Finite Group Databasebeta

← #20242020

Subgroups — #20242020

Order 6016.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689180C211yesmaximal, characteristic, complemented
3#15688864C212yesmaximal, complemented
4#15688862C212yesmaximal, complemented
5C47×#432C211yesmaximal, characteristic, complemented
6#13094018—21no—
7#13094016C2211yescharacteristic
8#13094012C2211yescharacteristic
9#13094007—21no—
10#13094003C411yescharacteristic
11#13093998C411yescharacteristic
12C4×Dic94C411yescharacteristic
13C4×D188C411yescharacteristic
14C4×C22⋊D47—21no—
15#13093981—21no—
16C4⋊(C47⋊C8)—21no—
17C22⋊(C47⋊C8)—21no—
18#13093935C2212yes—
19C2×C42×C47C2211yescharacteristic
20C4⋊C8×C47—21no—
21C22⋊C8×C47—21no—
22#97×C47C2212yes—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C2×C22⋊D47—21no—
27C2×D188C2×C411yescharacteristic
28C2×C4×D47—21no—
29C2×Dic94C2×C411yescharacteristic
30C2×C8×C47—22no—
31C42×C47C2×C411yescharacteristic
32C42×C47D411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47C2311yescharacteristic
35C22⋊Dic47—21no—
36(C2×D47)⋊C4—21no—
37(C2×D47)⋊C4—21no—
38(C2×D47)⋊C4—21no—
39(C2×D47)⋊C4—21no—
40C4⋊Dic47C2×C411yescharacteristic
41C4⋊Dic47C2×C411yescharacteristic
42Dic47⋊C4—21no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—22no—
48C23×C47C22⋊C411yescharacteristic
49C22×D47—21no—
50C2×C4×C47—41no—
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×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C22⋊D47—42no—
60C2×Dic47—21no—
61C2×Dic47—21no—
62C2×Dic47—21no—
63D188—41no—
64C4×D47—42no—
65Dic94—41no—
66C8×C47—42no—
67C47⋊C8—42no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47C2×C22⋊C411yescharacteristic
72C2×D47—41no—
73C2×D47—41no—
74C2×D47—41no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81Dic47—41no—
82Dic47—41no—
83Dic47—41no—
84#1535—471nomaximal, Sylow
85C2×C47—41no—
86C2×C47#41311yescharacteristic
87C2×C47#42111yescharacteristic
88C2×C47#42111yescharacteristic
89D47—81no—
90#529—471no—
91#432—471no—
92#432D4711yescharacteristic, complemented
93#330—472no—
94#329—472no—
95C47#153511yescharacteristic, complemented, Sylow
96#126—941no—
97#125—471no—
98#124—471no—
99#123—941no—
100C22⋊Q8—471no—
101#121—471no—
102C4×Q8—471no—
103C4×D4—471no—
104C4×D4—941no—
105#117—941no—
106C2×C42C2×D4711yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—941no—
109C22⋊C8—21no—
110C22⋊C8—941no—
111#97—472no—
112#97C2×D4712yes—
113C2×Q8—471no—
114C2×D4—471no—
115C2×D4—941no—
116C22×C4—941no—
117C22×C4C4×D4711yescharacteristic
118C22×C4D18811yescharacteristic
119C22×C4C22⋊D4711yescharacteristic
120C2×C8—22no—
121C2×C8—942no—
122C4⋊C4—471no—
123C4⋊C4—471no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C4⋊C4—941no—
128C22⋊C4—941no—
129C22⋊C4—941no—
130C22⋊C4—941no—
131C22⋊C4—941no—
132C22⋊C4—941no—
133C42—941no—
134C42C4×D4711yescharacteristic
135C42D18811yescharacteristic
136C42C22⋊D4711yescharacteristic
137C42C22×D4711yescharacteristic
138C23—941no—
139C23(C2×D47)⋊C411yescharacteristic
140Q8—1881no—
141D4—1881no—
142D4—1882no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—941no—
147C2×C4—941no—
148C2×C4—941no—
149C2×C4—1882no—
150C2×C4(C2×D47)⋊C411yescharacteristic
151C2×C4(C2×D47)⋊C411yescharacteristic
152C2×C4(C2×D47)⋊C411yescharacteristic
153C2×C4C2×C4×D4711yescharacteristic
154C2×C4C2×D18811yescharacteristic
155C2×C4C2×C22⋊D4711yescharacteristic
156C8—42no—
157C8—1882no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—1881no—
162C22—1881no—
163C22—1881no—
164C22C2×(C2×D47)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—1881no—
172C4—1881no—
173C4—1881no—
174C2—41no—
175C2—3761no—
176C2#1568910511yescharacteristic
177C2#1568913911yescharacteristic
178C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1535
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #15689180C2semidirect
3. #15688864C2semidirect
4. #15688862C2semidirect
5. C47×#432C2semidirect
92. #432D47semidirect
95. C47#1535semidirect