Finite Group Databasebeta

← #20242066

Subgroups — #20242066

Order 6016.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689673C211yesmaximal, characteristic
2C2×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#15688870C212yesmaximal, complemented
4#15688866C212yesmaximal, complemented
5C47×#423C211yesmaximal, characteristic, complemented
6C2×#10625350—21no—
7C22×C47⋊C8—21no—
8#13094024C2211yescharacteristic
9#13094021C2211yescharacteristic
10#13094012—21no—
11#13093998—21no—
12#13093998C412yes—
13C4×D188—21no—
14C4×D188C412yes—
15C4⋊(C47⋊C8)—21no—
16C4⋊(C47⋊C8)C2212yes—
17C2×M16×C47—21no—
18C2×C42×C47C2211yescharacteristic
19C4⋊C8×C47—21no—
20C4⋊C8×C47C2212yes—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C2×C22⋊D47—22no—
25#10625350—42no—
26#10625350—42no—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188C2×C412yes—
30C2×C4×D47—22no—
31C2×Dic94—21no—
32M16×C47—42no—
33C2×C8×C47—22no—
34C42×C47C2×C411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47D411yescharacteristic
37C42×C47C2311yescharacteristic
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40C4⋊Dic47—21no—
41C4⋊Dic47C2×C412yes—
42C2×C47⋊C8—22no—
43C2×C47⋊C8—42no—
44C23×C47C22⋊C411yescharacteristic
45C22×D47—22no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—41no—
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47D812yes—
53C2×C4×C47SD1612yes—
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C22⋊D47—44no—
58C2×Dic47—22no—
59D188—42no—
60D188—41no—
61D188—41no—
62D188—41no—
63D188—41no—
64C4×D47—44no—
65Dic94—41no—
66Dic94—41no—
67C8×C47—42no—
68C47⋊C8—42no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47#10212yes—
72C22×C47C2×C22⋊C411yescharacteristic
73C2×D47—42no—
74C2×D47—42no—
75C2×D47—42no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47#10212yes—
80C4×C47C2×D811yescharacteristic
81C4×C47C2×SD1611yescharacteristic
82C4×C47AGL(1,ℤ/8)11yescharacteristic
83C4×C47#13711yescharacteristic
84Dic47—42no—
85#1547—471nomaximal, Sylow
86C2×C47—22no—
87C2×C47#41311yescharacteristic
88C2×C47C2×#10211yescharacteristic
89C2×C47#41711yescharacteristic
90D47—82no—
91#532—471no—
92#423D4711yescharacteristic, complemented
93C2×C4⋊C8—471no—
94#332—472no—
95#331—472no—
96C47#154711yescharacteristic, complemented, Sylow
97C2×#41—941no—
98C2×M16—21no—
99C22×C8—941no—
100C4⋊Q8—471no—
101#127—471no—
102#124—941no—
103#121—472no—
104#121—941no—
105C4×D4—472no—
106C4×D4—941no—
107C2×C42C2×D4711yescharacteristic
108C4⋊C8—21no—
109C4⋊C8—472no—
110C4⋊C8—941no—
111C4⋊C8C2×D4712yes—
112#41—1882no—
113#41—1882no—
114C2×Q8—941no—
115C2×D4—472no—
116C2×D4—942no—
117C2×D4—941no—
118C2×D4—941no—
119C22×C4—942no—
120C22×C4C4×D4711yescharacteristic
121C22×C4D18811yescharacteristic
122C22×C4C22⋊D4711yescharacteristic
123M16—42no—
124C2×C8—22no—
125C2×C8—942no—
126C2×C8—1882no—
127C4⋊C4—472no—
128C4⋊C4—941no—
129C22⋊C4—942no—
130C22⋊C4—942no—
131C42C4×D4711yescharacteristic
132C42D18811yescharacteristic
133C42C22⋊D4711yescharacteristic
134C42C22×D4711yescharacteristic
135C23—942no—
136C23(C2×D47)⋊C411yescharacteristic
137Q8—1881no—
138Q8—1881no—
139D4—1882no—
140D4—1884no—
141D4—1881no—
142D4—1881no—
143D4—1881no—
144D4—1881no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—942no—
149C2×C4—1884no—
150C2×C4(C2×D47)⋊C411yescharacteristic
151C2×C4(C2×D47)⋊C411yescharacteristic
152C2×C4(C2×D47)⋊C411yescharacteristic
153C2×C4#1062533412yes—
154C2×C4#1062533612yes—
155C2×C4C2×C4×D4711yescharacteristic
156C2×C4C2×D18811yescharacteristic
157C2×C4C2×C22⋊D4711yescharacteristic
158C8—42no—
159C8—1882no—
160C22—21no—
161C22—21no—
162C22—1882no—
163C22—1882no—
164C22—1882no—
165C22#1309394412yes—
166C22C2×(C2×D47)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—1882no—
171C4#1309394412yes—
172C4C2×#1062533411yescharacteristic
173C4C2×#1062533611yescharacteristic
174C4#1309405211yescharacteristic
175C4#1309405711yescharacteristic
176C2—22no—
177C2—3762no—
178C2#1568910511yescharacteristic
179C2C2×#1309394411yescharacteristic
180C2#1568912511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#423C2
socleC22×C47C2×C22⋊C4
hypercenter#423D47
hypocenterC47#1547
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C47⋊C8)C2semidirect
3. #15688870C2semidirect
4. #15688866C2semidirect
5. C47×#423C2semidirect
92. #423D47semidirect
96. C47#1547semidirect