Finite Group Databasebeta

← #329×D47 #20241967

Subgroups — #329×D47 #20241967

Order 6016.

284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 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#124×D47C211yesmaximal, characteristic
2#97×D47C212yesmaximal, complemented
3#15688863C211yesmaximal, characteristic, complemented
4#15688862C212yesmaximal, complemented
5C47×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D47C411yescharacteristic
7C2×D4×D47C411yescharacteristic
8C2×C8×D47—22no—
9#13094013C411yescharacteristic
10#13094012C2211yescharacteristic
11#13094011C411yescharacteristic
12#13094010—22no—
13C22⋊C4×D47—22no—
14C42×D47C2211yescharacteristic
15#13093935C2212yescomplemented
16#13093934—22no—
17#124×C47C2211yescharacteristic
18#97×C47C2212yescomplemented
19C23×D47—21no—
20C2×Q8×C47C2×C411yescharacteristic
21C2×D4×C47C2×C411yescharacteristic
22C2×C22⋊D47—21no—
23Q8×D47—42no—
24D4×D47—42no—
25C2×D188C2×C411yescharacteristic
26C2×C4×D47—21no—
27C2×C4×D47C2×C411yescharacteristic
28C2×C4×D47D412yes—
29C2×Dic94—21no—
30C2×Dic94C2×C411yescharacteristic
31C2×C8×C47—22no—
32C22⋊C4×C47—22no—
33C42×C47C2311yescharacteristic
34C22⋊Dic47—22no—
35(C2×D47)⋊C4—22no—
36(C2×D47)⋊C4—22no—
37C4×Dic47C2×C411yescharacteristic
38C4×Dic47D412yes—
39C2×C47⋊C8—22no—
40C8×D47—28no—
41C23×C47—21no—
42C22×D47—21no—
43C22×D47—42no—
44C22×D47—44no—
45C22×D47C22⋊C411yescharacteristic
46Q8×C47—41no—
47D4×C47—41no—
48C2×C4×C47—21no—
49C2×C4×C47C22×C411yescharacteristic
50C2×C4×C47C2×D412yes—
51C22⋊D47—42no—
52C2×Dic47—21no—
53C2×Dic47C22⋊C412yes—
54C2×Dic47C22⋊C411yescharacteristic
55D188—41no—
56C4×D47—22no—
57C4×D47—24no—
58C4×D47—42no—
59Dic94—42no—
60Dic94—41no—
61C8×C47—24no—
62C47⋊C8—24no—
63C22×C47—41no—
64C22×C47—42no—
65C22×C47C2×C22⋊C411yescharacteristic
66C2×D47—41no—
67C2×D47—42no—
68C2×D47—84no—
69C2×D47#10012yes—
70C2×D47#10414yes—
71C4×C47—21no—
72C4×C47—22no—
73C4×C47—41no—
74Dic47—21no—
75Dic47—22no—
76Dic47—41no—
77C2×#329—471nomaximal, Sylow
78C2×C47—81no—
79C2×C47C2×#10011yescharacteristic
80C2×C47C2×#10412yes—
81D47—81no—
82D47#32914yesdirect product factor
83C2×#124—471no—
84C2×#97—472no—
85#329—471no—
86#329—472no—
87#329D4711yescharacteristic, direct product factor
88C47C2×#32911yescharacteristic, complemented, Sylow
89C22×Q8—471no—
90C22×D4—471no—
91C22×C8—942no—
92#124—471no—
93#124—471no—
94#124—471no—
95#124—942no—
96#124C2×D4711yescharacteristic
97C2×C22⋊C4—942no—
98C2×C42—471no—
99#97—472no—
100#97—942no—
101#97C2×D4712yescomplemented
102C24—941no—
103C2×Q8—471no—
104C2×Q8—941no—
105C2×Q8—1882no—
106C2×Q8C4×D4711yescharacteristic
107C2×D4—471no—
108C2×D4—941no—
109C2×D4—1882no—
110C2×D4C4×D4711yescharacteristic
111C22×C4—471no—
112C22×C4—472no—
113C22×C4—941no—
114C2×C8—22no—
115C2×C8—948no—
116C2×C8—942no—
117C22⋊C4—22no—
118C22⋊C4—942no—
119C22⋊C4—942no—
120C22⋊C4—942no—
121C42—471no—
122C42—472no—
123C42C22×D4711yescharacteristic
124C23—21no—
125C23—471no—
126C23—941no—
127C23—1882no—
128C23—1884no—
129Q8—41no—
130Q8—1881no—
131Q8—1882no—
132D4—41no—
133D4—1881no—
134D4—1882no—
135C2×C4—21no—
136C2×C4—472no—
137C2×C4—471no—
138C2×C4—944no—
139C2×C4—942no—
140C2×C4—941no—
141C2×C4—1882no—
142C2×C4C2×C4×D4711yescharacteristic
143C2×C4D4×D4712yes—
144C8—24no—
145C8—944no—
146C22—41no—
147C22—42no—
148C22—472no—
149C22—474no—
150C22—3764no—
151C22—1881no—
152C22—1882no—
153C22C22⋊C4×D4711yescharacteristic
154C4—21no—
155C4—22no—
156C4—41no—
157C4—941no—
158C4—942no—
159C4—1881no—
160C2—81no—
161C2—474no—
162C2—3761no—
163C2#100×D4711yescharacteristic
164C2#104×D4712yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47C2×C22⋊C4
hypercenter#329D47
hypocenterC47C2×#329
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #97×D47C2semidirect
3. #15688863C2semidirect
4. #15688862C2semidirect
5. C47×#329C2semidirect
15. #13093935C22semidirect
18. #97×C47C22semidirect
82. D47#329direct (N × H)
87. #329D47direct (N × H)
88. C47C2×#329semidirect
101. #97C2×D47semidirect