Finite Group Databasebeta

← #393×D47 #20246586

Subgroups — #393×D47 #20246586

Order 6016.

1036 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C22×Q8×D47C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D47C213yesmaximal
3#15689036C213yesmaximal, complemented
4#15689035C213yesmaximal, complemented
5#15689034C211yesmaximal, characteristic, complemented
6#95×D47C213yesmaximal, complemented
7C47×#393C211yesmaximal, characteristic, complemented
8C24×D47C2211yescharacteristic
9C22×Dic94C2213yescomplemented
10C2×Q8×D47—212no—
11C22×C4×D47C2213yes—
12C22×C4×D47C2213yes—
13C2×C22⋊Dic47C2213yes—
14C2×(C2×D47)⋊C4C2213yes—
15C2×(C2×D47)⋊C4C2213yes—
16C22⋊C4×D47—212no—
17C47⋊#95C2213yescomplemented
18C47⋊#95C2216yescomplemented
19C22×Q8×C47C2211yescharacteristic, complemented
20C2×C22⋊C4×C47C2213yes—
21#95×C47C2213yescomplemented
22C24×C47C2311yescharacteristic
23C23×D47—26no—
24C23×D47—26no—
25C23×D47Q814yescomplemented
26C23×D47C2311yescharacteristic
27C23×D47C2311yescharacteristic
28C2×Q8×C47—26no—
29C22×C4×C47C2313yes—
30C22×C4×C47C2313yes—
31C22×Dic47C2313yes—
32C22×Dic47C2313yes—
33Q8×D47—232no—
34C2×C4×D47—212no—
35C2×C4×D47—26no—
36C2×C4×D47—212no—
37C2×C4×D47D4112yes—
38C2×Dic94—26no—
39C2×Dic94—212no—
40C22⋊C4×C47—26no—
41C22⋊Dic47—26no—
42(C2×D47)⋊C4—26no—
43(C2×D47)⋊C4—26no—
44C23×C47—23no—
45C23×C47—23no—
46C23×C47C2×Q812yescomplemented
47C23×C47C2411yescharacteristic
48C22×D47—23no—
49C22×D47—23no—
50C22×D47—224no—
51C22×D47—44no—
52C22×D47—412no—
53C22×D47C2×D416yes—
54C22×D47C2×Q812yes—
55C22×D47C2×Q812yescomplemented
56C22×D47#4116yes—
57Q8×C47—28no—
58C2×C4×C47—26no—
59C2×C4×C47—23no—
60C2×C4×C47—26no—
61C2×C4×C47C2×D416yes—
62C2×Dic47—26no—
63C2×Dic47—23no—
64C2×Dic47—26no—
65C2×Dic47C2×D416yes—
66C4×D47—224no—
67C4×D47—412no—
68Dic94—224no—
69C22×C47—26no—
70C22×C47—41no—
71C22×C47—43no—
72C22×C47C22×D413yes—
73C22×C47C22×Q811yescharacteristic
74C22×C47C2×#4113yes—
75C2×D47—26no—
76C2×D47—41no—
77C2×D47—43no—
78C2×D47—416no—
79C2×D47#12014yes—
80C2×D47C22⋊Q8112yes—
81C2×D47#124112yes—
82C4×C47—26no—
83C4×C47—43no—
84Dic47—26no—
85Dic47—43no—
86C2×#393—471nomaximal, Sylow
87C2×C47—42no—
88C2×C47C2×#12011yescharacteristic
89C2×C47C2×C22⋊Q813yes—
90C2×C47C2×#12413yes—
91D47—42no—
92D47#39318yesdirect product factor
93C23×Q8—471no—
94C22×C22⋊C4—473no—
95#393—471no—
96#393—473no—
97#393—473no—
98#393D4711yescharacteristic, direct product factor
99C2×#95—473no—
100C47C2×#39311yescharacteristic, complemented, Sylow
101C25—471no—
102C22×Q8—473no—
103C22×Q8—9412no—
104C22×Q8C2×D4711yescharacteristic, complemented
105C23×C4—473no—
106C23×C4—473no—
107C2×C22⋊C4—473no—
108C2×C22⋊C4—473no—
109C2×C22⋊C4—473no—
110C2×C22⋊C4—9412no—
111C2×C22⋊C4C2×D4713yes—
112#95—476no—
113#95—473no—
114#95C2×D4713yescomplemented
115C24—471no—
116C24—474no—
117C24—471no—
118C24—946no—
119C24—946no—
120C24C22×D4711yescharacteristic
121C2×Q8—26no—
122C2×Q8—9412no—
123C2×Q8—9432no—
124C2×Q8—946no—
125C22×C4—473no—
126C22×C4—4712no—
127C22×C4—473no—
128C22×C4—9412no—
129C22×C4—946no—
130C22×C4—9412no—
131C22×C4C22×D4713yes—
132C22×C4C22×D4713yes—
133C22⋊C4—26no—
134C22⋊C4—946no—
135C22⋊C4—946no—
136C22⋊C4—946no—
137C23—23no—
138C23—23no—
139C23—476no—
140C23—472no—
141C23—476no—
142C23—472no—
143C23—9424no—
144C23—943no—
145C23—943no—
146C23—1884no—
147C23—18812no—
148C23Q8×D4712yescomplemented
149C23C23×D4711yescharacteristic
150Q8—28no—
151Q8—9424no—
152C2×C4—26no—
153C2×C4—23no—
154C2×C4—26no—
155C2×C4—476no—
156C2×C4—9424no—
157C2×C4—946no—
158C2×C4—943no—
159C2×C4—946no—
160C2×C4—18812no—
161C2×C4D4×D4716yes—
162C22—26no—
163C22—41no—
164C22—43no—
165C22—474no—
166C22—4712no—
167C22—4712no—
168C22—946no—
169C22—18816no—
170C22—1881no—
171C22—1883no—
172C22C2×D4×D4713yes—
173C22C2×Q8×D4711yescharacteristic
174C22#41×D4713yes—
175C4—26no—
176C4—43no—
177C4—946no—
178C4—1883no—
179C2—42no—
180C2—478no—
181C2—1882no—
182C2#120×D4711yescharacteristic
183C2C22⋊Q8×D4713yes—
184C2#124×D4713yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47C2×#393
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D47C2semidirect
3. #15689036C2semidirect
4. #15689035C2semidirect
5. #15689034C2semidirect
6. #95×D47C2semidirect
7. C47×#393C2semidirect
9. C22×Dic94C22semidirect
17. C47⋊#95C22semidirect
18. C47⋊#95C22semidirect
19. C22×Q8×C47C22semidirect
21. #95×C47C22semidirect
25. C23×D47Q8semidirect
46. C23×C47C2×Q8semidirect
55. C22×D47C2×Q8semidirect
92. D47#393direct (N × H)
98. #393D47direct (N × H)
100. C47C2×#393semidirect
104. C22×Q8C2×D47semidirect
114. #95C2×D47semidirect
148. C23Q8×D47semidirect