Finite Group Databasebeta

← #396×D47 #20246607

Subgroups — #396×D47 #20246607

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#15689047C211yesmaximal, characteristic, complemented
4#15689046C213yesmaximal, complemented
5#15689045C213yesmaximal, complemented
6#95×D47C211yesmaximal, characteristic, complemented
7C47×#396C211yesmaximal, characteristic, complemented
8C24×D47C2211yescharacteristic
9C22×C4×D47C2213yes—
10C22×C4×D47C2213yes—
11C2×C4⋊Dic47C2213yescomplemented
12C2×Dic47⋊C4C2213yescomplemented
13C2×Dic47⋊C4C2213yescomplemented
14C4⋊C4×D47—212no—
15C2×C22⋊Dic47C2213yes—
16C2×(C2×D47)⋊C4C2213yes—
17C2×(C2×D47)⋊C4C2213yes—
18C22⋊C4×D47—212no—
19C47⋊#95C2213yescomplemented
20C2×C4⋊C4×C47C2213yescomplemented
21C2×C22⋊C4×C47C2213yes—
22#95×C47C2211yescharacteristic, complemented
23C24×C47C2311yescharacteristic
24C23×D47—26no—
25C23×D47—26no—
26C23×D47Q814yes—
27C23×D47C2311yescharacteristic
28C23×D47C2311yescharacteristic
29C22×C4×C47C2313yes—
30C22×C4×C47C2313yes—
31C22×Dic47C2313yes—
32C22×Dic47C2313yes—
33C2×C4×D47—26no—
34C2×C4×D47—26no—
35C2×C4×D47—26no—
36C2×C4×D47—26no—
37C2×C4×D47—26no—
38C2×C4×D47D4112yes—
39C4⋊C4×C47—26no—
40C22⋊C4×C47—26no—
41C22⋊Dic47—26no—
42(C2×D47)⋊C4—26no—
43(C2×D47)⋊C4—26no—
44C4⋊Dic47—26no—
45Dic47⋊C4—26no—
46Dic47⋊C4—26no—
47C23×C47—23no—
48C23×C47—23no—
49C23×C47C2×Q812yes—
50C23×C47C2411yescharacteristic
51C22×D47—23no—
52C22×D47—23no—
53C22×D47—224no—
54C22×D47—412no—
55C22×D47—44no—
56C22×D47C2×D416yes—
57C22×D47C2×Q812yes—
58C22×D47C2×Q812yes—
59C22×D47#4116yes—
60C2×C4×C47—23no—
61C2×C4×C47—23no—
62C2×C4×C47—23no—
63C2×C4×C47—23no—
64C2×C4×C47—23no—
65C2×C4×C47C2×D416yes—
66C2×Dic47—23no—
67C2×Dic47—23no—
68C2×Dic47—23no—
69C2×Dic47—23no—
70C2×Dic47—23no—
71C2×Dic47C2×D416yes—
72C4×D47—224no—
73C4×D47—412no—
74C22×C47—26no—
75C22×C47—43no—
76C22×C47—41no—
77C22×C47C22×D413yes—
78C22×C47C22×Q811yescharacteristic
79C22×C47C2×#4113yes—
80C2×D47—26no—
81C2×D47—43no—
82C2×D47—41no—
83C2×D47—416no—
84C2×D47#121112yes—
85C2×D47C22⋊Q8112yes—
86C2×D47#12614yes—
87C4×C47—26no—
88C4×C47—43no—
89Dic47—26no—
90Dic47—43no—
91C2×#396—471nomaximal, Sylow
92C2×C47—42no—
93C2×C47C2×#12113yes—
94C2×C47C2×C22⋊Q813yes—
95C2×C47C2×#12611yescharacteristic
96D47—42no—
97D47#39618yesdirect product factor
98C22×C4⋊C4—473no—
99C22×C22⋊C4—473no—
100#396—473no—
101#396—473no—
102#396—471no—
103#396D4711yescharacteristic, direct product factor
104C2×#95—471no—
105C47C2×#39611yescharacteristic, complemented, Sylow
106C25—471no—
107C23×C4—473no—
108C23×C4—473no—
109C2×C4⋊C4—473no—
110C2×C4⋊C4—473no—
111C2×C4⋊C4—473no—
112C2×C4⋊C4—9412no—
113C2×C4⋊C4C2×D4713yescomplemented
114C2×C22⋊C4—473no—
115C2×C22⋊C4—473no—
116C2×C22⋊C4—473no—
117C2×C22⋊C4—9412no—
118C2×C22⋊C4C2×D4713yes—
119#95—473no—
120#95C2×D4711yescharacteristic, complemented
121C24—471no—
122C24—474no—
123C24—471no—
124C24—946no—
125C24—946no—
126C24C22×D4711yescharacteristic
127C22×C4—473no—
128C22×C4—4712no—
129C22×C4—473no—
130C22×C4—946no—
131C22×C4—946no—
132C22×C4—946no—
133C22×C4—946no—
134C22×C4—946no—
135C22×C4C22×D4713yes—
136C22×C4C22×D4713yes—
137C4⋊C4—26no—
138C4⋊C4—946no—
139C4⋊C4—946no—
140C4⋊C4—946no—
141C22⋊C4—26no—
142C22⋊C4—946no—
143C22⋊C4—946no—
144C22⋊C4—946no—
145C23—23no—
146C23—23no—
147C23—476no—
148C23—472no—
149C23—476no—
150C23—472no—
151C23—9424no—
152C23—943no—
153C23—943no—
154C23—18812no—
155C23—1884no—
156C23Q8×D4712yes—
157C23C23×D4711yescharacteristic
158C2×C4—23no—
159C2×C4—23no—
160C2×C4—23no—
161C2×C4—23no—
162C2×C4—23no—
163C2×C4—476no—
164C2×C4—9424no—
165C2×C4—943no—
166C2×C4—943no—
167C2×C4—943no—
168C2×C4—943no—
169C2×C4—943no—
170C2×C4—18812no—
171C2×C4D4×D4716yes—
172C22—26no—
173C22—43no—
174C22—41no—
175C22—4712no—
176C22—4712no—
177C22—474no—
178C22—946no—
179C22—18816no—
180C22—1883no—
181C22—1881no—
182C22C2×D4×D4713yes—
183C22C2×Q8×D4711yescharacteristic
184C22#41×D4713yes—
185C4—26no—
186C4—43no—
187C4—946no—
188C4—1883no—
189C2—42no—
190C2—478no—
191C2—1882no—
192C2#121×D4713yes—
193C2C22⋊Q8×D4713yes—
194C2#126×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47C2×#396
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D47C2semidirect
3. #15689047C2semidirect
4. #15689046C2semidirect
5. #15689045C2semidirect
6. #95×D47C2semidirect
7. C47×#396C2semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×Dic47⋊C4C22semidirect
13. C2×Dic47⋊C4C22semidirect
19. C47⋊#95C22semidirect
20. C2×C4⋊C4×C47C22semidirect
22. #95×C47C22semidirect
97. D47#396direct (N × H)
103. #396D47direct (N × H)
105. C47C2×#396semidirect
113. C2×C4⋊C4C2×D47semidirect
120. #95C2×D47semidirect