Finite Group Databasebeta

← #20244646

Subgroups — #20244646

Order 6016.

276 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 71 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#15689149C211yesmaximal, characteristic, complemented
2#15689132C211yesmaximal, characteristic, complemented
3#15689128C211yesmaximal, characteristic
4C2×#13093943C211yesmaximal, characteristic, complemented
5C2×#13093941C211yesmaximal, characteristic
6#15688888C211yesmaximal, characteristic, complemented
7C22×SD16×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13093983C2211yescharacteristic
12Dic47⋊C8—22no—
13#13093948—22no—
14#13093945—22no—
15#13093943—22no—
16#13093941—22no—
17C22×Q8×C47C2211yescharacteristic
18C22×D4×C47C2211yescharacteristic
19C2×SD16×C47—22no—
20C2×SD16×C47—22no—
21C2×SD16×C47—22no—
22C22×C8×C47C2211yescharacteristic
23C24×C47—21no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47D412yes—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47D412yes—
36C22×C4×C47—21no—
37C22×C4×C47C2311yescharacteristic
38SD16×C47—28no—
39C2×C8×C47—21no—
40C2×C8×C47—21no—
41C2×C8×C47D412yes—
42C22⋊Dic47—21no—
43C4⋊Dic47D412yes—
44C4×Dic47—21no—
45#10625329—21no—
46#10625329—21no—
47#10625329—21no—
48#10625329—21no—
49#10625329—21no—
50#10625329—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47—22no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47—82no—
58C23×C47#4111yescharacteristic
59Q8×C47—22no—
60Q8×C47—22no—
61Q8×C47—41no—
62Q8×C47—41no—
63D4×C47—22no—
64D4×C47—22no—
65D4×C47—41no—
66D4×C47—41no—
67C2×C4×C47—22no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×Dic47—22no—
77C8×C47—22no—
78C47⋊C8—41no—
79C47⋊C8—41no—
80C47⋊C8—41no—
81C22×C47—22no—
82C22×C47—42no—
83C22×C47—82no—
84C22×C47—82no—
85C22×C47—82no—
86C22×C47#12111yescharacteristic
87C22×C47#12311yescharacteristic
88C22×C47#12311yescharacteristic
89C4×C47—42no—
90C4×C47#12011yescharacteristic
91C4×C47#12111yescharacteristic
92C4×C47#12111yescharacteristic
93C4×C47#12411yescharacteristic
94Dic47—42no—
95#2046—471nomaximal, Sylow
96C2×C47—21no—
97C2×C47—21no—
98C2×C47—82no—
99C2×C47#39411yescharacteristic
100C2×C47#47112yes—
101C22×SD16D4711yescharacteristic
102#424—471no—
103#419—471no—
104#418—471no—
105C2×#101—471no—
106C2×#100—471no—
107#341—471no—
108C47#204611yescharacteristic, complemented, Sylow
109C22×Q8C2×D4711yescharacteristic
110C22×D4C2×D4711yescharacteristic
111C2×SD16—22no—
112C2×SD16—22no—
113C2×SD16—22no—
114C2×M16—471no—
115C2×M16—471no—
116C2×M16—471no—
117C22×C8C2×D4711yescharacteristic
118#117—471no—
119C4⋊C8—942no—
120#103—942no—
121#102—942no—
122#101—942no—
123#100—942no—
124C24—21no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8C22⋊D4712yes—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4C22⋊D4712yes—
137C22×C4—21no—
138C22×C4C22×D4711yescharacteristic
139SD16—28no—
140M16—941no—
141M16—941no—
142M16—941no—
143M16—941no—
144M16—941no—
145M16—941no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—941no—
149C2×C8—941no—
150C2×C8—941no—
151C2×C8C22⋊D4712yes—
152C4⋊C4—472no—
153C22⋊C4—941no—
154C42—941no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—82no—
159C23#1062535211yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164D4—22no—
165D4—22no—
166D4—41no—
167D4—41no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—942no—
172C2×C4D4×D4711yescharacteristic
173C2×C4#1062535211yescharacteristic
174C2×C4#1062535211yescharacteristic
175C2×C4C2×C22⋊D4711yescharacteristic
176C2×C4C2×C22⋊D4711yescharacteristic
177C2×C4C2×C22⋊D4711yescharacteristic
178C8—22no—
179C8—1881no—
180C8—1881no—
181C8—1881no—
182C22—22no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22#1309399511yescharacteristic
188C22#1309400511yescharacteristic
189C22#1309400511yescharacteristic
190C4—42no—
191C4—1882no—
192C4#1309399311yescharacteristic
193C4#1309399611yescharacteristic
194C4#1309399611yescharacteristic
195C4#1309401111yescharacteristic
196C2—21no—
197C2—21no—
198C2—82no—
199C2#1568903711yescharacteristic
200C2#1568938312yes—
subgroupG/H
centerC22#13093995
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC22×SD16×C47C2
socleC22×C47#121
hypercenterC22×SD16D47
hypocenterC47#2046
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. #15689149C2semidirect
2. #15689132C2semidirect
4. C2×#13093943C2semidirect
6. #15688888C2semidirect
108. C47#2046semidirect