Finite Group Databasebeta

← #20242453

Subgroups — #20242453

Order 6016.

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

normal subgroups only

This group has 278 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#15689499C211yesmaximal, characteristic, complemented
2#15689323C211yesmaximal, characteristic, complemented
3#15689318C211yesmaximal, characteristic, complemented
4#15688867C211yesmaximal, characteristic, complemented
5Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×#550C211yesmaximal, characteristic, complemented
8C2×#10625336—21no—
9C2×#10625334—22no—
10C2×#10625334—21no—
11#13094021C2211yescharacteristic
12C4⋊(C47⋊C8)C2211yescharacteristic
13C4⋊(C47⋊C8)C2211yescharacteristic
14#13093944—21no—
15#13093944—21no—
16C4×C47⋊C8C2211yescharacteristic
17C2×#41×C47—21no—
18#127×C47—21no—
19#127×C47C2211yescharacteristic
20#121×C47—22no—
21#121×C47—21no—
22C4×Q8×C47C2211yescharacteristic
23C4×D4×C47—21no—
24C4×D4×C47C2211yescharacteristic
25#41×C47—42no—
26#41×C47—42no—
27C2×Q8×C47D411yescharacteristic
28C2×D4×C47—22no—
29C2×D4×C47—22no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47D411yescharacteristic
33C2×D4×C47D412yes—
34C22×C4×C47—22no—
35C22×C4×C47—21no—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47D411yescharacteristic
41C4⋊C4×C47D411yescharacteristic
42C22⋊C4×C47—22no—
43C22⋊C4×C47—21no—
44C42×C47—21no—
45C42×C47C2311yescharacteristic
46#10625336—42no—
47#10625334—44no—
48#10625334—42no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C23×C47—21no—
53C23×C47—22no—
54C22×D47—41no—
55Q8×C47—21no—
56Q8×C47D812yescomplemented
57D4×C47—21no—
58D4×C47—21no—
59D4×C47—42no—
60D4×C47—44no—
61D4×C47—41no—
62D4×C47—41no—
63D4×C47—41no—
64D4×C47—41no—
65D4×C47—82no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—44no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75D188—42no—
76D188—41no—
77D188—41no—
78D188—41no—
79D188—41no—
80C47⋊C8—22no—
81C47⋊C8—41no—
82C47⋊C8—41no—
83C22×C47—42no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47—42no—
87C22×C47—42no—
88C22×C47—41no—
89C22×C47#12011yescharacteristic
90C2×D47—81no—
91C2×D47—81no—
92C2×D47—81no—
93C4×C47—22no—
94C4×C47—21no—
95C4×C47—41no—
96C4×C47—41no—
97C4×C47C2×D811yescharacteristic
98C4×C47#13511yescharacteristic
99C4×C47AGL(1,ℤ/8)11yescharacteristic
100C4×C47AGL(1,ℤ/8)11yescharacteristic
101#1621—471nomaximal, Sylow
102C2×C47—81no—
103C2×C47—82no—
104C2×C47#44711yescharacteristic
105C2×C47#44911yescharacteristic
106C2×C47#45311yescharacteristic
107D47—161no—
108#550D4711yescharacteristic, complemented
109#493—471no—
110#460—471no—
111#459—471no—
112#331—471no—
113Q8⋊C8—471no—
114D4⋊C8—471no—
115C47#162111yescharacteristic, complemented, Sylow
116C2×#41—21no—
117C2×SD16—941no—
118C2×D8—941no—
119C2×D8—942no—
120#127—21no—
121#127—471no—
122#127C2×D4711yescharacteristic
123#121—22no—
124#121—21no—
125C4×Q8C2×D4711yescharacteristic
126C4×D4—21no—
127C4×D4C2×D4711yescharacteristic
128C4⋊C8—471no—
129C4⋊C8—471no—
130#102—941no—
131#102—941no—
132C4×C8—471no—
133#41—42no—
134#41—42no—
135C2×Q8C22⋊D4711yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—941no—
141C2×D4—941no—
142C2×D4—941no—
143C2×D4C22⋊D4711yescharacteristic
144C2×D4C22⋊D4712yes—
145C22×C4—22no—
146C22×C4—21no—
147SD16—1882no—
148D8—1884no—
149D8—1882no—
150C2×C8—941no—
151C2×C8—941no—
152C2×C8—941no—
153C4⋊C4—21no—
154C4⋊C4C22⋊D4711yescharacteristic
155C4⋊C4C22⋊D4711yescharacteristic
156C22⋊C4—22no—
157C22⋊C4—21no—
158C42—21no—
159C42C22×D4711yescharacteristic
160C23—21no—
161C23—22no—
162C23—1881no—
163Q8—21no—
164Q8#1062533412yescomplemented
165D4—21no—
166D4—21no—
167D4—42no—
168D4—44no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—82no—
174D4—1882no—
175D4—1881no—
176D4—1881no—
177D4—1881no—
178D4—1881no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—44no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4C2×C22⋊D4711yescharacteristic
186C2×C4C2×C22⋊D4711yescharacteristic
187C2×C4C2×C22⋊D4711yescharacteristic
188C8—942no—
189C8—1881no—
190C8—1881no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—42no—
195C22—42no—
196C22—41no—
197C22—3761no—
198C22—3761no—
199C22—3761no—
200C22#1309399311yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4C2×#1062533411yescharacteristic
206C4#1309404411yescharacteristic
207C4#1309404911yescharacteristic
208C4#1309405011yescharacteristic
209C2—81no—
210C2—82no—
211C2—7521no—
212C2#1568925711yescharacteristic
213C2#1568926811yescharacteristic
214C2#1568929111yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#550C2
socleC22×C47#120
hypercenter#550D47
hypocenterC47#1621
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #15689499C2semidirect
2. #15689323C2semidirect
3. #15689318C2semidirect
4. #15688867C2semidirect
5. Q8⋊(C47⋊C8)C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×#550C2semidirect
56. Q8×C47D8semidirect
108. #550D47semidirect
115. C47#1621semidirect
164. Q8#10625334semidirect