Finite Group Databasebeta

← #20241875

Subgroups — #20241875

Order 6016.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689657C211yesmaximal, characteristic
2#15688969C211yesmaximal, characteristic, complemented
3#15688861C212yesmaximal, complemented
4#15688858C212yesmaximal
5C47×#431C211yesmaximal, characteristic, complemented
6#13094018—21no—
7#13094016C411yescharacteristic, complemented
8#13094012C411yescharacteristic, complemented
9#13094007—21no—
10#13094003C2211yescharacteristic
11#13093998C2211yescharacteristic
12C4×Dic94C411yescharacteristic, complemented
13C4×D188C411yescharacteristic, complemented
14C4×C22⋊D47—21no—
15#13093981—21no—
16C2×C4×Dic47—21no—
17C47⋊#95—21no—
18C47⋊#95C2212yes—
19C2×C42×C47C2211yescharacteristic
20C4⋊C8×C47—21no—
21C22⋊C8×C47C2212yes—
22C4×C8×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—21no—
27C22×Dic47—22no—
28C2×D188C2×C411yescharacteristic
29C2×C4×D47—21no—
30C2×Dic94C2×C411yescharacteristic
31C2×C8×C47—22no—
32C42×C47C2×C411yescharacteristic
33C42×C47C2×C411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36C22⋊Dic47—21no—
37(C2×D47)⋊C4—21no—
38(C2×D47)⋊C4—21no—
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47C2×C411yescharacteristic
42C4⋊Dic47C2×C411yescharacteristic
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—24no—
48C4×Dic47—21no—
49C23×C47C2×D411yescharacteristic
50C22×D47—21no—
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—41no—
54C2×C4×C47C22⋊C411yescharacteristic
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C22⋊D47—42no—
61C2×Dic47—24no—
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—42no—
66C2×Dic47—42no—
67D188—41no—
68C4×D47—42no—
69Dic94—41no—
70C8×C47—42no—
71C22×C47—21no—
72C22×C47—21no—
73C22×C47C2×C22⋊C411yescharacteristic
74C22×C47#13512yes—
75C2×D47—41no—
76C2×D47—41no—
77C2×D47—41no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47#10412yes—
84Dic47—44no—
85Dic47—41no—
86Dic47—41no—
87Dic47—41no—
88#1500—471nomaximal, Sylow
89C2×C47—22no—
90C2×C47#41011yescharacteristic
91C2×C47#41611yescharacteristic
92C2×C47C2×#10411yescharacteristic
93D47—81no—
94#529—471no—
95#431D4711yescharacteristic, complemented
96#376—471no—
97#328—472no—
98#327—472no—
99C47#150011yescharacteristic, complemented, Sylow
100#126—941no—
101#125—471no—
102#124—471no—
103#123—941no—
104C22⋊Q8—471no—
105#121—471no—
106C4×Q8—471no—
107C4×D4—471no—
108C4×D4—941no—
109#117—941no—
110C2×C42—941no—
111C2×C42C2×D4711yescharacteristic
112C4⋊C8—21no—
113C22⋊C8C2×D4712yes—
114C4×C8—21no—
115#95—472no—
116#95—941no—
117C2×Q8—471no—
118C2×D4—471no—
119C2×D4—941no—
120C22×C4—942no—
121C22×C4—941no—
122C22×C4D18811yescharacteristic
123C22×C4D18811yescharacteristic
124C22×C4C22×D4711yescharacteristic
125C2×C8—22no—
126C4⋊C4—471no—
127C4⋊C4—471no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C22⋊C4—941no—
133C22⋊C4—941no—
134C22⋊C4—941no—
135C22⋊C4—941no—
136C22⋊C4—941no—
137C42—944no—
138C42—941no—
139C42C4×D4711yescharacteristic
140C42C4×D4711yescharacteristic
141C42C22⋊D4711yescharacteristic
142C42C22⋊D4711yescharacteristic
143C23—941no—
144C23C2×D18811yescharacteristic
145Q8—1881no—
146D4—1881no—
147D4—1882no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—944no—
152C2×C4—941no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—1882no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4(C2×D47)⋊C411yescharacteristic
159C2×C4(C2×D47)⋊C411yescharacteristic
160C2×C4(C2×D47)⋊C411yescharacteristic
161C2×C4(C2×D47)⋊C411yescharacteristic
162C2×C4C2×C4×D4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—1881no—
168C22—1881no—
169C22—1881no—
170C22C2×(C2×D47)⋊C411yescharacteristic
171C22#1309404612yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—1884no—
178C4—1881no—
179C4—1881no—
180C4—1881no—
181C4#1309395012yes—
182C2—22no—
183C2—3761no—
184C2#1568909611yescharacteristic
185C2#1568912011yescharacteristic
186C2C2×#1309395011yescharacteristic
subgroupG/H
centerC2×C4(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#431C2
socleC22×C47C2×C22⋊C4
hypercenter#431D47
hypocenterC47#1500
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #15688969C2semidirect
3. #15688861C2semidirect
5. C47×#431C2semidirect
7. #13094016C4semidirect
8. #13094012C4semidirect
12. C4×Dic94C4semidirect
13. C4×D188C4semidirect
95. #431D47semidirect
99. C47#1500semidirect