Finite Group Databasebeta

← #20242460

Subgroups — #20242460

Order 6016.

236 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 61 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#15689497C211yesmaximal, characteristic, complemented
2#15689323C211yesmaximal, characteristic, complemented
3#15689318C211yesmaximal, characteristic
4#15688872C211yesmaximal, characteristic, complemented
5Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×#554C211yesmaximal, characteristic, complemented
8C2×#10625336—22no—
9C2×#10625336—21no—
10C2×#10625334—21no—
11#13094021C2211yescharacteristic
12C4⋊(C47⋊C8)C2211yescharacteristic
13C4⋊(C47⋊C8)C2211yescharacteristic
14#13093944—21no—
15#13093944—21no—
16C4×C47⋊C8C2211yescharacteristic
17C4⋊Q8×C47C2211yescharacteristic
18#125×C47—21no—
19C22⋊Q8×C47—21no—
20C22⋊Q8×C47—22no—
21C4×Q8×C47C2211yescharacteristic
22C4×D4×C47—21no—
23C4×D4×C47C2211yescharacteristic
24C2×C4⋊C4×C47—21no—
25C2×Q8×C47D411yescharacteristic
26C2×Q8×C47D412yes—
27C2×D4×C47D411yescharacteristic
28C22×C4×C47—22no—
29C22×C4×C47—21no—
30C2×D188—21no—
31C2×D188—21no—
32C2×D188—21no—
33C4⋊C4×C47—22no—
34C4⋊C4×C47—22no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47D411yescharacteristic
39C4⋊C4×C47D411yescharacteristic
40C22⋊C4×C47—22no—
41C22⋊C4×C47—21no—
42C42×C47—21no—
43C42×C47C2311yescharacteristic
44#10625336—44no—
45#10625336—42no—
46#10625334—42no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—21no—
51C22×D47—41no—
52Q8×C47—21no—
53Q8×C47—21no—
54Q8×C47—42no—
55D4×C47—21no—
56D4×C47SD1612yescomplemented
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—22no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—82no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67D188—42no—
68D188—41no—
69D188—41no—
70D188—41no—
71D188—41no—
72C47⋊C8—22no—
73C47⋊C8—41no—
74C47⋊C8—41no—
75C22×C47—22no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47#12011yescharacteristic
79C2×D47—81no—
80C2×D47—81no—
81C2×D47—81no—
82C4×C47—21no—
83C4×C47—41no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47—42no—
87C4×C47C2×SD1611yescharacteristic
88C4×C47#13511yescharacteristic
89C4×C47AGL(1,ℤ/8)11yescharacteristic
90C4×C47#13711yescharacteristic
91#1622—471nomaximal, Sylow
92C2×C47—42no—
93C2×C47#44811yescharacteristic
94C2×C47#44911yescharacteristic
95C2×C47#45311yescharacteristic
96D47—161no—
97#554D4711yescharacteristic, complemented
98#492—471no—
99#460—471no—
100#459—471no—
101#333—471no—
102Q8⋊C8—471no—
103D4⋊C8—471no—
104C47#162211yescharacteristic, complemented, Sylow
105C2×SD16—941no—
106C2×SD16—942no—
107C2×D8—941no—
108C4⋊Q8C2×D4711yescharacteristic
109#127—471no—
110#125—21no—
111C22⋊Q8—21no—
112C22⋊Q8—22no—
113C4×Q8C2×D4711yescharacteristic
114C4×D4—21no—
115C4×D4C2×D4711yescharacteristic
116C2×C4⋊C4—21no—
117C4⋊C8—471no—
118C4⋊C8—471no—
119#102—941no—
120#102—941no—
121C4×C8—471no—
122C2×Q8C22⋊D4711yescharacteristic
123C2×Q8C22⋊D4712yes—
124C2×D4—941no—
125C2×D4—941no—
126C2×D4—941no—
127C2×D4C22⋊D4711yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130SD16—1884no—
131SD16—1882no—
132D8—1882no—
133C2×C8—941no—
134C2×C8—941no—
135C2×C8—941no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4C22⋊D4711yescharacteristic
142C4⋊C4C22⋊D4711yescharacteristic
143C22⋊C4—22no—
144C22⋊C4—21no—
145C42—21no—
146C42C22×D4711yescharacteristic
147C23—21no—
148C23—1881no—
149Q8—21no—
150Q8—21no—
151Q8—42no—
152D4—21no—
153D4—1882no—
154D4—1881no—
155D4—1881no—
156D4—1881no—
157D4—1881no—
158D4#1062533612yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—82no—
166C2×C4C2×C22⋊D4711yescharacteristic
167C2×C4C2×C22⋊D4711yescharacteristic
168C2×C4C2×C22⋊D4711yescharacteristic
169C8—942no—
170C8—1881no—
171C8—1881no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—3761no—
176C22—3761no—
177C22—3761no—
178C22#1309399311yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—41no—
183C4—42no—
184C4C2×#1062533611yescharacteristic
185C4#1309404411yescharacteristic
186C4#1309404911yescharacteristic
187C4#1309405511yescharacteristic
188C2—42no—
189C2—7521no—
190C2#1568926211yescharacteristic
191C2#1568926811yescharacteristic
192C2#1568929111yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#554C2
socleC22×C47#120
hypercenter#554D47
hypocenterC47#1622
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #15689497C2semidirect
2. #15689323C2semidirect
4. #15688872C2semidirect
5. Q8⋊(C47⋊C8)C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×#554C2semidirect
56. D4×C47SD16semidirect
97. #554D47semidirect
104. C47#1622semidirect
158. D4#10625336semidirect