Finite Group Databasebeta

← #20244643

Subgroups — #20244643

Order 6016.

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

normal subgroups only

This group has 296 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
1C22×#10625334C211yesmaximal, characteristic
2#15689150C211yesmaximal, characteristic, complemented
3#15689127C211yesmaximal, characteristic, complemented
4C2×#13093941C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C47×#418C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625334—22no—
10C2×#10625334—22no—
11C2×#10625334—22no—
12C2×#10625329C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14C22×C47⋊C8C2211yescharacteristic
15C4⋊(C47⋊C8)—22no—
16#13093944—22no—
17#13093941—22no—
18#13093940—22no—
19C22×D4×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21#117×C47C2211yescharacteristic
22#102×C47—22no—
23C24×C47—21no—
24C23×D47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47D412yes—
31C22×C4×C47C2311yescharacteristic
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188D412yes—
38M16×C47—21no—
39M16×C47—21no—
40C2×C8×C47—21no—
41C4⋊C4×C47D412yes—
42C22⋊C4×C47—21no—
43C42×C47—21no—
44#10625334—28no—
45#10625329—21no—
46#10625329—21no—
47#10625329—21no—
48#10625329—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8D412yes—
54C23×C47—22no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47—82no—
58C23×C47#4111yescharacteristic
59C22×D47—22no—
60C22×D47—41no—
61C22×D47—41no—
62C22×D47—82no—
63D4×C47—22no—
64D4×C47—22no—
65D4×C47—41no—
66D4×C47—41no—
67C2×C4×C47—22no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74D188—22no—
75D188—22no—
76D188—41no—
77D188—41no—
78C8×C47—41no—
79C47⋊C8—22no—
80C47⋊C8—41no—
81C47⋊C8—41no—
82C22×C47—22no—
83C22×C47—42no—
84C22×C47—82no—
85C22×C47—82no—
86C22×C47—82no—
87C22×C47#12111yescharacteristic
88C22×C47#12311yescharacteristic
89C22×C47#12311yescharacteristic
90C2×D47—42no—
91C2×D47—82no—
92C2×D47—82no—
93C2×D47—82no—
94C4×C47—42no—
95C4×C47#12011yescharacteristic
96C4×C47#12111yescharacteristic
97C4×C47#12111yescharacteristic
98C4×C47#12411yescharacteristic
99#2045—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47—82no—
103C2×C47#39411yescharacteristic
104C2×C47#47212yes—
105D47—82no—
106C22×D8—471no—
107#424—471no—
108#418—471no—
109#418D4711yescharacteristic, complemented
110C2×#100—471no—
111C2×#100—471no—
112#341—471no—
113C47#204511yescharacteristic, complemented, Sylow
114C22×D4—471no—
115C22×D4C2×D4711yescharacteristic
116C2×D8—942no—
117C2×D8—942no—
118C2×D8—942no—
119C2×M16—471no—
120C2×M16—471no—
121C2×M16C2×D4711yescharacteristic
122C22×C8—471no—
123#117C2×D4711yescharacteristic
124C4⋊C8—942no—
125#102—22no—
126#102—942no—
127#100—942no—
128#100—942no—
129C24—21no—
130C24—941no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—472no—
137C2×D4—941no—
138C2×D4—941no—
139C2×D4—941no—
140C2×D4—941no—
141C2×D4—941no—
142C2×D4D18812yes—
143C22×C4C22×D4711yescharacteristic
144D8—948no—
145M16—21no—
146M16—21no—
147M16—941no—
148M16—941no—
149M16—941no—
150M16—941no—
151C2×C8—21no—
152C2×C8—472no—
153C2×C8—941no—
154C2×C8—941no—
155C2×C8—941no—
156C2×C8—941no—
157C4⋊C4C22⋊D4712yes—
158C22⋊C4—21no—
159C42—21no—
160C23—22no—
161C23—41no—
162C23—41no—
163C23—82no—
164C23—942no—
165C23—3762no—
166C23—1881no—
167C23—1881no—
168C23#1062535211yescharacteristic
169D4—22no—
170D4—22no—
171D4—41no—
172D4—41no—
173D4—942no—
174D4—942no—
175D4—1881no—
176D4—1881no—
177C2×C4—22no—
178C2×C4C2×D18811yescharacteristic
179C2×C4#1062535011yescharacteristic
180C2×C4D4×D4711yescharacteristic
181C2×C4D4×D4711yescharacteristic
182C2×C4#1062535211yescharacteristic
183C2×C4C2×C22⋊D4711yescharacteristic
184C8—41no—
185C8—942no—
186C8—1881no—
187C8—1881no—
188C22—22no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—3762no—
194C22—3762no—
195C22—3762no—
196C22—1882no—
197C22#1309399611yescharacteristic
198C22#1309400611yescharacteristic
199C22#1309400811yescharacteristic
200C4—42no—
201C4#1309399411yescharacteristic
202C4#1309399511yescharacteristic
203C4#1309399811yescharacteristic
204C4#1309401011yescharacteristic
205C2—21no—
206C2—21no—
207C2—82no—
208C2—3762no—
209C2#1568903911yescharacteristic
210C2#1568939112yes—
subgroupG/H
centerC22#13093996
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#418C2
socleC22×C47#121
hypercenter#418D47
hypocenterC47#2045
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #15689150C2semidirect
3. #15689127C2semidirect
4. C2×#13093941C2semidirect
5. C2×#13093940C2semidirect
6. #15688887C2semidirect
7. C47×#418C2semidirect
109. #418D47semidirect
113. C47#2045semidirect