Finite Group Databasebeta

← #20245323

Subgroups — #20245323

Order 6016.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D47C211yesmaximal, characteristic
2C2×Dic376C211yesmaximal, characteristic, complemented
3C2×#13093970C211yesmaximal, characteristic, complemented
4#15689365C211yesmaximal, characteristic
5#15688926C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C16C211yesmaximal, characteristic
7C47×#358C211yesmaximal, characteristic, complemented
8C2×Q8×D47—21no—
9C2×Dic188C2211yescharacteristic
10C2×Dic188C2211yescharacteristic
11C2×#10625337—21no—
12Q16×D47—22no—
13Q16×D47—22no—
14C2×C8×D47C2211yescharacteristic
15#13094004—21no—
16Dic376—22no—
17#13093970—22no—
18C2×C47⋊C16C2211yescharacteristic
19#13093947—21no—
20C2×Q16×C47C2211yescharacteristic
21C2×C16×C47C2211yescharacteristic
22#107×C47C2211yescharacteristic
23C2×Q8×C47—21no—
24Q8×D47—24no—
25Q8×D47—42no—
26C2×C4×D47—41no—
27C2×C4×D47D411yescharacteristic
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×Dic94—41no—
31Q16×C47—21no—
32Q16×C47D412yes—
33C2×C8×C47C2311yescharacteristic
34C4⋊C4×C47—21no—
35#10625337—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—
47C22×D47D811yescharacteristic
48Q8×C47—22no—
49Q8×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47C2×D411yescharacteristic
53C2×Dic47—41no—
54C2×Dic47—41no—
55C2×Dic47D811yescharacteristic
56C4×D47—21no—
57C4×D47—21no—
58C4×D47—44no—
59Dic94—22no—
60Dic94—44no—
61Dic94—41no—
62Dic94—41no—
63Dic94—41no—
64C8×C47C2×D411yescharacteristic
65C8×C47C2×D411yescharacteristic
66C47⋊C8—21no—
67C22×C47C2×D811yescharacteristic
68C2×D47—21no—
69C2×D47—21no—
70C2×D47Q3212yescomplemented
71C4×C47—42no—
72C4×C47—81no—
73C4×C47#12011yescharacteristic
74C4×C47AGL(1,ℤ/8)11yescharacteristic
75Dic47—21no—
76Dic47—42no—
77Dic47—81no—
78#2188—471nomaximal, Sylow
79C2×C47#44711yescharacteristic
80C2×C47C2×Q3211yescharacteristic
81C2×C47#51011yescharacteristic
82D47—22no—
83C22×Q16—471no—
84C2×Q32—471no—
85C2×Q32—471no—
86#467—471no—
87#358—471no—
88#358D4711yescharacteristic, complemented
89C22⋊C16—471no—
90C47#218811yescharacteristic, complemented, Sylow
91C22×Q8—941no—
92C2×Q16—471no—
93C2×Q16—471no—
94C2×Q16—941no—
95C2×Q16—942no—
96C2×Q16—942no—
97C2×Q16C2×D4711yescharacteristic
98C22×C8—471no—
99C22⋊Q8—941no—
100Q32—942no—
101Q32—942no—
102C2×C16—471no—
103C2×C16C2×D4711yescharacteristic
104#107C2×D4711yescharacteristic
105#103—941no—
106C2×Q8—21no—
107C2×Q8—944no—
108C2×Q8—941no—
109C2×Q8—941no—
110C2×Q8—1881no—
111C2×Q8—1882no—
112C22×C4—471no—
113C22×C4—1881no—
114Q16—21no—
115Q16—472no—
116Q16—944no—
117Q16—941no—
118Q16—941no—
119Q16—941no—
120Q16D18812yes—
121C2×C8—471no—
122C2×C8—941no—
123C2×C8—941no—
124C2×C8C22×D4711yescharacteristic
125C4⋊C4—21no—
126C4⋊C4—1881no—
127C22⋊C4—1881no—
128C16—21no—
129C16—941no—
130C23—471no—
131Q8—22no—
132Q8—41no—
133Q8—942no—
134Q8—1884no—
135Q8—1881no—
136Q8—1881no—
137Q8—1881no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—471no—
141C2×C4—941no—
142C2×C4—941no—
143C2×C4—1884no—
144C2×C4—1881no—
145C2×C4—1881no—
146C2×C4D4×D4711yescharacteristic
147C8—941no—
148C8C2×D18811yescharacteristic
149C8D4×D4711yescharacteristic
150C22—472no—
151C22—941no—
152C22—941no—
153C22D8×D4711yescharacteristic
154C4—42no—
155C4—81no—
156C4—941no—
157C4—3761no—
158C4—1882no—
159C4#1309399411yescharacteristic
160C4#1309405111yescharacteristic
161C2—942no—
162C2#1568925811yescharacteristic
163C2Q32×D4711yescharacteristic
164C2#1568956211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2188
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
2. C2×Dic376C2semidirect
3. C2×#13093970C2semidirect
5. #15688926C2semidirect
7. C47×#358C2semidirect
70. C2×D47Q32semidirect
88. #358D47semidirect
90. C47#2188semidirect