Finite Group Databasebeta

← #20241874

Subgroups — #20241874

Order 6016.

238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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#15689176C211yesmaximal, characteristic, complemented
2#15688969C211yesmaximal, characteristic, complemented
3#15688860C212yesmaximal, complemented
4#15688857C212yesmaximal
5C47×#529C211yesmaximal, characteristic
6C2×C4×Dic47—21no—
7C4⋊(C47⋊C8)—21no—
8C22⋊(C47⋊C8)C2212yes—
9C4×C47⋊C8—21no—
10C47⋊#95—21no—
11C47⋊#95C2212yes—
12#126×C47—21no—
13#125×C47C411yescharacteristic, complemented
14#124×C47C411yescharacteristic, complemented
15#123×C47—21no—
16C22⋊Q8×C47C2211yescharacteristic
17#121×C47C2211yescharacteristic
18C4×Q8×C47C411yescharacteristic, complemented
19C4×D4×C47—21no—
20C4×D4×C47C411yescharacteristic, complemented
21#117×C47—21no—
22C2×C42×C47C2211yescharacteristic
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47—21no—
25C2×D4×C47C2×C411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—22no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47C2×C411yescharacteristic
36C4⋊C4×C47C2×C411yescharacteristic
37C22⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C22⋊C4×C47—21no—
42C42×C47—21no—
43C42×C47C2×C411yescharacteristic
44C42×C47C2×C411yescharacteristic
45C42×C47D411yescharacteristic
46C42×C47D411yescharacteristic
47C4×Dic47—24no—
48C2×C47⋊C8—22no—
49C23×C47—21no—
50C23×C47C2×D411yescharacteristic
51Q8×C47—41no—
52D4×C47—41no—
53D4×C47—42no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—41no—
60C2×C4×C47—42no—
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×Dic47—24no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70C47⋊C8—42no—
71C22×C47—21no—
72C22×C47—21no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47—41no—
76C22×C47C2×C22⋊C411yescharacteristic
77C22×C47#13512yes—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—41no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47#10412yes—
87Dic47—44no—
88#1500—471nomaximal, Sylow
89C2×C47—22no—
90C2×C47—81no—
91C2×C47#41011yescharacteristic
92C2×C47#41611yescharacteristic
93C2×C47C2×#10411yescharacteristic
94#529D4711yescharacteristic
95#431—471no—
96#376—471no—
97#328—472no—
98#327—472no—
99C47#150011yescharacteristic, complemented, Sylow
100#126—21no—
101#125Dic4711yescharacteristic, complemented
102#124Dic4711yescharacteristic, complemented
103#123—21no—
104C22⋊Q8C2×D4711yescharacteristic
105#121C2×D4711yescharacteristic
106C4×Q8Dic4711yescharacteristic, complemented
107C4×D4—21no—
108C4×D4Dic4711yescharacteristic, complemented
109#117—21no—
110C2×C42—941no—
111C2×C42C2×D4711yescharacteristic
112C4⋊C8—941no—
113C22⋊C8—472no—
114C4×C8—941no—
115#95—472no—
116#95—941no—
117C2×Q8C2×Dic4711yescharacteristic
118C2×D4—21no—
119C2×D4C2×Dic4711yescharacteristic
120C22×C4—21no—
121C22×C4—942no—
122C22×C4C22⋊D4711yescharacteristic
123C22×C4C22⋊D4711yescharacteristic
124C22×C4C22×D4711yescharacteristic
125C2×C8—942no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4C2×Dic4711yescharacteristic
131C4⋊C4C2×Dic4711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C42—21no—
138C42—944no—
139C42C2×Dic4711yescharacteristic
140C42C2×Dic4711yescharacteristic
141C42C22⋊D4711yescharacteristic
142C42C22⋊D4711yescharacteristic
143C23—21no—
144C23C2×C22⋊D4711yescharacteristic
145Q8—41no—
146D4—41no—
147D4—42no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—944no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4C22⋊Dic4711yescharacteristic
159C2×C4C22⋊Dic4711yescharacteristic
160C2×C4C22⋊Dic4711yescharacteristic
161C2×C4C22⋊Dic4711yescharacteristic
162C2×C4C22×Dic4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—1882no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×C22⋊Dic4711yescharacteristic
171C22#1309404412yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—41no—
179C4—41no—
180C4—1884no—
181C4#1309395112yes—
182C2—22no—
183C2—81no—
184C2#1568909711yescharacteristic
185C2#1568911911yescharacteristic
186C2C2×#1309395111yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#529C2
socleC22×C47C2×C22⋊C4
hypercenter#529D47
hypocenterC47#1500
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #15689176C2semidirect
2. #15688969C2semidirect
3. #15688860C2semidirect
13. #125×C47C4semidirect
14. #124×C47C4semidirect
18. C4×Q8×C47C4semidirect
20. C4×D4×C47C4semidirect
99. C47#1500semidirect
101. #125Dic47semidirect
102. #124Dic47semidirect
106. C4×Q8Dic47semidirect
108. C4×D4Dic47semidirect