no—
30C2×C8×D47D416yes—
31#13094024C2313yes—
32#13094023—26no—
33#13094022—23no—
34#13094021C2311yescharacteristic
35#13094020—23no—
36C4⋊C4×D47—26no—
37C42×D47C2311yescharacteristic
38#13093956—26no—
39#13093955—212no—
40C4×C47⋊C8C2313yes—
41C8×Dic47D416yes—
42C2×SD16×C47—26no—
43C4⋊Q8×C47C2313yes—
44#127×C47C2311yescharacteristic
45#106×C47—26no—
46C4×C8×C47C2313yes—
47C23×D47—41no—
48C2×Q8×C47—23no—
49C2×D4×C47—23no—
50C2×C22⋊D47—43no—
51Q8×D47—412no—
52D4×D47—412no—
53C2×D188—23no—
54C2×C4×D47—43no—
55C2×C4×D47C2×D413yes—
56C2×Dic94—23no—
57C2×Dic94—43no—
58SD16×C47—412no—
59C2×C8×C47C2×D416yes—
60C4⋊C4×C47—26no—
61C42×C47C2411yescharacteristic
62#10625336—412no—
63#10625335—412no—
64C4⋊Dic47—26no—
65Dic47⋊C4—46no—
66C4×Dic47C2×D413yes—
67C2×C47⋊C8C2×D416yes—
68#10625325—412no—
69C8×D47SD16124yescomplemented
70C23×C47—41no—
71C22×D47—41no—
72C22×D47—86no—
73C22×D47#12711yescharacteristic
74Q8×C47—46no—
75D4×C47—46no—
76C2×C4×C47—43no—
77C2×C4×C47C22×D413yes—
78C22⋊D47—86no—
79C2×Dic47—43no—
80C2×Dic47#12713yes—
81D188—46no—
82C4×D47—86no—
83C4×D47C2×SD16112yes—
84Dic94—46no—
85Dic94—86no—
86C8×C47C2×SD16112yescomplemented
87C47⋊C8C2×SD16112yescomplemented
88C2×#1705—471nomaximal, Sylow
89C22×C47—83no—
90C22×C47C2×#12711yescharacteristic
91C2×D47—83no—
92C2×D47—164no—
93C2×D47#49216yes—
94C4×C47—83no—
95C4×C47C22×SD1616yes—
96Dic47—83no—
97Dic47#49216yes—
98C2×#498—473no—
99C2×#492—473no—
100#1705—473no—
101#1705—473no—
102#1705—471no—
103#1705D4711yescharacteristic, direct product factor
104C2×C82—471no—
105C2×C47—161no—
106C2×C47C2×#49213yes—
107D47—161no—
108D47#170514yesdirect product factor
109C22×SD16—946no—
110C2×C4⋊Q8—473no—
111C2×#127—471no—
112#498—476no—
113#498—473no—
114#498—946no—
115#498C2×D4713yescomplemented
116#492—473no—
117#492—473no—
118#492—473no—
119#492—946no—
120#492C2×D4713yes—
121C2×#106—946no—
122C2×C4×C8—473no—
123C82—473no—
124C82C2×D4711yescharacteristic, complemented
125C47C2×#170511yescharacteristic, complemented, Sylow
126C22×Q8—943no—
127C22×D4—943no—
128C2×SD16—26no—
129C2×SD16—946no—
130C2×SD16—946no—
131C2×SD16—946no—
132C2×SD16—18824no—
133C22×C8—476no—
134C4⋊Q8—473no—
135C4⋊Q8—946no—
136C4⋊Q8—943no—
137C4⋊Q8C22×D4713yes—
138#127—471no—
139#127—943no—
140#127C22×D4711yescharacteristic
141C2×C4⋊C4—946no—
142C2×C42—471no—
143#106—26no—
144#106—9412no—
145#106—946no—
146C4×C8—476no—
147C4×C8—473no—
148C4×C8C22×D4713yes—
149C24—1881no—
150C2×Q8—23no—
151C2×Q8—943no—
152C2×Q8—1883no—
153C2×Q8—18812no—
154C2×D4—23no—
155C2×D4—943no—
156C2×D4—18812no—
157C2×D4—1883no—
158C22×C4—473no—
159C22×C4—1883no—
160SD16—412no—
161SD16—18812no—
162SD16—18812no—
163SD16—18812no—
164C2×C8—476no—
165C2×C8—4724no—
166C2×C8D4×D4716yes—
167C4⋊C4—26no—
168C4⋊C4—946no—
169C4⋊C4—1886no—
170C42—473no—
171C42C23×D4711yescharacteristic
172C23—41no—
173C23—471no—
174C23—3766no—
175C23—1881no—
176Q8—46no—
177Q8—3766no—
178Q8—1886no—
179D4—46no—
180D4—3766no—
181D4—1886no—
182C2×C4—43no—
183C2×C4—473no—
184C2×C4—4712no—
185C2×C4—3766no—
186C2×C4—1883no—
187C2×C4C2×D4×D4713yes—
188C8—4712no—
189C8SD16×D47112yescomplemented
190C22—83no—
191C22—476no—
192C22—3763no—
193C22—7524no—
194C22#127×D4711yescharacteristic
195C4—83no—
196C4—476no—
197C4—3763no—
198C4C2×SD16×D4716yes—
199C2—161no—
200C2—474no—
201C2—7521no—
202C2#492×D4713yes—
subgroupG/H
centerC22#127×D47
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#1705C2
socleC22×C47C2×#127
prime radical#127×D47C22
hypercenter#1705D47
hypocenterC47C2×#1705
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #1705

Complements

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

NH ≅ G/Ntype
1. #498×D47C2semidirect
3. #20242976C2semidirect
4. #20242975C2semidirect
5. #20242974C2semidirect
6. C82×D47C2semidirect
7. C47×#1705C2semidirect
11. #15689521C22semidirect
13. #15689519C22semidirect
20. C8×C47⋊C8C22semidirect
21. C47×#498C22semidirect
23. C82×C47C22semidirect
69. C8×D47SD16semidirect
86. C8×C47C2×SD16semidirect
87. C47⋊C8C2×SD16semidirect
103. #1705D47direct (N × H)
108. D47#1705direct (N × H)
115. #498C2×D47semidirect
124. C82C2×D47semidirect
125. C47C2×#1705semidirect
189. C8SD16×D47semidirect

Maximal subgroups

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

subgroupindex
#498×D472
#492×D472
#202429762
#202429752
#202429742
C82×D472
C47×#17052
C2×#170547