Finite Group Databasebeta

← #20242021

Subgroups — #20242021

Order 6016.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#15689672C211yesmaximal, characteristic
2#15689178C212yesmaximal, complemented
3#15688863C211yesmaximal, characteristic, complemented
4#15688862C212yesmaximal, complemented
5C47×#329C211yesmaximal, characteristic, complemented
6C2×#10625354C411yescharacteristic
7C2×#10625352C411yescharacteristic
8#13094022C411yescharacteristic
9#13094020C411yescharacteristic
10#13094012C2211yescharacteristic
11#13093997—22no—
12(C22⋊D47)⋊C4—22no—
13C42×D47C2211yescharacteristic
14Dic47⋊C8—22no—
15(C2×D47)⋊C8—22no—
16#13093935C2212yes—
17#124×C47C2211yescharacteristic
18#97×C47C2212yes—
19C2×Q8×C47C2×C411yescharacteristic
20C2×D4×C47C2×C411yescharacteristic
21C2×C22⋊D47—21no—
22C2×C22⋊D47—22no—
23C22×Dic47—21no—
24#10625354—42no—
25#10625352—42no—
26C2×D188—21no—
27C2×D188C2×C411yescharacteristic
28C2×C4×D47—21no—
29C2×C4×D47C2×C411yescharacteristic
30C2×C4×D47D412yes—
31C2×Dic94C2×C411yescharacteristic
32C2×C8×C47—22no—
33C22⋊C4×C47—22no—
34C42×C47C2311yescharacteristic
35(C2×D47)⋊C4—22no—
36Dic47⋊C4—22no—
37C4×Dic47C2×C411yescharacteristic
38C4×Dic47D412yes—
39C2×C47⋊C8—22no—
40C23×C47—21no—
41C22×D47—21no—
42C22×D47C22⋊C411yescharacteristic
43Q8×C47—41no—
44D4×C47—41no—
45C2×C4×C47—21no—
46C2×C4×C47C22×C411yescharacteristic
47C2×C4×C47C2×D412yes—
48C22⋊D47—44no—
49C22⋊D47—42no—
50C2×Dic47—21no—
51C2×Dic47—42no—
52C2×Dic47C22⋊C412yes—
53C2×Dic47C22⋊C411yescharacteristic
54D188—41no—
55D188—42no—
56C4×D47—22no—
57C4×D47—42no—
58C4×D47—42no—
59Dic94—41no—
60C8×C47—42no—
61C47⋊C8—42no—
62C22×C47—41no—
63C22×C47—42no—
64C22×C47C2×C22⋊C411yescharacteristic
65C2×D47—21no—
66C2×D47—22no—
67C2×D47—41no—
68C2×D47—42no—
69C4×C47—21no—
70C4×C47—22no—
71C4×C47—41no—
72Dic47—22no—
73Dic47—41no—
74Dic47#10012yes—
75#1536—471nomaximal, Sylow
76C2×C47—81no—
77C2×C47C2×#10011yescharacteristic
78C2×C47#42112yes—
79D47—41no—
80D47—81no—
81#532—471no—
82#432—472no—
83#329—471no—
84#329—472no—
85#329D4711yescharacteristic, complemented
86C47#153611yescharacteristic, complemented, Sylow
87C2×#41—471no—
88C2×#41—471no—
89C4⋊Q8—471no—
90#127—471no—
91#124—471no—
92#124C2×D4711yescharacteristic
93#121—942no—
94C4×D4—942no—
95C2×C42—471no—
96C4⋊C8—942no—
97C22⋊C8—942no—
98#97—472no—
99#97C2×D4712yes—
100#41—1882no—
101#41—1882no—
102C2×Q8—471no—
103C2×Q8C4×D4711yescharacteristic
104C2×D4—471no—
105C2×D4—941no—
106C2×D4—942no—
107C2×D4—941no—
108C2×D4C4×D4711yescharacteristic
109C22×C4—471no—
110C22×C4—472no—
111C22×C4—941no—
112C22×C4—941no—
113C2×C8—22no—
114C2×C8—942no—
115C4⋊C4—942no—
116C22⋊C4—22no—
117C22⋊C4—942no—
118C42—471no—
119C42—472no—
120C42C22×D4711yescharacteristic
121C23—21no—
122C23—471no—
123C23—941no—
124Q8—41no—
125Q8—1881no—
126D4—41no—
127D4—1881no—
128D4—1882no—
129D4—1884no—
130D4—1882no—
131C2×C4—21no—
132C2×C4—471no—
133C2×C4—472no—
134C2×C4—942no—
135C2×C4—941no—
136C2×C4—1882no—
137C2×C4—1882no—
138C2×C4—1882no—
139C2×C4C2×C4×D4711yescharacteristic
140C2×C4D4×D4712yes—
141C8—42no—
142C8—1882no—
143C22—41no—
144C22—42no—
145C22—941no—
146C22—942no—
147C22—1881no—
148C22—1882no—
149C22C22⋊C4×D4711yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—472no—
154C4—942no—
155C4—1881no—
156C2—81no—
157C2—3761no—
158C2—1881no—
159C2#100×D4711yescharacteristic
160C2#1568913812yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47C2×C22⋊C4
hypercenter#329D47
hypocenterC47#1536
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. #15689178C2semidirect
3. #15688863C2semidirect
4. #15688862C2semidirect
5. C47×#329C2semidirect
85. #329D47semidirect
86. C47#1536semidirect