Finite Group Databasebeta

← #20241755

Subgroups — #20241755

Order 6016.

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

normal subgroups only

This group has 214 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
1C2×#13094018C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic, complemented
3#15688848C212yesmaximal, complemented
4#15688846C212yesmaximal
5C47×#431C211yesmaximal, characteristic, complemented
6#13094018—21no—
7#13094018—21no—
8#13094018—21no—
9#13094018—21no—
10C2×Dic47⋊C4C411yescharacteristic
11C2×Dic47⋊C4C411yescharacteristic
12C2×Dic47⋊C4C2211yescharacteristic
13C2×(C2×D47)⋊C4C411yescharacteristic
14C2×(C2×D47)⋊C4C411yescharacteristic
15C2×(C2×D47)⋊C4C2211yescharacteristic
16C4⋊(C47⋊C8)—21no—
17C22⋊(C47⋊C8)C2212yes—
18#13093935—21no—
19C2×C42×C47C2211yescharacteristic
20C4⋊C8×C47—21no—
21C22⋊C8×C47C2212yes—
22C4×C8×C47—21no—
23C23×D47C2×C411yescharacteristic
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C22×Dic47C2×C411yescharacteristic
28C22×Dic47C2×C411yescharacteristic
29C22×Dic47C2×C411yescharacteristic
30C2×C8×C47—22no—
31C42×C47D411yescharacteristic
32C42×C47D411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35(C2×D47)⋊C4—21no—
36(C2×D47)⋊C4—21no—
37(C2×D47)⋊C4—21no—
38(C2×D47)⋊C4—21no—
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41Dic47⋊C4—21no—
42Dic47⋊C4—21no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C2×C47⋊C8—22no—
48C23×C47C22×C411yescharacteristic
49C22×D47—21no—
50C22×D47—22no—
51C22×D47—41no—
52C22×D47—41no—
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C22⋊C411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—22no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C8×C47—42no—
69C47⋊C8—42no—
70C22×C47—21no—
71C22×C47—21no—
72C22×C47C2×C22⋊C411yescharacteristic
73C22×C47#13112yes—
74C2×D47—41no—
75C2×D47—41no—
76C2×D47—41no—
77C2×D47—82no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—21no—
84Dic47—41no—
85Dic47—41no—
86Dic47—41no—
87#1473—471nomaximal, Sylow
88C2×C47—22no—
89C2×C47#40811yescharacteristic
90C2×C47#41011yescharacteristic
91C2×C47#41311yescharacteristic
92D47—81no—
93C2×#126—471no—
94#432—471no—
95#431D4711yescharacteristic, complemented
96#324—472no—
97#323—472no—
98C47#147311yescharacteristic, complemented, Sylow
99#126—941no—
100#126—941no—
101#126—941no—
102#126—941no—
103C2×C4⋊C4—471no—
104C2×C4⋊C4—471no—
105C2×C4⋊C4—471no—
106C2×C22⋊C4—471no—
107C2×C22⋊C4—471no—
108C2×C22⋊C4—471no—
109C2×C42C2×D4711yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—941no—
112C22⋊C8—472no—
113C22⋊C8C2×D4712yes—
114#97—941no—
115C4×C8—21no—
116C24—471no—
117C22×C4—471no—
118C22×C4—471no—
119C22×C4—471no—
120C22×C4C4×D4711yescharacteristic
121C22×C4C4×D4711yescharacteristic
122C22×C4C22×D4711yescharacteristic
123C2×C8—22no—
124C2×C8—942no—
125C4⋊C4—941no—
126C4⋊C4—941no—
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—
136C22⋊C4—941no—
137C42D18811yescharacteristic
138C42D18811yescharacteristic
139C42C22⋊D4711yescharacteristic
140C42C22⋊D4711yescharacteristic
141C23—942no—
142C23—941no—
143C23—1881no—
144C23—1881no—
145C23C2×C4×D4711yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—941no—
150C2×C4—941no—
151C2×C4—941no—
152C2×C4—942no—
153C2×C4—1881no—
154C2×C4—1881no—
155C2×C4(C2×D47)⋊C411yescharacteristic
156C2×C4(C2×D47)⋊C411yescharacteristic
157C2×C4(C2×D47)⋊C411yescharacteristic
158C2×C4(C2×D47)⋊C411yescharacteristic
159C2×C4C2×D18811yescharacteristic
160C2×C4C2×C22⋊D4711yescharacteristic
161C8—42no—
162C8—1882no—
163C22—21no—
164C22—21no—
165C22—3762no—
166C22—1881no—
167C22—1881no—
168C22—1881no—
169C22C2×(C2×D47)⋊C411yescharacteristic
170C22#1309403012yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—1881no—
178C4—1881no—
179C4—1881no—
180C2—22no—
181C2—3761no—
182C2#1568908911yescharacteristic
183C2#1568909611yescharacteristic
184C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#431C2
socleC22×C47C2×C22⋊C4
hypercenter#431D47
hypocenterC47#1473
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #15689180C2semidirect
3. #15688848C2semidirect
5. C47×#431C2semidirect
95. #431D47semidirect
98. C47#1473semidirect