Finite Group Databasebeta

← #20245358

Subgroups — #20245358

Order 6016.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#15689924C211yesmaximal, characteristic
2#15689564C211yesmaximal, characteristic, complemented
3#15689395C211yesmaximal, characteristic, complemented
4#15688936C211yesmaximal, characteristic, complemented
5#15688931C211yesmaximal, characteristic, complemented
6#15688906C211yesmaximal, characteristic, complemented
7C2×SD32×C47C211yesmaximal, characteristic, complemented
8#13094069—21no—
9#13094055—21no—
10#13094050—21no—
11#13094048—22no—
12#13094046C2211yescharacteristic
13#13094043—21no—
14D8×D47—21no—
15#13094030C2211yescharacteristic
16#13093970—21no—
17#13093967—21no—
18#13093964C2211yescharacteristic, complemented
19#13093960C2211yescharacteristic, complemented
20#13093943—21no—
21C2×Q16×C47C2211yescharacteristic, complemented
22C2×D8×C47C2211yescharacteristic
23SD32×C47—22no—
24C2×C16×C47C2211yescharacteristic, complemented
25C2×Q8×C47—21no—
26C2×D4×C47—21no—
27C2×C22⋊D47—42no—
28#10625352—22no—
29#10625352—41no—
30D4×D47—22no—
31D4×D47—41no—
32#10625350—21no—
33#10625350D411yescharacteristic
34Q16×C47—21no—
35Q16×C47—21no—
36D8×C47—21no—
37D8×C47D412yes—
38C2×C8×C47C2311yescharacteristic
39#10625337—41no—
40#10625336—41no—
41#10625335—22no—
42#10625334—22no—
43#10625329—21no—
44#10625329D411yescharacteristic
45Dic188D411yescharacteristic
46D376D411yescharacteristic
47#10625325—21no—
48#10625324—21no—
49C8×D47—21no—
50C16×C47—21no—
51C47⋊C16—21no—
52C23×C47—41no—
53C22×D47—42no—
54Q8×C47—41no—
55Q8×C47—41no—
56D4×C47—22no—
57D4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C22⋊D47—21no—
61C22⋊D47—42no—
62C22⋊D47—42no—
63C22⋊D47—41no—
64C2×Dic47—42no—
65D188—21no—
66D188D811yescharacteristic
67C4×D47—21no—
68C4×D47—41no—
69Dic94—21no—
70Dic94D811yescharacteristic
71C8×C47C2×D411yescharacteristic
72C8×C47C2×D411yescharacteristic
73C47⋊C8—21no—
74C47⋊C8—41no—
75C22×C47—42no—
76C22×C47—161no—
77C22×C47AGL(1,ℤ/8)11yescharacteristic
78C2×D47—21no—
79C2×D47—41no—
80C2×D47—162no—
81C4×C47—81no—
82C4×C47#12011yescharacteristic
83C4×C47C2×D811yescharacteristic
84Dic47—21no—
85Dic47—41no—
86#2194—471nomaximal, Sylow
87C2×C47—21no—
88C2×C47—82no—
89C2×C47#44711yescharacteristic
90D47—41no—
91D47—81no—
92#576—471no—
93#510—471no—
94C2×SD32D4711yescharacteristic, complemented
95#473—471no—
96#361—471no—
97#359—471no—
98#350—471no—
99C47#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—941no—
101#137—941no—
102AGL(1,ℤ/8)—941no—
103AGL(1,ℤ/8)—942no—
104#135—471no—
105#135—941no—
106C2×Q16C2×D4711yescharacteristic, complemented
107C2×D8—941no—
108C2×D8C2×D4711yescharacteristic
109#131—471no—
110Q32—941no—
111SD32—22no—
112SD32—941no—
113M32—471no—
114C2×C16C2×D4711yescharacteristic, complemented
115#108—471no—
116#101—941no—
117#41—471no—
118#41—942no—
119#41—941no—
120#41—1881no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—942no—
124C2×D4—1881no—
125C2×D4—1882no—
126Q16—21no—
127Q16—21no—
128Q16—471no—
129Q16—1881no—
130SD16—942no—
131SD16—941no—
132SD16—1881no—
133D8—21no—
134D8—471no—
135D8—942no—
136D8C22⋊D4712yes—
137M16—471no—
138M16—941no—
139M16—941no—
140C2×C8—941no—
141C2×C8C22×D4711yescharacteristic
142C16—21no—
143C16—941no—
144C23—41no—
145C23—1882no—
146Q8—41no—
147Q8—41no—
148Q8—471no—
149Q8—941no—
150D4—22no—
151D4—41no—
152D4—471no—
153D4—941no—
154D4—941no—
155D4—1882no—
156D4—1882no—
157D4—1881no—
158C2×C4—41no—
159C2×C4—941no—
160C2×C4—1882no—
161C2×C4—1881no—
162C2×C4D4×D4711yescharacteristic
163C8—941no—
164C8—1881no—
165C8D4×D4711yescharacteristic
166C8C2×C22⋊D4711yescharacteristic
167C22—42no—
168C22—161no—
169C22—941no—
170C22—1881no—
171C22—7522no—
172C22#1309404811yescharacteristic
173C4—81no—
174C4—941no—
175C4—1881no—
176C4#1309399211yescharacteristic
177C4D8×D4711yescharacteristic
178C2—21no—
179C2—82no—
180C2—3761no—
181C2—1881no—
182C2#1568925511yescharacteristic
subgroupG/H
centerC2#15689255
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC2×SD32×C47C2
socleC2×C47#447
hypercenterC2×SD32D47
hypocenterC47#2194
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #15689564C2semidirect
3. #15689395C2semidirect
4. #15688936C2semidirect
5. #15688931C2semidirect
6. #15688906C2semidirect
7. C2×SD32×C47C2semidirect
18. #13093964C22semidirect
19. #13093960C22semidirect
21. C2×Q16×C47C22semidirect
24. C2×C16×C47C22semidirect
94. C2×SD32D47semidirect
99. C47#2194semidirect
106. C2×Q16C2×D47semidirect
114. C2×C16C2×D47semidirect