Finite Group Databasebeta

← #20244281

Subgroups — #20244281

Order 6016.

292 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094046C211yesmaximal, characteristic
2C2×#13093960C211yesmaximal, characteristic, complemented
3C2×#13093952C212yesmaximal, complemented
4#15689089C212yesmaximal, complemented
5C2×#97×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C2212yes—
7#13094046—22no—
8#13094046—22no—
9C2×Dic188C411yescharacteristic, complemented
10C2×#10625325C412yescomplemented
11C2×D376C411yescharacteristic, complemented
12C2×#10625329C2212yes—
13#13093960—22no—
14#13093952—24no—
15(C2×D47)⋊C8—24no—
16C22×C8×C47C2211yescharacteristic
17C22×C8×C47C2211yescharacteristic
18C2×C42×C47C2211yescharacteristic
19#97×C47—22no—
20C22×C4×C47—21no—
21C22×C4×C47C2311yescharacteristic
22C2×C22⋊D47—22no—
23#10625350—22no—
24#10625350—22no—
25#10625350—22no—
26#10625350—22no—
27C2×D188C2×C412yes—
28C2×C4×D47—22no—
29C2×Dic94C2×C412yes—
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C2×C8×C47C2×C411yescharacteristic
33C2×C8×C47C2×C411yescharacteristic
34C2×C8×C47D412yes—
35C2×C8×C47D412yes—
36C2×C8×C47D412yes—
37C42×C47—21no—
38C42×C47D412yes—
39#10625329—22no—
40#10625329—22no—
41C2×C47⋊C8—22no—
42Dic188—22no—
43D376—22no—
44#10625325—24no—
45C23×C47#4111yescharacteristic
46C22×D47—22no—
47C2×C4×C47—22no—
48C2×C4×C47—42no—
49C2×C4×C47C22×C411yescharacteristic
50C2×C4×C47C2×D411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47#4111yescharacteristic
55C22⋊D47—42no—
56C22⋊D47—42no—
57C2×Dic47—22no—
58D188—22no—
59D188—22no—
60C4×D47—42no—
61C4×D47—42no—
62Dic94—22no—
63Dic94—22no—
64C8×C47—22no—
65C8×C47C22⋊C412yes—
66C8×C47C22⋊C412yes—
67C47⋊C8—42no—
68C22×C47—22no—
69C22×C47C4×D411yescharacteristic
70C22×C47#12111yescharacteristic
71C22×C47#12411yescharacteristic
72C2×D47—42no—
73C2×D47—44no—
74C4×C47—42no—
75C4×C47C2×C22⋊C411yescharacteristic
76C4×C47C4×D411yescharacteristic
77C4×C47#12111yescharacteristic
78C4×C47#12711yescharacteristic
79Dic47—42no—
80#1975—471nomaximal, Sylow
81C2×C47—21no—
82C2×C47—21no—
83C2×C47#39011yescharacteristic
84C2×C47#44412yes—
85D47—82no—
86C2×#135—471no—
87C2×#108—471no—
88C2×#104—472no—
89#408—472no—
90C2×#97D4711yescharacteristic, complemented
91C47#197511yescharacteristic, complemented, Sylow
92C2×#41—472no—
93#135—942no—
94#135—942no—
95C2×Q16—471no—
96C2×SD16—472no—
97C2×D8—471no—
98C2×M16—472no—
99C22×C8C2×D4711yescharacteristic
100C22×C8C2×D4711yescharacteristic
101C2×C42C2×D4711yescharacteristic
102#108—942no—
103#104—944no—
104C22⋊C8—944no—
105#97—22no—
106#41—942no—
107#41—942no—
108#41—942no—
109#41—942no—
110C2×Q8—472no—
111C2×D4—472no—
112C2×D4—942no—
113C22×C4—21no—
114C22×C4—942no—
115C22×C4C22×D4711yescharacteristic
116Q16—942no—
117SD16—944no—
118D8—942no—
119M16—942no—
120M16—942no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—942no—
124C2×C8C4×D4711yescharacteristic
125C2×C8C4×D4711yescharacteristic
126C2×C8D18812yes—
127C2×C8D18812yes—
128C2×C8C22⋊D4712yes—
129C42—21no—
130C42D18812yes—
131C23—942no—
132C23#1062535011yescharacteristic
133Q8—942no—
134Q8—942no—
135D4—942no—
136D4—942no—
137D4—1882no—
138D4—1882no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—942no—
142C2×C4—1882no—
143C2×C4—1882no—
144C2×C4C2×C4×D4711yescharacteristic
145C2×C4C2×D18811yescharacteristic
146C2×C4C2×D18811yescharacteristic
147C2×C4C2×D18811yescharacteristic
148C2×C4#1062535011yescharacteristic
149C2×C4C2×C22⋊D4711yescharacteristic
150C8—22no—
151C8—1882no—
152C8(C2×D47)⋊C412yes—
153C8(C2×D47)⋊C412yes—
154C22—22no—
155C22—1884no—
156C22—1882no—
157C22C4×D18811yescharacteristic
158C22#1309399811yescharacteristic
159C22#1309401211yescharacteristic
160C4—42no—
161C4—1882no—
162C4C2×(C2×D47)⋊C411yescharacteristic
163C4C4×D18811yescharacteristic
164C4#1309399811yescharacteristic
165C4#1309402111yescharacteristic
166C2—21no—
167C2—21no—
168C2—3762no—
169C2#1568902511yescharacteristic
170C2#1568924612yes—
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#97×C47C2
socleC22×C47C4×D4
hypercenterC2×#97D47
hypocenterC47#1975
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×#13093960C2semidirect
3. C2×#13093952C2semidirect
4. #15689089C2semidirect
5. C2×#97×C47C2semidirect
9. C2×Dic188C4semidirect
10. C2×#10625325C4semidirect
11. C2×D376C4semidirect
90. C2×#97D47semidirect
91. C47#1975semidirect