Finite Group Databasebeta

← #399×D47 #20246634

Subgroups — #399×D47 #20246634

Order 6016.

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

normal subgroups only

This group has 908 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
1C2×C4⋊C4×D47C213yesmaximal, complemented
2C2×C22⋊C4×D47C213yesmaximal
3#15689060C211yesmaximal, characteristic, complemented
4#15689059C213yesmaximal, complemented
5#15689058C213yesmaximal, complemented
6#95×D47C211yesmaximal, characteristic, complemented
7C47×#399C211yesmaximal, characteristic, complemented
8C24×D47C2211yescharacteristic
9C22×C4×D47C2213yes—
10C22×C4×D47C2213yes—
11C2×C4⋊Dic47C2213yescomplemented
12C2×Dic47⋊C4C2216yescomplemented
13C4⋊C4×D47—212no—
14C2×C22⋊Dic47C2213yes—
15C2×(C2×D47)⋊C4C2213yes—
16C2×(C2×D47)⋊C4C2213yes—
17C22⋊C4×D47—212no—
18C47⋊#95C2213yescomplemented
19C2×C4⋊C4×C47C2213yescomplemented
20C2×C22⋊C4×C47C2213yes—
21#95×C47C2211yescharacteristic, complemented
22C24×C47C2311yescharacteristic
23C23×D47—26no—
24C23×D47—26no—
25C23×D47Q814yes—
26C23×D47C2311yescharacteristic
27C23×D47C2311yescharacteristic
28C22×C4×C47C2313yes—
29C22×C4×C47C2313yes—
30C22×Dic47C2313yes—
31C22×Dic47C2313yes—
32C2×C4×D47—212no—
33C2×C4×D47—26no—
34C2×C4×D47—212no—
35C2×C4×D47D4112yes—
36C4⋊C4×C47—26no—
37C22⋊C4×C47—26no—
38C22⋊Dic47—26no—
39(C2×D47)⋊C4—26no—
40(C2×D47)⋊C4—26no—
41C4⋊Dic47—26no—
42Dic47⋊C4—212no—
43C23×C47—23no—
44C23×C47—23no—
45C23×C47C2×Q812yes—
46C23×C47C2411yescharacteristic
47C22×D47—23no—
48C22×D47—23no—
49C22×D47—224no—
50C22×D47—412no—
51C22×D47—44no—
52C22×D47C2×D416yes—
53C22×D47C2×Q812yes—
54C22×D47C2×Q812yes—
55C22×D47#4116yes—
56C2×C4×C47—26no—
57C2×C4×C47—26no—
58C2×C4×C47—23no—
59C2×C4×C47C2×D416yes—
60C2×Dic47—26no—
61C2×Dic47—26no—
62C2×Dic47—23no—
63C2×Dic47C2×D416yes—
64C4×D47—224no—
65C4×D47—412no—
66C22×C47—26no—
67C22×C47—43no—
68C22×C47—41no—
69C22×C47C22×D413yes—
70C22×C47C22×Q811yescharacteristic
71C22×C47C2×#4113yes—
72C2×D47—26no—
73C2×D47—43no—
74C2×D47—41no—
75C2×D47—416no—
76C2×D47C22⋊Q8112yes—
77C2×D47#123112yes—
78C2×D47#12714yes—
79C4×C47—26no—
80C4×C47—43no—
81Dic47—26no—
82Dic47—43no—
83C2×#399—471nomaximal, Sylow
84C2×C47—42no—
85C2×C47C2×C22⋊Q813yes—
86C2×C47C2×#12313yes—
87C2×C47C2×#12711yescharacteristic
88D47—42no—
89D47#39918yesdirect product factor
90C22×C4⋊C4—473no—
91C22×C22⋊C4—473no—
92#399—473no—
93#399—473no—
94#399—471no—
95#399D4711yescharacteristic, direct product factor
96C2×#95—471no—
97C47C2×#39911yescharacteristic, complemented, Sylow
98C25—471no—
99C23×C4—473no—
100C23×C4—473no—
101C2×C4⋊C4—476no—
102C2×C4⋊C4—473no—
103C2×C4⋊C4—9412no—
104C2×C4⋊C4C2×D4713yescomplemented
105C2×C22⋊C4—473no—
106C2×C22⋊C4—473no—
107C2×C22⋊C4—473no—
108C2×C22⋊C4—9412no—
109C2×C22⋊C4C2×D4713yes—
110#95—473no—
111#95C2×D4711yescharacteristic, complemented
112C24—471no—
113C24—474no—
114C24—471no—
115C24—946no—
116C24—946no—
117C24C22×D4711yescharacteristic
118C22×C4—473no—
119C22×C4—4712no—
120C22×C4—473no—
121C22×C4—9412no—
122C22×C4—946no—
123C22×C4—9412no—
124C22×C4C22×D4713yes—
125C22×C4C22×D4713yes—
126C4⋊C4—26no—
127C4⋊C4—9412no—
128C4⋊C4—946no—
129C22⋊C4—26no—
130C22⋊C4—946no—
131C22⋊C4—946no—
132C22⋊C4—946no—
133C23—23no—
134C23—23no—
135C23—476no—
136C23—472no—
137C23—476no—
138C23—472no—
139C23—9424no—
140C23—943no—
141C23—943no—
142C23—18812no—
143C23—1884no—
144C23Q8×D4712yes—
145C23C23×D4711yescharacteristic
146C2×C4—26no—
147C2×C4—23no—
148C2×C4—26no—
149C2×C4—476no—
150C2×C4—9424no—
151C2×C4—946no—
152C2×C4—943no—
153C2×C4—946no—
154C2×C4—18812no—
155C2×C4D4×D4716yes—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—4712no—
160C22—4712no—
161C22—474no—
162C22—946no—
163C22—18816no—
164C22—1883no—
165C22—1881no—
166C22C2×D4×D4713yes—
167C22C2×Q8×D4711yescharacteristic
168C22#41×D4713yes—
169C4—26no—
170C4—43no—
171C4—946no—
172C4—1883no—
173C2—42no—
174C2—478no—
175C2—1882no—
176C2C22⋊Q8×D4713yes—
177C2#123×D4713yes—
178C2#127×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47C2×#399
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D47C2semidirect
3. #15689060C2semidirect
4. #15689059C2semidirect
5. #15689058C2semidirect
6. #95×D47C2semidirect
7. C47×#399C2semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×Dic47⋊C4C22semidirect
18. C47⋊#95C22semidirect
19. C2×C4⋊C4×C47C22semidirect
21. #95×C47C22semidirect
89. D47#399direct (N × H)
95. #399D47direct (N × H)
97. C47C2×#399semidirect
104. C2×C4⋊C4C2×D47semidirect
111. #95C2×D47semidirect