Finite Group Databasebeta

← D47×#1711 #26203952

Subgroups — D47×#1711 #26203952

Order 12032.

802 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 179 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#487×D47C213yesmaximal, complemented
2#486×D47C213yesmaximal
3#20243001C213yesmaximal, complemented
4#20243000C211yesmaximal, characteristic, complemented
5#20242999C213yesmaximal, complemented
6C82×D47C211yesmaximal, characteristic, complemented
7C47×#1711C211yesmaximal, characteristic, complemented
8C4⋊Q8×D47C2213yes—
9#127×D47C2211yescharacteristic
10#15689475C2213yescomplemented
11#15689474C2213yescomplemented
12#15689473C2213yescomplemented
13#15689472—26no—
14#15689471C2213yes—
15#15689470C2213yes—
16#15689469C2213yes—
17#15689468—26no—
18#103×D47—26no—
19#102×D47—26no—
20C4×C8×D47C2213yes—
21C8×C47⋊C8C2213yescomplemented
22C47×#487C2213yescomplemented
23C47×#486C2213yes—
24C82×C47C2211yescharacteristic, complemented
25C2×Q8×D47—23no—
26C2×D4×D47—23no—
27C2×C8×D47D416yes—
28#13094024C2313yes—
29#13094023—23no—
30#13094023—23no—
31#13094022—23no—
32#13094021C2311yescharacteristic
33#13094020—23no—
34C4⋊C4×D47—23no—
35C4⋊C4×D47—23no—
36C42×D47C2311yescharacteristic
37#13093949—26no—
38#13093948—26no—
39#13093947—26no—
40#13093946—26no—
41#13093945—26no—
42#13093944—26no—
43C4×C47⋊C8C2313yes—
44C8×Dic47D416yes—
45C4⋊Q8×C47C2313yes—
46#127×C47C2311yescharacteristic
47#103×C47—26no—
48#102×C47—26no—
49C4×C8×C47C2313yes—
50C23×D47—41no—
51C2×Q8×C47—23no—
52C2×D4×C47—23no—
53C2×C22⋊D47—43no—
54Q8×D47—412no—
55D4×D47—412no—
56C2×D188—23no—
57C2×C4×D47—43no—
58C2×C4×D47C2×D413yes—
59C2×Dic94—23no—
60C2×Dic94—43no—
61C2×C8×C47C2×D416yes—
62C4⋊C4×C47—23no—
63C4⋊C4×C47—23no—
64C42×C47C2411yescharacteristic
65C4⋊Dic47—23no—
66C4⋊Dic47—23no—
67Dic47⋊C4—43no—
68Dic47⋊C4—43no—
69C4×Dic47C2×D413yes—
70C2×C47⋊C8C2×D416yes—
71C8×D47—212no—
72C23×C47—41no—
73C22×D47—41no—
74C22×D47—86no—
75C22×D47#12711yescharacteristic
76Q8×C47—46no—
77D4×C47—46no—
78C2×C4×C47—43no—
79C2×C4×C47C22×D413yes—
80C22⋊D47—86no—
81C2×Dic47—43no—
82C2×Dic47#12713yes—
83D188—46no—
84C4×D47—86no—
85C4×D47#135112yes—
86Dic94—46no—
87Dic94—86no—
88C8×C47—26no—
89C47⋊C8—26no—
90C2×#1711—471nomaximal, Sylow
91C22×C47—83no—
92C22×C47C2×#12711yescharacteristic
93C2×D47—83no—
94C2×D47—164no—
95C2×D47#49516yes—
96C4×C47—83no—
97C4×C47C2×#13516yes—
98Dic47—83no—
99Dic47#49516yes—
100C2×#487—473no—
101C2×#486—473no—
102#1711—473no—
103#1711—473no—
104#1711—471no—
105#1711D4711yescharacteristic, direct product factor
106C2×C82—471no—
107C2×C47—161no—
108C2×C47C2×#49513yes—
109D47—161no—
110D47#171114yesdirect product factor
111C2×C4⋊Q8—473no—
112C2×#127—471no—
113#487—473no—
114#487—473no—
115#487—473no—
116#487—946no—
117#487C2×D4713yescomplemented
118#486—473no—
119#486—473no—
120#486—473no—
121#486—946no—
122#486C2×D4713yes—
123C2×#103—946no—
124C2×#102—946no—
125C2×C4×C8—473no—
126C82—473no—
127C82C2×D4711yescharacteristic, complemented
128C47C2×#171111yescharacteristic, complemented, Sylow
129C22×Q8—943no—
130C22×D4—943no—
131C22×C8—476no—
132C4⋊Q8—473no—
133C4⋊Q8—943no—
134C4⋊Q8—943no—
135C4⋊Q8—943no—
136C4⋊Q8C22×D4713yes—
137#127—471no—
138#127—943no—
139#127C22×D4711yescharacteristic
140C2×C4⋊C4—943no—
141C2×C4⋊C4—943no—
142C2×C42—471no—
143#103—26no—
144#103—946no—
145#103—946no—
146#103—946no—
147#102—26no—
148#102—946no—
149#102—946no—
150#102—946no—
151C4×C8—476no—
152C4×C8—473no—
153C4×C8C22×D4713yes—
154C24—1881no—
155C2×Q8—23no—
156C2×Q8—943no—
157C2×Q8—1883no—
158C2×Q8—18812no—
159C2×D4—23no—
160C2×D4—943no—
161C2×D4—18812no—
162C2×D4—1883no—
163C22×C4—473no—
164C22×C4—1883no—
165C2×C8—476no—
166C2×C8—9412no—
167C2×C8D4×D4716yes—
168C4⋊C4—23no—
169C4⋊C4—23no—
170C4⋊C4—943no—
171C4⋊C4—943no—
172C4⋊C4—1883no—
173C4⋊C4—1883no—
174C42—473no—
175C42C23×D4711yescharacteristic
176C23—41no—
177C23—471no—
178C23—3766no—
179C23—1881no—
180Q8—46no—
181Q8—3766no—
182Q8—1886no—
183D4—46no—
184D4—3766no—
185D4—1886no—
186C2×C4—43no—
187C2×C4—473no—
188C2×C4—4712no—
189C2×C4—3766no—
190C2×C4—1883no—
191C2×C4C2×D4×D4713yes—
192C8—26no—
193C8—946no—
194C22—83no—
195C22—476no—
196C22—3763no—
197C22—7524no—
198C22#127×D4711yescharacteristic
199C4—83no—
200C4—476no—
201C4—3763no—
202C4#135×D4716yes—
203C2—161no—
204C2—474no—
205C2—7521no—
206C2#495×D4713yes—
subgroupG/H
centerC22#127×D47
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#1711C2
socleC22×C47C2×#127
prime radical#127×D47C22
hypercenter#1711D47
hypocenterC47C2×#1711
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #1711

Complements

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

NH ≅ G/Ntype
1. #487×D47C2semidirect
3. #20243001C2semidirect
4. #20243000C2semidirect
5. #20242999C2semidirect
6. C82×D47C2semidirect
7. C47×#1711C2semidirect
10. #15689475C22semidirect
11. #15689474C22semidirect
12. #15689473C22semidirect
21. C8×C47⋊C8C22semidirect
22. C47×#487C22semidirect
24. C82×C47C22semidirect
105. #1711D47direct (N × H)
110. D47#1711direct (N × H)
117. #487C2×D47semidirect
127. C82C2×D47semidirect
128. C47C2×#1711semidirect

Maximal subgroups

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

subgroupindex
#487×D472
#486×D472
#202430012
#202430002
#202429992
C82×D472
C47×#17112
C2×#171147