Finite Group Databasebeta

← #20241966

Subgroups — #20241966

Order 6016.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#15688991C211yesmaximal, 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—
16C47⋊#95—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—21no—
48C23×C47C2×D411yescharacteristic
49C22×D47—21no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47C22⋊C411yescharacteristic
54C2×C4×C47C22⋊C411yescharacteristic
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22×C411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C22⋊D47—42no—
60C2×Dic47—21no—
61C2×Dic47—21no—
62C2×Dic47—21no—
63C2×Dic47—42no—
64C2×Dic47—42no—
65C2×Dic47—42no—
66D188—41no—
67C4×D47—42no—
68Dic94—41no—
69C8×C47—42no—
70C22×C47—21no—
71C22×C47—21no—
72C22×C47C2×C22⋊C411yescharacteristic
73C22×C47#13512yes—
74C2×D47—41no—
75C2×D47—41no—
76C2×D47—41no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83Dic47—41no—
84Dic47—41no—
85Dic47—41no—
86Dic47—82no—
87#1521—471nomaximal, Sylow
88C2×C47—22no—
89C2×C47#41011yescharacteristic
90C2×C47#41611yescharacteristic
91C2×C47#42111yescharacteristic
92D47—81no—
93#529—471no—
94#431D4711yescharacteristic, complemented
95#383—471no—
96#328—472no—
97#327—472no—
98C47#152111yescharacteristic, complemented, Sylow
99#126—941no—
100#125—471no—
101#124—471no—
102#123—941no—
103C22⋊Q8—471no—
104#121—471no—
105C4×Q8—471no—
106C4×D4—471no—
107C4×D4—941no—
108#117—941no—
109C2×C42C2×D4711yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D4712yes—
112C4×C8—21no—
113#95—472no—
114#95—941no—
115#95—941no—
116C2×Q8—471no—
117C2×D4—471no—
118C2×D4—941no—
119C22×C4—941no—
120C22×C4—942no—
121C22×C4D18811yescharacteristic
122C22×C4D18811yescharacteristic
123C22×C4C22×D4711yescharacteristic
124C2×C8—22no—
125C4⋊C4—471no—
126C4⋊C4—471no—
127C4⋊C4—941no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C22⋊C4—941no—
132C22⋊C4—941no—
133C22⋊C4—941no—
134C22⋊C4—941no—
135C22⋊C4—941no—
136C42—941no—
137C42C4×D4711yescharacteristic
138C42C4×D4711yescharacteristic
139C42C22⋊D4711yescharacteristic
140C42C22⋊D4711yescharacteristic
141C23—941no—
142C23C2×D18811yescharacteristic
143Q8—1881no—
144D4—1881no—
145D4—1882no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—941no—
150C2×C4—941no—
151C2×C4—941no—
152C2×C4—1882no—
153C2×C4—1882no—
154C2×C4—1882no—
155C2×C4—1882no—
156C2×C4(C2×D47)⋊C411yescharacteristic
157C2×C4(C2×D47)⋊C411yescharacteristic
158C2×C4(C2×D47)⋊C411yescharacteristic
159C2×C4(C2×D47)⋊C411yescharacteristic
160C2×C4C2×C4×D4711yescharacteristic
161C2×C4C2×C22⋊D4711yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—1881no—
166C22—1881no—
167C22—1881no—
168C22C2×(C2×D47)⋊C411yescharacteristic
169C22#1309404612yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—3762no—
177C4—1881no—
178C4—1881no—
179C4—1881no—
180C2—22no—
181C2—3761no—
182C2#1568909611yescharacteristic
183C2#1568912011yescharacteristic
184C2#1568913911yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#431C2
socleC22×C47C2×C22⋊C4
hypercenter#431D47
hypocenterC47#1521
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #15688991C2semidirect
3. #15688861C2semidirect
5. C47×#431C2semidirect
7. #13094016C4semidirect
8. #13094012C4semidirect
12. C4×Dic94C4semidirect
13. C4×D188C4semidirect
94. #431D47semidirect
98. C47#1521semidirect