Finite Group Databasebeta

← #20245306

Subgroups — #20245306

Order 6016.

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

normal subgroups only

This group has 226 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, complemented
2C2×#13093969C211yesmaximal, characteristic, complemented
3C2×#13093967C211yesmaximal, characteristic, complemented
4#15689360C211yesmaximal, characteristic
5#15688926C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C16C211yesmaximal, characteristic, complemented
7C47×#358C211yesmaximal, characteristic, complemented
8C2×Q8×D47—21no—
9C2×Dic188C2211yescharacteristic
10C2×#10625337—21no—
11Q16×D47—22no—
12Q16×D47—22no—
13C2×D376C2211yescharacteristic
14C2×C8×D47C2211yescharacteristic
15#13093999—21no—
16#13093969—22no—
17#13093967—22no—
18C2×C47⋊C16C2211yescharacteristic
19#13093944—21no—
20C2×Q16×C47C2211yescharacteristic
21C2×C16×C47C2211yescharacteristic
22#107×C47C2211yescharacteristic
23C2×Q8×C47—21no—
24Q8×D47—24no—
25Q8×D47—42no—
26C2×D188—21no—
27C2×D188—41no—
28C2×C4×D47—41no—
29C2×C4×D47D411yescharacteristic
30C2×Dic94—21no—
31C2×Dic94—41no—
32Q16×C47—21no—
33Q16×C47D412yescomplemented
34C2×C8×C47C2311yescharacteristic
35C4⋊C4×C47—21no—
36#10625337—24no—
37(C2×D47)⋊C4—41no—
38C2×C47⋊C8D411yescharacteristic
39Dic188—21no—
40Dic188D412yescomplemented
41D376—21no—
42D376—21no—
43C8×D47—21no—
44C8×D47—21no—
45C16×C47—21no—
46C47⋊C16—21no—
47C22×D47—41no—
48C22×D47D811yescharacteristic
49Q8×C47—22no—
50Q8×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47C2×D411yescharacteristic
54C2×Dic47—41no—
55C2×Dic47D811yescharacteristic
56D188—41no—
57D188—41no—
58D188—82no—
59C4×D47—21no—
60C4×D47—21no—
61C4×D47—44no—
62Dic94—22no—
63Dic94—44no—
64Dic94—41no—
65C8×C47C2×D411yescharacteristic
66C8×C47C2×D411yescharacteristic
67C47⋊C8—21no—
68C22×C47C2×D811yescharacteristic
69C2×D47—21no—
70C2×D47—21no—
71C2×D47—81no—
72C2×D47—81no—
73C2×D47—81no—
74C2×D47SD3212yescomplemented
75C4×C47—42no—
76C4×C47—81no—
77C4×C47#12011yescharacteristic
78C4×C47AGL(1,ℤ/8)11yescharacteristic
79Dic47—21no—
80Dic47—42no—
81#2185—471nomaximal, Sylow
82C2×C47#44711yescharacteristic
83C2×C47C2×SD3211yescharacteristic
84C2×C47#51011yescharacteristic
85D47—22no—
86D47—161no—
87C22×Q16—471no—
88C2×SD32—471no—
89C2×SD32—471no—
90#466—471no—
91#358—471no—
92#358D4711yescharacteristic, complemented
93C22⋊C16—471no—
94C47#218511yescharacteristic, complemented, Sylow
95C22×Q8—941no—
96C2×Q16—471no—
97C2×Q16—941no—
98C2×Q16—942no—
99C2×Q16—942no—
100C2×Q16C2×D4711yescharacteristic
101C2×D8—471no—
102C22×C8—471no—
103#121—941no—
104SD32—942no—
105SD32—942no—
106C2×C16—471no—
107C2×C16C2×D4711yescharacteristic
108#107C2×D4711yescharacteristic
109#102—941no—
110C2×Q8—21no—
111C2×Q8—944no—
112C2×Q8—941no—
113C2×Q8—1881no—
114C2×Q8—1882no—
115C2×D4—941no—
116C2×D4—1881no—
117C22×C4—471no—
118C22×C4—1881no—
119Q16—21no—
120Q16—472no—
121Q16—944no—
122Q16—941no—
123Q16D18812yescomplemented
124D8—941no—
125D8—941no—
126C2×C8—471no—
127C2×C8—941no—
128C2×C8—941no—
129C2×C8C22×D4711yescharacteristic
130C4⋊C4—21no—
131C22⋊C4—1881no—
132C16—21no—
133C16—941no—
134C23—471no—
135C23—1881no—
136Q8—22no—
137Q8—41no—
138Q8—942no—
139Q8—1884no—
140Q8—1881no—
141D4—3762no—
142D4—1881no—
143D4—1881no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—471no—
147C2×C4—941no—
148C2×C4—941no—
149C2×C4—1884no—
150C2×C4—1881no—
151C2×C4D4×D4711yescharacteristic
152C8—941no—
153C8C2×D18811yescharacteristic
154C8D4×D4711yescharacteristic
155C22—472no—
156C22—941no—
157C22—941no—
158C22—3761no—
159C22—3761no—
160C22—3761no—
161C22D8×D4711yescharacteristic
162C4—42no—
163C4—81no—
164C4—941no—
165C4—1882no—
166C4#1309399411yescharacteristic
167C4#1309405111yescharacteristic
168C2—942no—
169C2—7521no—
170C2#1568925811yescharacteristic
171C2SD32×D4711yescharacteristic
172C2#1568956511yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2185
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
1. C2×Q16×D47C2semidirect
2. C2×#13093969C2semidirect
3. C2×#13093967C2semidirect
5. #15688926C2semidirect
6. (C2×D47)⋊C16C2semidirect
7. C47×#358C2semidirect
33. Q16×C47D4semidirect
40. Dic188D4semidirect
74. C2×D47SD32semidirect
92. #358D47semidirect
94. C47#2185semidirect
123. Q16D188semidirect