Finite Group Databasebeta

← #20245329

Subgroups — #20245329

Order 6016.

220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#13094043C211yesmaximal, characteristic
2C2×Dic376C211yesmaximal, characteristic, complemented
3C2×#13093968C211yesmaximal, characteristic, complemented
4#15689365C211yesmaximal, characteristic, complemented
5#15688926C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C16C211yesmaximal, characteristic, complemented
7C47×#357C211yesmaximal, characteristic, complemented
8C2×#10625352—21no—
9#13094043—22no—
10#13094043—22no—
11C2×Dic188C2211yescharacteristic
12C2×Dic188C2211yescharacteristic
13C2×#10625335—21no—
14C2×C8×D47C2211yescharacteristic
15#13094004—21no—
16Dic376—22no—
17#13093968—22no—
18C2×C47⋊C16C2211yescharacteristic
19#13093947—21no—
20C2×D8×C47C2211yescharacteristic
21C2×C16×C47C2211yescharacteristic
22#107×C47C2211yescharacteristic
23C2×D4×C47—21no—
24C2×C22⋊D47—41no—
25C22×Dic47—41no—
26#10625352—24no—
27#10625352—42no—
28C2×C4×D47D411yescharacteristic
29C2×Dic94—21no—
30C2×Dic94—21no—
31D8×C47—21no—
32D8×C47D412yes—
33C2×C8×C47C2311yescharacteristic
34C4⋊C4×C47—21no—
35#10625335—24no—
36(C2×D47)⋊C4—41no—
37C4⋊Dic47—41no—
38C2×C47⋊C8D411yescharacteristic
39Dic188—21no—
40Dic188—21no—
41Dic188—21no—
42Dic188D412yes—
43C8×D47—21no—
44C8×D47—21no—
45C16×C47—21no—
46C47⋊C16—21no—
47C23×C47—41no—
48C22×D47D811yescharacteristic
49D4×C47—22no—
50D4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47C2×D411yescharacteristic
53C22⋊D47—44no—
54C2×Dic47—44no—
55C2×Dic47—41no—
56C2×Dic47—41no—
57C2×Dic47D811yescharacteristic
58C4×D47—21no—
59C4×D47—21no—
60Dic94—22no—
61Dic94—41no—
62Dic94—41no—
63Dic94—41no—
64C8×C47C2×D411yescharacteristic
65C8×C47C2×D411yescharacteristic
66C47⋊C8—21no—
67C22×C47—42no—
68C22×C47—81no—
69C22×C47—81no—
70C22×C47C2×D811yescharacteristic
71C2×D47—21no—
72C2×D47—21no—
73C2×D47—21no—
74C4×C47—81no—
75C4×C47#12011yescharacteristic
76C4×C47AGL(1,ℤ/8)11yescharacteristic
77Dic47—21no—
78Dic47—42no—
79Dic47—81no—
80#2189—471nomaximal, Sylow
81C2×C47—82no—
82C2×C47#44711yescharacteristic
83C2×C47#50811yescharacteristic
84C2×C47#51011yescharacteristic
85D47—41no—
86C2×#135—471no—
87C2×Q32—471no—
88C2×SD32—471no—
89#467—471no—
90#358—471no—
91#357D4711yescharacteristic, complemented
92C22⋊C16—471no—
93C47#218911yescharacteristic, complemented, Sylow
94C2×#41—941no—
95#135—942no—
96#135—942no—
97C2×Q16—471no—
98C2×Q16—471no—
99C2×SD16—941no—
100C2×D8C2×D4711yescharacteristic
101C22×C8—471no—
102C22⋊Q8—941no—
103Q32—942no—
104SD32—942no—
105C2×C16—471no—
106C2×C16C2×D4711yescharacteristic
107#107C2×D4711yescharacteristic
108#103—941no—
109#41—944no—
110#41—1882no—
111C2×Q8—941no—
112C2×Q8—941no—
113C2×D4—21no—
114C2×D4—1881no—
115C22×C4—471no—
116C22×C4—1881no—
117Q16—472no—
118Q16—941no—
119Q16—941no—
120Q16—941no—
121SD16—944no—
122D8—21no—
123D8D18812yes—
124C2×C8—471no—
125C2×C8—941no—
126C2×C8—941no—
127C2×C8C22×D4711yescharacteristic
128C4⋊C4—21no—
129C4⋊C4—1881no—
130C22⋊C4—1881no—
131C16—21no—
132C16—941no—
133C23—41no—
134C23—471no—
135Q8—942no—
136Q8—1881no—
137Q8—1881no—
138Q8—1881no—
139D4—22no—
140D4—41no—
141D4—1884no—
142C2×C4—41no—
143C2×C4—471no—
144C2×C4—941no—
145C2×C4—941no—
146C2×C4—1884no—
147C2×C4—1881no—
148C2×C4—1881no—
149C2×C4D4×D4711yescharacteristic
150C8—941no—
151C8C2×D18811yescharacteristic
152C8D4×D4711yescharacteristic
153C22—42no—
154C22—81no—
155C22—81no—
156C22—941no—
157C22—941no—
158C22—941no—
159C22D8×D4711yescharacteristic
160C4—81no—
161C4—941no—
162C4—3761no—
163C4—1882no—
164C4#1309399411yescharacteristic
165C4#1309405111yescharacteristic
166C2—82no—
167C2—1881no—
168C2#1568925811yescharacteristic
169C2#1568955211yescharacteristic
170C2#1568956211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47#2189
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×Dic376C2semidirect
3. C2×#13093968C2semidirect
4. #15689365C2semidirect
5. #15688926C2semidirect
6. (C2×D47)⋊C16C2semidirect
7. C47×#357C2semidirect
91. #357D47semidirect
93. C47#2189semidirect