Finite Group Databasebeta

← D47×#2845 #26422865

Subgroups — D47×#2845 #26422865

Order 12032.

1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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#20251663C213yesmaximal, complemented
2#20251662C2112yesmaximal, complemented
3#398×D47C2112yesmaximal
4#382×D47C213yesmaximal
5C47×#2845C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D47C2216yes—
7C2×C4⋊C4×D47C22112yes—
8C2×C42×D47C2211yescharacteristic
9#15689057C22112yes—
10#15689057C22112yes—
11#15689056C22112yes—
12#15689056C22112yes—
13#15689055C22112yes—
14#15689054C22112yes—
15#15689053C22112yes—
16#15688989C2213yes—
17#15688988C2216yes—
18#15688987C22112yes—
19#95×D47C22112yes—
20#95×D47C2214yes—
21C47×#398C22112yes—
22C47×#382C2213yes—
23C22×C4×D47C23112yes—
24C22×C4×D47C2313yes—
25C2×C4⋊Dic47C2316yes—
26C2×C4⋊Dic47C23112yes—
27C2×Dic47⋊C4C23112yes—
28C2×Dic47⋊C4C23112yes—
29C2×Dic47⋊C4C23112yes—
30C4⋊C4×D47—412no—
31C4⋊C4×D47—424no—
32C2×C4×Dic47C2313yes—
33C42×D47Q818yes—
34C47⋊#95C23112yes—
35C47⋊#95C23112yes—
36C47⋊#95C23112yes—
37C47⋊#95C23112yes—
38C2×C4⋊C4×C47C2316yes—
39C2×C4⋊C4×C47C23112yes—
40C2×C42×C47C2311yescharacteristic
41#95×C47C23112yes—
42#95×C47C2314yes—
43C23×D47C2411yescharacteristic
44C22×C4×C47C24112yes—
45C22×C4×C47C2413yes—
46C22×Dic47C24112yes—
47C22×Dic47C2413yes—
48C2×C4×D47—26no—
49C2×C4×D47—26no—
50C2×C4×D47—224no—
51C2×C4×D47—224no—
52C2×C4×D47—224no—
53C2×C4×D47C2×Q8112yes—
54C4⋊C4×C47—46no—
55C4⋊C4×C47—412no—
56C42×C47C2×Q814yes—
57C4⋊Dic47—412no—
58C4⋊Dic47—46no—
59Dic47⋊C4—412no—
60Dic47⋊C4—412no—
61Dic47⋊C4—412no—
62C4×Dic47C2×Q8112yes—
63C23×C47C2511yescharacteristic
64C22×D47C22×Q812yes—
65C22×D47H(5,𝔽2)16yes—
66C22×D472−1+416yes—
67C2×C4×C47—23no—
68C2×C4×C47—23no—
69C2×C4×C47—212no—
70C2×C4×C47—212no—
71C2×C4×C47—212no—
72C2×C4×C47C22×Q816yes—
73C2×Dic47—23no—
74C2×Dic47—23no—
75C2×Dic47—212no—
76C2×Dic47—212no—
77C2×Dic47—212no—
78C2×Dic47C22×Q816yes—
79C4×D47—224no—
80C4×D47—448no—
81C2×#2845—471nomaximal, Sylow
82C22×C47C23×Q811yescharacteristic
83C22×C47C2×H(5,𝔽2)13yes—
84C22×C47C2×2−1+413yes—
85C2×D47#544112yes—
86C2×D47#562112yes—
87C2×D47#56414yes—
88C4×C47—26no—
89C4×C47—412no—
90Dic47—26no—
91Dic47—412no—
92#2845—4712no—
93#2845—473no—
94#2845D4711yescharacteristic, direct product factor
95C2×#398—4712no—
96C2×#382—473no—
97C2×C47C2×#54413yes—
98C2×C47C2×#56213yes—
99C2×C47C2×#56411yescharacteristic
100D47#284518yesdirect product factor
101C22×C4⋊C4—4712no—
102C22×C4⋊C4—476no—
103C22×C42—471no—
104#398—4712no—
105#398—4712no—
106#398—4712no—
107#398—4712no—
108#398—4712no—
109#398—4712no—
110#398—4712no—
111#398C2×D47112yes—
112#382—476no—
113#382—473no—
114#382—4712no—
115#382C2×D4713yes—
116C2×#95—474no—
117C2×#95—4712no—
118C47C2×#284511yescharacteristic, complemented, Sylow
119C23×C4—473no—
120C23×C4—4712no—
121C2×C4⋊C4—4712no—
122C2×C4⋊C4—4712no—
123C2×C4⋊C4—4712no—
124C2×C4⋊C4—476no—
125C2×C4⋊C4—4712no—
126C2×C4⋊C4—18812no—
127C2×C4⋊C4—18824no—
128C2×C4⋊C4C22×D4716yes—
129C2×C4⋊C4C22×D47112yes—
130C2×C42—473no—
131C2×C42—478no—
132C2×C42C22×D4711yescharacteristic
133#95—4712no—
134#95—4712no—
135#95—4712no—
136#95—4712no—
137#95C22×D47112yes—
138#95C22×D4714yes—
139C24—471no—
140C22×C4—473no—
141C22×C4—4712no—
142C22×C4—4712no—
143C22×C4—946no—
144C22×C4—946no—
145C22×C4—9424no—
146C22×C4—9424no—
147C22×C4—9424no—
148C22×C4C23×D47112yes—
149C22×C4C23×D4713yes—
150C4⋊C4—46no—
151C4⋊C4—412no—
152C4⋊C4—18812no—
153C4⋊C4—18812no—
154C4⋊C4—18812no—
155C4⋊C4—1886no—
156C4⋊C4—18812no—
157C42—4712no—
158C42Q8×D4714yes—
159C23—472no—
160C23—476no—
161C23—476no—
162C23C24×D4711yescharacteristic
163C2×C4—23no—
164C2×C4—23no—
165C2×C4—212no—
166C2×C4—212no—
167C2×C4—212no—
168C2×C4—476no—
169C2×C4—9424no—
170C2×C4—943no—
171C2×C4—943no—
172C2×C4—9412no—
173C2×C4—9412no—
174C2×C4—9412no—
175C2×C4—18848no—
176C2×C4C2×Q8×D4716yes—
177C22—4712no—
178C22—4712no—
179C22—474no—
180C22C22×Q8×D4711yescharacteristic
181C22H(5,𝔽2)×D4713yes—
182C222−1+4×D4713yes—
183C4—26no—
184C4—412no—
185C4—946no—
186C4—18812no—
187C2—478no—
188C2#544×D4713yes—
189C2#562×D4713yes—
190C2#564×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2845C2
prime radicalC23×D47C24
hypercenter#2845D47
hypocenterC47C2×#2845
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2845

Complements

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

NH ≅ G/Ntype
1. #20251663C2semidirect
2. #20251662C2semidirect
5. C47×#2845C2semidirect
94. #2845D47direct (N × H)
100. D47#2845direct (N × H)
118. C47C2×#2845semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202516622
#398×D472
#382×D472
C47×#28452
C2×#284547